id	sid	tid	token	lemma	pos
ejpam-4316	1	1	european	european	PROPN
ejpam-4316	1	2	journal	journal	PROPN
ejpam-4316	1	3	of	of	ADP
ejpam-4316	1	4	pure	pure	ADJ
ejpam-4316	1	5	and	and	CCONJ
ejpam-4316	1	6	applied	apply	VERB
ejpam-4316	1	7	mathematics	mathematic	NOUN
ejpam-4316	1	8	vol	vol	NOUN
ejpam-4316	1	9	.	.	PROPN
ejpam-4316	2	1	15	15	NUM
ejpam-4316	2	2	,	,	PUNCT
ejpam-4316	2	3	no	no	INTJ
ejpam-4316	2	4	.	.	NOUN
ejpam-4316	2	5	2	2	NUM
ejpam-4316	2	6	,	,	PUNCT
ejpam-4316	2	7	2022	2022	NUM
ejpam-4316	2	8	,	,	PUNCT
ejpam-4316	2	9	602	602	NUM
ejpam-4316	2	10	-	-	SYM
ejpam-4316	2	11	619	619	NUM
ejpam-4316	2	12	issn	issn	PROPN
ejpam-4316	2	13	1307	1307	NUM
ejpam-4316	2	14	-	-	SYM
ejpam-4316	2	15	5543	5543	NUM
ejpam-4316	2	16	–	–	PUNCT
ejpam-4316	2	17	ejpam.com	ejpam.com	X
ejpam-4316	2	18	published	publish	VERB
ejpam-4316	2	19	by	by	ADP
ejpam-4316	2	20	new	new	PROPN
ejpam-4316	2	21	york	york	PROPN
ejpam-4316	2	22	business	business	PROPN
ejpam-4316	2	23	global	global	PROPN
ejpam-4316	2	24	on	on	ADP
ejpam-4316	2	25	the	the	DET
ejpam-4316	2	26	weiner	weiner	NOUN
ejpam-4316	2	27	and	and	CCONJ
ejpam-4316	2	28	harary	harary	ADJ
ejpam-4316	2	29	index	index	NOUN
ejpam-4316	2	30	of	of	ADP
ejpam-4316	2	31	splitting	splitting	NOUN
ejpam-4316	2	32	graphs	graph	NOUN
ejpam-4316	2	33	francis	francis	PROPN
ejpam-4316	2	34	joseph	joseph	PROPN
ejpam-4316	2	35	h.	h.	PROPN
ejpam-4316	2	36	campeña1	campeña1	PROPN
ejpam-4316	2	37	,	,	PUNCT
ejpam-4316	2	38	ma	ma	PROPN
ejpam-4316	2	39	.	.	PROPN
ejpam-4316	2	40	christine	christine	PROPN
ejpam-4316	2	41	g.	g.	PROPN
ejpam-4316	2	42	egan1,∗	egan1,∗	PROPN
ejpam-4316	2	43	,	,	PUNCT
ejpam-4316	2	44	john	john	PROPN
ejpam-4316	2	45	rafael	rafael	PROPN
ejpam-4316	2	46	m.	m.	PROPN
ejpam-4316	2	47	antalan1,2	antalan1,2	PROPN
ejpam-4316	2	48	1	1	NUM
ejpam-4316	2	49	mathematics	mathematic	NOUN
ejpam-4316	2	50	and	and	CCONJ
ejpam-4316	2	51	statistics	statistics	PROPN
ejpam-4316	2	52	department	department	PROPN
ejpam-4316	2	53	college	college	PROPN
ejpam-4316	2	54	of	of	ADP
ejpam-4316	2	55	science	science	NOUN
ejpam-4316	2	56	,	,	PUNCT
ejpam-4316	2	57	de	de	X
ejpam-4316	2	58	la	la	X
ejpam-4316	2	59	salle	salle	PROPN
ejpam-4316	2	60	university	university	PROPN
ejpam-4316	2	61	,	,	PUNCT
ejpam-4316	2	62	2401	2401	NUM
ejpam-4316	2	63	taft	taft	PROPN
ejpam-4316	2	64	avenue	avenue	PROPN
ejpam-4316	2	65	malate	malate	PROPN
ejpam-4316	2	66	manila	manila	PROPN
ejpam-4316	2	67	,	,	PUNCT
ejpam-4316	2	68	philippines	philippine	NOUN
ejpam-4316	2	69	.	.	PUNCT
ejpam-4316	3	1	2	2	NUM
ejpam-4316	3	2	department	department	NOUN
ejpam-4316	3	3	of	of	ADP
ejpam-4316	3	4	mathematics	mathematics	PROPN
ejpam-4316	3	5	and	and	CCONJ
ejpam-4316	3	6	physics	physics	PROPN
ejpam-4316	3	7	,	,	PUNCT
ejpam-4316	3	8	college	college	NOUN
ejpam-4316	3	9	of	of	ADP
ejpam-4316	3	10	science	science	NOUN
ejpam-4316	3	11	,	,	PUNCT
ejpam-4316	3	12	central	central	ADJ
ejpam-4316	3	13	luzon	luzon	PROPN
ejpam-4316	3	14	state	state	PROPN
ejpam-4316	3	15	university	university	PROPN
ejpam-4316	3	16	,	,	PUNCT
ejpam-4316	3	17	science	science	NOUN
ejpam-4316	3	18	city	city	NOUN
ejpam-4316	3	19	of	of	ADP
ejpam-4316	3	20	muñoz	muñoz	PROPN
ejpam-4316	3	21	,	,	PUNCT
ejpam-4316	3	22	3120	3120	NUM
ejpam-4316	3	23	nueva	nueva	NOUN
ejpam-4316	3	24	ecija	ecija	NOUN
ejpam-4316	3	25	,	,	PUNCT
ejpam-4316	3	26	philippines	philippine	NOUN
ejpam-4316	3	27	.	.	PUNCT
ejpam-4316	4	1	abstract	abstract	ADJ
ejpam-4316	4	2	.	.	PUNCT
ejpam-4316	5	1	in	in	ADP
ejpam-4316	5	2	this	this	DET
ejpam-4316	5	3	study	study	NOUN
ejpam-4316	5	4	we	we	PRON
ejpam-4316	5	5	define	define	VERB
ejpam-4316	5	6	a	a	DET
ejpam-4316	5	7	graph	graph	NOUN
ejpam-4316	5	8	operation	operation	NOUN
ejpam-4316	5	9	on	on	ADP
ejpam-4316	5	10	a	a	DET
ejpam-4316	5	11	finite	finite	ADJ
ejpam-4316	5	12	simple	simple	ADJ
ejpam-4316	5	13	graph	graph	NOUN
ejpam-4316	5	14	g	g	PROPN
ejpam-4316	5	15	=	=	PUNCT
ejpam-4316	5	16	(	(	PUNCT
ejpam-4316	5	17	v	v	NOUN
ejpam-4316	5	18	,	,	PUNCT
ejpam-4316	5	19	e	e	NOUN
ejpam-4316	5	20	)	)	PUNCT
ejpam-4316	5	21	called	call	VERB
ejpam-4316	5	22	the	the	DET
ejpam-4316	5	23	s	s	NOUN
ejpam-4316	5	24	-	-	PUNCT
ejpam-4316	5	25	splitting	splitting	NOUN
ejpam-4316	5	26	graph	graph	NOUN
ejpam-4316	5	27	of	of	ADP
ejpam-4316	5	28	g	g	NOUN
ejpam-4316	5	29	where	where	SCONJ
ejpam-4316	5	30	s	s	VERB
ejpam-4316	5	31	is	be	AUX
ejpam-4316	5	32	a	a	DET
ejpam-4316	5	33	non	non	ADJ
ejpam-4316	5	34	-	-	ADJ
ejpam-4316	5	35	empty	empty	ADJ
ejpam-4316	5	36	subset	subset	NOUN
ejpam-4316	5	37	of	of	ADP
ejpam-4316	5	38	vertices	vertex	NOUN
ejpam-4316	5	39	of	of	ADP
ejpam-4316	5	40	g.	g.	PROPN
ejpam-4316	5	41	if	if	SCONJ
ejpam-4316	5	42	s	s	VERB
ejpam-4316	5	43	=	=	X
ejpam-4316	5	44	v	v	PROPN
ejpam-4316	5	45	,	,	PUNCT
ejpam-4316	5	46	then	then	ADV
ejpam-4316	5	47	it	it	PRON
ejpam-4316	5	48	is	be	AUX
ejpam-4316	5	49	the	the	DET
ejpam-4316	5	50	splitting	splitting	NOUN
ejpam-4316	5	51	graph	graph	NOUN
ejpam-4316	5	52	of	of	ADP
ejpam-4316	5	53	g	g	PROPN
ejpam-4316	5	54	defined	define	VERB
ejpam-4316	5	55	by	by	ADP
ejpam-4316	5	56	e.	e.	PROPN
ejpam-4316	5	57	sampathkumar	sampathkumar	PROPN
ejpam-4316	5	58	,	,	PUNCT
ejpam-4316	5	59	and	and	CCONJ
ejpam-4316	5	60	h.b	h.b	PROPN
ejpam-4316	5	61	.	.	PROPN
ejpam-4316	5	62	walikar	walikar	NOUN
ejpam-4316	5	63	in	in	ADP
ejpam-4316	5	64	the	the	DET
ejpam-4316	5	65	1980	1980	NUM
ejpam-4316	5	66	’s	’s	NOUN
ejpam-4316	5	67	.	.	PUNCT
ejpam-4316	6	1	this	this	DET
ejpam-4316	6	2	paper	paper	NOUN
ejpam-4316	6	3	investigates	investigate	VERB
ejpam-4316	6	4	the	the	DET
ejpam-4316	6	5	wiener	wiener	NOUN
ejpam-4316	6	6	and	and	CCONJ
ejpam-4316	6	7	harary	harary	NOUN
ejpam-4316	6	8	indices	index	NOUN
ejpam-4316	6	9	of	of	ADP
ejpam-4316	6	10	the	the	DET
ejpam-4316	6	11	s	s	NOUN
ejpam-4316	6	12	-	-	PUNCT
ejpam-4316	6	13	splitting	splitting	NOUN
ejpam-4316	6	14	graph	graph	NOUN
ejpam-4316	6	15	of	of	ADP
ejpam-4316	6	16	g	g	NOUN
ejpam-4316	6	17	for	for	ADP
ejpam-4316	6	18	some	some	DET
ejpam-4316	6	19	families	family	NOUN
ejpam-4316	6	20	of	of	ADP
ejpam-4316	6	21	graph	graph	NOUN
ejpam-4316	6	22	.	.	PUNCT
ejpam-4316	7	1	2020	2020	NUM
ejpam-4316	7	2	mathematics	mathematic	NOUN
ejpam-4316	7	3	subject	subject	NOUN
ejpam-4316	7	4	classifications	classification	NOUN
ejpam-4316	7	5	:	:	PUNCT
ejpam-4316	7	6	05c50	05c50	NUM
ejpam-4316	7	7	,	,	PUNCT
ejpam-4316	7	8	05c09	05c09	NUM
ejpam-4316	7	9	,	,	PUNCT
ejpam-4316	7	10	key	key	ADJ
ejpam-4316	7	11	words	word	NOUN
ejpam-4316	7	12	and	and	CCONJ
ejpam-4316	7	13	phrases	phrase	NOUN
ejpam-4316	7	14	:	:	PUNCT
ejpam-4316	7	15	wiener	wiener	NOUN
ejpam-4316	7	16	index	index	NOUN
ejpam-4316	7	17	,	,	PUNCT
ejpam-4316	7	18	harary	harary	PROPN
ejpam-4316	7	19	index	index	NOUN
ejpam-4316	7	20	,	,	PUNCT
ejpam-4316	7	21	splitting	splitting	NOUN
ejpam-4316	7	22	graph	graph	NOUN
ejpam-4316	7	23	1	1	NUM
ejpam-4316	7	24	.	.	PUNCT
ejpam-4316	8	1	introduction	introduction	NOUN
ejpam-4316	8	2	mathematical	mathematical	ADJ
ejpam-4316	8	3	objects	object	NOUN
ejpam-4316	8	4	have	have	AUX
ejpam-4316	8	5	been	be	AUX
ejpam-4316	8	6	used	use	VERB
ejpam-4316	8	7	to	to	PART
ejpam-4316	8	8	represent	represent	VERB
ejpam-4316	8	9	the	the	DET
ejpam-4316	8	10	structure	structure	NOUN
ejpam-4316	8	11	of	of	ADP
ejpam-4316	8	12	a	a	DET
ejpam-4316	8	13	chemical	chemical	NOUN
ejpam-4316	8	14	compound	compound	NOUN
ejpam-4316	8	15	.	.	PUNCT
ejpam-4316	9	1	one	one	NUM
ejpam-4316	9	2	such	such	ADJ
ejpam-4316	9	3	representation	representation	NOUN
ejpam-4316	9	4	is	be	AUX
ejpam-4316	9	5	that	that	SCONJ
ejpam-4316	9	6	each	each	DET
ejpam-4316	9	7	atom	atom	NOUN
ejpam-4316	9	8	is	be	AUX
ejpam-4316	9	9	described	describe	VERB
ejpam-4316	9	10	by	by	ADP
ejpam-4316	9	11	vertices	vertex	NOUN
ejpam-4316	9	12	and	and	CCONJ
ejpam-4316	9	13	the	the	DET
ejpam-4316	9	14	bond	bond	NOUN
ejpam-4316	9	15	between	between	ADP
ejpam-4316	9	16	atoms	atom	NOUN
ejpam-4316	9	17	is	be	AUX
ejpam-4316	9	18	described	describe	VERB
ejpam-4316	9	19	by	by	ADP
ejpam-4316	9	20	an	an	DET
ejpam-4316	9	21	edge	edge	NOUN
ejpam-4316	9	22	.	.	PUNCT
ejpam-4316	10	1	with	with	ADP
ejpam-4316	10	2	this	this	PRON
ejpam-4316	10	3	,	,	PUNCT
ejpam-4316	10	4	mathematical	mathematical	ADJ
ejpam-4316	10	5	tools	tool	NOUN
ejpam-4316	10	6	can	can	AUX
ejpam-4316	10	7	now	now	ADV
ejpam-4316	10	8	be	be	AUX
ejpam-4316	10	9	used	use	VERB
ejpam-4316	10	10	to	to	PART
ejpam-4316	10	11	analyze	analyze	VERB
ejpam-4316	10	12	the	the	DET
ejpam-4316	10	13	properties	property	NOUN
ejpam-4316	10	14	of	of	ADP
ejpam-4316	10	15	chemical	chemical	NOUN
ejpam-4316	10	16	compounds	compound	NOUN
ejpam-4316	10	17	that	that	PRON
ejpam-4316	10	18	may	may	AUX
ejpam-4316	10	19	be	be	AUX
ejpam-4316	10	20	related	relate	VERB
ejpam-4316	10	21	to	to	ADP
ejpam-4316	10	22	its	its	PRON
ejpam-4316	10	23	structure	structure	NOUN
ejpam-4316	10	24	.	.	PUNCT
ejpam-4316	11	1	a	a	DET
ejpam-4316	11	2	mathematical	mathematical	ADJ
ejpam-4316	11	3	formula	formula	NOUN
ejpam-4316	11	4	that	that	PRON
ejpam-4316	11	5	represents	represent	VERB
ejpam-4316	11	6	chemical	chemical	ADJ
ejpam-4316	11	7	species	specie	NOUN
ejpam-4316	11	8	which	which	PRON
ejpam-4316	11	9	have	have	AUX
ejpam-4316	11	10	made	make	VERB
ejpam-4316	11	11	a	a	DET
ejpam-4316	11	12	variety	variety	NOUN
ejpam-4316	11	13	of	of	ADP
ejpam-4316	11	14	methods	method	NOUN
ejpam-4316	11	15	of	of	ADP
ejpam-4316	11	16	chemical	chemical	ADJ
ejpam-4316	11	17	structure	structure	NOUN
ejpam-4316	11	18	is	be	AUX
ejpam-4316	11	19	called	call	VERB
ejpam-4316	11	20	the	the	DET
ejpam-4316	11	21	topological	topological	ADJ
ejpam-4316	11	22	indices	index	NOUN
ejpam-4316	11	23	[	[	X
ejpam-4316	11	24	18	18	NUM
ejpam-4316	11	25	]	]	PUNCT
ejpam-4316	11	26	.	.	PUNCT
ejpam-4316	12	1	topological	topological	ADJ
ejpam-4316	12	2	indices	index	NOUN
ejpam-4316	12	3	are	be	AUX
ejpam-4316	12	4	helpful	helpful	ADJ
ejpam-4316	12	5	when	when	SCONJ
ejpam-4316	12	6	interpreting	interpret	VERB
ejpam-4316	12	7	chemical	chemical	ADJ
ejpam-4316	12	8	constitution	constitution	NOUN
ejpam-4316	12	9	into	into	ADP
ejpam-4316	12	10	numerical	numerical	ADJ
ejpam-4316	12	11	values	value	NOUN
ejpam-4316	12	12	which	which	PRON
ejpam-4316	12	13	can	can	AUX
ejpam-4316	12	14	be	be	AUX
ejpam-4316	12	15	used	use	VERB
ejpam-4316	12	16	for	for	ADP
ejpam-4316	12	17	correlation	correlation	NOUN
ejpam-4316	12	18	with	with	ADP
ejpam-4316	12	19	physical	physical	ADJ
ejpam-4316	12	20	properties	property	NOUN
ejpam-4316	12	21	in	in	ADP
ejpam-4316	12	22	quantitative	quantitative	ADJ
ejpam-4316	12	23	structureproperty	structureproperty	NOUN
ejpam-4316	12	24	/	/	SYM
ejpam-4316	12	25	activity	activity	NOUN
ejpam-4316	12	26	relationship	relationship	NOUN
ejpam-4316	12	27	(	(	PUNCT
ejpam-4316	12	28	qspr	qspr	NOUN
ejpam-4316	12	29	/	/	SYM
ejpam-4316	12	30	qsar	qsar	PROPN
ejpam-4316	12	31	)	)	PUNCT
ejpam-4316	12	32	studies	study	NOUN
ejpam-4316	12	33	.	.	PUNCT
ejpam-4316	13	1	quantitative	quantitative	ADJ
ejpam-4316	13	2	structure	structure	NOUN
ejpam-4316	13	3	-	-	PUNCT
ejpam-4316	13	4	property	property	NOUN
ejpam-4316	13	5	relationship	relationship	NOUN
ejpam-4316	13	6	(	(	PUNCT
ejpam-4316	13	7	qspr	qspr	NOUN
ejpam-4316	13	8	)	)	PUNCT
ejpam-4316	13	9	mathematical	mathematical	ADJ
ejpam-4316	13	10	modeling	modeling	NOUN
ejpam-4316	13	11	method	method	NOUN
ejpam-4316	13	12	connects	connect	VERB
ejpam-4316	13	13	physical	physical	ADJ
ejpam-4316	13	14	or	or	CCONJ
ejpam-4316	13	15	chemical	chemical	NOUN
ejpam-4316	13	16	properties	property	NOUN
ejpam-4316	13	17	with	with	ADP
ejpam-4316	13	18	a	a	DET
ejpam-4316	13	19	structure	structure	NOUN
ejpam-4316	13	20	of	of	ADP
ejpam-4316	13	21	a	a	DET
ejpam-4316	13	22	molecule	molecule	NOUN
ejpam-4316	13	23	[	[	X
ejpam-4316	13	24	1	1	NUM
ejpam-4316	13	25	]	]	PUNCT
ejpam-4316	13	26	.	.	PUNCT
ejpam-4316	14	1	meanwhile	meanwhile	ADV
ejpam-4316	14	2	,	,	PUNCT
ejpam-4316	14	3	quantitative	quantitative	ADJ
ejpam-4316	14	4	structure	structure	NOUN
ejpam-4316	14	5	-	-	PUNCT
ejpam-4316	14	6	activity	activity	NOUN
ejpam-4316	14	7	relationship	relationship	NOUN
ejpam-4316	14	8	(	(	PUNCT
ejpam-4316	14	9	qsar	qsar	NOUN
ejpam-4316	14	10	)	)	PUNCT
ejpam-4316	14	11	is	be	AUX
ejpam-4316	14	12	a	a	DET
ejpam-4316	14	13	mathematical	mathematical	ADJ
ejpam-4316	14	14	modeling	modeling	NOUN
ejpam-4316	14	15	method	method	NOUN
ejpam-4316	14	16	that	that	PRON
ejpam-4316	14	17	show	show	VERB
ejpam-4316	14	18	relationships	relationship	NOUN
ejpam-4316	14	19	between	between	ADP
ejpam-4316	14	20	biological	biological	ADJ
ejpam-4316	14	21	activities	activity	NOUN
ejpam-4316	14	22	and	and	CCONJ
ejpam-4316	14	23	the	the	DET
ejpam-4316	14	24	structural	structural	ADJ
ejpam-4316	14	25	properties	property	NOUN
ejpam-4316	14	26	of	of	ADP
ejpam-4316	14	27	chemical	chemical	NOUN
ejpam-4316	14	28	compounds	compound	NOUN
ejpam-4316	14	29	[	[	X
ejpam-4316	14	30	13	13	NUM
ejpam-4316	14	31	]	]	PUNCT
ejpam-4316	14	32	.	.	PUNCT
ejpam-4316	15	1	we	we	PRON
ejpam-4316	15	2	have	have	VERB
ejpam-4316	15	3	here	here	ADV
ejpam-4316	15	4	some	some	DET
ejpam-4316	15	5	studies	study	NOUN
ejpam-4316	15	6	of	of	ADP
ejpam-4316	15	7	toplogical	toplogical	ADJ
ejpam-4316	15	8	indices	index	NOUN
ejpam-4316	15	9	in	in	ADP
ejpam-4316	15	10	qspr	qspr	NOUN
ejpam-4316	15	11	/	/	SYM
ejpam-4316	15	12	qsar	qsar	NOUN
ejpam-4316	15	13	.	.	PUNCT
ejpam-4316	16	1	shanmukha	shanmukha	PROPN
ejpam-4316	16	2	,	,	PUNCT
ejpam-4316	16	3	et	et	PROPN
ejpam-4316	16	4	.	.	PUNCT
ejpam-4316	17	1	al	al	PROPN
ejpam-4316	17	2	used	use	VERB
ejpam-4316	17	3	13	13	NUM
ejpam-4316	17	4	degreebased	degreebase	VERB
ejpam-4316	17	5	topological	topological	ADJ
ejpam-4316	17	6	indices	index	NOUN
ejpam-4316	17	7	to	to	PART
ejpam-4316	17	8	study	study	VERB
ejpam-4316	17	9	anticancer	anticancer	NOUN
ejpam-4316	17	10	drugs	drug	NOUN
ejpam-4316	17	11	in	in	ADP
ejpam-4316	17	12	terms	term	NOUN
ejpam-4316	17	13	of	of	ADP
ejpam-4316	17	14	qspr	qspr	NOUN
ejpam-4316	17	15	[	[	X
ejpam-4316	17	16	20	20	NUM
ejpam-4316	17	17	]	]	PUNCT
ejpam-4316	17	18	.	.	PUNCT
ejpam-4316	18	1	hosamani	hosamani	PROPN
ejpam-4316	18	2	∗corresponding	∗corresponde	VERB
ejpam-4316	18	3	author	author	NOUN
ejpam-4316	18	4	.	.	PUNCT
ejpam-4316	19	1	doi	doi	NOUN
ejpam-4316	19	2	:	:	PUNCT
ejpam-4316	19	3	https://doi.org/10.29020/nybg.ejpam.v15i2.4316	https://doi.org/10.29020/nybg.ejpam.v15i2.4316	ADJ
ejpam-4316	19	4	email	email	NOUN
ejpam-4316	19	5	addresses	address	NOUN
ejpam-4316	19	6	:	:	PUNCT
ejpam-4316	20	1	francis.campena@dlsu.edu.ph	francis.campena@dlsu.edu.ph	PROPN
ejpam-4316	20	2	(	(	PUNCT
ejpam-4316	20	3	f.j.h	f.j.h	ADJ
ejpam-4316	20	4	.	.	PUNCT
ejpam-4316	20	5	campeña	campeña	PROPN
ejpam-4316	20	6	)	)	PUNCT
ejpam-4316	20	7	,	,	PUNCT
ejpam-4316	20	8	ma_christine_egan@dlsu.edu.ph	ma_christine_egan@dlsu.edu.ph	PROPN
ejpam-4316	20	9	(	(	PUNCT
ejpam-4316	20	10	m.c.g	m.c.g	PROPN
ejpam-4316	20	11	.	.	PUNCT
ejpam-4316	20	12	egan	egan	PROPN
ejpam-4316	20	13	)	)	PUNCT
ejpam-4316	20	14	,	,	PUNCT
ejpam-4316	20	15	jrantalan@clsu.edu.ph	jrantalan@clsu.edu.ph	PROPN
ejpam-4316	20	16	(	(	PUNCT
ejpam-4316	20	17	j.r.m	j.r.m	PROPN
ejpam-4316	20	18	.	.	PUNCT
ejpam-4316	20	19	antalan	antalan	PROPN
ejpam-4316	20	20	)	)	PUNCT
ejpam-4316	20	21	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-4316	20	22	602	602	NUM
ejpam-4316	21	1	©	©	ADP
ejpam-4316	21	2	2022	2022	NUM
ejpam-4316	21	3	ejpam	ejpam	VERB
ejpam-4316	21	4	all	all	DET
ejpam-4316	21	5	rights	right	NOUN
ejpam-4316	21	6	reserved	reserve	VERB
ejpam-4316	21	7	.	.	PUNCT
ejpam-4316	22	1	f.j.h	f.j.h	ADJ
ejpam-4316	22	2	.	.	PUNCT
ejpam-4316	23	1	campeña	campeña	NOUN
ejpam-4316	23	2	,	,	PUNCT
ejpam-4316	23	3	m.c.g	m.c.g	PROPN
ejpam-4316	23	4	.	.	PUNCT
ejpam-4316	23	5	egan	egan	PROPN
ejpam-4316	23	6	,	,	PUNCT
ejpam-4316	23	7	j.r.m	j.r.m	PROPN
ejpam-4316	23	8	.	.	PUNCT
ejpam-4316	24	1	antalan	antalan	PROPN
ejpam-4316	24	2	/	/	SYM
ejpam-4316	24	3	eur	eur	PROPN
ejpam-4316	24	4	.	.	PUNCT
ejpam-4316	25	1	j.	j.	PROPN
ejpam-4316	25	2	pure	pure	PROPN
ejpam-4316	25	3	appl	appl	PROPN
ejpam-4316	25	4	.	.	PROPN
ejpam-4316	25	5	math	math	PROPN
ejpam-4316	25	6	,	,	PUNCT
ejpam-4316	25	7	15	15	NUM
ejpam-4316	25	8	(	(	PUNCT
ejpam-4316	25	9	2	2	NUM
ejpam-4316	25	10	)	)	PUNCT
ejpam-4316	25	11	(	(	PUNCT
ejpam-4316	25	12	2022	2022	NUM
ejpam-4316	25	13	)	)	PUNCT
ejpam-4316	25	14	,	,	PUNCT
ejpam-4316	25	15	602	602	NUM
ejpam-4316	25	16	-	-	SYM
ejpam-4316	25	17	619	619	NUM
ejpam-4316	25	18	603	603	NUM
ejpam-4316	25	19	studied	study	VERB
ejpam-4316	25	20	the	the	DET
ejpam-4316	25	21	qspr	qspr	NOUN
ejpam-4316	25	22	of	of	ADP
ejpam-4316	25	23	phytochemicals	phytochemical	NOUN
ejpam-4316	25	24	screened	screen	VERB
ejpam-4316	25	25	against	against	ADP
ejpam-4316	25	26	sars	sar	NOUN
ejpam-4316	25	27	-	-	PUNCT
ejpam-4316	25	28	cov-2	cov-2	NOUN
ejpam-4316	25	29	3clpro	3clpro	NUM
ejpam-4316	25	30	with	with	ADP
ejpam-4316	25	31	the	the	DET
ejpam-4316	25	32	help	help	NOUN
ejpam-4316	25	33	of	of	ADP
ejpam-4316	25	34	several	several	ADJ
ejpam-4316	25	35	topological	topological	ADJ
ejpam-4316	25	36	indices	index	NOUN
ejpam-4316	25	37	[	[	X
ejpam-4316	25	38	10	10	NUM
ejpam-4316	25	39	]	]	PUNCT
ejpam-4316	25	40	.	.	PUNCT
ejpam-4316	26	1	in	in	ADP
ejpam-4316	26	2	general	general	ADJ
ejpam-4316	26	3	,	,	PUNCT
ejpam-4316	26	4	a	a	DET
ejpam-4316	26	5	topological	topological	ADJ
ejpam-4316	26	6	index	index	NOUN
ejpam-4316	26	7	,	,	PUNCT
ejpam-4316	26	8	also	also	ADV
ejpam-4316	26	9	known	know	VERB
ejpam-4316	26	10	as	as	ADP
ejpam-4316	26	11	a	a	DET
ejpam-4316	26	12	graph	graph	NOUN
ejpam-4316	26	13	-	-	PUNCT
ejpam-4316	26	14	theoretic	theoretic	NOUN
ejpam-4316	26	15	index	index	NOUN
ejpam-4316	26	16	,	,	PUNCT
ejpam-4316	26	17	is	be	AUX
ejpam-4316	26	18	a	a	DET
ejpam-4316	26	19	numerical	numerical	ADJ
ejpam-4316	26	20	invariant	invariant	NOUN
ejpam-4316	26	21	of	of	ADP
ejpam-4316	26	22	a	a	DET
ejpam-4316	26	23	chemical	chemical	NOUN
ejpam-4316	26	24	graph	graph	NOUN
ejpam-4316	26	25	.	.	PUNCT
ejpam-4316	27	1	harary	harary	PROPN
ejpam-4316	27	2	index	index	PROPN
ejpam-4316	27	3	,	,	PUNCT
ejpam-4316	27	4	balaban	balaban	PROPN
ejpam-4316	27	5	index	index	NOUN
ejpam-4316	27	6	,	,	PUNCT
ejpam-4316	27	7	molecular	molecular	ADJ
ejpam-4316	27	8	topological	topological	ADJ
ejpam-4316	27	9	index	index	NOUN
ejpam-4316	27	10	,	,	PUNCT
ejpam-4316	27	11	wiener	wiener	NOUN
ejpam-4316	27	12	index	index	NOUN
ejpam-4316	27	13	,	,	PUNCT
ejpam-4316	27	14	hyper	hyper	NOUN
ejpam-4316	27	15	-	-	ADJ
ejpam-4316	27	16	wiener	wiener	NOUN
ejpam-4316	27	17	index	index	NOUN
ejpam-4316	27	18	,	,	PUNCT
ejpam-4316	27	19	and	and	CCONJ
ejpam-4316	27	20	zagreb	zagreb	PROPN
ejpam-4316	27	21	indices	index	NOUN
ejpam-4316	27	22	are	be	AUX
ejpam-4316	27	23	some	some	PRON
ejpam-4316	27	24	of	of	ADP
ejpam-4316	27	25	the	the	DET
ejpam-4316	27	26	well	well	ADV
ejpam-4316	27	27	-	-	PUNCT
ejpam-4316	27	28	studied	study	VERB
ejpam-4316	27	29	topological	topological	ADJ
ejpam-4316	27	30	indices	index	NOUN
ejpam-4316	27	31	.	.	PUNCT
ejpam-4316	28	1	topological	topological	ADJ
ejpam-4316	28	2	indices	index	NOUN
ejpam-4316	28	3	are	be	AUX
ejpam-4316	28	4	used	use	VERB
ejpam-4316	28	5	to	to	PART
ejpam-4316	28	6	represent	represent	VERB
ejpam-4316	28	7	each	each	DET
ejpam-4316	28	8	chemical	chemical	ADJ
ejpam-4316	28	9	structure	structure	NOUN
ejpam-4316	28	10	with	with	ADP
ejpam-4316	28	11	a	a	DET
ejpam-4316	28	12	numerical	numerical	ADJ
ejpam-4316	28	13	value	value	NOUN
ejpam-4316	28	14	.	.	PUNCT
ejpam-4316	29	1	these	these	DET
ejpam-4316	29	2	values	value	NOUN
ejpam-4316	29	3	are	be	AUX
ejpam-4316	29	4	used	use	VERB
ejpam-4316	29	5	to	to	PART
ejpam-4316	29	6	model	model	VERB
ejpam-4316	29	7	different	different	ADJ
ejpam-4316	29	8	physicochemical	physicochemical	ADJ
ejpam-4316	29	9	properties	property	NOUN
ejpam-4316	29	10	and	and	CCONJ
ejpam-4316	29	11	biological	biological	ADJ
ejpam-4316	29	12	activities	activity	NOUN
ejpam-4316	29	13	of	of	ADP
ejpam-4316	29	14	chemical	chemical	ADJ
ejpam-4316	29	15	compounds	compound	NOUN
ejpam-4316	29	16	[	[	X
ejpam-4316	29	17	15	15	NUM
ejpam-4316	29	18	]	]	PUNCT
ejpam-4316	29	19	.	.	PUNCT
ejpam-4316	30	1	the	the	DET
ejpam-4316	30	2	first	first	ADJ
ejpam-4316	30	3	topological	topological	ADJ
ejpam-4316	30	4	index	index	NOUN
ejpam-4316	30	5	was	be	AUX
ejpam-4316	30	6	introduced	introduce	VERB
ejpam-4316	30	7	by	by	ADP
ejpam-4316	30	8	harry	harry	PROPN
ejpam-4316	30	9	wiener	wiener	NOUN
ejpam-4316	30	10	in	in	ADP
ejpam-4316	30	11	1947	1947	NUM
ejpam-4316	30	12	.	.	PUNCT
ejpam-4316	31	1	he	he	PRON
ejpam-4316	31	2	computed	compute	VERB
ejpam-4316	31	3	the	the	DET
ejpam-4316	31	4	sum	sum	NOUN
ejpam-4316	31	5	of	of	ADP
ejpam-4316	31	6	the	the	DET
ejpam-4316	31	7	distances	distance	NOUN
ejpam-4316	31	8	of	of	ADP
ejpam-4316	31	9	the	the	DET
ejpam-4316	31	10	shortest	short	ADJ
ejpam-4316	31	11	path	path	NOUN
ejpam-4316	31	12	between	between	ADP
ejpam-4316	31	13	all	all	DET
ejpam-4316	31	14	pairs	pair	NOUN
ejpam-4316	31	15	of	of	ADP
ejpam-4316	31	16	vertices	vertex	NOUN
ejpam-4316	31	17	of	of	ADP
ejpam-4316	31	18	a	a	DET
ejpam-4316	31	19	graph	graph	NOUN
ejpam-4316	31	20	called	call	VERB
ejpam-4316	31	21	wiener	wiener	NOUN
ejpam-4316	31	22	index	index	NOUN
ejpam-4316	31	23	[	[	X
ejpam-4316	31	24	24	24	NUM
ejpam-4316	31	25	]	]	PUNCT
ejpam-4316	31	26	.	.	PUNCT
ejpam-4316	32	1	the	the	DET
ejpam-4316	32	2	concept	concept	NOUN
ejpam-4316	32	3	of	of	ADP
ejpam-4316	32	4	the	the	DET
ejpam-4316	32	5	wiener	wiener	NOUN
ejpam-4316	32	6	index	index	NOUN
ejpam-4316	32	7	was	be	AUX
ejpam-4316	32	8	generalized	generalize	VERB
ejpam-4316	32	9	by	by	ADP
ejpam-4316	32	10	milan	milan	PROPN
ejpam-4316	32	11	randic	randic	ADJ
ejpam-4316	32	12	in	in	ADP
ejpam-4316	32	13	1993	1993	NUM
ejpam-4316	32	14	.	.	PUNCT
ejpam-4316	33	1	it	it	PRON
ejpam-4316	33	2	was	be	AUX
ejpam-4316	33	3	the	the	DET
ejpam-4316	33	4	extension	extension	NOUN
ejpam-4316	33	5	for	for	ADP
ejpam-4316	33	6	all	all	DET
ejpam-4316	33	7	connected	connected	ADJ
ejpam-4316	33	8	graphs	graph	NOUN
ejpam-4316	33	9	and	and	CCONJ
ejpam-4316	33	10	called	call	VERB
ejpam-4316	33	11	it	it	PRON
ejpam-4316	33	12	hyper	hyper	ADJ
ejpam-4316	33	13	-	-	ADJ
ejpam-4316	33	14	wiener	wiener	NOUN
ejpam-4316	33	15	index	index	NOUN
ejpam-4316	33	16	[	[	X
ejpam-4316	33	17	14	14	NUM
ejpam-4316	33	18	]	]	PUNCT
ejpam-4316	33	19	.	.	PUNCT
ejpam-4316	34	1	the	the	DET
ejpam-4316	34	2	sum	sum	NOUN
ejpam-4316	34	3	of	of	ADP
ejpam-4316	34	4	reciprocals	reciprocal	NOUN
ejpam-4316	34	5	of	of	ADP
ejpam-4316	34	6	distances	distance	NOUN
ejpam-4316	34	7	between	between	ADP
ejpam-4316	34	8	all	all	DET
ejpam-4316	34	9	pairs	pair	NOUN
ejpam-4316	34	10	of	of	ADP
ejpam-4316	34	11	vertices	vertex	NOUN
ejpam-4316	34	12	in	in	ADP
ejpam-4316	34	13	a	a	DET
ejpam-4316	34	14	graph	graph	NOUN
ejpam-4316	34	15	g	g	NOUN
ejpam-4316	34	16	is	be	AUX
ejpam-4316	34	17	called	call	VERB
ejpam-4316	34	18	the	the	DET
ejpam-4316	34	19	harary	harary	PROPN
ejpam-4316	34	20	index	index	NOUN
ejpam-4316	34	21	,	,	PUNCT
ejpam-4316	34	22	denoted	denote	VERB
ejpam-4316	34	23	by	by	ADP
ejpam-4316	34	24	h(g	h(g	NOUN
ejpam-4316	34	25	)	)	PUNCT
ejpam-4316	34	26	.	.	PUNCT
ejpam-4316	35	1	it	it	PRON
ejpam-4316	35	2	was	be	AUX
ejpam-4316	35	3	introduced	introduce	VERB
ejpam-4316	35	4	independently	independently	ADV
ejpam-4316	35	5	by	by	ADP
ejpam-4316	35	6	plavšić	plavšić	PROPN
ejpam-4316	35	7	et	et	PROPN
ejpam-4316	35	8	al	al	PROPN
ejpam-4316	35	9	.	.	PUNCT
ejpam-4316	36	1	[	[	X
ejpam-4316	36	2	17	17	NUM
ejpam-4316	36	3	]	]	PUNCT
ejpam-4316	36	4	and	and	CCONJ
ejpam-4316	36	5	by	by	ADP
ejpam-4316	36	6	ivanciuc	ivanciuc	PROPN
ejpam-4316	36	7	et	et	PROPN
ejpam-4316	36	8	al	al	PROPN
ejpam-4316	36	9	.	.	PUNCT
ejpam-4316	37	1	[	[	X
ejpam-4316	37	2	11	11	NUM
ejpam-4316	37	3	]	]	PUNCT
ejpam-4316	37	4	in	in	ADP
ejpam-4316	37	5	1993	1993	NUM
ejpam-4316	37	6	.	.	PUNCT
ejpam-4316	38	1	a	a	DET
ejpam-4316	38	2	variety	variety	NOUN
ejpam-4316	38	3	of	of	ADP
ejpam-4316	38	4	topological	topological	ADJ
ejpam-4316	38	5	indices	index	NOUN
ejpam-4316	38	6	have	have	AUX
ejpam-4316	38	7	been	be	AUX
ejpam-4316	38	8	studied	study	VERB
ejpam-4316	38	9	.	.	PUNCT
ejpam-4316	39	1	in	in	ADP
ejpam-4316	39	2	particular	particular	ADJ
ejpam-4316	39	3	,	,	PUNCT
ejpam-4316	39	4	the	the	DET
ejpam-4316	39	5	balaban	balaban	PROPN
ejpam-4316	39	6	index	index	NOUN
ejpam-4316	39	7	,	,	PUNCT
ejpam-4316	39	8	also	also	ADV
ejpam-4316	39	9	called	call	VERB
ejpam-4316	39	10	j	j	PROPN
ejpam-4316	39	11	index	index	NOUN
ejpam-4316	39	12	was	be	AUX
ejpam-4316	39	13	developed	develop	VERB
ejpam-4316	39	14	by	by	ADP
ejpam-4316	39	15	balaban	balaban	NOUN
ejpam-4316	40	1	[	[	X
ejpam-4316	40	2	2	2	NUM
ejpam-4316	40	3	]	]	PUNCT
ejpam-4316	40	4	.	.	PUNCT
ejpam-4316	41	1	de	de	ADP
ejpam-4316	41	2	first	first	ADJ
ejpam-4316	41	3	derived	derive	VERB
ejpam-4316	41	4	explicit	explicit	ADJ
ejpam-4316	41	5	expression	expression	NOUN
ejpam-4316	41	6	of	of	ADP
ejpam-4316	41	7	reformulated	reformulate	VERB
ejpam-4316	41	8	first	first	ADJ
ejpam-4316	41	9	zagreb	zagreb	PROPN
ejpam-4316	41	10	index	index	NOUN
ejpam-4316	41	11	of	of	ADP
ejpam-4316	41	12	generalized	generalized	ADJ
ejpam-4316	41	13	hierarchical	hierarchical	ADJ
ejpam-4316	41	14	product	product	NOUN
ejpam-4316	41	15	of	of	ADP
ejpam-4316	41	16	two	two	NUM
ejpam-4316	41	17	connected	connected	ADJ
ejpam-4316	41	18	graphs	graph	NOUN
ejpam-4316	41	19	[	[	X
ejpam-4316	41	20	3	3	NUM
ejpam-4316	41	21	]	]	PUNCT
ejpam-4316	41	22	.	.	PUNCT
ejpam-4316	42	1	gao	gao	PROPN
ejpam-4316	42	2	et	et	PROPN
ejpam-4316	42	3	.	.	PUNCT
ejpam-4316	43	1	al	al	PROPN
ejpam-4316	43	2	developed	develop	VERB
ejpam-4316	43	3	some	some	DET
ejpam-4316	43	4	degree	degree	NOUN
ejpam-4316	43	5	-	-	PUNCT
ejpam-4316	43	6	based	base	VERB
ejpam-4316	43	7	topological	topological	ADJ
ejpam-4316	43	8	indices	index	NOUN
ejpam-4316	43	9	of	of	ADP
ejpam-4316	43	10	networks	network	NOUN
ejpam-4316	43	11	derived	derive	VERB
ejpam-4316	43	12	from	from	ADP
ejpam-4316	43	13	honey	honey	NOUN
ejpam-4316	43	14	comb	comb	NOUN
ejpam-4316	43	15	networks	network	NOUN
ejpam-4316	43	16	[	[	X
ejpam-4316	43	17	6	6	NUM
ejpam-4316	43	18	]	]	PUNCT
ejpam-4316	43	19	.	.	PUNCT
ejpam-4316	44	1	recently	recently	ADV
ejpam-4316	44	2	,	,	PUNCT
ejpam-4316	44	3	mondal	mondal	PROPN
ejpam-4316	44	4	et	et	PROPN
ejpam-4316	44	5	.	.	PUNCT
ejpam-4316	45	1	al	al	PROPN
ejpam-4316	45	2	obtained	obtain	VERB
ejpam-4316	45	3	some	some	PRON
ejpam-4316	45	4	of	of	ADP
ejpam-4316	45	5	the	the	DET
ejpam-4316	45	6	topological	topological	ADJ
ejpam-4316	45	7	properties	property	NOUN
ejpam-4316	45	8	of	of	ADP
ejpam-4316	45	9	some	some	DET
ejpam-4316	45	10	chemical	chemical	NOUN
ejpam-4316	45	11	structures	structure	NOUN
ejpam-4316	45	12	used	use	VERB
ejpam-4316	45	13	to	to	PART
ejpam-4316	45	14	inhibit	inhibit	VERB
ejpam-4316	45	15	the	the	DET
ejpam-4316	45	16	outbreak	outbreak	NOUN
ejpam-4316	45	17	and	and	CCONJ
ejpam-4316	45	18	transmission	transmission	NOUN
ejpam-4316	45	19	of	of	ADP
ejpam-4316	45	20	covid-19	covid-19	PROPN
ejpam-4316	45	21	in	in	ADP
ejpam-4316	45	22	terms	term	NOUN
ejpam-4316	45	23	of	of	ADP
ejpam-4316	45	24	some	some	PRON
ejpam-4316	45	25	degree	degree	NOUN
ejpam-4316	45	26	-	-	PUNCT
ejpam-4316	45	27	based	base	VERB
ejpam-4316	45	28	and	and	CCONJ
ejpam-4316	45	29	some	some	DET
ejpam-4316	45	30	neighborhood	neighborhood	NOUN
ejpam-4316	45	31	degree	degree	NOUN
ejpam-4316	45	32	sum	sum	NOUN
ejpam-4316	45	33	-	-	PUNCT
ejpam-4316	45	34	based	base	VERB
ejpam-4316	45	35	indices	index	NOUN
ejpam-4316	45	36	[	[	X
ejpam-4316	45	37	15	15	NUM
ejpam-4316	45	38	]	]	PUNCT
ejpam-4316	45	39	.	.	PUNCT
ejpam-4316	46	1	while	while	SCONJ
ejpam-4316	46	2	other	other	ADJ
ejpam-4316	46	3	researchers	researcher	NOUN
ejpam-4316	46	4	focused	focus	VERB
ejpam-4316	46	5	on	on	ADP
ejpam-4316	46	6	the	the	DET
ejpam-4316	46	7	wiener	wiener	NOUN
ejpam-4316	46	8	index	index	NOUN
ejpam-4316	46	9	of	of	ADP
ejpam-4316	46	10	a	a	DET
ejpam-4316	46	11	graph	graph	NOUN
ejpam-4316	46	12	obtained	obtain	VERB
ejpam-4316	46	13	by	by	ADP
ejpam-4316	46	14	some	some	DET
ejpam-4316	46	15	graph	graph	NOUN
ejpam-4316	46	16	operations	operation	NOUN
ejpam-4316	46	17	such	such	ADJ
ejpam-4316	46	18	as	as	ADP
ejpam-4316	46	19	yeh	yeh	PROPN
ejpam-4316	46	20	and	and	CCONJ
ejpam-4316	46	21	gutman	gutman	NOUN
ejpam-4316	46	22	in	in	ADP
ejpam-4316	46	23	[	[	X
ejpam-4316	46	24	25	25	NUM
ejpam-4316	46	25	]	]	PUNCT
ejpam-4316	46	26	studied	study	VERB
ejpam-4316	46	27	the	the	DET
ejpam-4316	46	28	wiener	wiener	NOUN
ejpam-4316	46	29	index	index	NOUN
ejpam-4316	46	30	of	of	ADP
ejpam-4316	46	31	graphs	graph	NOUN
ejpam-4316	46	32	obtained	obtain	VERB
ejpam-4316	46	33	by	by	ADP
ejpam-4316	46	34	means	mean	NOUN
ejpam-4316	46	35	of	of	ADP
ejpam-4316	46	36	certain	certain	ADJ
ejpam-4316	46	37	binary	binary	ADJ
ejpam-4316	46	38	operations	operation	NOUN
ejpam-4316	46	39	on	on	ADP
ejpam-4316	46	40	pairs	pair	NOUN
ejpam-4316	46	41	of	of	ADP
ejpam-4316	46	42	graphs	graph	NOUN
ejpam-4316	46	43	.	.	PUNCT
ejpam-4316	47	1	stevanović	stevanović	PROPN
ejpam-4316	47	2	generalized	generalize	VERB
ejpam-4316	47	3	these	these	DET
ejpam-4316	47	4	results	result	NOUN
ejpam-4316	47	5	to	to	PART
ejpam-4316	47	6	determine	determine	VERB
ejpam-4316	47	7	the	the	DET
ejpam-4316	47	8	wiener	wiener	NOUN
ejpam-4316	47	9	polynomial	polynomial	NOUN
ejpam-4316	47	10	of	of	ADP
ejpam-4316	47	11	the	the	DET
ejpam-4316	47	12	composite	composite	ADJ
ejpam-4316	47	13	graphs	graph	NOUN
ejpam-4316	47	14	[	[	X
ejpam-4316	47	15	21	21	NUM
ejpam-4316	47	16	]	]	PUNCT
ejpam-4316	47	17	.	.	PUNCT
ejpam-4316	48	1	the	the	DET
ejpam-4316	48	2	hyper	hyper	ADJ
ejpam-4316	48	3	-	-	ADJ
ejpam-4316	48	4	wiener	wiener	NOUN
ejpam-4316	48	5	index	index	NOUN
ejpam-4316	48	6	of	of	ADP
ejpam-4316	48	7	these	these	DET
ejpam-4316	48	8	operations	operation	NOUN
ejpam-4316	48	9	determined	determine	VERB
ejpam-4316	48	10	by	by	ADP
ejpam-4316	48	11	khalifeh	khalifeh	PROPN
ejpam-4316	48	12	et	et	PROPN
ejpam-4316	48	13	.	.	PUNCT
ejpam-4316	49	1	al	al	PROPN
ejpam-4316	49	2	in	in	ADP
ejpam-4316	49	3	[	[	X
ejpam-4316	49	4	12	12	NUM
ejpam-4316	49	5	]	]	PUNCT
ejpam-4316	49	6	.	.	PUNCT
ejpam-4316	50	1	eliasi	eliasi	PROPN
ejpam-4316	50	2	et	et	PROPN
ejpam-4316	50	3	.	.	PUNCT
ejpam-4316	51	1	al	al	PROPN
ejpam-4316	51	2	computed	compute	VERB
ejpam-4316	51	3	the	the	DET
ejpam-4316	51	4	values	value	NOUN
ejpam-4316	51	5	of	of	ADP
ejpam-4316	51	6	the	the	DET
ejpam-4316	51	7	wiener	wiener	NOUN
ejpam-4316	51	8	index	index	NOUN
ejpam-4316	51	9	of	of	ADP
ejpam-4316	51	10	a	a	DET
ejpam-4316	51	11	graph	graph	NOUN
ejpam-4316	51	12	obtained	obtain	VERB
ejpam-4316	51	13	by	by	ADP
ejpam-4316	51	14	some	some	DET
ejpam-4316	51	15	graph	graph	NOUN
ejpam-4316	51	16	operations	operation	NOUN
ejpam-4316	51	17	[	[	X
ejpam-4316	51	18	5	5	NUM
ejpam-4316	51	19	]	]	PUNCT
ejpam-4316	51	20	.	.	PUNCT
ejpam-4316	52	1	moreover	moreover	ADV
ejpam-4316	52	2	,	,	PUNCT
ejpam-4316	52	3	a	a	DET
ejpam-4316	52	4	study	study	NOUN
ejpam-4316	52	5	on	on	ADP
ejpam-4316	52	6	the	the	DET
ejpam-4316	52	7	wiener	wiener	NOUN
ejpam-4316	52	8	index	index	NOUN
ejpam-4316	52	9	of	of	ADP
ejpam-4316	52	10	a	a	DET
ejpam-4316	52	11	graph	graph	NOUN
ejpam-4316	52	12	obtained	obtain	VERB
ejpam-4316	52	13	from	from	ADP
ejpam-4316	52	14	some	some	DET
ejpam-4316	52	15	graph	graph	NOUN
ejpam-4316	52	16	operation	operation	NOUN
ejpam-4316	52	17	is	be	AUX
ejpam-4316	52	18	called	call	VERB
ejpam-4316	52	19	sum	sum	NOUN
ejpam-4316	52	20	of	of	ADP
ejpam-4316	52	21	shadow	shadow	NOUN
ejpam-4316	52	22	graphs	graph	NOUN
ejpam-4316	52	23	[	[	X
ejpam-4316	52	24	7	7	NUM
ejpam-4316	52	25	]	]	PUNCT
ejpam-4316	52	26	.	.	PUNCT
ejpam-4316	53	1	in	in	ADP
ejpam-4316	53	2	this	this	DET
ejpam-4316	53	3	paper	paper	NOUN
ejpam-4316	53	4	we	we	PRON
ejpam-4316	53	5	only	only	ADV
ejpam-4316	53	6	consider	consider	VERB
ejpam-4316	53	7	a	a	DET
ejpam-4316	53	8	finite	finite	ADJ
ejpam-4316	53	9	simple	simple	ADJ
ejpam-4316	53	10	undirected	undirected	ADJ
ejpam-4316	53	11	graph	graph	NOUN
ejpam-4316	53	12	g	g	PROPN
ejpam-4316	53	13	=	=	PUNCT
ejpam-4316	53	14	(	(	PUNCT
ejpam-4316	53	15	v	v	NOUN
ejpam-4316	53	16	,	,	PUNCT
ejpam-4316	53	17	e	e	NOUN
ejpam-4316	53	18	)	)	PUNCT
ejpam-4316	53	19	and	and	CCONJ
ejpam-4316	53	20	s	s	VERB
ejpam-4316	53	21	⊆	⊆	NUM
ejpam-4316	53	22	v	v	NOUN
ejpam-4316	53	23	=	=	SYM
ejpam-4316	53	24	{	{	PUNCT
ejpam-4316	53	25	x1	x1	PROPN
ejpam-4316	53	26	,	,	PUNCT
ejpam-4316	53	27	x2	x2	PROPN
ejpam-4316	53	28	,	,	PUNCT
ejpam-4316	53	29	.	.	PUNCT
ejpam-4316	53	30	.	.	PUNCT
ejpam-4316	54	1	.	.	PUNCT
ejpam-4316	55	1	,	,	PUNCT
ejpam-4316	55	2	xn	xn	X
ejpam-4316	55	3	}	}	PUNCT
ejpam-4316	55	4	where	where	SCONJ
ejpam-4316	55	5	n	n	PRON
ejpam-4316	55	6	≥	≥	NOUN
ejpam-4316	55	7	1	1	NUM
ejpam-4316	55	8	.	.	PUNCT
ejpam-4316	55	9	define	define	VERB
ejpam-4316	55	10	a	a	DET
ejpam-4316	55	11	graph	graph	NOUN
ejpam-4316	55	12	γ	γ	X
ejpam-4316	55	13	=	=	SYM
ejpam-4316	55	14	γ(g	γ(g	PROPN
ejpam-4316	55	15	,	,	PUNCT
ejpam-4316	55	16	s	s	PART
ejpam-4316	55	17	)	)	PUNCT
ejpam-4316	55	18	to	to	PART
ejpam-4316	55	19	be	be	AUX
ejpam-4316	55	20	a	a	DET
ejpam-4316	55	21	graph	graph	NOUN
ejpam-4316	55	22	obtained	obtain	VERB
ejpam-4316	55	23	from	from	ADP
ejpam-4316	55	24	g	g	NOUN
ejpam-4316	55	25	by	by	ADP
ejpam-4316	55	26	replicating	replicate	VERB
ejpam-4316	55	27	the	the	DET
ejpam-4316	55	28	vertices	vertex	NOUN
ejpam-4316	55	29	x	x	X
ejpam-4316	55	30	in	in	ADP
ejpam-4316	55	31	s	s	PRON
ejpam-4316	55	32	as	as	ADV
ejpam-4316	55	33	well	well	ADV
ejpam-4316	55	34	as	as	ADP
ejpam-4316	55	35	the	the	DET
ejpam-4316	55	36	edges	edge	NOUN
ejpam-4316	55	37	adjacent	adjacent	ADJ
ejpam-4316	55	38	to	to	ADP
ejpam-4316	55	39	it	it	PRON
ejpam-4316	55	40	,	,	PUNCT
ejpam-4316	55	41	that	that	PRON
ejpam-4316	55	42	is	be	AUX
ejpam-4316	55	43	;	;	PUNCT
ejpam-4316	55	44	v	v	X
ejpam-4316	55	45	(	(	PUNCT
ejpam-4316	55	46	γ	γ	NOUN
ejpam-4316	55	47	)	)	PUNCT
ejpam-4316	55	48	=	=	SYM
ejpam-4316	55	49	v	v	ADP
ejpam-4316	55	50	∪{x′|x	∪{x′|x	NOUN
ejpam-4316	55	51	∈	∈	PROPN
ejpam-4316	55	52	s	s	X
ejpam-4316	55	53	}	}	PUNCT
ejpam-4316	55	54	and	and	CCONJ
ejpam-4316	55	55	e(γ	e(γ	NOUN
ejpam-4316	55	56	)	)	PUNCT
ejpam-4316	56	1	=	=	SYM
ejpam-4316	56	2	e	e	X
ejpam-4316	56	3	∪{x′u|u	∪{x′u|u	NOUN
ejpam-4316	56	4	∈	∈	PROPN
ejpam-4316	56	5	ng(x	ng(x	NUM
ejpam-4316	56	6	)	)	PUNCT
ejpam-4316	56	7	}	}	PUNCT
ejpam-4316	56	8	where	where	SCONJ
ejpam-4316	56	9	n(x	n(x	PROPN
ejpam-4316	56	10	)	)	PUNCT
ejpam-4316	56	11	is	be	AUX
ejpam-4316	56	12	the	the	DET
ejpam-4316	56	13	set	set	NOUN
ejpam-4316	56	14	of	of	ADP
ejpam-4316	56	15	vertices	vertex	NOUN
ejpam-4316	56	16	in	in	ADP
ejpam-4316	56	17	g	g	PROPN
ejpam-4316	56	18	adjacent	adjacent	ADJ
ejpam-4316	56	19	to	to	PART
ejpam-4316	56	20	x.	x.	VERB
ejpam-4316	56	21	the	the	DET
ejpam-4316	56	22	graph	graph	NOUN
ejpam-4316	56	23	γ(g	γ(g	PROPN
ejpam-4316	56	24	,	,	PUNCT
ejpam-4316	56	25	s	s	PART
ejpam-4316	56	26	)	)	PUNCT
ejpam-4316	56	27	obtained	obtain	VERB
ejpam-4316	56	28	is	be	AUX
ejpam-4316	56	29	called	call	VERB
ejpam-4316	56	30	an	an	DET
ejpam-4316	56	31	s	s	NOUN
ejpam-4316	56	32	-	-	PUNCT
ejpam-4316	56	33	splitting	splitting	NOUN
ejpam-4316	56	34	of	of	ADP
ejpam-4316	56	35	g.	g.	PROPN
ejpam-4316	56	36	if	if	SCONJ
ejpam-4316	56	37	s	s	VERB
ejpam-4316	56	38	=	=	SYM
ejpam-4316	56	39	v	v	NOUN
ejpam-4316	56	40	,	,	PUNCT
ejpam-4316	56	41	then	then	ADV
ejpam-4316	56	42	the	the	DET
ejpam-4316	56	43	graph	graph	NOUN
ejpam-4316	56	44	γ(g	γ(g	PROPN
ejpam-4316	56	45	,	,	PUNCT
ejpam-4316	56	46	v	v	NOUN
ejpam-4316	56	47	)	)	PUNCT
ejpam-4316	56	48	is	be	AUX
ejpam-4316	56	49	the	the	DET
ejpam-4316	56	50	splitting	splitting	NOUN
ejpam-4316	56	51	graph	graph	NOUN
ejpam-4316	56	52	of	of	ADP
ejpam-4316	56	53	a	a	DET
ejpam-4316	56	54	graph	graph	NOUN
ejpam-4316	56	55	g	g	NOUN
ejpam-4316	56	56	as	as	SCONJ
ejpam-4316	56	57	defined	define	VERB
ejpam-4316	56	58	by	by	ADP
ejpam-4316	56	59	sampathkumar	sampathkumar	PROPN
ejpam-4316	56	60	et	et	PROPN
ejpam-4316	56	61	al	al	PROPN
ejpam-4316	56	62	.	.	PUNCT
ejpam-4316	57	1	[	[	X
ejpam-4316	57	2	19	19	NUM
ejpam-4316	57	3	]	]	PUNCT
ejpam-4316	57	4	.	.	PUNCT
ejpam-4316	58	1	it	it	PRON
ejpam-4316	58	2	is	be	AUX
ejpam-4316	58	3	worthwhile	worthwhile	ADJ
ejpam-4316	58	4	to	to	PART
ejpam-4316	58	5	note	note	VERB
ejpam-4316	58	6	that	that	SCONJ
ejpam-4316	58	7	the	the	DET
ejpam-4316	58	8	definition	definition	NOUN
ejpam-4316	58	9	of	of	ADP
ejpam-4316	58	10	an	an	DET
ejpam-4316	58	11	s	s	NOUN
ejpam-4316	58	12	-	-	PUNCT
ejpam-4316	58	13	splitting	splitting	NOUN
ejpam-4316	58	14	graph	graph	NOUN
ejpam-4316	58	15	of	of	ADP
ejpam-4316	58	16	g	g	PROPN
ejpam-4316	58	17	is	be	AUX
ejpam-4316	58	18	similar	similar	ADJ
ejpam-4316	58	19	to	to	ADP
ejpam-4316	58	20	the	the	DET
ejpam-4316	58	21	double	double	ADJ
ejpam-4316	58	22	graph	graph	NOUN
ejpam-4316	58	23	d[g	d[g	NOUN
ejpam-4316	58	24	]	]	PUNCT
ejpam-4316	58	25	defined	define	VERB
ejpam-4316	58	26	in	in	ADP
ejpam-4316	58	27	[	[	X
ejpam-4316	58	28	16	16	NUM
ejpam-4316	58	29	]	]	PUNCT
ejpam-4316	58	30	.	.	PUNCT
ejpam-4316	59	1	in	in	ADP
ejpam-4316	59	2	particular	particular	ADJ
ejpam-4316	59	3	,	,	PUNCT
ejpam-4316	59	4	γ(g	γ(g	PROPN
ejpam-4316	59	5	)	)	PUNCT
ejpam-4316	59	6	⊆	⊆	NUM
ejpam-4316	59	7	d[g	d[g	NOUN
ejpam-4316	59	8	]	]	PUNCT
ejpam-4316	59	9	.	.	PUNCT
ejpam-4316	60	1	the	the	DET
ejpam-4316	60	2	case	case	NOUN
ejpam-4316	60	3	of	of	ADP
ejpam-4316	60	4	double	double	ADJ
ejpam-4316	60	5	graphs	graph	NOUN
ejpam-4316	60	6	is	be	AUX
ejpam-4316	60	7	more	more	ADV
ejpam-4316	60	8	simple	simple	ADJ
ejpam-4316	60	9	than	than	ADP
ejpam-4316	60	10	an	an	DET
ejpam-4316	60	11	s	s	NOUN
ejpam-4316	60	12	-	-	NOUN
ejpam-4316	60	13	splitting	splitting	NOUN
ejpam-4316	60	14	of	of	ADP
ejpam-4316	60	15	g	g	NOUN
ejpam-4316	60	16	in	in	ADP
ejpam-4316	60	17	terms	term	NOUN
ejpam-4316	60	18	of	of	ADP
ejpam-4316	60	19	computing	compute	VERB
ejpam-4316	60	20	some	some	DET
ejpam-4316	60	21	topological	topological	ADJ
ejpam-4316	60	22	indices	index	NOUN
ejpam-4316	60	23	.	.	PUNCT
ejpam-4316	61	1	the	the	DET
ejpam-4316	61	2	preliminary	preliminary	ADJ
ejpam-4316	61	3	concepts	concept	NOUN
ejpam-4316	61	4	are	be	AUX
ejpam-4316	61	5	presented	present	VERB
ejpam-4316	61	6	in	in	ADP
ejpam-4316	61	7	section	section	NOUN
ejpam-4316	61	8	2	2	NUM
ejpam-4316	61	9	.	.	PUNCT
ejpam-4316	62	1	the	the	DET
ejpam-4316	62	2	s	s	NOUN
ejpam-4316	62	3	-	-	PUNCT
ejpam-4316	62	4	splitting	splitting	NOUN
ejpam-4316	62	5	graph	graph	NOUN
ejpam-4316	62	6	of	of	ADP
ejpam-4316	62	7	g	g	NOUN
ejpam-4316	62	8	,	,	PUNCT
ejpam-4316	62	9	f.j.h	f.j.h	ADJ
ejpam-4316	62	10	.	.	PUNCT
ejpam-4316	63	1	campeña	campeña	NOUN
ejpam-4316	63	2	,	,	PUNCT
ejpam-4316	63	3	m.c.g	m.c.g	PROPN
ejpam-4316	63	4	.	.	PUNCT
ejpam-4316	63	5	egan	egan	PROPN
ejpam-4316	63	6	,	,	PUNCT
ejpam-4316	63	7	j.r.m	j.r.m	PROPN
ejpam-4316	63	8	.	.	PUNCT
ejpam-4316	64	1	antalan	antalan	PROPN
ejpam-4316	64	2	/	/	SYM
ejpam-4316	64	3	eur	eur	PROPN
ejpam-4316	64	4	.	.	PUNCT
ejpam-4316	65	1	j.	j.	PROPN
ejpam-4316	65	2	pure	pure	PROPN
ejpam-4316	65	3	appl	appl	PROPN
ejpam-4316	65	4	.	.	PROPN
ejpam-4316	65	5	math	math	PROPN
ejpam-4316	65	6	,	,	PUNCT
ejpam-4316	65	7	15	15	NUM
ejpam-4316	65	8	(	(	PUNCT
ejpam-4316	65	9	2	2	NUM
ejpam-4316	65	10	)	)	PUNCT
ejpam-4316	65	11	(	(	PUNCT
ejpam-4316	65	12	2022	2022	NUM
ejpam-4316	65	13	)	)	PUNCT
ejpam-4316	65	14	,	,	PUNCT
ejpam-4316	65	15	602	602	NUM
ejpam-4316	65	16	-	-	SYM
ejpam-4316	65	17	619	619	NUM
ejpam-4316	65	18	604	604	NUM
ejpam-4316	65	19	denoted	denote	VERB
ejpam-4316	65	20	by	by	ADP
ejpam-4316	65	21	γ(g	γ(g	PROPN
ejpam-4316	65	22	,	,	PUNCT
ejpam-4316	65	23	s	s	PART
ejpam-4316	65	24	)	)	PUNCT
ejpam-4316	65	25	is	be	AUX
ejpam-4316	65	26	formally	formally	ADV
ejpam-4316	65	27	defined	define	VERB
ejpam-4316	65	28	in	in	ADP
ejpam-4316	65	29	section	section	NOUN
ejpam-4316	65	30	3	3	NUM
ejpam-4316	65	31	.	.	PUNCT
ejpam-4316	66	1	the	the	DET
ejpam-4316	66	2	computations	computation	NOUN
ejpam-4316	66	3	for	for	ADP
ejpam-4316	66	4	the	the	DET
ejpam-4316	66	5	weiner	weiner	NOUN
ejpam-4316	66	6	index	index	NOUN
ejpam-4316	66	7	of	of	ADP
ejpam-4316	66	8	the	the	DET
ejpam-4316	66	9	s	s	NOUN
ejpam-4316	66	10	-	-	PUNCT
ejpam-4316	66	11	splitting	splitting	NOUN
ejpam-4316	66	12	graph	graph	NOUN
ejpam-4316	66	13	γ(g	γ(g	PROPN
ejpam-4316	66	14	,	,	PUNCT
ejpam-4316	66	15	s	s	PART
ejpam-4316	66	16	)	)	PUNCT
ejpam-4316	66	17	are	be	AUX
ejpam-4316	66	18	also	also	ADV
ejpam-4316	66	19	included	include	VERB
ejpam-4316	66	20	in	in	ADP
ejpam-4316	66	21	this	this	DET
ejpam-4316	66	22	section	section	NOUN
ejpam-4316	66	23	.	.	PUNCT
ejpam-4316	67	1	in	in	ADP
ejpam-4316	67	2	chapter	chapter	NOUN
ejpam-4316	67	3	4	4	NUM
ejpam-4316	67	4	,	,	PUNCT
ejpam-4316	67	5	we	we	PRON
ejpam-4316	67	6	have	have	VERB
ejpam-4316	67	7	the	the	DET
ejpam-4316	67	8	computations	computation	NOUN
ejpam-4316	67	9	for	for	ADP
ejpam-4316	67	10	the	the	DET
ejpam-4316	67	11	harary	harary	PROPN
ejpam-4316	67	12	index	index	NOUN
ejpam-4316	67	13	of	of	ADP
ejpam-4316	67	14	γ(g	γ(g	PROPN
ejpam-4316	67	15	,	,	PUNCT
ejpam-4316	67	16	s	s	PART
ejpam-4316	67	17	)	)	PUNCT
ejpam-4316	67	18	.	.	PUNCT
ejpam-4316	68	1	2	2	X
ejpam-4316	68	2	.	.	X
ejpam-4316	68	3	preliminary	preliminary	ADJ
ejpam-4316	68	4	concepts	concept	NOUN
ejpam-4316	68	5	in	in	ADP
ejpam-4316	68	6	this	this	DET
ejpam-4316	68	7	study	study	NOUN
ejpam-4316	68	8	we	we	PRON
ejpam-4316	68	9	only	only	ADV
ejpam-4316	68	10	consider	consider	VERB
ejpam-4316	68	11	a	a	DET
ejpam-4316	68	12	simple	simple	ADJ
ejpam-4316	68	13	undirected	undirected	ADJ
ejpam-4316	68	14	graph	graph	NOUN
ejpam-4316	68	15	g	g	NOUN
ejpam-4316	68	16	with	with	ADP
ejpam-4316	68	17	a	a	DET
ejpam-4316	68	18	non	non	ADJ
ejpam-4316	68	19	-	-	ADJ
ejpam-4316	68	20	empty	empty	ADJ
ejpam-4316	68	21	finite	finite	NOUN
ejpam-4316	68	22	set	set	VERB
ejpam-4316	68	23	v	v	NOUN
ejpam-4316	68	24	of	of	ADP
ejpam-4316	68	25	vertices	vertex	NOUN
ejpam-4316	68	26	and	and	CCONJ
ejpam-4316	68	27	a	a	DET
ejpam-4316	68	28	finite	finite	ADJ
ejpam-4316	68	29	set	set	VERB
ejpam-4316	68	30	e	e	NOUN
ejpam-4316	68	31	of	of	ADP
ejpam-4316	68	32	edges	edge	NOUN
ejpam-4316	68	33	.	.	PUNCT
ejpam-4316	69	1	we	we	PRON
ejpam-4316	69	2	say	say	VERB
ejpam-4316	69	3	v	v	INTJ
ejpam-4316	69	4	(	(	PUNCT
ejpam-4316	69	5	g	g	NOUN
ejpam-4316	69	6	)	)	PUNCT
ejpam-4316	69	7	as	as	ADP
ejpam-4316	69	8	the	the	DET
ejpam-4316	69	9	vertex	vertex	NOUN
ejpam-4316	69	10	set	set	NOUN
ejpam-4316	69	11	and	and	CCONJ
ejpam-4316	69	12	e(g	e(g	PROPN
ejpam-4316	69	13	)	)	PUNCT
ejpam-4316	69	14	as	as	SCONJ
ejpam-4316	69	15	the	the	DET
ejpam-4316	69	16	edge	edge	NOUN
ejpam-4316	69	17	set	set	NOUN
ejpam-4316	69	18	.	.	PUNCT
ejpam-4316	70	1	we	we	PRON
ejpam-4316	70	2	denote	denote	VERB
ejpam-4316	70	3	any	any	DET
ejpam-4316	70	4	edge	edge	NOUN
ejpam-4316	70	5	in	in	ADP
ejpam-4316	70	6	e(g	e(g	NOUN
ejpam-4316	70	7	)	)	PUNCT
ejpam-4316	70	8	by	by	ADP
ejpam-4316	70	9	{	{	PUNCT
ejpam-4316	70	10	xi	xi	PROPN
ejpam-4316	70	11	,	,	PUNCT
ejpam-4316	70	12	xj	xj	PROPN
ejpam-4316	70	13	}	}	PUNCT
ejpam-4316	70	14	.	.	PUNCT
ejpam-4316	71	1	we	we	PRON
ejpam-4316	71	2	call	call	VERB
ejpam-4316	71	3	adjacent	adjacent	ADJ
ejpam-4316	71	4	these	these	DET
ejpam-4316	71	5	two	two	NUM
ejpam-4316	71	6	distinct	distinct	ADJ
ejpam-4316	71	7	vertices	vertex	NOUN
ejpam-4316	71	8	xi	xi	X
ejpam-4316	71	9	and	and	CCONJ
ejpam-4316	71	10	xj	xj	PROPN
ejpam-4316	71	11	in	in	ADP
ejpam-4316	71	12	e(g	e(g	PROPN
ejpam-4316	71	13	)	)	PUNCT
ejpam-4316	71	14	.	.	PUNCT
ejpam-4316	72	1	a	a	DET
ejpam-4316	72	2	set	set	NOUN
ejpam-4316	72	3	containing	contain	VERB
ejpam-4316	72	4	those	those	DET
ejpam-4316	72	5	vertices	vertex	NOUN
ejpam-4316	72	6	of	of	ADP
ejpam-4316	72	7	g	g	PROPN
ejpam-4316	72	8	that	that	PRON
ejpam-4316	72	9	are	be	AUX
ejpam-4316	72	10	adjacent	adjacent	ADJ
ejpam-4316	72	11	to	to	ADP
ejpam-4316	72	12	some	some	DET
ejpam-4316	72	13	vertex	vertex	NOUN
ejpam-4316	72	14	a	a	PRON
ejpam-4316	72	15	is	be	AUX
ejpam-4316	72	16	called	call	VERB
ejpam-4316	72	17	the	the	DET
ejpam-4316	72	18	neighbor	neighbor	NOUN
ejpam-4316	72	19	set	set	NOUN
ejpam-4316	72	20	of	of	ADP
ejpam-4316	72	21	a	a	PRON
ejpam-4316	72	22	,	,	PUNCT
ejpam-4316	72	23	denoted	denote	VERB
ejpam-4316	72	24	by	by	ADP
ejpam-4316	72	25	n(a	n(a	NOUN
ejpam-4316	72	26	)	)	PUNCT
ejpam-4316	72	27	.	.	PUNCT
ejpam-4316	73	1	a	a	DET
ejpam-4316	73	2	graph	graph	NOUN
ejpam-4316	73	3	g	g	NOUN
ejpam-4316	73	4	is	be	AUX
ejpam-4316	73	5	said	say	VERB
ejpam-4316	73	6	to	to	PART
ejpam-4316	73	7	be	be	AUX
ejpam-4316	73	8	a	a	DET
ejpam-4316	73	9	triangle	triangle	NOUN
ejpam-4316	73	10	free	free	ADJ
ejpam-4316	73	11	graph	graph	NOUN
ejpam-4316	73	12	if	if	SCONJ
ejpam-4316	73	13	no	no	DET
ejpam-4316	73	14	three	three	NUM
ejpam-4316	73	15	vertices	vertex	NOUN
ejpam-4316	73	16	form	form	VERB
ejpam-4316	73	17	a	a	DET
ejpam-4316	73	18	triangle	triangle	NOUN
ejpam-4316	73	19	of	of	ADP
ejpam-4316	73	20	edges	edge	NOUN
ejpam-4316	73	21	.	.	PUNCT
ejpam-4316	74	1	the	the	DET
ejpam-4316	74	2	adjacency	adjacency	NOUN
ejpam-4316	74	3	matrix	matrix	NOUN
ejpam-4316	74	4	denoted	denote	VERB
ejpam-4316	74	5	by	by	ADP
ejpam-4316	74	6	a(g	a(g	PROPN
ejpam-4316	74	7	)	)	PUNCT
ejpam-4316	74	8	with	with	ADP
ejpam-4316	74	9	vertex	vertex	NOUN
ejpam-4316	74	10	set	set	NOUN
ejpam-4316	74	11	{	{	PUNCT
ejpam-4316	74	12	x1	x1	PROPN
ejpam-4316	74	13	,	,	PUNCT
ejpam-4316	74	14	x2	x2	PROPN
ejpam-4316	74	15	,	,	PUNCT
ejpam-4316	74	16	.	.	PUNCT
ejpam-4316	74	17	.	.	PUNCT
ejpam-4316	74	18	.	.	PUNCT
ejpam-4316	75	1	,	,	PUNCT
ejpam-4316	75	2	xn	xn	X
ejpam-4316	75	3	}	}	PUNCT
ejpam-4316	75	4	is	be	AUX
ejpam-4316	75	5	the	the	DET
ejpam-4316	75	6	n	n	NUM
ejpam-4316	75	7	×	×	NOUN
ejpam-4316	75	8	n	n	CCONJ
ejpam-4316	75	9	binary	binary	ADJ
ejpam-4316	75	10	matrix	matrix	NOUN
ejpam-4316	76	1	a	a	PRON
ejpam-4316	76	2	=	=	X
ejpam-4316	77	1	[	[	X
ejpam-4316	77	2	aij	aij	X
ejpam-4316	77	3	]	]	PUNCT
ejpam-4316	77	4	where	where	SCONJ
ejpam-4316	77	5	aij	aij	PROPN
ejpam-4316	77	6	=	=	SYM
ejpam-4316	77	7	1	1	NUM
ejpam-4316	77	8	if	if	SCONJ
ejpam-4316	77	9	the	the	DET
ejpam-4316	77	10	vertices	vertex	NOUN
ejpam-4316	77	11	xi	xi	PROPN
ejpam-4316	77	12	,	,	PUNCT
ejpam-4316	77	13	xj	xj	PROPN
ejpam-4316	77	14	are	be	AUX
ejpam-4316	77	15	adjacent	adjacent	ADJ
ejpam-4316	77	16	,	,	PUNCT
ejpam-4316	77	17	and	and	CCONJ
ejpam-4316	77	18	aij	aij	PROPN
ejpam-4316	77	19	=	=	SYM
ejpam-4316	77	20	0	0	NUM
ejpam-4316	77	21	otherwise	otherwise	ADV
ejpam-4316	77	22	.	.	PUNCT
ejpam-4316	78	1	the	the	DET
ejpam-4316	78	2	distance	distance	NOUN
ejpam-4316	78	3	d(xi	d(xi	PROPN
ejpam-4316	78	4	,	,	PUNCT
ejpam-4316	78	5	xj	xj	NOUN
ejpam-4316	78	6	)	)	PUNCT
ejpam-4316	78	7	between	between	ADP
ejpam-4316	78	8	two	two	NUM
ejpam-4316	78	9	vertices	vertex	NOUN
ejpam-4316	78	10	xi	xi	ADP
ejpam-4316	78	11	,	,	PUNCT
ejpam-4316	78	12	and	and	CCONJ
ejpam-4316	78	13	xj	xj	PROPN
ejpam-4316	78	14	is	be	AUX
ejpam-4316	78	15	the	the	DET
ejpam-4316	78	16	length	length	NOUN
ejpam-4316	78	17	of	of	ADP
ejpam-4316	78	18	the	the	DET
ejpam-4316	78	19	shortest	short	ADJ
ejpam-4316	78	20	path	path	NOUN
ejpam-4316	78	21	between	between	ADP
ejpam-4316	78	22	the	the	DET
ejpam-4316	78	23	vertices	vertex	NOUN
ejpam-4316	78	24	xi	xi	X
ejpam-4316	78	25	and	and	CCONJ
ejpam-4316	78	26	xj	xj	PROPN
ejpam-4316	78	27	.	.	PUNCT
ejpam-4316	79	1	note	note	VERB
ejpam-4316	79	2	that	that	SCONJ
ejpam-4316	79	3	the	the	DET
ejpam-4316	79	4	sum	sum	NOUN
ejpam-4316	79	5	of	of	ADP
ejpam-4316	79	6	the	the	DET
ejpam-4316	79	7	degree	degree	NOUN
ejpam-4316	79	8	of	of	ADP
ejpam-4316	79	9	all	all	DET
ejpam-4316	79	10	vertices	vertex	NOUN
ejpam-4316	79	11	in	in	ADP
ejpam-4316	79	12	a	a	DET
ejpam-4316	79	13	graph	graph	NOUN
ejpam-4316	79	14	g	g	NOUN
ejpam-4316	79	15	is	be	AUX
ejpam-4316	79	16	twice	twice	DET
ejpam-4316	79	17	the	the	DET
ejpam-4316	79	18	number	number	NOUN
ejpam-4316	79	19	of	of	ADP
ejpam-4316	79	20	edges	edge	NOUN
ejpam-4316	79	21	in	in	ADP
ejpam-4316	79	22	g.	g.	PROPN
ejpam-4316	79	23	d(g	d(g	PROPN
ejpam-4316	79	24	)	)	PUNCT
ejpam-4316	79	25	is	be	AUX
ejpam-4316	79	26	the	the	DET
ejpam-4316	79	27	matrix	matrix	NOUN
ejpam-4316	80	1	[	[	X
ejpam-4316	80	2	dij	dij	X
ejpam-4316	80	3	]	]	PUNCT
ejpam-4316	80	4	where	where	SCONJ
ejpam-4316	80	5	dij	dij	PROPN
ejpam-4316	80	6	=	=	SYM
ejpam-4316	80	7	d(xi	d(xi	PROPN
ejpam-4316	80	8	,	,	PUNCT
ejpam-4316	80	9	xj	xj	NOUN
ejpam-4316	80	10	)	)	PUNCT
ejpam-4316	80	11	is	be	AUX
ejpam-4316	80	12	called	call	VERB
ejpam-4316	80	13	the	the	DET
ejpam-4316	80	14	distance	distance	NOUN
ejpam-4316	80	15	matrix	matrix	NOUN
ejpam-4316	80	16	of	of	ADP
ejpam-4316	80	17	a	a	DET
ejpam-4316	80	18	graph	graph	NOUN
ejpam-4316	80	19	g.	g.	NOUN
ejpam-4316	80	20	readers	reader	NOUN
ejpam-4316	80	21	are	be	AUX
ejpam-4316	80	22	referred	refer	VERB
ejpam-4316	80	23	to	to	ADP
ejpam-4316	80	24	[	[	X
ejpam-4316	80	25	4	4	NUM
ejpam-4316	80	26	,	,	PUNCT
ejpam-4316	80	27	9	9	NUM
ejpam-4316	80	28	]	]	PUNCT
ejpam-4316	80	29	for	for	ADP
ejpam-4316	80	30	other	other	ADJ
ejpam-4316	80	31	elementary	elementary	ADJ
ejpam-4316	80	32	graph	graph	NOUN
ejpam-4316	80	33	theoretic	theoretic	ADJ
ejpam-4316	80	34	concepts	concept	NOUN
ejpam-4316	80	35	.	.	PUNCT
ejpam-4316	81	1	in	in	ADP
ejpam-4316	81	2	this	this	DET
ejpam-4316	81	3	study	study	NOUN
ejpam-4316	81	4	,	,	PUNCT
ejpam-4316	81	5	we	we	PRON
ejpam-4316	81	6	focus	focus	VERB
ejpam-4316	81	7	on	on	ADP
ejpam-4316	81	8	the	the	DET
ejpam-4316	81	9	wiener	wiener	NOUN
ejpam-4316	81	10	index	index	NOUN
ejpam-4316	81	11	,	,	PUNCT
ejpam-4316	81	12	and	and	CCONJ
ejpam-4316	81	13	harary	harary	PROPN
ejpam-4316	81	14	index	index	NOUN
ejpam-4316	81	15	of	of	ADP
ejpam-4316	81	16	a	a	DET
ejpam-4316	81	17	graph	graph	NOUN
ejpam-4316	81	18	.	.	PUNCT
ejpam-4316	82	1	the	the	DET
ejpam-4316	82	2	wiener	wiener	NOUN
ejpam-4316	82	3	index	index	NOUN
ejpam-4316	82	4	w	w	PROPN
ejpam-4316	82	5	(	(	PUNCT
ejpam-4316	82	6	g	g	NOUN
ejpam-4316	82	7	)	)	PUNCT
ejpam-4316	82	8	of	of	ADP
ejpam-4316	82	9	a	a	DET
ejpam-4316	82	10	graph	graph	NOUN
ejpam-4316	82	11	g	g	NOUN
ejpam-4316	82	12	is	be	AUX
ejpam-4316	82	13	defined	define	VERB
ejpam-4316	82	14	as	as	ADP
ejpam-4316	82	15	w	w	PROPN
ejpam-4316	82	16	(	(	PUNCT
ejpam-4316	82	17	g	g	NOUN
ejpam-4316	82	18	)	)	PUNCT
ejpam-4316	82	19	=	=	SYM
ejpam-4316	82	20	∑	∑	PROPN
ejpam-4316	82	21	{	{	PUNCT
ejpam-4316	82	22	vi	vi	PROPN
ejpam-4316	82	23	,	,	PUNCT
ejpam-4316	82	24	vj}⊆v	vj}⊆v	NUM
ejpam-4316	82	25	(	(	PUNCT
ejpam-4316	82	26	g	g	NOUN
ejpam-4316	82	27	)	)	PUNCT
ejpam-4316	82	28	d(vi	d(vi	PROPN
ejpam-4316	82	29	,	,	PUNCT
ejpam-4316	82	30	vj	vj	NOUN
ejpam-4316	82	31	)	)	PUNCT
ejpam-4316	82	32	=	=	SYM
ejpam-4316	82	33	1	1	NUM
ejpam-4316	82	34	2	2	NUM
ejpam-4316	82	35	n∑	n∑	NOUN
ejpam-4316	82	36	i=1	i=1	PROPN
ejpam-4316	82	37	n∑	n∑	PROPN
ejpam-4316	82	38	j=1	j=1	PROPN
ejpam-4316	82	39	d(vi	d(vi	PROPN
ejpam-4316	82	40	,	,	PUNCT
ejpam-4316	82	41	vj	vj	PROPN
ejpam-4316	82	42	)	)	PUNCT
ejpam-4316	82	43	.	.	PUNCT
ejpam-4316	83	1	the	the	DET
ejpam-4316	83	2	harary	harary	PROPN
ejpam-4316	83	3	index	index	NOUN
ejpam-4316	83	4	h(g	h(g	NOUN
ejpam-4316	83	5	)	)	PUNCT
ejpam-4316	83	6	of	of	ADP
ejpam-4316	83	7	a	a	DET
ejpam-4316	83	8	graph	graph	NOUN
ejpam-4316	83	9	g	g	NOUN
ejpam-4316	83	10	is	be	AUX
ejpam-4316	83	11	defined	define	VERB
ejpam-4316	83	12	as	as	ADP
ejpam-4316	83	13	h(g	h(g	NOUN
ejpam-4316	83	14	)	)	PUNCT
ejpam-4316	83	15	=	=	PUNCT
ejpam-4316	83	16	∑	∑	PUNCT
ejpam-4316	83	17	{	{	PUNCT
ejpam-4316	83	18	vi	vi	PROPN
ejpam-4316	83	19	,	,	PUNCT
ejpam-4316	83	20	vj}⊆v	vj}⊆v	NOUN
ejpam-4316	83	21	(	(	PUNCT
ejpam-4316	83	22	g	g	NOUN
ejpam-4316	83	23	)	)	PUNCT
ejpam-4316	83	24	1	1	NUM
ejpam-4316	83	25	d(vi	d(vi	PROPN
ejpam-4316	83	26	,	,	PUNCT
ejpam-4316	83	27	vj	vj	NOUN
ejpam-4316	83	28	)	)	PUNCT
ejpam-4316	83	29	=	=	SYM
ejpam-4316	83	30	1	1	NUM
ejpam-4316	83	31	2	2	NUM
ejpam-4316	83	32	n∑	n∑	NOUN
ejpam-4316	83	33	i=1	i=1	PROPN
ejpam-4316	83	34	n∑	n∑	PROPN
ejpam-4316	84	1	j=1	j=1	NOUN
ejpam-4316	84	2	1	1	NUM
ejpam-4316	84	3	d(vi	d(vi	PROPN
ejpam-4316	84	4	,	,	PUNCT
ejpam-4316	84	5	vj	vj	PROPN
ejpam-4316	84	6	)	)	PUNCT
ejpam-4316	84	7	.	.	PUNCT
ejpam-4316	85	1	the	the	DET
ejpam-4316	85	2	following	follow	VERB
ejpam-4316	85	3	are	be	AUX
ejpam-4316	85	4	the	the	DET
ejpam-4316	85	5	exact	exact	ADJ
ejpam-4316	85	6	values	value	NOUN
ejpam-4316	85	7	of	of	ADP
ejpam-4316	85	8	weiner	weiner	NOUN
ejpam-4316	85	9	and	and	CCONJ
ejpam-4316	85	10	harary	harary	NOUN
ejpam-4316	85	11	indices	index	NOUN
ejpam-4316	85	12	for	for	ADP
ejpam-4316	85	13	some	some	DET
ejpam-4316	85	14	families	family	NOUN
ejpam-4316	85	15	of	of	ADP
ejpam-4316	85	16	graphs	graph	NOUN
ejpam-4316	85	17	.	.	PUNCT
ejpam-4316	86	1	we	we	PRON
ejpam-4316	86	2	denote	denote	VERB
ejpam-4316	86	3	hn	hn	PRON
ejpam-4316	86	4	be	be	AUX
ejpam-4316	86	5	the	the	DET
ejpam-4316	86	6	nth	nth	NOUN
ejpam-4316	86	7	harmonic	harmonic	ADJ
ejpam-4316	86	8	number	number	NOUN
ejpam-4316	86	9	.	.	PUNCT
ejpam-4316	87	1	that	that	PRON
ejpam-4316	87	2	is	be	AUX
ejpam-4316	87	3	,	,	PUNCT
ejpam-4316	88	1	hn	hn	PROPN
ejpam-4316	88	2	=	=	PUNCT
ejpam-4316	88	3	∑n	∑n	NOUN
ejpam-4316	89	1	k=1	k=1	NOUN
ejpam-4316	89	2	1	1	NUM
ejpam-4316	89	3	k	k	X
ejpam-4316	89	4	.	.	PUNCT
ejpam-4316	89	5	theorem	theorem	NOUN
ejpam-4316	89	6	1	1	NUM
ejpam-4316	89	7	.	.	PUNCT
ejpam-4316	90	1	[	[	X
ejpam-4316	90	2	17	17	NUM
ejpam-4316	90	3	,	,	PUNCT
ejpam-4316	90	4	23	23	NUM
ejpam-4316	90	5	]	]	PUNCT
ejpam-4316	90	6	the	the	DET
ejpam-4316	90	7	wiener	wiener	NOUN
ejpam-4316	90	8	and	and	CCONJ
ejpam-4316	90	9	harary	harary	PROPN
ejpam-4316	90	10	index	index	NOUN
ejpam-4316	90	11	of	of	ADP
ejpam-4316	90	12	the	the	DET
ejpam-4316	90	13	path	path	NOUN
ejpam-4316	90	14	graph	graph	NOUN
ejpam-4316	90	15	on	on	ADP
ejpam-4316	90	16	n	n	PRON
ejpam-4316	90	17	vertices	vertex	NOUN
ejpam-4316	90	18	for	for	ADP
ejpam-4316	90	19	n	n	PRON
ejpam-4316	90	20	≥	≥	NOUN
ejpam-4316	90	21	1	1	NUM
ejpam-4316	90	22	is	be	AUX
ejpam-4316	90	23	given	give	VERB
ejpam-4316	90	24	by	by	ADP
ejpam-4316	90	25	w	w	PROPN
ejpam-4316	90	26	(	(	PUNCT
ejpam-4316	90	27	pn	pn	NOUN
ejpam-4316	90	28	)	)	PUNCT
ejpam-4316	90	29	=	=	SYM
ejpam-4316	90	30	1	1	NUM
ejpam-4316	90	31	6n(n	6n(n	NUM
ejpam-4316	90	32	2	2	NUM
ejpam-4316	90	33	−	−	NOUN
ejpam-4316	90	34	1	1	NUM
ejpam-4316	90	35	)	)	PUNCT
ejpam-4316	90	36	and	and	CCONJ
ejpam-4316	90	37	h(pn	h(pn	NOUN
ejpam-4316	90	38	)	)	PUNCT
ejpam-4316	90	39	=	=	SYM
ejpam-4316	90	40	nhn	nhn	PROPN
ejpam-4316	91	1	−	−	PROPN
ejpam-4316	91	2	1	1	X
ejpam-4316	91	3	.	.	PUNCT
ejpam-4316	91	4	theorem	theorem	NOUN
ejpam-4316	91	5	2	2	NUM
ejpam-4316	91	6	.	.	PUNCT
ejpam-4316	92	1	[	[	X
ejpam-4316	92	2	17	17	NUM
ejpam-4316	92	3	,	,	PUNCT
ejpam-4316	92	4	23	23	NUM
ejpam-4316	92	5	]	]	PUNCT
ejpam-4316	92	6	the	the	DET
ejpam-4316	92	7	wiener	wiener	NOUN
ejpam-4316	92	8	and	and	CCONJ
ejpam-4316	92	9	harary	harary	PROPN
ejpam-4316	92	10	index	index	NOUN
ejpam-4316	92	11	of	of	ADP
ejpam-4316	92	12	the	the	DET
ejpam-4316	92	13	cycle	cycle	NOUN
ejpam-4316	92	14	graph	graph	NOUN
ejpam-4316	92	15	on	on	ADP
ejpam-4316	92	16	n	n	PRON
ejpam-4316	92	17	vertices	vertex	NOUN
ejpam-4316	92	18	for	for	ADP
ejpam-4316	92	19	n	n	PRON
ejpam-4316	92	20	≥	≥	NOUN
ejpam-4316	92	21	3	3	NUM
ejpam-4316	92	22	is	be	AUX
ejpam-4316	92	23	given	give	VERB
ejpam-4316	92	24	by	by	ADP
ejpam-4316	92	25	w	w	PROPN
ejpam-4316	92	26	(	(	PUNCT
ejpam-4316	92	27	cn	cn	PROPN
ejpam-4316	92	28	)	)	PUNCT
ejpam-4316	92	29	=	=	SYM
ejpam-4316	93	1			PROPN
ejpam-4316	93	2	n3	n3	VERB
ejpam-4316	93	3	8	8	NUM
ejpam-4316	93	4	n	n	NOUN
ejpam-4316	93	5	even	even	ADV
ejpam-4316	93	6	(	(	PUNCT
ejpam-4316	93	7	n−	n−	NOUN
ejpam-4316	93	8	1)(n+	1)(n+	NUM
ejpam-4316	93	9	1)n	1)n	NUM
ejpam-4316	93	10	8	8	NUM
ejpam-4316	93	11	n	n	PRON
ejpam-4316	93	12	odd	odd	ADJ
ejpam-4316	93	13	f.j.h	f.j.h	NOUN
ejpam-4316	93	14	.	.	PUNCT
ejpam-4316	94	1	campeña	campeña	NOUN
ejpam-4316	94	2	,	,	PUNCT
ejpam-4316	94	3	m.c.g	m.c.g	PROPN
ejpam-4316	94	4	.	.	PUNCT
ejpam-4316	94	5	egan	egan	PROPN
ejpam-4316	94	6	,	,	PUNCT
ejpam-4316	94	7	j.r.m	j.r.m	PROPN
ejpam-4316	94	8	.	.	PUNCT
ejpam-4316	95	1	antalan	antalan	PROPN
ejpam-4316	95	2	/	/	SYM
ejpam-4316	95	3	eur	eur	PROPN
ejpam-4316	95	4	.	.	PUNCT
ejpam-4316	96	1	j.	j.	PROPN
ejpam-4316	96	2	pure	pure	PROPN
ejpam-4316	96	3	appl	appl	PROPN
ejpam-4316	96	4	.	.	PROPN
ejpam-4316	96	5	math	math	PROPN
ejpam-4316	96	6	,	,	PUNCT
ejpam-4316	96	7	15	15	NUM
ejpam-4316	96	8	(	(	PUNCT
ejpam-4316	96	9	2	2	NUM
ejpam-4316	96	10	)	)	PUNCT
ejpam-4316	96	11	(	(	PUNCT
ejpam-4316	96	12	2022	2022	NUM
ejpam-4316	96	13	)	)	PUNCT
ejpam-4316	96	14	,	,	PUNCT
ejpam-4316	96	15	602	602	NUM
ejpam-4316	96	16	-	-	SYM
ejpam-4316	96	17	619	619	NUM
ejpam-4316	96	18	605	605	NUM
ejpam-4316	96	19	and	and	CCONJ
ejpam-4316	96	20	h(cn	h(cn	PROPN
ejpam-4316	96	21	)	)	PUNCT
ejpam-4316	96	22	=	=	SYM
ejpam-4316	96	23	1	1	NUM
ejpam-4316	96	24	2	2	NUM
ejpam-4316	96	25	(	(	PUNCT
ejpam-4316	96	26	1	1	NUM
ejpam-4316	96	27	+	+	CCONJ
ejpam-4316	96	28	(	(	PUNCT
ejpam-4316	96	29	−1)n	−1)n	PROPN
ejpam-4316	96	30	)	)	PUNCT
ejpam-4316	96	31	+	+	CCONJ
ejpam-4316	96	32	nhb(n−1)/2c	nhb(n−1)/2c	ADJ
ejpam-4316	96	33	.	.	PUNCT
ejpam-4316	97	1	theorem	theorem	VERB
ejpam-4316	97	2	3	3	NUM
ejpam-4316	97	3	.	.	PUNCT
ejpam-4316	98	1	[	[	X
ejpam-4316	98	2	22	22	NUM
ejpam-4316	98	3	,	,	PUNCT
ejpam-4316	98	4	23	23	NUM
ejpam-4316	98	5	]	]	PUNCT
ejpam-4316	98	6	the	the	DET
ejpam-4316	98	7	wiener	wiener	NOUN
ejpam-4316	98	8	and	and	CCONJ
ejpam-4316	98	9	harary	harary	PROPN
ejpam-4316	98	10	index	index	NOUN
ejpam-4316	98	11	of	of	ADP
ejpam-4316	98	12	the	the	DET
ejpam-4316	98	13	complete	complete	ADJ
ejpam-4316	98	14	graph	graph	NOUN
ejpam-4316	98	15	on	on	ADP
ejpam-4316	98	16	n	n	PRON
ejpam-4316	98	17	vertices	vertex	NOUN
ejpam-4316	98	18	for	for	ADP
ejpam-4316	98	19	n	n	PRON
ejpam-4316	98	20	≥	≥	NOUN
ejpam-4316	98	21	1	1	NUM
ejpam-4316	98	22	is	be	AUX
ejpam-4316	98	23	given	give	VERB
ejpam-4316	98	24	by	by	ADP
ejpam-4316	98	25	w	w	PROPN
ejpam-4316	98	26	(	(	PUNCT
ejpam-4316	98	27	kn	kn	PROPN
ejpam-4316	98	28	)	)	PUNCT
ejpam-4316	98	29	=	=	SYM
ejpam-4316	98	30	h(kn	h(kn	NOUN
ejpam-4316	98	31	)	)	PUNCT
ejpam-4316	98	32	=	=	PRON
ejpam-4316	98	33	n(n−	n(n−	VERB
ejpam-4316	98	34	1	1	NUM
ejpam-4316	98	35	)	)	PUNCT
ejpam-4316	98	36	2	2	NUM
ejpam-4316	98	37	.	.	PUNCT
ejpam-4316	99	1	theorem	theorem	VERB
ejpam-4316	99	2	4	4	NUM
ejpam-4316	99	3	.	.	PUNCT
ejpam-4316	100	1	[	[	X
ejpam-4316	100	2	22	22	NUM
ejpam-4316	100	3	,	,	PUNCT
ejpam-4316	100	4	23	23	NUM
ejpam-4316	100	5	]	]	PUNCT
ejpam-4316	100	6	the	the	DET
ejpam-4316	100	7	wiener	wiener	NOUN
ejpam-4316	100	8	and	and	CCONJ
ejpam-4316	100	9	harary	harary	PROPN
ejpam-4316	100	10	index	index	NOUN
ejpam-4316	100	11	of	of	ADP
ejpam-4316	100	12	the	the	DET
ejpam-4316	100	13	star	star	NOUN
ejpam-4316	100	14	graph	graph	NOUN
ejpam-4316	100	15	on	on	ADP
ejpam-4316	100	16	n	n	PRON
ejpam-4316	100	17	vertices	vertex	NOUN
ejpam-4316	100	18	for	for	ADP
ejpam-4316	100	19	n	n	PRON
ejpam-4316	100	20	≥	≥	NOUN
ejpam-4316	100	21	1	1	NUM
ejpam-4316	100	22	is	be	AUX
ejpam-4316	100	23	given	give	VERB
ejpam-4316	100	24	by	by	ADP
ejpam-4316	100	25	w	w	PROPN
ejpam-4316	100	26	(	(	PUNCT
ejpam-4316	100	27	sn	sn	NOUN
ejpam-4316	100	28	)	)	PUNCT
ejpam-4316	100	29	=	=	PUNCT
ejpam-4316	100	30	(	(	PUNCT
ejpam-4316	100	31	n−	n−	NOUN
ejpam-4316	100	32	1)2	1)2	NUM
ejpam-4316	100	33	and	and	CCONJ
ejpam-4316	100	34	h(sn	h(sn	NUM
ejpam-4316	100	35	)	)	PUNCT
ejpam-4316	100	36	=	=	SYM
ejpam-4316	100	37	1	1	NUM
ejpam-4316	100	38	4(n+	4(n+	NUM
ejpam-4316	100	39	2)(n−	2)(n−	NUM
ejpam-4316	100	40	1	1	NUM
ejpam-4316	100	41	)	)	PUNCT
ejpam-4316	100	42	.	.	PUNCT
ejpam-4316	101	1	theorem	theorem	ADJ
ejpam-4316	101	2	5	5	NUM
ejpam-4316	101	3	.	.	PUNCT
ejpam-4316	102	1	[	[	X
ejpam-4316	102	2	22	22	NUM
ejpam-4316	102	3	,	,	PUNCT
ejpam-4316	102	4	23	23	NUM
ejpam-4316	102	5	]	]	PUNCT
ejpam-4316	102	6	for	for	ADP
ejpam-4316	102	7	n	n	X
ejpam-4316	102	8	≥	≥	NOUN
ejpam-4316	102	9	4	4	NUM
ejpam-4316	102	10	,	,	PUNCT
ejpam-4316	102	11	the	the	DET
ejpam-4316	102	12	wiener	wiener	NOUN
ejpam-4316	102	13	and	and	CCONJ
ejpam-4316	102	14	harary	harary	ADJ
ejpam-4316	102	15	index	index	NOUN
ejpam-4316	102	16	of	of	ADP
ejpam-4316	102	17	the	the	DET
ejpam-4316	102	18	wheel	wheel	NOUN
ejpam-4316	102	19	graph	graph	NOUN
ejpam-4316	102	20	on	on	ADP
ejpam-4316	102	21	n	n	DET
ejpam-4316	102	22	vertices	vertex	NOUN
ejpam-4316	102	23	is	be	AUX
ejpam-4316	102	24	given	give	VERB
ejpam-4316	102	25	by	by	ADP
ejpam-4316	102	26	w	w	PROPN
ejpam-4316	102	27	(	(	PUNCT
ejpam-4316	102	28	wn	wn	PROPN
ejpam-4316	102	29	)	)	PUNCT
ejpam-4316	102	30	=	=	PUNCT
ejpam-4316	103	1	(	(	PUNCT
ejpam-4316	103	2	n−	n−	NOUN
ejpam-4316	103	3	1)(n−	1)(n−	PROPN
ejpam-4316	103	4	2	2	NUM
ejpam-4316	103	5	)	)	PUNCT
ejpam-4316	103	6	and	and	CCONJ
ejpam-4316	103	7	h(wn	h(wn	NUM
ejpam-4316	103	8	)	)	PUNCT
ejpam-4316	103	9	=	=	SYM
ejpam-4316	104	1	1	1	NUM
ejpam-4316	104	2	4(n+	4(n+	NUM
ejpam-4316	104	3	4)(n−	4)(n−	NUM
ejpam-4316	104	4	1	1	NUM
ejpam-4316	104	5	)	)	PUNCT
ejpam-4316	104	6	.	.	PUNCT
ejpam-4316	105	1	theorem	theorem	VERB
ejpam-4316	105	2	6	6	NUM
ejpam-4316	105	3	.	.	PUNCT
ejpam-4316	106	1	[	[	X
ejpam-4316	106	2	8	8	NUM
ejpam-4316	106	3	,	,	PUNCT
ejpam-4316	106	4	23	23	NUM
ejpam-4316	106	5	]	]	PUNCT
ejpam-4316	106	6	for	for	ADP
ejpam-4316	106	7	m	m	PROPN
ejpam-4316	106	8	,	,	PUNCT
ejpam-4316	106	9	n	n	PRON
ejpam-4316	106	10	≥	≥	NOUN
ejpam-4316	106	11	1	1	NUM
ejpam-4316	106	12	,	,	PUNCT
ejpam-4316	106	13	the	the	DET
ejpam-4316	106	14	wiener	wiener	NOUN
ejpam-4316	106	15	and	and	CCONJ
ejpam-4316	106	16	harary	harary	ADJ
ejpam-4316	106	17	index	index	NOUN
ejpam-4316	106	18	of	of	ADP
ejpam-4316	106	19	the	the	DET
ejpam-4316	106	20	complete	complete	ADJ
ejpam-4316	106	21	bipartite	bipartite	PROPN
ejpam-4316	106	22	graph	graph	NOUN
ejpam-4316	106	23	km	km	PROPN
ejpam-4316	106	24	,	,	PUNCT
ejpam-4316	106	25	n	n	PUNCT
ejpam-4316	106	26	is	be	AUX
ejpam-4316	106	27	given	give	VERB
ejpam-4316	106	28	w	w	PROPN
ejpam-4316	106	29	(	(	PUNCT
ejpam-4316	106	30	km	km	PROPN
ejpam-4316	106	31	,	,	PUNCT
ejpam-4316	106	32	n	n	CCONJ
ejpam-4316	106	33	)	)	PUNCT
ejpam-4316	106	34	=	=	SYM
ejpam-4316	106	35	m2+mn+n2−m−n	m2+mn+n2−m−n	PROPN
ejpam-4316	106	36	and	and	CCONJ
ejpam-4316	106	37	h(km	h(km	PROPN
ejpam-4316	106	38	,	,	PUNCT
ejpam-4316	106	39	n	n	CCONJ
ejpam-4316	106	40	)	)	PUNCT
ejpam-4316	106	41	=	=	SYM
ejpam-4316	107	1	1	1	NUM
ejpam-4316	107	2	4(m	4(m	NUM
ejpam-4316	107	3	2+n2−m−	2+n2−m−	NUM
ejpam-4316	107	4	n	n	CCONJ
ejpam-4316	107	5	)	)	PUNCT
ejpam-4316	107	6	+	+	PROPN
ejpam-4316	107	7	mn	mn	PROPN
ejpam-4316	107	8	.	.	PROPN
ejpam-4316	108	1	3	3	NUM
ejpam-4316	108	2	.	.	X
ejpam-4316	108	3	s	s	X
ejpam-4316	108	4	-	-	PUNCT
ejpam-4316	108	5	splitting	split	VERB
ejpam-4316	108	6	graphs	graph	NOUN
ejpam-4316	108	7	sampathkumar	sampathkumar	NOUN
ejpam-4316	108	8	and	and	CCONJ
ejpam-4316	108	9	walikar	walikar	NOUN
ejpam-4316	108	10	introduced	introduce	VERB
ejpam-4316	108	11	the	the	DET
ejpam-4316	108	12	splitting	splitting	NOUN
ejpam-4316	108	13	graph	graph	NOUN
ejpam-4316	108	14	in	in	ADP
ejpam-4316	108	15	1980	1980	NUM
ejpam-4316	108	16	[	[	X
ejpam-4316	108	17	19	19	NUM
ejpam-4316	108	18	]	]	PUNCT
ejpam-4316	108	19	and	and	CCONJ
ejpam-4316	108	20	defined	define	VERB
ejpam-4316	108	21	it	it	PRON
ejpam-4316	108	22	as	as	SCONJ
ejpam-4316	108	23	follows	follow	VERB
ejpam-4316	108	24	.	.	PUNCT
ejpam-4316	109	1	for	for	ADP
ejpam-4316	109	2	each	each	DET
ejpam-4316	109	3	vertex	vertex	NOUN
ejpam-4316	109	4	v	v	NOUN
ejpam-4316	109	5	of	of	ADP
ejpam-4316	109	6	a	a	DET
ejpam-4316	109	7	graph	graph	NOUN
ejpam-4316	109	8	g	g	NOUN
ejpam-4316	109	9	,	,	PUNCT
ejpam-4316	109	10	we	we	PRON
ejpam-4316	109	11	have	have	VERB
ejpam-4316	109	12	a	a	DET
ejpam-4316	109	13	new	new	ADJ
ejpam-4316	109	14	vertex	vertex	NOUN
ejpam-4316	109	15	v′	v′	NOUN
ejpam-4316	109	16	,	,	PUNCT
ejpam-4316	109	17	and	and	CCONJ
ejpam-4316	109	18	connect	connect	VERB
ejpam-4316	109	19	v′	v′	NOUN
ejpam-4316	109	20	to	to	ADP
ejpam-4316	109	21	all	all	DET
ejpam-4316	109	22	the	the	DET
ejpam-4316	109	23	vertices	vertex	NOUN
ejpam-4316	109	24	of	of	ADP
ejpam-4316	109	25	g	g	NOUN
ejpam-4316	109	26	adjacent	adjacent	ADJ
ejpam-4316	109	27	to	to	ADP
ejpam-4316	109	28	v.	v.	ADP
ejpam-4316	109	29	in	in	ADP
ejpam-4316	109	30	this	this	DET
ejpam-4316	109	31	study	study	NOUN
ejpam-4316	109	32	,	,	PUNCT
ejpam-4316	109	33	we	we	PRON
ejpam-4316	109	34	look	look	VERB
ejpam-4316	109	35	into	into	ADP
ejpam-4316	109	36	a	a	DET
ejpam-4316	109	37	variation	variation	NOUN
ejpam-4316	109	38	of	of	ADP
ejpam-4316	109	39	the	the	DET
ejpam-4316	109	40	splitting	splitting	NOUN
ejpam-4316	109	41	graph	graph	NOUN
ejpam-4316	109	42	and	and	CCONJ
ejpam-4316	109	43	define	define	VERB
ejpam-4316	109	44	what	what	PRON
ejpam-4316	109	45	we	we	PRON
ejpam-4316	109	46	call	call	VERB
ejpam-4316	109	47	an	an	DET
ejpam-4316	109	48	s	s	NOUN
ejpam-4316	109	49	-	-	PUNCT
ejpam-4316	109	50	splitting	splitting	NOUN
ejpam-4316	109	51	graph	graph	NOUN
ejpam-4316	109	52	of	of	ADP
ejpam-4316	109	53	g	g	NOUN
ejpam-4316	109	54	where	where	SCONJ
ejpam-4316	109	55	s	s	VERB
ejpam-4316	109	56	is	be	AUX
ejpam-4316	109	57	a	a	DET
ejpam-4316	109	58	non	non	ADJ
ejpam-4316	109	59	-	-	ADJ
ejpam-4316	109	60	empty	empty	ADJ
ejpam-4316	109	61	subset	subset	NOUN
ejpam-4316	109	62	of	of	ADP
ejpam-4316	109	63	vertices	vertex	NOUN
ejpam-4316	109	64	in	in	ADP
ejpam-4316	109	65	g.	g.	PROPN
ejpam-4316	109	66	3.1	3.1	NUM
ejpam-4316	109	67	.	.	PUNCT
ejpam-4316	110	1	the	the	DET
ejpam-4316	110	2	s	s	NOUN
ejpam-4316	110	3	-	-	PUNCT
ejpam-4316	110	4	splitting	splitting	NOUN
ejpam-4316	110	5	graph	graph	NOUN
ejpam-4316	110	6	γ(g	γ(g	PROPN
ejpam-4316	110	7	,	,	PUNCT
ejpam-4316	110	8	s	s	PART
ejpam-4316	110	9	)	)	PUNCT
ejpam-4316	110	10	throughout	throughout	ADV
ejpam-4316	110	11	,	,	PUNCT
ejpam-4316	110	12	we	we	PRON
ejpam-4316	110	13	consider	consider	VERB
ejpam-4316	110	14	a	a	DET
ejpam-4316	110	15	finite	finite	ADJ
ejpam-4316	110	16	connected	connect	VERB
ejpam-4316	110	17	simple	simple	ADJ
ejpam-4316	110	18	graph	graph	NOUN
ejpam-4316	110	19	g	g	PROPN
ejpam-4316	110	20	=	=	PUNCT
ejpam-4316	110	21	(	(	PUNCT
ejpam-4316	110	22	v	v	NOUN
ejpam-4316	110	23	,	,	PUNCT
ejpam-4316	110	24	e	e	NOUN
ejpam-4316	110	25	)	)	PUNCT
ejpam-4316	110	26	and	and	CCONJ
ejpam-4316	110	27	s	s	VERB
ejpam-4316	110	28	⊆	⊆	NUM
ejpam-4316	110	29	v	v	NOUN
ejpam-4316	110	30	=	=	SYM
ejpam-4316	110	31	{	{	PUNCT
ejpam-4316	110	32	x1	x1	PROPN
ejpam-4316	110	33	,	,	PUNCT
ejpam-4316	110	34	x2	x2	PROPN
ejpam-4316	110	35	,	,	PUNCT
ejpam-4316	110	36	.	.	PUNCT
ejpam-4316	110	37	.	.	PUNCT
ejpam-4316	110	38	.	.	PUNCT
ejpam-4316	111	1	,	,	PUNCT
ejpam-4316	111	2	xn	xn	X
ejpam-4316	111	3	}	}	PUNCT
ejpam-4316	111	4	where	where	SCONJ
ejpam-4316	111	5	n	n	NUM
ejpam-4316	111	6	≥	≥	X
ejpam-4316	111	7	2	2	NUM
ejpam-4316	111	8	and	and	CCONJ
ejpam-4316	111	9	|e|	|e|	NOUN
ejpam-4316	111	10	=	=	NOUN
ejpam-4316	111	11	m	m	NOUN
ejpam-4316	111	12	≥	≥	NOUN
ejpam-4316	111	13	1	1	NUM
ejpam-4316	111	14	.	.	PUNCT
ejpam-4316	112	1	the	the	DET
ejpam-4316	112	2	graph	graph	NOUN
ejpam-4316	112	3	γ(g	γ(g	PROPN
ejpam-4316	112	4	,	,	PUNCT
ejpam-4316	112	5	s	s	PART
ejpam-4316	112	6	)	)	PUNCT
ejpam-4316	112	7	or	or	CCONJ
ejpam-4316	112	8	simply	simply	ADV
ejpam-4316	112	9	γ	γ	PROPN
ejpam-4316	112	10	is	be	AUX
ejpam-4316	112	11	an	an	DET
ejpam-4316	112	12	s	s	NOUN
ejpam-4316	112	13	-	-	PUNCT
ejpam-4316	112	14	splitting	splitting	NOUN
ejpam-4316	112	15	graph	graph	NOUN
ejpam-4316	112	16	of	of	ADP
ejpam-4316	112	17	g	g	PROPN
ejpam-4316	112	18	is	be	AUX
ejpam-4316	112	19	the	the	DET
ejpam-4316	112	20	graph	graph	NOUN
ejpam-4316	112	21	obtained	obtain	VERB
ejpam-4316	112	22	from	from	ADP
ejpam-4316	112	23	g	g	NOUN
ejpam-4316	112	24	with	with	ADP
ejpam-4316	112	25	the	the	DET
ejpam-4316	112	26	vertex	vertex	NOUN
ejpam-4316	112	27	set	set	VERB
ejpam-4316	112	28	v	v	NOUN
ejpam-4316	112	29	(	(	PUNCT
ejpam-4316	112	30	γ	γ	NOUN
ejpam-4316	112	31	)	)	PUNCT
ejpam-4316	112	32	=	=	NOUN
ejpam-4316	112	33	v	v	NOUN
ejpam-4316	112	34	∪	∪	ADJ
ejpam-4316	112	35	s′	s′	NUM
ejpam-4316	112	36	where	where	SCONJ
ejpam-4316	112	37	s′	s′	ADJ
ejpam-4316	112	38	=	=	SYM
ejpam-4316	112	39	{	{	PUNCT
ejpam-4316	112	40	x′|x	x′|x	NOUN
ejpam-4316	112	41	∈	∈	PROPN
ejpam-4316	112	42	s	s	PART
ejpam-4316	112	43	}	}	PUNCT
ejpam-4316	112	44	and	and	CCONJ
ejpam-4316	112	45	the	the	DET
ejpam-4316	112	46	edge	edge	NOUN
ejpam-4316	112	47	set	set	VERB
ejpam-4316	112	48	e(γ	e(γ	NOUN
ejpam-4316	112	49	)	)	PUNCT
ejpam-4316	113	1	=	=	PUNCT
ejpam-4316	113	2	e	e	NOUN
ejpam-4316	113	3	∪	∪	X
ejpam-4316	113	4	{	{	PUNCT
ejpam-4316	113	5	{	{	PUNCT
ejpam-4316	113	6	x′	x′	PROPN
ejpam-4316	113	7	,	,	PUNCT
ejpam-4316	113	8	u}|u	u}|u	PROPN
ejpam-4316	113	9	∈	∈	PROPN
ejpam-4316	113	10	ng(x	ng(x	NUM
ejpam-4316	113	11	)	)	PUNCT
ejpam-4316	113	12	}	}	PUNCT
ejpam-4316	113	13	where	where	SCONJ
ejpam-4316	113	14	ng(x	ng(x	NUM
ejpam-4316	113	15	)	)	PUNCT
ejpam-4316	113	16	is	be	AUX
ejpam-4316	113	17	the	the	DET
ejpam-4316	113	18	set	set	NOUN
ejpam-4316	113	19	of	of	ADP
ejpam-4316	113	20	vertices	vertex	NOUN
ejpam-4316	113	21	in	in	ADP
ejpam-4316	113	22	g	g	PROPN
ejpam-4316	113	23	adjacent	adjacent	ADJ
ejpam-4316	113	24	to	to	PART
ejpam-4316	113	25	x.	x.	VERB
ejpam-4316	113	26	if	if	SCONJ
ejpam-4316	113	27	s	s	PART
ejpam-4316	113	28	=	=	X
ejpam-4316	113	29	v	v	PROPN
ejpam-4316	113	30	,	,	PUNCT
ejpam-4316	113	31	then	then	ADV
ejpam-4316	113	32	γ(g	γ(g	PROPN
ejpam-4316	113	33	)	)	PUNCT
ejpam-4316	113	34	or	or	CCONJ
ejpam-4316	113	35	a	a	DET
ejpam-4316	113	36	v	v	NUM
ejpam-4316	113	37	-splitting	-splitte	VERB
ejpam-4316	113	38	graph	graph	NOUN
ejpam-4316	113	39	of	of	ADP
ejpam-4316	113	40	g	g	PROPN
ejpam-4316	113	41	is	be	AUX
ejpam-4316	113	42	splitting	split	VERB
ejpam-4316	113	43	graph	graph	NOUN
ejpam-4316	113	44	of	of	ADP
ejpam-4316	113	45	a	a	DET
ejpam-4316	113	46	graph	graph	NOUN
ejpam-4316	113	47	g	g	NOUN
ejpam-4316	113	48	as	as	SCONJ
ejpam-4316	113	49	defined	define	VERB
ejpam-4316	113	50	by	by	ADP
ejpam-4316	113	51	sampathkumar	sampathkumar	NOUN
ejpam-4316	113	52	in	in	ADP
ejpam-4316	113	53	[	[	X
ejpam-4316	113	54	19	19	NUM
ejpam-4316	113	55	]	]	PUNCT
ejpam-4316	113	56	.	.	PUNCT
ejpam-4316	114	1	from	from	ADP
ejpam-4316	114	2	the	the	DET
ejpam-4316	114	3	definition	definition	NOUN
ejpam-4316	114	4	of	of	ADP
ejpam-4316	114	5	the	the	DET
ejpam-4316	114	6	s	s	NOUN
ejpam-4316	114	7	-	-	PUNCT
ejpam-4316	114	8	splitting	splitting	NOUN
ejpam-4316	114	9	graph	graph	NOUN
ejpam-4316	114	10	of	of	ADP
ejpam-4316	114	11	g	g	NOUN
ejpam-4316	114	12	,	,	PUNCT
ejpam-4316	114	13	the	the	DET
ejpam-4316	114	14	following	follow	VERB
ejpam-4316	114	15	statements	statement	NOUN
ejpam-4316	114	16	can	can	AUX
ejpam-4316	114	17	be	be	AUX
ejpam-4316	114	18	easily	easily	ADV
ejpam-4316	114	19	shown	show	VERB
ejpam-4316	114	20	.	.	PUNCT
ejpam-4316	115	1	lemma	lemma	PROPN
ejpam-4316	115	2	1	1	X
ejpam-4316	115	3	.	.	PUNCT
ejpam-4316	116	1	let	let	VERB
ejpam-4316	116	2	g	g	PROPN
ejpam-4316	116	3	=	=	SYM
ejpam-4316	116	4	(	(	PUNCT
ejpam-4316	116	5	v	v	NOUN
ejpam-4316	116	6	,	,	PUNCT
ejpam-4316	116	7	e	e	NOUN
ejpam-4316	116	8	)	)	PUNCT
ejpam-4316	116	9	is	be	AUX
ejpam-4316	116	10	a	a	DET
ejpam-4316	116	11	simple	simple	ADJ
ejpam-4316	116	12	graph	graph	NOUN
ejpam-4316	116	13	on	on	ADP
ejpam-4316	116	14	n	n	PRON
ejpam-4316	116	15	≥	≥	NUM
ejpam-4316	116	16	2	2	NUM
ejpam-4316	116	17	vertices	vertex	NOUN
ejpam-4316	116	18	and	and	CCONJ
ejpam-4316	116	19	m	m	PRON
ejpam-4316	116	20	≥	≥	NOUN
ejpam-4316	116	21	1	1	NUM
ejpam-4316	116	22	edges	edge	NOUN
ejpam-4316	116	23	.	.	PUNCT
ejpam-4316	117	1	let	let	VERB
ejpam-4316	117	2	s	s	PRON
ejpam-4316	117	3	be	be	AUX
ejpam-4316	117	4	a	a	DET
ejpam-4316	117	5	non	non	ADJ
ejpam-4316	117	6	-	-	ADJ
ejpam-4316	117	7	empty	empty	ADJ
ejpam-4316	117	8	subset	subset	NOUN
ejpam-4316	117	9	of	of	ADP
ejpam-4316	117	10	v	v	NUM
ejpam-4316	117	11	and	and	CCONJ
ejpam-4316	117	12	|s|	|s|	PROPN
ejpam-4316	117	13	=	=	SYM
ejpam-4316	117	14	r.	r.	PROPN
ejpam-4316	117	15	consider	consider	VERB
ejpam-4316	117	16	the	the	DET
ejpam-4316	117	17	s	s	NOUN
ejpam-4316	117	18	-	-	PUNCT
ejpam-4316	117	19	splitting	splitting	NOUN
ejpam-4316	117	20	graph	graph	NOUN
ejpam-4316	117	21	of	of	ADP
ejpam-4316	117	22	g	g	PROPN
ejpam-4316	117	23	,	,	PUNCT
ejpam-4316	117	24	γ(g	γ(g	PROPN
ejpam-4316	117	25	,	,	PUNCT
ejpam-4316	117	26	s	s	PART
ejpam-4316	117	27	)	)	PUNCT
ejpam-4316	117	28	with	with	ADP
ejpam-4316	117	29	v	v	NUM
ejpam-4316	117	30	(	(	PUNCT
ejpam-4316	117	31	γ	γ	NOUN
ejpam-4316	117	32	)	)	PUNCT
ejpam-4316	117	33	=	=	SYM
ejpam-4316	117	34	v	v	NOUN
ejpam-4316	117	35	∪	∪	ADP
ejpam-4316	117	36	s′	s′	NOUN
ejpam-4316	117	37	,	,	PUNCT
ejpam-4316	117	38	where	where	SCONJ
ejpam-4316	117	39	s′	s′	ADJ
ejpam-4316	117	40	=	=	SYM
ejpam-4316	117	41	{	{	PUNCT
ejpam-4316	117	42	x′|x	x′|x	NOUN
ejpam-4316	117	43	∈	∈	PROPN
ejpam-4316	117	44	s	s	PART
ejpam-4316	117	45	}	}	PUNCT
ejpam-4316	117	46	.	.	PUNCT
ejpam-4316	118	1	(	(	PUNCT
ejpam-4316	118	2	i	i	NOUN
ejpam-4316	118	3	)	)	PUNCT
ejpam-4316	118	4	if	if	SCONJ
ejpam-4316	118	5	s	s	VERB
ejpam-4316	118	6	=	=	SYM
ejpam-4316	118	7	v	v	PROPN
ejpam-4316	118	8	,	,	PUNCT
ejpam-4316	118	9	then	then	ADV
ejpam-4316	118	10	|v	|v	PROPN
ejpam-4316	118	11	(	(	PUNCT
ejpam-4316	118	12	γ)|	γ)|	NOUN
ejpam-4316	118	13	=	=	SYM
ejpam-4316	118	14	2n	2n	NUM
ejpam-4316	118	15	,	,	PUNCT
ejpam-4316	118	16	|e(γ)|	|e(γ)|	PROPN
ejpam-4316	118	17	=	=	SYM
ejpam-4316	118	18	3	3	NUM
ejpam-4316	118	19	m.	m.	NOUN
ejpam-4316	118	20	(	(	PUNCT
ejpam-4316	118	21	ii	ii	NOUN
ejpam-4316	118	22	)	)	PUNCT
ejpam-4316	118	23	if	if	SCONJ
ejpam-4316	118	24	s	s	VERB
ejpam-4316	118	25	=	=	SYM
ejpam-4316	118	26	v	v	NOUN
ejpam-4316	118	27	and	and	CCONJ
ejpam-4316	118	28	v	v	ADP
ejpam-4316	118	29	∈	∈	NOUN
ejpam-4316	118	30	s	s	NOUN
ejpam-4316	118	31	,	,	PUNCT
ejpam-4316	118	32	then	then	ADV
ejpam-4316	118	33	degγ(v	degγ(v	NOUN
ejpam-4316	118	34	)	)	PUNCT
ejpam-4316	118	35	=	=	SYM
ejpam-4316	118	36	2degg(v	2degg(v	NUM
ejpam-4316	118	37	)	)	PUNCT
ejpam-4316	118	38	.	.	PUNCT
ejpam-4316	119	1	(	(	PUNCT
ejpam-4316	119	2	iii	iii	X
ejpam-4316	119	3	)	)	PUNCT
ejpam-4316	119	4	if	if	SCONJ
ejpam-4316	119	5	v	v	NUM
ejpam-4316	119	6	∈	∈	PROPN
ejpam-4316	119	7	s′	s′	NOUN
ejpam-4316	119	8	,	,	PUNCT
ejpam-4316	119	9	then	then	ADV
ejpam-4316	119	10	degγ(v	degγ(v	VERB
ejpam-4316	119	11	′	′	NOUN
ejpam-4316	119	12	)	)	PUNCT
ejpam-4316	120	1	=	=	SYM
ejpam-4316	120	2	degg(v	degg(v	PROPN
ejpam-4316	120	3	)	)	PUNCT
ejpam-4316	120	4	.	.	PUNCT
ejpam-4316	121	1	(	(	PUNCT
ejpam-4316	121	2	iv	iv	X
ejpam-4316	121	3	)	)	PUNCT
ejpam-4316	121	4	if	if	SCONJ
ejpam-4316	121	5	g	g	PROPN
ejpam-4316	121	6	is	be	AUX
ejpam-4316	121	7	a	a	DET
ejpam-4316	121	8	connected	connected	ADJ
ejpam-4316	121	9	graph	graph	NOUN
ejpam-4316	121	10	,	,	PUNCT
ejpam-4316	121	11	then	then	ADV
ejpam-4316	121	12	γ(g	γ(g	PROPN
ejpam-4316	121	13	,	,	PUNCT
ejpam-4316	121	14	s	s	PART
ejpam-4316	121	15	)	)	PUNCT
ejpam-4316	121	16	is	be	AUX
ejpam-4316	121	17	also	also	ADV
ejpam-4316	121	18	connected	connect	VERB
ejpam-4316	121	19	.	.	PUNCT
ejpam-4316	122	1	f.j.h	f.j.h	ADJ
ejpam-4316	122	2	.	.	PUNCT
ejpam-4316	123	1	campeña	campeña	NOUN
ejpam-4316	123	2	,	,	PUNCT
ejpam-4316	123	3	m.c.g	m.c.g	PROPN
ejpam-4316	123	4	.	.	PUNCT
ejpam-4316	123	5	egan	egan	PROPN
ejpam-4316	123	6	,	,	PUNCT
ejpam-4316	123	7	j.r.m	j.r.m	PROPN
ejpam-4316	123	8	.	.	PUNCT
ejpam-4316	124	1	antalan	antalan	PROPN
ejpam-4316	124	2	/	/	SYM
ejpam-4316	124	3	eur	eur	PROPN
ejpam-4316	124	4	.	.	PUNCT
ejpam-4316	125	1	j.	j.	PROPN
ejpam-4316	125	2	pure	pure	PROPN
ejpam-4316	125	3	appl	appl	PROPN
ejpam-4316	125	4	.	.	PROPN
ejpam-4316	125	5	math	math	PROPN
ejpam-4316	125	6	,	,	PUNCT
ejpam-4316	125	7	15	15	NUM
ejpam-4316	125	8	(	(	PUNCT
ejpam-4316	125	9	2	2	NUM
ejpam-4316	125	10	)	)	PUNCT
ejpam-4316	125	11	(	(	PUNCT
ejpam-4316	125	12	2022	2022	NUM
ejpam-4316	125	13	)	)	PUNCT
ejpam-4316	125	14	,	,	PUNCT
ejpam-4316	125	15	602	602	NUM
ejpam-4316	125	16	-	-	SYM
ejpam-4316	125	17	619	619	NUM
ejpam-4316	125	18	606	606	NUM
ejpam-4316	125	19	proof	proof	NOUN
ejpam-4316	125	20	.	.	PUNCT
ejpam-4316	126	1	let	let	VERB
ejpam-4316	126	2	γ	γ	NOUN
ejpam-4316	126	3	be	be	AUX
ejpam-4316	126	4	the	the	DET
ejpam-4316	126	5	s	s	NOUN
ejpam-4316	126	6	-	-	PUNCT
ejpam-4316	126	7	splitting	splitting	NOUN
ejpam-4316	126	8	graph	graph	NOUN
ejpam-4316	126	9	of	of	ADP
ejpam-4316	126	10	g.	g.	PROPN
ejpam-4316	126	11	for	for	ADP
ejpam-4316	126	12	(	(	PUNCT
ejpam-4316	126	13	i	i	NOUN
ejpam-4316	126	14	)	)	PUNCT
ejpam-4316	126	15	,	,	PUNCT
ejpam-4316	126	16	suppose	suppose	VERB
ejpam-4316	126	17	s	s	VERB
ejpam-4316	126	18	=	=	ADJ
ejpam-4316	126	19	v	v	PROPN
ejpam-4316	126	20	.	.	PUNCT
ejpam-4316	127	1	then	then	ADV
ejpam-4316	127	2	|s|	|s|	PROPN
ejpam-4316	127	3	=	=	PROPN
ejpam-4316	127	4	|v	|v	PROPN
ejpam-4316	127	5	|	|	NOUN
ejpam-4316	127	6	.	.	PUNCT
ejpam-4316	128	1	since	since	SCONJ
ejpam-4316	128	2	v	v	X
ejpam-4316	128	3	(	(	PUNCT
ejpam-4316	128	4	γ	γ	NOUN
ejpam-4316	128	5	)	)	PUNCT
ejpam-4316	128	6	=	=	NOUN
ejpam-4316	128	7	v	v	NOUN
ejpam-4316	128	8	∪v	∪v	NOUN
ejpam-4316	128	9	′	′	NUM
ejpam-4316	128	10	and	and	CCONJ
ejpam-4316	128	11	v	v	NOUN
ejpam-4316	128	12	′	′	NUM
ejpam-4316	128	13	is	be	AUX
ejpam-4316	128	14	the	the	DET
ejpam-4316	128	15	new	new	ADJ
ejpam-4316	128	16	set	set	NOUN
ejpam-4316	128	17	of	of	ADP
ejpam-4316	128	18	the	the	DET
ejpam-4316	128	19	vertices	vertex	NOUN
ejpam-4316	128	20	obtained	obtain	VERB
ejpam-4316	128	21	from	from	ADP
ejpam-4316	128	22	v	v	NUM
ejpam-4316	128	23	(	(	PUNCT
ejpam-4316	128	24	g	g	NOUN
ejpam-4316	128	25	)	)	PUNCT
ejpam-4316	128	26	,	,	PUNCT
ejpam-4316	128	27	then	then	ADV
ejpam-4316	128	28	v	v	ADP
ejpam-4316	128	29	∩v	∩v	NOUN
ejpam-4316	129	1	′	′	NUM
ejpam-4316	130	1	=	=	PUNCT
ejpam-4316	131	1	∅.	∅.	PRON
ejpam-4316	131	2	this	this	PRON
ejpam-4316	131	3	implies	imply	VERB
ejpam-4316	131	4	that	that	SCONJ
ejpam-4316	131	5	|v	|v	PROPN
ejpam-4316	131	6	(	(	PUNCT
ejpam-4316	131	7	γ)|	γ)|	NOUN
ejpam-4316	131	8	=	=	SYM
ejpam-4316	131	9	|v	|v	PROPN
ejpam-4316	131	10	|+	|+	NOUN
ejpam-4316	131	11	|v	|v	VERB
ejpam-4316	131	12	′|	′|	NUM
ejpam-4316	131	13	=	=	SYM
ejpam-4316	131	14	2|v	2|v	PROPN
ejpam-4316	131	15	(	(	PUNCT
ejpam-4316	131	16	g)|	g)|	NOUN
ejpam-4316	131	17	.	.	PUNCT
ejpam-4316	132	1	meanwhile	meanwhile	ADV
ejpam-4316	132	2	,	,	PUNCT
ejpam-4316	132	3	from	from	ADP
ejpam-4316	132	4	the	the	DET
ejpam-4316	132	5	definition	definition	NOUN
ejpam-4316	132	6	of	of	ADP
ejpam-4316	132	7	γ(g	γ(g	PROPN
ejpam-4316	132	8	,	,	PUNCT
ejpam-4316	132	9	s	s	PART
ejpam-4316	132	10	)	)	PUNCT
ejpam-4316	132	11	,	,	PUNCT
ejpam-4316	132	12	for	for	ADP
ejpam-4316	132	13	every	every	DET
ejpam-4316	132	14	edge	edge	NOUN
ejpam-4316	132	15	in	in	ADP
ejpam-4316	132	16	g	g	NOUN
ejpam-4316	132	17	,	,	PUNCT
ejpam-4316	132	18	2	2	NUM
ejpam-4316	132	19	new	new	ADJ
ejpam-4316	132	20	edges	edge	NOUN
ejpam-4316	132	21	are	be	AUX
ejpam-4316	132	22	formed	form	VERB
ejpam-4316	132	23	.	.	PUNCT
ejpam-4316	133	1	so	so	ADV
ejpam-4316	133	2	,	,	PUNCT
ejpam-4316	133	3	|e(γ)|	|e(γ)|	PROPN
ejpam-4316	133	4	=	=	NOUN
ejpam-4316	133	5	|e(g)|+	|e(g)|+	ADJ
ejpam-4316	133	6	2|e(g)|	2|e(g)|	NUM
ejpam-4316	133	7	=	=	SYM
ejpam-4316	133	8	3|e(g)|	3|e(g)|	NUM
ejpam-4316	133	9	.	.	PUNCT
ejpam-4316	134	1	for	for	ADP
ejpam-4316	134	2	(	(	PUNCT
ejpam-4316	134	3	ii	ii	NOUN
ejpam-4316	134	4	)	)	PUNCT
ejpam-4316	134	5	,	,	PUNCT
ejpam-4316	134	6	let	let	VERB
ejpam-4316	134	7	s	s	PRON
ejpam-4316	134	8	=	=	VERB
ejpam-4316	134	9	v	v	PROPN
ejpam-4316	134	10	.	.	PUNCT
ejpam-4316	135	1	from	from	ADP
ejpam-4316	135	2	γ	γ	PROPN
ejpam-4316	135	3	,	,	PUNCT
ejpam-4316	135	4	suppose	suppose	VERB
ejpam-4316	135	5	degg(v	degg(v	VERB
ejpam-4316	135	6	)	)	PUNCT
ejpam-4316	135	7	=	=	SYM
ejpam-4316	136	1	p	p	NOUN
ejpam-4316	136	2	and	and	CCONJ
ejpam-4316	136	3	v	v	ADP
ejpam-4316	136	4	∈	∈	NOUN
ejpam-4316	136	5	s	s	NOUN
ejpam-4316	136	6	,	,	PUNCT
ejpam-4316	136	7	then	then	ADV
ejpam-4316	136	8	there	there	PRON
ejpam-4316	136	9	are	be	VERB
ejpam-4316	136	10	p	p	ADJ
ejpam-4316	136	11	new	new	ADJ
ejpam-4316	136	12	vertices	vertex	NOUN
ejpam-4316	136	13	connected	connect	VERB
ejpam-4316	136	14	to	to	ADP
ejpam-4316	136	15	v.	v.	PROPN
ejpam-4316	136	16	thus	thus	ADV
ejpam-4316	136	17	,	,	PUNCT
ejpam-4316	136	18	degγ(v	degγ(v	NOUN
ejpam-4316	136	19	)	)	PUNCT
ejpam-4316	136	20	=	=	SYM
ejpam-4316	136	21	2degg(v	2degg(v	NUM
ejpam-4316	136	22	)	)	PUNCT
ejpam-4316	136	23	.	.	PUNCT
ejpam-4316	137	1	for	for	ADP
ejpam-4316	137	2	(	(	PUNCT
ejpam-4316	137	3	iii	iii	NOUN
ejpam-4316	137	4	)	)	PUNCT
ejpam-4316	137	5	,	,	PUNCT
ejpam-4316	137	6	let	let	VERB
ejpam-4316	137	7	v	v	ADP
ejpam-4316	137	8	∈	∈	PROPN
ejpam-4316	137	9	v	v	ADP
ejpam-4316	137	10	′.	′.	NOUN
ejpam-4316	137	11	since	since	SCONJ
ejpam-4316	137	12	v′	v′	PROPN
ejpam-4316	137	13	is	be	AUX
ejpam-4316	137	14	the	the	DET
ejpam-4316	137	15	new	new	ADJ
ejpam-4316	137	16	vertex	vertex	NOUN
ejpam-4316	137	17	that	that	PRON
ejpam-4316	137	18	connects	connect	VERB
ejpam-4316	137	19	to	to	ADP
ejpam-4316	137	20	all	all	DET
ejpam-4316	137	21	vertices	vertex	NOUN
ejpam-4316	137	22	of	of	ADP
ejpam-4316	137	23	g	g	NOUN
ejpam-4316	137	24	adjacent	adjacent	ADJ
ejpam-4316	137	25	to	to	ADP
ejpam-4316	137	26	v	v	NOUN
ejpam-4316	137	27	,	,	PUNCT
ejpam-4316	137	28	then	then	ADV
ejpam-4316	137	29	degγ(v	degγ(v	VERB
ejpam-4316	137	30	′	′	NOUN
ejpam-4316	137	31	)	)	PUNCT
ejpam-4316	138	1	=	=	SYM
ejpam-4316	138	2	degg(v	degg(v	PROPN
ejpam-4316	138	3	)	)	PUNCT
ejpam-4316	138	4	.	.	PUNCT
ejpam-4316	139	1	for	for	ADP
ejpam-4316	139	2	(	(	PUNCT
ejpam-4316	139	3	iv	iv	NOUN
ejpam-4316	139	4	)	)	PUNCT
ejpam-4316	139	5	,	,	PUNCT
ejpam-4316	139	6	to	to	PART
ejpam-4316	139	7	show	show	VERB
ejpam-4316	139	8	that	that	SCONJ
ejpam-4316	139	9	γ	γ	PROPN
ejpam-4316	139	10	is	be	AUX
ejpam-4316	139	11	connected	connect	VERB
ejpam-4316	139	12	,	,	PUNCT
ejpam-4316	139	13	we	we	PRON
ejpam-4316	139	14	need	need	VERB
ejpam-4316	139	15	to	to	PART
ejpam-4316	139	16	show	show	VERB
ejpam-4316	139	17	that	that	SCONJ
ejpam-4316	139	18	for	for	ADP
ejpam-4316	139	19	any	any	DET
ejpam-4316	139	20	pair	pair	NOUN
ejpam-4316	139	21	of	of	ADP
ejpam-4316	139	22	vertices	vertex	NOUN
ejpam-4316	139	23	x	x	X
ejpam-4316	139	24	,	,	PUNCT
ejpam-4316	139	25	y	y	PROPN
ejpam-4316	139	26	in	in	ADP
ejpam-4316	139	27	γ	γ	PROPN
ejpam-4316	139	28	,	,	PUNCT
ejpam-4316	139	29	there	there	PRON
ejpam-4316	139	30	exists	exist	VERB
ejpam-4316	139	31	a	a	DET
ejpam-4316	139	32	path	path	NOUN
ejpam-4316	139	33	from	from	ADP
ejpam-4316	139	34	vertex	vertex	NOUN
ejpam-4316	139	35	x	x	PUNCT
ejpam-4316	139	36	to	to	ADP
ejpam-4316	139	37	vertex	vertex	NOUN
ejpam-4316	139	38	y.	y.	NOUN
ejpam-4316	139	39	we	we	PRON
ejpam-4316	139	40	consider	consider	VERB
ejpam-4316	139	41	three	three	NUM
ejpam-4316	139	42	cases	case	NOUN
ejpam-4316	139	43	:	:	PUNCT
ejpam-4316	139	44	x	x	X
ejpam-4316	139	45	,	,	PUNCT
ejpam-4316	139	46	y	y	PROPN
ejpam-4316	139	47	∈	∈	PROPN
ejpam-4316	139	48	v	v	NOUN
ejpam-4316	139	49	;	;	PUNCT
ejpam-4316	139	50	x	x	X
ejpam-4316	139	51	∈	∈	PROPN
ejpam-4316	139	52	v	v	NOUN
ejpam-4316	139	53	,	,	PUNCT
ejpam-4316	139	54	y	y	PROPN
ejpam-4316	139	55	∈	∈	PROPN
ejpam-4316	139	56	v	v	ADP
ejpam-4316	139	57	′	′	NUM
ejpam-4316	139	58	;	;	PUNCT
ejpam-4316	139	59	and	and	CCONJ
ejpam-4316	139	60	x	x	X
ejpam-4316	139	61	,	,	PUNCT
ejpam-4316	139	62	y	y	PROPN
ejpam-4316	139	63	∈	∈	PROPN
ejpam-4316	139	64	v	v	ADP
ejpam-4316	139	65	′.	′.	NOUN
ejpam-4316	139	66	since	since	SCONJ
ejpam-4316	139	67	g	g	PROPN
ejpam-4316	139	68	is	be	AUX
ejpam-4316	139	69	a	a	DET
ejpam-4316	139	70	connected	connected	ADJ
ejpam-4316	139	71	graph	graph	NOUN
ejpam-4316	139	72	,	,	PUNCT
ejpam-4316	139	73	then	then	ADV
ejpam-4316	139	74	there	there	PRON
ejpam-4316	139	75	is	be	VERB
ejpam-4316	139	76	a	a	DET
ejpam-4316	139	77	path	path	NOUN
ejpam-4316	139	78	between	between	ADP
ejpam-4316	139	79	any	any	DET
ejpam-4316	139	80	pair	pair	NOUN
ejpam-4316	139	81	of	of	ADP
ejpam-4316	139	82	vertices	vertex	NOUN
ejpam-4316	139	83	x	x	X
ejpam-4316	139	84	,	,	PUNCT
ejpam-4316	139	85	y	y	PROPN
ejpam-4316	139	86	in	in	ADP
ejpam-4316	139	87	v	v	NUM
ejpam-4316	139	88	.	.	PUNCT
ejpam-4316	140	1	let	let	VERB
ejpam-4316	140	2	x	x	PUNCT
ejpam-4316	140	3	∈	∈	PROPN
ejpam-4316	140	4	v	v	NOUN
ejpam-4316	140	5	,	,	PUNCT
ejpam-4316	140	6	y	y	PROPN
ejpam-4316	140	7	∈	∈	PROPN
ejpam-4316	140	8	v	v	ADP
ejpam-4316	140	9	′	′	NOUN
ejpam-4316	140	10	,	,	PUNCT
ejpam-4316	140	11	if	if	SCONJ
ejpam-4316	140	12	y	y	PROPN
ejpam-4316	140	13	=	=	SYM
ejpam-4316	140	14	x′	x′	PROPN
ejpam-4316	140	15	then	then	ADV
ejpam-4316	140	16	d(x	d(x	PROPN
ejpam-4316	140	17	,	,	PUNCT
ejpam-4316	140	18	y	y	PROPN
ejpam-4316	140	19	)	)	PUNCT
ejpam-4316	140	20	≥	≥	NOUN
ejpam-4316	140	21	2	2	NUM
ejpam-4316	140	22	from	from	ADP
ejpam-4316	140	23	the	the	DET
ejpam-4316	140	24	definition	definition	NOUN
ejpam-4316	140	25	of	of	ADP
ejpam-4316	140	26	an	an	DET
ejpam-4316	140	27	s	s	NOUN
ejpam-4316	140	28	-	-	PUNCT
ejpam-4316	140	29	splitting	splitting	NOUN
ejpam-4316	140	30	of	of	ADP
ejpam-4316	140	31	g.	g.	PROPN
ejpam-4316	140	32	moreover	moreover	ADV
ejpam-4316	140	33	,	,	PUNCT
ejpam-4316	140	34	y	y	PROPN
ejpam-4316	140	35	must	must	AUX
ejpam-4316	140	36	be	be	AUX
ejpam-4316	140	37	adjacent	adjacent	ADJ
ejpam-4316	140	38	to	to	ADP
ejpam-4316	140	39	a	a	DET
ejpam-4316	140	40	vertex	vertex	NOUN
ejpam-4316	140	41	in	in	ADP
ejpam-4316	140	42	ng(x	ng(x	NUM
ejpam-4316	140	43	)	)	PUNCT
ejpam-4316	140	44	and	and	CCONJ
ejpam-4316	140	45	thus	thus	ADV
ejpam-4316	140	46	there	there	PRON
ejpam-4316	140	47	exist	exist	VERB
ejpam-4316	140	48	a	a	DET
ejpam-4316	140	49	path	path	NOUN
ejpam-4316	140	50	of	of	ADP
ejpam-4316	140	51	length	length	NOUN
ejpam-4316	140	52	2	2	NUM
ejpam-4316	140	53	from	from	ADP
ejpam-4316	140	54	x	x	PUNCT
ejpam-4316	140	55	to	to	ADP
ejpam-4316	140	56	y	y	PROPN
ejpam-4316	140	57	,	,	PUNCT
ejpam-4316	140	58	which	which	PRON
ejpam-4316	140	59	shows	show	VERB
ejpam-4316	140	60	that	that	SCONJ
ejpam-4316	140	61	d(x	d(x	PROPN
ejpam-4316	140	62	,	,	PUNCT
ejpam-4316	140	63	y	y	NOUN
ejpam-4316	140	64	)	)	PUNCT
ejpam-4316	140	65	=	=	SYM
ejpam-4316	141	1	2	2	X
ejpam-4316	141	2	.	.	X
ejpam-4316	141	3	we	we	PRON
ejpam-4316	141	4	now	now	ADV
ejpam-4316	141	5	consider	consider	VERB
ejpam-4316	141	6	vertex	vertex	NOUN
ejpam-4316	141	7	u	u	NOUN
ejpam-4316	141	8	∈	∈	PROPN
ejpam-4316	141	9	v	v	ADP
ejpam-4316	141	10	associated	associate	VERB
ejpam-4316	141	11	to	to	ADP
ejpam-4316	141	12	y	y	PROPN
ejpam-4316	141	13	from	from	ADP
ejpam-4316	141	14	the	the	DET
ejpam-4316	141	15	definition	definition	NOUN
ejpam-4316	141	16	of	of	ADP
ejpam-4316	141	17	γ	γ	PROPN
ejpam-4316	141	18	where	where	SCONJ
ejpam-4316	141	19	y	y	PROPN
ejpam-4316	141	20	6=	6=	PROPN
ejpam-4316	141	21	x′.	x′.	PROPN
ejpam-4316	141	22	since	since	SCONJ
ejpam-4316	141	23	g	g	PROPN
ejpam-4316	141	24	is	be	AUX
ejpam-4316	141	25	connected	connect	VERB
ejpam-4316	141	26	,	,	PUNCT
ejpam-4316	141	27	then	then	ADV
ejpam-4316	141	28	there	there	PRON
ejpam-4316	141	29	must	must	AUX
ejpam-4316	141	30	be	be	AUX
ejpam-4316	141	31	a	a	DET
ejpam-4316	141	32	path	path	NOUN
ejpam-4316	141	33	from	from	ADP
ejpam-4316	141	34	x	x	PUNCT
ejpam-4316	141	35	to	to	PART
ejpam-4316	141	36	u.	u.	PROPN
ejpam-4316	141	37	suppose	suppose	VERB
ejpam-4316	141	38	the	the	DET
ejpam-4316	141	39	sequence	sequence	NOUN
ejpam-4316	141	40	of	of	ADP
ejpam-4316	141	41	vertices	vertex	NOUN
ejpam-4316	141	42	from	from	ADP
ejpam-4316	141	43	this	this	DET
ejpam-4316	141	44	path	path	NOUN
ejpam-4316	141	45	is	be	AUX
ejpam-4316	141	46	x	x	NOUN
ejpam-4316	141	47	=	=	NOUN
ejpam-4316	141	48	a1	a1	NOUN
ejpam-4316	141	49	,	,	PUNCT
ejpam-4316	141	50	.	.	PUNCT
ejpam-4316	141	51	.	.	PUNCT
ejpam-4316	142	1	.	.	PUNCT
ejpam-4316	143	1	,	,	PUNCT
ejpam-4316	143	2	ak	ak	PROPN
ejpam-4316	143	3	=	=	SYM
ejpam-4316	143	4	u	u	PROPN
ejpam-4316	143	5	,	,	PUNCT
ejpam-4316	143	6	then	then	ADV
ejpam-4316	143	7	there	there	PRON
ejpam-4316	143	8	is	be	VERB
ejpam-4316	143	9	a	a	DET
ejpam-4316	143	10	path	path	NOUN
ejpam-4316	143	11	from	from	ADP
ejpam-4316	143	12	x	x	PUNCT
ejpam-4316	143	13	to	to	ADP
ejpam-4316	143	14	y	y	NOUN
ejpam-4316	143	15	using	use	VERB
ejpam-4316	143	16	the	the	DET
ejpam-4316	143	17	sequence	sequence	NOUN
ejpam-4316	143	18	of	of	ADP
ejpam-4316	143	19	vertices	vertex	NOUN
ejpam-4316	143	20	x	x	X
ejpam-4316	143	21	=	=	SYM
ejpam-4316	143	22	a1	a1	NOUN
ejpam-4316	143	23	,	,	PUNCT
ejpam-4316	143	24	.	.	PUNCT
ejpam-4316	143	25	.	.	PUNCT
ejpam-4316	144	1	.	.	PUNCT
ejpam-4316	145	1	,	,	PUNCT
ejpam-4316	145	2	ak−1	ak−1	INTJ
ejpam-4316	145	3	=	=	PUNCT
ejpam-4316	145	4	y.	y.	NOUN
ejpam-4316	145	5	for	for	ADP
ejpam-4316	145	6	the	the	DET
ejpam-4316	145	7	last	last	ADJ
ejpam-4316	145	8	case	case	NOUN
ejpam-4316	145	9	,	,	PUNCT
ejpam-4316	145	10	suppose	suppose	VERB
ejpam-4316	145	11	both	both	DET
ejpam-4316	145	12	x	x	NOUN
ejpam-4316	145	13	,	,	PUNCT
ejpam-4316	145	14	y	y	PROPN
ejpam-4316	145	15	are	be	AUX
ejpam-4316	145	16	in	in	ADP
ejpam-4316	145	17	v	v	NUM
ejpam-4316	145	18	′.	′.	NOUN
ejpam-4316	145	19	let	let	VERB
ejpam-4316	145	20	u	u	NOUN
ejpam-4316	145	21	,	,	PUNCT
ejpam-4316	145	22	v	v	X
ejpam-4316	145	23	be	be	AUX
ejpam-4316	145	24	the	the	DET
ejpam-4316	145	25	vertices	vertex	NOUN
ejpam-4316	145	26	in	in	ADP
ejpam-4316	145	27	v	v	NUM
ejpam-4316	145	28	associated	associate	VERB
ejpam-4316	145	29	with	with	ADP
ejpam-4316	145	30	x	x	PROPN
ejpam-4316	145	31	,	,	PUNCT
ejpam-4316	145	32	y	y	PROPN
ejpam-4316	145	33	respectively	respectively	ADV
ejpam-4316	145	34	from	from	ADP
ejpam-4316	145	35	the	the	DET
ejpam-4316	145	36	definition	definition	NOUN
ejpam-4316	145	37	of	of	ADP
ejpam-4316	145	38	γ	γ	PROPN
ejpam-4316	145	39	.	.	PROPN
ejpam-4316	146	1	since	since	SCONJ
ejpam-4316	146	2	g	g	PROPN
ejpam-4316	146	3	is	be	AUX
ejpam-4316	146	4	connected	connect	VERB
ejpam-4316	146	5	,	,	PUNCT
ejpam-4316	146	6	then	then	ADV
ejpam-4316	146	7	there	there	PRON
ejpam-4316	146	8	must	must	AUX
ejpam-4316	146	9	be	be	AUX
ejpam-4316	146	10	a	a	DET
ejpam-4316	146	11	path	path	NOUN
ejpam-4316	146	12	from	from	ADP
ejpam-4316	146	13	u	u	NOUN
ejpam-4316	146	14	to	to	ADP
ejpam-4316	146	15	v	v	NOUN
ejpam-4316	146	16	in	in	ADP
ejpam-4316	146	17	g.	g.	PROPN
ejpam-4316	146	18	suppose	suppose	VERB
ejpam-4316	146	19	a1	a1	PROPN
ejpam-4316	146	20	,	,	PUNCT
ejpam-4316	146	21	a2	a2	PROPN
ejpam-4316	146	22	,	,	PUNCT
ejpam-4316	146	23	.	.	PUNCT
ejpam-4316	146	24	.	.	PUNCT
ejpam-4316	147	1	.	.	PUNCT
ejpam-4316	148	1	,	,	PUNCT
ejpam-4316	148	2	ak−1	ak−1	PROPN
ejpam-4316	148	3	,	,	PUNCT
ejpam-4316	148	4	ak	ak	PROPN
ejpam-4316	148	5	is	be	AUX
ejpam-4316	148	6	the	the	DET
ejpam-4316	148	7	sequence	sequence	NOUN
ejpam-4316	148	8	of	of	ADP
ejpam-4316	148	9	vertices	vertex	NOUN
ejpam-4316	148	10	from	from	ADP
ejpam-4316	148	11	this	this	DET
ejpam-4316	148	12	path	path	NOUN
ejpam-4316	148	13	.	.	PUNCT
ejpam-4316	149	1	from	from	ADP
ejpam-4316	149	2	the	the	DET
ejpam-4316	149	3	definition	definition	NOUN
ejpam-4316	149	4	of	of	ADP
ejpam-4316	149	5	γ	γ	PROPN
ejpam-4316	149	6	,	,	PUNCT
ejpam-4316	149	7	x	x	X
ejpam-4316	149	8	is	be	AUX
ejpam-4316	149	9	adjacent	adjacent	ADJ
ejpam-4316	149	10	to	to	ADP
ejpam-4316	149	11	a2	a2	PROPN
ejpam-4316	149	12	and	and	CCONJ
ejpam-4316	149	13	y	y	PROPN
ejpam-4316	149	14	is	be	AUX
ejpam-4316	149	15	adjacent	adjacent	ADJ
ejpam-4316	149	16	to	to	ADP
ejpam-4316	149	17	ak−1	ak−1	VERB
ejpam-4316	149	18	,	,	PUNCT
ejpam-4316	149	19	thus	thus	ADV
ejpam-4316	149	20	there	there	PRON
ejpam-4316	149	21	is	be	VERB
ejpam-4316	149	22	a	a	DET
ejpam-4316	149	23	path	path	NOUN
ejpam-4316	149	24	from	from	ADP
ejpam-4316	149	25	x	x	PUNCT
ejpam-4316	149	26	to	to	ADP
ejpam-4316	149	27	y	y	PROPN
ejpam-4316	149	28	in	in	ADP
ejpam-4316	149	29	γ	γ	PROPN
ejpam-4316	149	30	.	.	PROPN
ejpam-4316	149	31	therefore	therefore	ADV
ejpam-4316	149	32	,	,	PUNCT
ejpam-4316	149	33	γ(g	γ(g	PROPN
ejpam-4316	149	34	,	,	PUNCT
ejpam-4316	149	35	s	s	PART
ejpam-4316	149	36	)	)	PUNCT
ejpam-4316	149	37	is	be	AUX
ejpam-4316	149	38	a	a	DET
ejpam-4316	149	39	connected	connected	ADJ
ejpam-4316	149	40	graph	graph	NOUN
ejpam-4316	149	41	.	.	PUNCT
ejpam-4316	150	1	lemma	lemma	PROPN
ejpam-4316	150	2	2	2	X
ejpam-4316	150	3	.	.	PUNCT
ejpam-4316	151	1	let	let	VERB
ejpam-4316	151	2	g	g	PRON
ejpam-4316	151	3	be	be	AUX
ejpam-4316	151	4	a	a	DET
ejpam-4316	151	5	connected	connected	ADJ
ejpam-4316	151	6	graph	graph	NOUN
ejpam-4316	151	7	triangle	triangle	NOUN
ejpam-4316	151	8	free	free	ADJ
ejpam-4316	151	9	graph	graph	NOUN
ejpam-4316	151	10	with	with	ADP
ejpam-4316	151	11	at	at	ADV
ejpam-4316	151	12	least	least	ADV
ejpam-4316	151	13	two	two	NUM
ejpam-4316	151	14	vertices	vertex	NOUN
ejpam-4316	151	15	.	.	PUNCT
ejpam-4316	152	1	consider	consider	VERB
ejpam-4316	152	2	γ(g	γ(g	PROPN
ejpam-4316	152	3	)	)	PUNCT
ejpam-4316	152	4	,	,	PUNCT
ejpam-4316	152	5	then	then	ADV
ejpam-4316	152	6	we	we	PRON
ejpam-4316	152	7	have	have	VERB
ejpam-4316	152	8	,	,	PUNCT
ejpam-4316	152	9	(	(	PUNCT
ejpam-4316	152	10	i	i	NOUN
ejpam-4316	152	11	)	)	PUNCT
ejpam-4316	152	12	d(xi	d(xi	PROPN
ejpam-4316	152	13	,	,	PUNCT
ejpam-4316	152	14	x	x	NOUN
ejpam-4316	153	1	′	′	NUM
ejpam-4316	154	1	i	i	NOUN
ejpam-4316	154	2	)	)	PUNCT
ejpam-4316	154	3	=	=	PUNCT
ejpam-4316	154	4	2	2	NUM
ejpam-4316	154	5	,	,	PUNCT
ejpam-4316	154	6	for	for	ADP
ejpam-4316	154	7	i	i	PROPN
ejpam-4316	154	8	=	=	NOUN
ejpam-4316	154	9	1	1	NUM
ejpam-4316	154	10	,	,	PUNCT
ejpam-4316	154	11	.	.	PUNCT
ejpam-4316	154	12	.	.	PUNCT
ejpam-4316	154	13	.	.	PUNCT
ejpam-4316	155	1	,	,	PUNCT
ejpam-4316	155	2	n	n	CCONJ
ejpam-4316	155	3	;	;	PUNCT
ejpam-4316	155	4	(	(	PUNCT
ejpam-4316	155	5	ii	ii	NOUN
ejpam-4316	155	6	)	)	PUNCT
ejpam-4316	155	7	d(xi	d(xi	PROPN
ejpam-4316	155	8	,	,	PUNCT
ejpam-4316	155	9	xj	xj	PROPN
ejpam-4316	155	10	)	)	PUNCT
ejpam-4316	155	11	=	=	SYM
ejpam-4316	155	12	d(x′i	d(x′i	PROPN
ejpam-4316	155	13	,	,	PUNCT
ejpam-4316	155	14	xj	xj	PROPN
ejpam-4316	155	15	)	)	PUNCT
ejpam-4316	155	16	,	,	PUNCT
ejpam-4316	155	17	for	for	ADP
ejpam-4316	155	18	1	1	NUM
ejpam-4316	155	19	≤	≤	NOUN
ejpam-4316	155	20	i	i	PRON
ejpam-4316	155	21	,	,	PUNCT
ejpam-4316	155	22	j	j	PROPN
ejpam-4316	155	23	≤	≤	PROPN
ejpam-4316	155	24	n	n	CCONJ
ejpam-4316	155	25	,	,	PUNCT
ejpam-4316	155	26	i	i	PROPN
ejpam-4316	155	27	6=	6=	PROPN
ejpam-4316	155	28	j	j	PROPN
ejpam-4316	155	29	;	;	PUNCT
ejpam-4316	155	30	(	(	PUNCT
ejpam-4316	155	31	iii	iii	X
ejpam-4316	155	32	)	)	PUNCT
ejpam-4316	155	33	d(x′i	d(x′i	NOUN
ejpam-4316	155	34	,	,	PUNCT
ejpam-4316	155	35	x	x	PROPN
ejpam-4316	155	36	′	′	NUM
ejpam-4316	155	37	j	j	NOUN
ejpam-4316	155	38	)	)	PUNCT
ejpam-4316	156	1	=	=	SYM
ejpam-4316	156	2	3	3	NUM
ejpam-4316	156	3	for	for	ADP
ejpam-4316	156	4	adjacent	adjacent	ADJ
ejpam-4316	156	5	vertices	vertex	NOUN
ejpam-4316	156	6	xi	xi	X
ejpam-4316	156	7	and	and	CCONJ
ejpam-4316	156	8	xj	xj	NOUN
ejpam-4316	156	9	;	;	PUNCT
ejpam-4316	156	10	(	(	PUNCT
ejpam-4316	156	11	iv	iv	X
ejpam-4316	156	12	)	)	PUNCT
ejpam-4316	156	13	d(xi	d(xi	PROPN
ejpam-4316	156	14	,	,	PUNCT
ejpam-4316	156	15	xj	xj	PROPN
ejpam-4316	156	16	)	)	PUNCT
ejpam-4316	156	17	=	=	SYM
ejpam-4316	156	18	d(x′i	d(x′i	NOUN
ejpam-4316	156	19	,	,	PUNCT
ejpam-4316	156	20	x	x	PROPN
ejpam-4316	156	21	′	′	NUM
ejpam-4316	156	22	j	j	NOUN
ejpam-4316	156	23	)	)	PUNCT
ejpam-4316	156	24	where	where	SCONJ
ejpam-4316	156	25	xi	xi	PROPN
ejpam-4316	156	26	and	and	CCONJ
ejpam-4316	156	27	xj	xj	PROPN
ejpam-4316	156	28	are	be	AUX
ejpam-4316	156	29	non	non	ADJ
ejpam-4316	156	30	-	-	ADJ
ejpam-4316	156	31	adjacent	adjacent	ADJ
ejpam-4316	156	32	vertices	vertex	NOUN
ejpam-4316	156	33	where	where	SCONJ
ejpam-4316	156	34	v	v	X
ejpam-4316	156	35	(	(	PUNCT
ejpam-4316	156	36	γ	γ	NOUN
ejpam-4316	156	37	)	)	PUNCT
ejpam-4316	156	38	=	=	SYM
ejpam-4316	156	39	{	{	PUNCT
ejpam-4316	156	40	x1	x1	PROPN
ejpam-4316	156	41	,	,	PUNCT
ejpam-4316	156	42	.	.	PUNCT
ejpam-4316	156	43	.	.	PUNCT
ejpam-4316	156	44	.	.	PUNCT
ejpam-4316	157	1	,	,	PUNCT
ejpam-4316	157	2	xn	xn	PROPN
ejpam-4316	157	3	,	,	PUNCT
ejpam-4316	157	4	x′1	x′1	PROPN
ejpam-4316	157	5	,	,	PUNCT
ejpam-4316	157	6	.	.	PUNCT
ejpam-4316	157	7	.	.	PUNCT
ejpam-4316	157	8	.	.	PUNCT
ejpam-4316	158	1	,	,	PUNCT
ejpam-4316	158	2	x′n	x′n	PROPN
ejpam-4316	158	3	}	}	PUNCT
ejpam-4316	158	4	.	.	PUNCT
ejpam-4316	159	1	lemma	lemma	PROPN
ejpam-4316	159	2	3	3	X
ejpam-4316	159	3	.	.	PUNCT
ejpam-4316	160	1	let	let	VERB
ejpam-4316	160	2	g	g	PRON
ejpam-4316	160	3	be	be	AUX
ejpam-4316	160	4	a	a	DET
ejpam-4316	160	5	connected	connected	ADJ
ejpam-4316	160	6	graph	graph	NOUN
ejpam-4316	160	7	with	with	ADP
ejpam-4316	160	8	at	at	ADV
ejpam-4316	160	9	least	least	ADV
ejpam-4316	160	10	two	two	NUM
ejpam-4316	160	11	vertices	vertex	NOUN
ejpam-4316	160	12	such	such	ADJ
ejpam-4316	160	13	that	that	SCONJ
ejpam-4316	160	14	any	any	DET
ejpam-4316	160	15	pair	pair	NOUN
ejpam-4316	160	16	of	of	ADP
ejpam-4316	160	17	adjacent	adjacent	ADJ
ejpam-4316	160	18	vertices	vertex	NOUN
ejpam-4316	160	19	has	have	VERB
ejpam-4316	160	20	a	a	DET
ejpam-4316	160	21	common	common	ADJ
ejpam-4316	160	22	neighbor	neighbor	NOUN
ejpam-4316	160	23	.	.	PUNCT
ejpam-4316	161	1	then	then	ADV
ejpam-4316	161	2	we	we	PRON
ejpam-4316	161	3	have	have	VERB
ejpam-4316	161	4	the	the	DET
ejpam-4316	161	5	following	following	NOUN
ejpam-4316	161	6	:	:	PUNCT
ejpam-4316	161	7	(	(	PUNCT
ejpam-4316	161	8	i	i	NOUN
ejpam-4316	161	9	)	)	PUNCT
ejpam-4316	161	10	d(xi	d(xi	PROPN
ejpam-4316	161	11	,	,	PUNCT
ejpam-4316	161	12	x	x	NOUN
ejpam-4316	161	13	′	′	NUM
ejpam-4316	162	1	i	i	NOUN
ejpam-4316	162	2	)	)	PUNCT
ejpam-4316	162	3	=	=	SYM
ejpam-4316	162	4	2	2	NUM
ejpam-4316	162	5	for	for	ADP
ejpam-4316	162	6	i	i	PRON
ejpam-4316	162	7	=	=	NOUN
ejpam-4316	162	8	1	1	NUM
ejpam-4316	162	9	,	,	PUNCT
ejpam-4316	162	10	.	.	PUNCT
ejpam-4316	162	11	.	.	PUNCT
ejpam-4316	162	12	.	.	PUNCT
ejpam-4316	163	1	n	n	CCONJ
ejpam-4316	163	2	;	;	PUNCT
ejpam-4316	163	3	(	(	PUNCT
ejpam-4316	163	4	ii	ii	NOUN
ejpam-4316	163	5	)	)	PUNCT
ejpam-4316	163	6	d(xi	d(xi	PROPN
ejpam-4316	163	7	,	,	PUNCT
ejpam-4316	163	8	xj	xj	PROPN
ejpam-4316	163	9	)	)	PUNCT
ejpam-4316	163	10	=	=	SYM
ejpam-4316	163	11	d(x′i	d(x′i	PROPN
ejpam-4316	163	12	,	,	PUNCT
ejpam-4316	163	13	xj	xj	PROPN
ejpam-4316	163	14	)	)	PUNCT
ejpam-4316	163	15	for	for	ADP
ejpam-4316	163	16	1	1	NUM
ejpam-4316	163	17	≤	≤	NOUN
ejpam-4316	164	1	i	i	PRON
ejpam-4316	164	2	,	,	PUNCT
ejpam-4316	164	3	j	j	PROPN
ejpam-4316	164	4	≤	≤	PROPN
ejpam-4316	164	5	n	n	CCONJ
ejpam-4316	164	6	,	,	PUNCT
ejpam-4316	164	7	i	i	PROPN
ejpam-4316	164	8	6=	6=	PROPN
ejpam-4316	164	9	j	j	PROPN
ejpam-4316	164	10	;	;	PUNCT
ejpam-4316	164	11	(	(	PUNCT
ejpam-4316	164	12	iii	iii	X
ejpam-4316	164	13	)	)	PUNCT
ejpam-4316	164	14	d(x′i	d(x′i	NOUN
ejpam-4316	164	15	,	,	PUNCT
ejpam-4316	164	16	x	x	PROPN
ejpam-4316	164	17	′	′	NUM
ejpam-4316	164	18	j	j	NOUN
ejpam-4316	164	19	)	)	PUNCT
ejpam-4316	164	20	=	=	SYM
ejpam-4316	164	21	2	2	NUM
ejpam-4316	164	22	for	for	ADP
ejpam-4316	164	23	adjacent	adjacent	ADJ
ejpam-4316	164	24	vertices	vertex	NOUN
ejpam-4316	164	25	xi	xi	X
ejpam-4316	164	26	and	and	CCONJ
ejpam-4316	164	27	xj	xj	PROPN
ejpam-4316	164	28	;	;	PUNCT
ejpam-4316	164	29	f.j.h	f.j.h	ADJ
ejpam-4316	164	30	.	.	PUNCT
ejpam-4316	165	1	campeña	campeña	NOUN
ejpam-4316	165	2	,	,	PUNCT
ejpam-4316	165	3	m.c.g	m.c.g	PROPN
ejpam-4316	165	4	.	.	PUNCT
ejpam-4316	165	5	egan	egan	PROPN
ejpam-4316	165	6	,	,	PUNCT
ejpam-4316	165	7	j.r.m	j.r.m	PROPN
ejpam-4316	165	8	.	.	PUNCT
ejpam-4316	166	1	antalan	antalan	PROPN
ejpam-4316	166	2	/	/	SYM
ejpam-4316	166	3	eur	eur	PROPN
ejpam-4316	166	4	.	.	PUNCT
ejpam-4316	167	1	j.	j.	PROPN
ejpam-4316	167	2	pure	pure	PROPN
ejpam-4316	167	3	appl	appl	PROPN
ejpam-4316	167	4	.	.	PROPN
ejpam-4316	167	5	math	math	PROPN
ejpam-4316	167	6	,	,	PUNCT
ejpam-4316	167	7	15	15	NUM
ejpam-4316	167	8	(	(	PUNCT
ejpam-4316	167	9	2	2	NUM
ejpam-4316	167	10	)	)	PUNCT
ejpam-4316	167	11	(	(	PUNCT
ejpam-4316	167	12	2022	2022	NUM
ejpam-4316	167	13	)	)	PUNCT
ejpam-4316	167	14	,	,	PUNCT
ejpam-4316	167	15	602	602	NUM
ejpam-4316	167	16	-	-	SYM
ejpam-4316	167	17	619	619	NUM
ejpam-4316	167	18	607	607	NUM
ejpam-4316	167	19	(	(	PUNCT
ejpam-4316	167	20	iv	iv	X
ejpam-4316	167	21	)	)	PUNCT
ejpam-4316	167	22	d(xi	d(xi	PROPN
ejpam-4316	167	23	,	,	PUNCT
ejpam-4316	167	24	xj	xj	PROPN
ejpam-4316	167	25	)	)	PUNCT
ejpam-4316	167	26	=	=	SYM
ejpam-4316	167	27	d(x′i	d(x′i	NOUN
ejpam-4316	167	28	,	,	PUNCT
ejpam-4316	167	29	x	x	PROPN
ejpam-4316	167	30	′	′	NUM
ejpam-4316	167	31	j	j	NOUN
ejpam-4316	167	32	)	)	PUNCT
ejpam-4316	167	33	where	where	SCONJ
ejpam-4316	167	34	xi	xi	PROPN
ejpam-4316	167	35	and	and	CCONJ
ejpam-4316	167	36	xj	xj	PROPN
ejpam-4316	167	37	are	be	AUX
ejpam-4316	167	38	non	non	ADJ
ejpam-4316	167	39	-	-	ADJ
ejpam-4316	167	40	adjacent	adjacent	ADJ
ejpam-4316	167	41	vertices	vertex	NOUN
ejpam-4316	167	42	in	in	ADP
ejpam-4316	167	43	g	g	PROPN
ejpam-4316	167	44	where	where	SCONJ
ejpam-4316	167	45	v	v	NOUN
ejpam-4316	167	46	(	(	PUNCT
ejpam-4316	167	47	γ	γ	NOUN
ejpam-4316	167	48	)	)	PUNCT
ejpam-4316	167	49	=	=	SYM
ejpam-4316	167	50	{	{	PUNCT
ejpam-4316	167	51	x1	x1	PROPN
ejpam-4316	167	52	,	,	PUNCT
ejpam-4316	167	53	.	.	PUNCT
ejpam-4316	167	54	.	.	PUNCT
ejpam-4316	167	55	.	.	PUNCT
ejpam-4316	168	1	,	,	PUNCT
ejpam-4316	168	2	xn	xn	PROPN
ejpam-4316	168	3	,	,	PUNCT
ejpam-4316	168	4	x′1	x′1	PROPN
ejpam-4316	168	5	,	,	PUNCT
ejpam-4316	168	6	.	.	PUNCT
ejpam-4316	168	7	.	.	PUNCT
ejpam-4316	168	8	.	.	PUNCT
ejpam-4316	169	1	,	,	PUNCT
ejpam-4316	169	2	x′n	x′n	PROPN
ejpam-4316	169	3	}	}	PUNCT
ejpam-4316	169	4	.	.	PUNCT
ejpam-4316	170	1	if	if	SCONJ
ejpam-4316	170	2	g	g	PROPN
ejpam-4316	170	3	is	be	AUX
ejpam-4316	170	4	a	a	DET
ejpam-4316	170	5	triangle	triangle	NOUN
ejpam-4316	170	6	free	free	ADJ
ejpam-4316	170	7	graph	graph	NOUN
ejpam-4316	170	8	,	,	PUNCT
ejpam-4316	170	9	then	then	ADV
ejpam-4316	170	10	by	by	ADP
ejpam-4316	170	11	lemma	lemma	PROPN
ejpam-4316	170	12	2	2	NUM
ejpam-4316	170	13	the	the	DET
ejpam-4316	170	14	distance	distance	NOUN
ejpam-4316	170	15	matrix	matrix	NOUN
ejpam-4316	170	16	of	of	ADP
ejpam-4316	170	17	the	the	DET
ejpam-4316	170	18	v	v	NOUN
ejpam-4316	170	19	-splitting	-splitting	NOUN
ejpam-4316	170	20	of	of	ADP
ejpam-4316	170	21	g	g	PROPN
ejpam-4316	170	22	,	,	PUNCT
ejpam-4316	170	23	γ(g	γ(g	PROPN
ejpam-4316	170	24	)	)	PUNCT
ejpam-4316	171	1	=	=	SYM
ejpam-4316	171	2	γ	γ	NOUN
ejpam-4316	171	3	can	can	AUX
ejpam-4316	171	4	view	view	VERB
ejpam-4316	171	5	as	as	ADP
ejpam-4316	171	6	a	a	DET
ejpam-4316	171	7	block	block	NOUN
ejpam-4316	171	8	matrix	matrix	NOUN
ejpam-4316	171	9	given	give	VERB
ejpam-4316	171	10	by	by	ADP
ejpam-4316	171	11	d(γ	d(γ	PROPN
ejpam-4316	171	12	)	)	PUNCT
ejpam-4316	171	13	=	=	PUNCT
ejpam-4316	171	14	[	[	PUNCT
ejpam-4316	171	15	d(g	d(g	PROPN
ejpam-4316	171	16	)	)	PUNCT
ejpam-4316	171	17	d(g	d(g	PROPN
ejpam-4316	171	18	)	)	PUNCT
ejpam-4316	172	1	+	+	CCONJ
ejpam-4316	172	2	2	2	NUM
ejpam-4316	172	3	in	in	ADP
ejpam-4316	172	4	(	(	PUNCT
ejpam-4316	172	5	d(g	d(g	PROPN
ejpam-4316	172	6	)	)	PUNCT
ejpam-4316	172	7	+	+	CCONJ
ejpam-4316	172	8	2	2	NUM
ejpam-4316	172	9	in	in	ADP
ejpam-4316	172	10	)	)	PUNCT
ejpam-4316	172	11	d(g	d(g	PROPN
ejpam-4316	172	12	)	)	PUNCT
ejpam-4316	172	13	+	+	NUM
ejpam-4316	172	14	2a(g	2a(g	NUM
ejpam-4316	172	15	)	)	PUNCT
ejpam-4316	172	16	]	]	PUNCT
ejpam-4316	172	17	while	while	SCONJ
ejpam-4316	172	18	,	,	PUNCT
ejpam-4316	172	19	in	in	ADP
ejpam-4316	172	20	view	view	NOUN
ejpam-4316	172	21	of	of	ADP
ejpam-4316	172	22	lemma	lemma	PROPN
ejpam-4316	172	23	3	3	NUM
ejpam-4316	172	24	,	,	PUNCT
ejpam-4316	172	25	if	if	SCONJ
ejpam-4316	172	26	every	every	DET
ejpam-4316	172	27	pair	pair	NOUN
ejpam-4316	172	28	of	of	ADP
ejpam-4316	172	29	adjacent	adjacent	ADJ
ejpam-4316	172	30	vertices	vertex	NOUN
ejpam-4316	172	31	of	of	ADP
ejpam-4316	172	32	a	a	DET
ejpam-4316	172	33	graph	graph	NOUN
ejpam-4316	172	34	g	g	NOUN
ejpam-4316	172	35	has	have	VERB
ejpam-4316	172	36	a	a	DET
ejpam-4316	172	37	common	common	ADJ
ejpam-4316	172	38	neighbor	neighbor	NOUN
ejpam-4316	172	39	,	,	PUNCT
ejpam-4316	172	40	then	then	ADV
ejpam-4316	172	41	the	the	DET
ejpam-4316	172	42	distance	distance	NOUN
ejpam-4316	172	43	matrix	matrix	NOUN
ejpam-4316	172	44	of	of	ADP
ejpam-4316	172	45	γ	γ	X
ejpam-4316	172	46	can	can	AUX
ejpam-4316	172	47	be	be	AUX
ejpam-4316	172	48	written	write	VERB
ejpam-4316	172	49	as	as	ADP
ejpam-4316	172	50	the	the	DET
ejpam-4316	172	51	block	block	NOUN
ejpam-4316	172	52	matrix	matrix	NOUN
ejpam-4316	172	53	given	give	VERB
ejpam-4316	172	54	by	by	ADP
ejpam-4316	172	55	d(γ	d(γ	PROPN
ejpam-4316	172	56	)	)	PUNCT
ejpam-4316	172	57	=	=	PUNCT
ejpam-4316	172	58	[	[	PUNCT
ejpam-4316	172	59	d(g	d(g	PROPN
ejpam-4316	172	60	)	)	PUNCT
ejpam-4316	172	61	d(g	d(g	PROPN
ejpam-4316	172	62	)	)	PUNCT
ejpam-4316	173	1	+	+	CCONJ
ejpam-4316	173	2	2	2	NUM
ejpam-4316	173	3	in	in	ADP
ejpam-4316	173	4	d(g	d(g	PROPN
ejpam-4316	173	5	)	)	PUNCT
ejpam-4316	173	6	+	+	CCONJ
ejpam-4316	173	7	2	2	NUM
ejpam-4316	173	8	in	in	ADP
ejpam-4316	173	9	d(g	d(g	PROPN
ejpam-4316	173	10	)	)	PUNCT
ejpam-4316	174	1	+	+	NOUN
ejpam-4316	174	2	a(g	a(g	PROPN
ejpam-4316	174	3	)	)	PUNCT
ejpam-4316	174	4	]	]	PUNCT
ejpam-4316	174	5	where	where	SCONJ
ejpam-4316	174	6	d(g	d(g	NOUN
ejpam-4316	174	7	)	)	PUNCT
ejpam-4316	174	8	is	be	AUX
ejpam-4316	174	9	the	the	DET
ejpam-4316	174	10	distance	distance	NOUN
ejpam-4316	174	11	matrix	matrix	NOUN
ejpam-4316	174	12	of	of	ADP
ejpam-4316	174	13	a	a	DET
ejpam-4316	174	14	graph	graph	NOUN
ejpam-4316	174	15	g	g	NOUN
ejpam-4316	174	16	,	,	PUNCT
ejpam-4316	174	17	a(g	a(g	PROPN
ejpam-4316	174	18	)	)	PUNCT
ejpam-4316	174	19	is	be	AUX
ejpam-4316	174	20	the	the	DET
ejpam-4316	174	21	adjacency	adjacency	NOUN
ejpam-4316	174	22	matrix	matrix	NOUN
ejpam-4316	174	23	,	,	PUNCT
ejpam-4316	174	24	and	and	CCONJ
ejpam-4316	174	25	in	in	SCONJ
ejpam-4316	174	26	is	be	AUX
ejpam-4316	174	27	the	the	DET
ejpam-4316	174	28	identity	identity	NOUN
ejpam-4316	174	29	matrix	matrix	NOUN
ejpam-4316	174	30	with	with	ADP
ejpam-4316	174	31	size	size	NOUN
ejpam-4316	174	32	n.	n.	NOUN
ejpam-4316	174	33	the	the	DET
ejpam-4316	174	34	following	follow	VERB
ejpam-4316	174	35	theorem	theorem	NOUN
ejpam-4316	174	36	now	now	ADV
ejpam-4316	174	37	gives	give	VERB
ejpam-4316	174	38	us	we	PRON
ejpam-4316	174	39	a	a	DET
ejpam-4316	174	40	general	general	ADJ
ejpam-4316	174	41	description	description	NOUN
ejpam-4316	174	42	of	of	ADP
ejpam-4316	174	43	the	the	DET
ejpam-4316	174	44	distance	distance	NOUN
ejpam-4316	174	45	matrix	matrix	NOUN
ejpam-4316	174	46	of	of	ADP
ejpam-4316	174	47	a	a	DET
ejpam-4316	174	48	v	v	NUM
ejpam-4316	174	49	-splitting	-splitte	VERB
ejpam-4316	174	50	graph	graph	NOUN
ejpam-4316	174	51	of	of	ADP
ejpam-4316	174	52	g.	g.	PROPN
ejpam-4316	174	53	theorem	theorem	VERB
ejpam-4316	174	54	7	7	NUM
ejpam-4316	174	55	.	.	PUNCT
ejpam-4316	175	1	the	the	DET
ejpam-4316	175	2	distance	distance	NOUN
ejpam-4316	175	3	matrix	matrix	NOUN
ejpam-4316	175	4	of	of	ADP
ejpam-4316	175	5	the	the	DET
ejpam-4316	175	6	v	v	NOUN
ejpam-4316	175	7	-splitting	-splitting	ADJ
ejpam-4316	175	8	graph	graph	NOUN
ejpam-4316	175	9	of	of	ADP
ejpam-4316	175	10	g	g	NOUN
ejpam-4316	175	11	can	can	AUX
ejpam-4316	175	12	be	be	AUX
ejpam-4316	175	13	viewed	view	VERB
ejpam-4316	175	14	as	as	ADP
ejpam-4316	175	15	a	a	DET
ejpam-4316	175	16	2×	2×	NUM
ejpam-4316	175	17	2	2	NUM
ejpam-4316	175	18	block	block	NOUN
ejpam-4316	175	19	matrix	matrix	NOUN
ejpam-4316	175	20	given	give	VERB
ejpam-4316	175	21	by	by	ADP
ejpam-4316	175	22	d(γ	d(γ	PROPN
ejpam-4316	175	23	)	)	PUNCT
ejpam-4316	175	24	=	=	PUNCT
ejpam-4316	176	1	[	[	PUNCT
ejpam-4316	176	2	x	x	X
ejpam-4316	176	3	y	y	PROPN
ejpam-4316	176	4	z	z	PROPN
ejpam-4316	176	5	w	w	PROPN
ejpam-4316	176	6	]	]	X
ejpam-4316	176	7	x	x	PUNCT
ejpam-4316	176	8	=	=	SYM
ejpam-4316	176	9	d(g	d(g	PROPN
ejpam-4316	176	10	)	)	PUNCT
ejpam-4316	176	11	,	,	PUNCT
ejpam-4316	177	1	y	y	NOUN
ejpam-4316	177	2	=	=	PUNCT
ejpam-4316	177	3	z	z	PROPN
ejpam-4316	177	4	=	=	SYM
ejpam-4316	177	5	d(g	d(g	PROPN
ejpam-4316	177	6	)	)	PUNCT
ejpam-4316	178	1	+	+	CCONJ
ejpam-4316	178	2	2	2	NUM
ejpam-4316	178	3	in	in	ADP
ejpam-4316	178	4	and	and	CCONJ
ejpam-4316	178	5	w	w	ADP
ejpam-4316	178	6	where	where	SCONJ
ejpam-4316	178	7	w	w	NOUN
ejpam-4316	178	8	=	=	PUNCT
ejpam-4316	179	1	[	[	X
ejpam-4316	179	2	wij	wij	X
ejpam-4316	179	3	]	]	PUNCT
ejpam-4316	179	4	is	be	AUX
ejpam-4316	179	5	the	the	DET
ejpam-4316	179	6	matrix	matrix	NOUN
ejpam-4316	179	7	given	give	VERB
ejpam-4316	179	8	by	by	ADP
ejpam-4316	179	9	:	:	PUNCT
ejpam-4316	179	10	wij	wij	X
ejpam-4316	179	11	=	=	SYM
ejpam-4316	179	12			NOUN
ejpam-4316	179	13	2	2	NUM
ejpam-4316	179	14	if	if	SCONJ
ejpam-4316	179	15	{	{	PUNCT
ejpam-4316	179	16	xi	xi	PROPN
ejpam-4316	179	17	,	,	PUNCT
ejpam-4316	179	18	xj	xj	ADJ
ejpam-4316	179	19	}	}	PUNCT
ejpam-4316	179	20	∈	∈	PROPN
ejpam-4316	179	21	e(g	e(g	PROPN
ejpam-4316	179	22	)	)	PUNCT
ejpam-4316	179	23	and	and	CCONJ
ejpam-4316	179	24	ng(i	ng(i	NOUN
ejpam-4316	179	25	)	)	PUNCT
ejpam-4316	179	26	∩ng(j	∩ng(j	PROPN
ejpam-4316	179	27	)	)	PUNCT
ejpam-4316	179	28	6=	6=	ADP
ejpam-4316	179	29	∅	∅	NOUN
ejpam-4316	179	30	3	3	NUM
ejpam-4316	179	31	if	if	SCONJ
ejpam-4316	179	32	{	{	PUNCT
ejpam-4316	179	33	xi	xi	PROPN
ejpam-4316	179	34	,	,	PUNCT
ejpam-4316	179	35	xj	xj	ADJ
ejpam-4316	179	36	}	}	PUNCT
ejpam-4316	179	37	∈	∈	PROPN
ejpam-4316	179	38	e(g	e(g	PROPN
ejpam-4316	179	39	)	)	PUNCT
ejpam-4316	179	40	and	and	CCONJ
ejpam-4316	179	41	ng(i	ng(i	NOUN
ejpam-4316	179	42	)	)	PUNCT
ejpam-4316	179	43	∩ng(j	∩ng(j	PROPN
ejpam-4316	179	44	)	)	PUNCT
ejpam-4316	180	1	=	=	NOUN
ejpam-4316	180	2	∅	∅	NOUN
ejpam-4316	180	3	0	0	PUNCT
ejpam-4316	181	1	if	if	SCONJ
ejpam-4316	181	2	i	i	PRON
ejpam-4316	181	3	=	=	SYM
ejpam-4316	181	4	j	j	PROPN
ejpam-4316	181	5	d(xi	d(xi	PROPN
ejpam-4316	181	6	,	,	PUNCT
ejpam-4316	181	7	xj	xj	NOUN
ejpam-4316	181	8	)	)	PUNCT
ejpam-4316	181	9	otherwise	otherwise	ADV
ejpam-4316	181	10	.	.	PUNCT
ejpam-4316	182	1	proof	proof	NOUN
ejpam-4316	182	2	.	.	PUNCT
ejpam-4316	183	1	consider	consider	VERB
ejpam-4316	183	2	the	the	DET
ejpam-4316	183	3	distance	distance	NOUN
ejpam-4316	183	4	matrix	matrix	NOUN
ejpam-4316	183	5	of	of	ADP
ejpam-4316	183	6	the	the	DET
ejpam-4316	183	7	v	v	NOUN
ejpam-4316	183	8	-splitting	-splitting	ADJ
ejpam-4316	183	9	graph	graph	NOUN
ejpam-4316	183	10	of	of	ADP
ejpam-4316	183	11	g	g	NOUN
ejpam-4316	183	12	where	where	SCONJ
ejpam-4316	183	13	first	first	ADJ
ejpam-4316	183	14	n	n	NOUN
ejpam-4316	183	15	rows	row	NOUN
ejpam-4316	183	16	and	and	CCONJ
ejpam-4316	183	17	columns	column	NOUN
ejpam-4316	183	18	are	be	AUX
ejpam-4316	183	19	indexed	index	VERB
ejpam-4316	183	20	by	by	ADP
ejpam-4316	183	21	the	the	DET
ejpam-4316	183	22	vertices	vertex	NOUN
ejpam-4316	183	23	in	in	ADP
ejpam-4316	183	24	g	g	PROPN
ejpam-4316	183	25	say	say	VERB
ejpam-4316	183	26	x1	x1	PROPN
ejpam-4316	183	27	,	,	PUNCT
ejpam-4316	183	28	.	.	PUNCT
ejpam-4316	183	29	.	.	PUNCT
ejpam-4316	184	1	.	.	PUNCT
ejpam-4316	185	1	,	,	PUNCT
ejpam-4316	185	2	xn	xn	PROPN
ejpam-4316	185	3	and	and	CCONJ
ejpam-4316	185	4	the	the	DET
ejpam-4316	185	5	last	last	ADJ
ejpam-4316	185	6	n	n	NOUN
ejpam-4316	185	7	and	and	CCONJ
ejpam-4316	185	8	columns	column	NOUN
ejpam-4316	185	9	rows	row	NOUN
ejpam-4316	185	10	by	by	ADP
ejpam-4316	185	11	the	the	DET
ejpam-4316	185	12	new	new	ADJ
ejpam-4316	185	13	vertices	vertex	NOUN
ejpam-4316	185	14	say	say	VERB
ejpam-4316	185	15	x′1	x′1	PROPN
ejpam-4316	185	16	,	,	PUNCT
ejpam-4316	185	17	.	.	PUNCT
ejpam-4316	185	18	.	.	PUNCT
ejpam-4316	185	19	.	.	PUNCT
ejpam-4316	186	1	,	,	PUNCT
ejpam-4316	186	2	x	x	X
ejpam-4316	186	3	′	′	NUM
ejpam-4316	186	4	n.	n.	NOUN
ejpam-4316	186	5	from	from	ADP
ejpam-4316	186	6	lemma	lemma	PROPN
ejpam-4316	186	7	2	2	PROPN
ejpam-4316	186	8	and	and	CCONJ
ejpam-4316	186	9	lemma	lemma	PROPN
ejpam-4316	186	10	3	3	NUM
ejpam-4316	186	11	,	,	PUNCT
ejpam-4316	186	12	it	it	PRON
ejpam-4316	186	13	is	be	AUX
ejpam-4316	186	14	easy	easy	ADJ
ejpam-4316	186	15	to	to	PART
ejpam-4316	186	16	see	see	VERB
ejpam-4316	186	17	that	that	PRON
ejpam-4316	186	18	x	x	PROPN
ejpam-4316	187	1	=	=	SYM
ejpam-4316	187	2	d(g	d(g	PROPN
ejpam-4316	187	3	)	)	PUNCT
ejpam-4316	187	4	,	,	PUNCT
ejpam-4316	188	1	y	y	NOUN
ejpam-4316	188	2	=	=	PUNCT
ejpam-4316	188	3	z	z	PROPN
ejpam-4316	188	4	=	=	SYM
ejpam-4316	188	5	d(g)+2	d(g)+2	PROPN
ejpam-4316	188	6	in	in	ADV
ejpam-4316	188	7	.	.	PUNCT
ejpam-4316	189	1	let	let	VERB
ejpam-4316	189	2	us	we	PRON
ejpam-4316	189	3	now	now	ADV
ejpam-4316	189	4	consider	consider	VERB
ejpam-4316	189	5	the	the	DET
ejpam-4316	189	6	entries	entry	NOUN
ejpam-4316	189	7	in	in	ADP
ejpam-4316	189	8	w	w	NOUN
ejpam-4316	189	9	=	=	PUNCT
ejpam-4316	190	1	[	[	X
ejpam-4316	190	2	wij	wij	X
ejpam-4316	190	3	]	]	PUNCT
ejpam-4316	190	4	.	.	PUNCT
ejpam-4316	191	1	first	first	ADV
ejpam-4316	191	2	note	note	VERB
ejpam-4316	191	3	that	that	SCONJ
ejpam-4316	191	4	in	in	ADP
ejpam-4316	191	5	the	the	DET
ejpam-4316	191	6	distance	distance	NOUN
ejpam-4316	191	7	matrix	matrix	NOUN
ejpam-4316	191	8	of	of	ADP
ejpam-4316	191	9	g	g	NOUN
ejpam-4316	191	10	,	,	PUNCT
ejpam-4316	191	11	d(g	d(g	PROPN
ejpam-4316	191	12	)	)	PUNCT
ejpam-4316	191	13	=	=	PUNCT
ejpam-4316	192	1	[	[	X
ejpam-4316	192	2	dij	dij	X
ejpam-4316	192	3	]	]	X
ejpam-4316	192	4	,	,	PUNCT
ejpam-4316	192	5	dij	dij	PROPN
ejpam-4316	192	6	=	=	SYM
ejpam-4316	192	7	1	1	NUM
ejpam-4316	192	8	whenever	whenever	SCONJ
ejpam-4316	192	9	vertex	vertex	NOUN
ejpam-4316	192	10	xi	xi	PROPN
ejpam-4316	192	11	is	be	AUX
ejpam-4316	192	12	adjacent	adjacent	ADJ
ejpam-4316	192	13	to	to	PART
ejpam-4316	192	14	vertex	vertex	VERB
ejpam-4316	192	15	xj	xj	PROPN
ejpam-4316	192	16	in	in	ADP
ejpam-4316	192	17	g.	g.	PROPN
ejpam-4316	192	18	thus	thus	ADV
ejpam-4316	192	19	,	,	PUNCT
ejpam-4316	192	20	the	the	DET
ejpam-4316	192	21	non	non	ADJ
ejpam-4316	192	22	-	-	ADJ
ejpam-4316	192	23	zero	zero	NUM
ejpam-4316	192	24	entries	entry	NOUN
ejpam-4316	192	25	in	in	ADP
ejpam-4316	192	26	d(g)−a(g	d(g)−a(g	NOUN
ejpam-4316	192	27	)	)	PUNCT
ejpam-4316	192	28	denotes	denote	VERB
ejpam-4316	192	29	the	the	DET
ejpam-4316	192	30	distances	distance	NOUN
ejpam-4316	192	31	of	of	ADP
ejpam-4316	192	32	two	two	NUM
ejpam-4316	192	33	distinct	distinct	ADJ
ejpam-4316	192	34	non	non	ADJ
ejpam-4316	192	35	-	-	ADJ
ejpam-4316	192	36	adjacent	adjacent	ADJ
ejpam-4316	192	37	vertices	vertex	NOUN
ejpam-4316	192	38	in	in	ADP
ejpam-4316	192	39	g.	g.	PROPN
ejpam-4316	192	40	by	by	ADP
ejpam-4316	192	41	lemma	lemma	PROPN
ejpam-4316	192	42	2	2	PROPN
ejpam-4316	192	43	and	and	CCONJ
ejpam-4316	192	44	lemma	lemma	PROPN
ejpam-4316	192	45	3	3	NUM
ejpam-4316	192	46	,	,	PUNCT
ejpam-4316	192	47	wij	wij	PROPN
ejpam-4316	192	48	=	=	SYM
ejpam-4316	192	49	d(xi	d(xi	PROPN
ejpam-4316	192	50	,	,	PUNCT
ejpam-4316	192	51	xj	xj	NOUN
ejpam-4316	192	52	)	)	PUNCT
ejpam-4316	192	53	for	for	ADP
ejpam-4316	192	54	any	any	DET
ejpam-4316	192	55	two	two	NUM
ejpam-4316	192	56	distinct	distinct	ADJ
ejpam-4316	192	57	non	non	ADJ
ejpam-4316	192	58	-	-	ADJ
ejpam-4316	192	59	adjacent	adjacent	ADJ
ejpam-4316	192	60	vertices	vertex	NOUN
ejpam-4316	192	61	in	in	ADP
ejpam-4316	192	62	g.	g.	PROPN
ejpam-4316	192	63	now	now	ADV
ejpam-4316	192	64	,	,	PUNCT
ejpam-4316	192	65	we	we	PRON
ejpam-4316	192	66	partition	partition	VERB
ejpam-4316	192	67	the	the	DET
ejpam-4316	192	68	set	set	NOUN
ejpam-4316	192	69	of	of	ADP
ejpam-4316	192	70	all	all	DET
ejpam-4316	192	71	pairs	pair	NOUN
ejpam-4316	192	72	of	of	ADP
ejpam-4316	192	73	adjacent	adjacent	ADJ
ejpam-4316	192	74	vertices	vertex	NOUN
ejpam-4316	192	75	in	in	ADP
ejpam-4316	192	76	g	g	PROPN
ejpam-4316	192	77	say	say	VERB
ejpam-4316	192	78	v1	v1	NOUN
ejpam-4316	192	79	,	,	PUNCT
ejpam-4316	192	80	v2	v2	PROPN
ejpam-4316	192	81	where	where	SCONJ
ejpam-4316	192	82	v1	v1	NOUN
ejpam-4316	192	83	contains	contain	VERB
ejpam-4316	192	84	all	all	DET
ejpam-4316	192	85	pairs	pair	NOUN
ejpam-4316	192	86	having	have	VERB
ejpam-4316	192	87	a	a	DET
ejpam-4316	192	88	common	common	ADJ
ejpam-4316	192	89	neighbor	neighbor	NOUN
ejpam-4316	192	90	and	and	CCONJ
ejpam-4316	192	91	v2	v2	NOUN
ejpam-4316	192	92	contains	contain	VERB
ejpam-4316	192	93	pairs	pair	NOUN
ejpam-4316	192	94	of	of	ADP
ejpam-4316	192	95	adjacent	adjacent	ADJ
ejpam-4316	192	96	vertices	vertex	NOUN
ejpam-4316	192	97	having	have	VERB
ejpam-4316	192	98	no	no	DET
ejpam-4316	192	99	common	common	ADJ
ejpam-4316	192	100	neighbor	neighbor	NOUN
ejpam-4316	192	101	.	.	PUNCT
ejpam-4316	193	1	for	for	ADP
ejpam-4316	193	2	the	the	DET
ejpam-4316	193	3	pair	pair	NOUN
ejpam-4316	193	4	of	of	ADP
ejpam-4316	193	5	vertices	vertex	NOUN
ejpam-4316	193	6	f.j.h	f.j.h	ADJ
ejpam-4316	193	7	.	.	PUNCT
ejpam-4316	194	1	campeña	campeña	NOUN
ejpam-4316	194	2	,	,	PUNCT
ejpam-4316	194	3	m.c.g	m.c.g	PROPN
ejpam-4316	194	4	.	.	PUNCT
ejpam-4316	194	5	egan	egan	PROPN
ejpam-4316	194	6	,	,	PUNCT
ejpam-4316	194	7	j.r.m	j.r.m	PROPN
ejpam-4316	194	8	.	.	PUNCT
ejpam-4316	195	1	antalan	antalan	PROPN
ejpam-4316	195	2	/	/	SYM
ejpam-4316	195	3	eur	eur	PROPN
ejpam-4316	195	4	.	.	PUNCT
ejpam-4316	196	1	j.	j.	PROPN
ejpam-4316	196	2	pure	pure	PROPN
ejpam-4316	196	3	appl	appl	PROPN
ejpam-4316	196	4	.	.	PROPN
ejpam-4316	196	5	math	math	PROPN
ejpam-4316	196	6	,	,	PUNCT
ejpam-4316	196	7	15	15	NUM
ejpam-4316	196	8	(	(	PUNCT
ejpam-4316	196	9	2	2	NUM
ejpam-4316	196	10	)	)	PUNCT
ejpam-4316	196	11	(	(	PUNCT
ejpam-4316	196	12	2022	2022	NUM
ejpam-4316	196	13	)	)	PUNCT
ejpam-4316	196	14	,	,	PUNCT
ejpam-4316	196	15	602	602	NUM
ejpam-4316	196	16	-	-	SYM
ejpam-4316	196	17	619	619	NUM
ejpam-4316	196	18	608	608	NUM
ejpam-4316	196	19	xi	xi	NOUN
ejpam-4316	196	20	,	,	PUNCT
ejpam-4316	196	21	xj	xj	PROPN
ejpam-4316	196	22	in	in	ADP
ejpam-4316	196	23	v1	v1	PROPN
ejpam-4316	196	24	,	,	PUNCT
ejpam-4316	196	25	by	by	ADP
ejpam-4316	196	26	lemma	lemma	PROPN
ejpam-4316	196	27	3	3	NUM
ejpam-4316	196	28	(	(	PUNCT
ejpam-4316	196	29	iii	iii	NOUN
ejpam-4316	196	30	)	)	PUNCT
ejpam-4316	196	31	,	,	PUNCT
ejpam-4316	196	32	wij	wij	PROPN
ejpam-4316	196	33	=	=	SYM
ejpam-4316	196	34	d(x′i	d(x′i	PROPN
ejpam-4316	196	35	,	,	PUNCT
ejpam-4316	196	36	x	x	PROPN
ejpam-4316	196	37	′	′	NUM
ejpam-4316	196	38	j	j	NOUN
ejpam-4316	196	39	)	)	PUNCT
ejpam-4316	196	40	=	=	SYM
ejpam-4316	196	41	2	2	NUM
ejpam-4316	196	42	and	and	CCONJ
ejpam-4316	196	43	for	for	ADP
ejpam-4316	196	44	the	the	DET
ejpam-4316	196	45	pairs	pair	NOUN
ejpam-4316	196	46	of	of	ADP
ejpam-4316	196	47	vertices	vertex	NOUN
ejpam-4316	196	48	xi	xi	PROPN
ejpam-4316	196	49	,	,	PUNCT
ejpam-4316	196	50	xj	xj	PROPN
ejpam-4316	196	51	in	in	ADP
ejpam-4316	196	52	v2	v2	PROPN
ejpam-4316	196	53	,	,	PUNCT
ejpam-4316	196	54	by	by	ADP
ejpam-4316	196	55	lemma	lemma	PROPN
ejpam-4316	196	56	3	3	NUM
ejpam-4316	196	57	(	(	PUNCT
ejpam-4316	196	58	iii	iii	NOUN
ejpam-4316	196	59	)	)	PUNCT
ejpam-4316	196	60	,	,	PUNCT
ejpam-4316	196	61	wij	wij	PROPN
ejpam-4316	196	62	=	=	SYM
ejpam-4316	196	63	d(x′i	d(x′i	PROPN
ejpam-4316	196	64	,	,	PUNCT
ejpam-4316	196	65	x	x	PROPN
ejpam-4316	196	66	′	′	NUM
ejpam-4316	196	67	j	j	NOUN
ejpam-4316	196	68	)	)	PUNCT
ejpam-4316	196	69	=	=	SYM
ejpam-4316	197	1	3	3	X
ejpam-4316	197	2	.	.	X
ejpam-4316	197	3	note	note	VERB
ejpam-4316	197	4	that	that	SCONJ
ejpam-4316	197	5	the	the	DET
ejpam-4316	197	6	matrix	matrix	NOUN
ejpam-4316	197	7	w	w	NOUN
ejpam-4316	197	8	in	in	ADP
ejpam-4316	197	9	theorem	theorem	NOUN
ejpam-4316	197	10	3.1.7	3.1.7	PRON
ejpam-4316	197	11	can	can	AUX
ejpam-4316	197	12	be	be	AUX
ejpam-4316	197	13	expressed	express	VERB
ejpam-4316	197	14	as	as	ADP
ejpam-4316	197	15	w	w	PROPN
ejpam-4316	197	16	=	=	PUNCT
ejpam-4316	197	17	d(g)−a(g	d(g)−a(g	NOUN
ejpam-4316	197	18	)	)	PUNCT
ejpam-4316	197	19	+	+	NUM
ejpam-4316	197	20	2a′(g	2a′(g	NUM
ejpam-4316	197	21	)	)	PUNCT
ejpam-4316	198	1	+	+	CCONJ
ejpam-4316	198	2	3a′′(g	3a′′(g	X
ejpam-4316	198	3	)	)	PUNCT
ejpam-4316	198	4	where	where	SCONJ
ejpam-4316	198	5	d(g	d(g	NOUN
ejpam-4316	198	6	)	)	PUNCT
ejpam-4316	198	7	,	,	PUNCT
ejpam-4316	198	8	a(g	a(g	PROPN
ejpam-4316	198	9	)	)	PUNCT
ejpam-4316	198	10	is	be	AUX
ejpam-4316	198	11	the	the	DET
ejpam-4316	198	12	distance	distance	NOUN
ejpam-4316	198	13	matrix	matrix	NOUN
ejpam-4316	198	14	and	and	CCONJ
ejpam-4316	198	15	adjacency	adjacency	NOUN
ejpam-4316	198	16	matrix	matrix	NOUN
ejpam-4316	198	17	of	of	ADP
ejpam-4316	198	18	g	g	NOUN
ejpam-4316	198	19	respectively	respectively	ADV
ejpam-4316	198	20	,	,	PUNCT
ejpam-4316	198	21	and	and	CCONJ
ejpam-4316	198	22	a′(g	a′(g	PROPN
ejpam-4316	198	23	)	)	PUNCT
ejpam-4316	198	24	is	be	AUX
ejpam-4316	198	25	an	an	DET
ejpam-4316	198	26	n×	n×	PROPN
ejpam-4316	198	27	n	n	NOUN
ejpam-4316	198	28	matrix	matrix	NOUN
ejpam-4316	198	29	whose	whose	DET
ejpam-4316	198	30	ij	ij	NOUN
ejpam-4316	198	31	-	-	NOUN
ejpam-4316	198	32	entry	entry	NOUN
ejpam-4316	198	33	is	be	AUX
ejpam-4316	198	34	1	1	NUM
ejpam-4316	198	35	if	if	SCONJ
ejpam-4316	198	36	vertex	vertex	NOUN
ejpam-4316	198	37	i	i	PRON
ejpam-4316	198	38	is	be	AUX
ejpam-4316	198	39	adjacent	adjacent	ADJ
ejpam-4316	198	40	to	to	PART
ejpam-4316	198	41	vertex	vertex	VERB
ejpam-4316	198	42	j	j	PROPN
ejpam-4316	198	43	in	in	ADP
ejpam-4316	198	44	g	g	PROPN
ejpam-4316	198	45	such	such	ADJ
ejpam-4316	198	46	that	that	DET
ejpam-4316	198	47	ng(i	ng(i	NOUN
ejpam-4316	198	48	)	)	PUNCT
ejpam-4316	198	49	∩ng(j	∩ng(j	PROPN
ejpam-4316	198	50	)	)	PUNCT
ejpam-4316	198	51	6=	6=	ADP
ejpam-4316	198	52	∅	∅	NOUN
ejpam-4316	198	53	and	and	CCONJ
ejpam-4316	198	54	0	0	NUM
ejpam-4316	198	55	otherwise	otherwise	ADV
ejpam-4316	198	56	;	;	PUNCT
ejpam-4316	198	57	and	and	CCONJ
ejpam-4316	198	58	a′′(g	a′′(g	ADJ
ejpam-4316	198	59	)	)	PUNCT
ejpam-4316	198	60	is	be	AUX
ejpam-4316	198	61	an	an	DET
ejpam-4316	198	62	n×	n×	PROPN
ejpam-4316	198	63	n	n	NOUN
ejpam-4316	198	64	matrix	matrix	NOUN
ejpam-4316	198	65	whose	whose	DET
ejpam-4316	198	66	ij	ij	NOUN
ejpam-4316	198	67	-	-	NOUN
ejpam-4316	198	68	entry	entry	NOUN
ejpam-4316	198	69	is	be	AUX
ejpam-4316	198	70	1	1	NUM
ejpam-4316	198	71	if	if	SCONJ
ejpam-4316	198	72	vertex	vertex	NOUN
ejpam-4316	198	73	i	i	PRON
ejpam-4316	198	74	is	be	AUX
ejpam-4316	198	75	adjacent	adjacent	ADJ
ejpam-4316	198	76	to	to	PART
ejpam-4316	198	77	vertex	vertex	VERB
ejpam-4316	198	78	j	j	PROPN
ejpam-4316	198	79	in	in	ADP
ejpam-4316	198	80	g	g	PROPN
ejpam-4316	199	1	such	such	ADJ
ejpam-4316	199	2	that	that	DET
ejpam-4316	199	3	ng(i	ng(i	NOUN
ejpam-4316	199	4	)	)	PUNCT
ejpam-4316	199	5	∩ng(j	∩ng(j	PROPN
ejpam-4316	199	6	)	)	PUNCT
ejpam-4316	200	1	=	=	NOUN
ejpam-4316	200	2	∅	∅	NOUN
ejpam-4316	200	3	and	and	CCONJ
ejpam-4316	200	4	0	0	NUM
ejpam-4316	200	5	otherwise	otherwise	ADV
ejpam-4316	200	6	.	.	PUNCT
ejpam-4316	201	1	3.2	3.2	NUM
ejpam-4316	201	2	.	.	PUNCT
ejpam-4316	201	3	wiener	wiener	NOUN
ejpam-4316	201	4	index	index	NOUN
ejpam-4316	201	5	of	of	ADP
ejpam-4316	201	6	γ(g	γ(g	PROPN
ejpam-4316	201	7	,	,	PUNCT
ejpam-4316	201	8	v	v	NOUN
ejpam-4316	201	9	)	)	PUNCT
ejpam-4316	201	10	to	to	PART
ejpam-4316	201	11	simplify	simplify	VERB
ejpam-4316	201	12	our	our	PRON
ejpam-4316	201	13	computations	computation	NOUN
ejpam-4316	201	14	for	for	ADP
ejpam-4316	201	15	the	the	DET
ejpam-4316	201	16	wiener	wiener	NOUN
ejpam-4316	201	17	index	index	NOUN
ejpam-4316	201	18	of	of	ADP
ejpam-4316	201	19	a	a	DET
ejpam-4316	201	20	graph	graph	NOUN
ejpam-4316	201	21	we	we	PRON
ejpam-4316	201	22	use	use	VERB
ejpam-4316	201	23	the	the	DET
ejpam-4316	201	24	following	following	ADJ
ejpam-4316	201	25	notation	notation	NOUN
ejpam-4316	201	26	,	,	PUNCT
ejpam-4316	201	27	for	for	ADP
ejpam-4316	201	28	any	any	DET
ejpam-4316	201	29	matrix	matrix	NOUN
ejpam-4316	201	30	a	a	PRON
ejpam-4316	201	31	we	we	PRON
ejpam-4316	201	32	denote	denote	VERB
ejpam-4316	201	33	the	the	DET
ejpam-4316	201	34	sum	sum	NOUN
ejpam-4316	201	35	of	of	ADP
ejpam-4316	201	36	all	all	DET
ejpam-4316	201	37	entries	entry	NOUN
ejpam-4316	201	38	in	in	ADP
ejpam-4316	201	39	a	a	DET
ejpam-4316	201	40	by	by	ADP
ejpam-4316	201	41	∑	∑	PROPN
ejpam-4316	201	42	a.	a.	NOUN
ejpam-4316	201	43	recall	recall	NOUN
ejpam-4316	201	44	that	that	PRON
ejpam-4316	201	45	for	for	ADP
ejpam-4316	201	46	a	a	DET
ejpam-4316	201	47	constant	constant	ADJ
ejpam-4316	201	48	c	c	NOUN
ejpam-4316	201	49	,	,	PUNCT
ejpam-4316	201	50	then	then	ADV
ejpam-4316	201	51	∑	∑	ADP
ejpam-4316	201	52	ca	ca	NOUN
ejpam-4316	201	53	=	=	SYM
ejpam-4316	201	54	c	c	X
ejpam-4316	201	55	∑	∑	PUNCT
ejpam-4316	201	56	a.	a.	NOUN
ejpam-4316	201	57	theorem	theorem	NOUN
ejpam-4316	201	58	8	8	NUM
ejpam-4316	201	59	.	.	PUNCT
ejpam-4316	202	1	let	let	VERB
ejpam-4316	202	2	g	g	PRON
ejpam-4316	202	3	be	be	AUX
ejpam-4316	202	4	a	a	DET
ejpam-4316	202	5	connected	connected	ADJ
ejpam-4316	202	6	triangle	triangle	NOUN
ejpam-4316	202	7	free	free	ADJ
ejpam-4316	202	8	graph	graph	NOUN
ejpam-4316	202	9	on	on	ADP
ejpam-4316	202	10	n	n	DET
ejpam-4316	202	11	vertices	vertex	NOUN
ejpam-4316	202	12	and	and	CCONJ
ejpam-4316	202	13	m	m	PRON
ejpam-4316	202	14	edges	edge	NOUN
ejpam-4316	202	15	.	.	PUNCT
ejpam-4316	203	1	suppose	suppose	VERB
ejpam-4316	203	2	v	v	X
ejpam-4316	203	3	=	=	SYM
ejpam-4316	203	4	s	s	PROPN
ejpam-4316	203	5	,	,	PUNCT
ejpam-4316	203	6	the	the	DET
ejpam-4316	203	7	splitting	splitting	NOUN
ejpam-4316	203	8	graph	graph	NOUN
ejpam-4316	203	9	of	of	ADP
ejpam-4316	203	10	g	g	PROPN
ejpam-4316	203	11	γ	γ	X
ejpam-4316	203	12	=	=	SYM
ejpam-4316	203	13	γ(g	γ(g	PROPN
ejpam-4316	203	14	)	)	PUNCT
ejpam-4316	203	15	has	have	VERB
ejpam-4316	203	16	wiener	wiener	NOUN
ejpam-4316	203	17	index	index	NOUN
ejpam-4316	203	18	given	give	VERB
ejpam-4316	203	19	by	by	ADP
ejpam-4316	203	20	w	w	PROPN
ejpam-4316	203	21	(	(	PUNCT
ejpam-4316	203	22	γ	γ	NOUN
ejpam-4316	203	23	)	)	PUNCT
ejpam-4316	204	1	=	=	SYM
ejpam-4316	204	2	4w	4w	NOUN
ejpam-4316	204	3	(	(	PUNCT
ejpam-4316	204	4	g	g	NOUN
ejpam-4316	204	5	)	)	PUNCT
ejpam-4316	204	6	+	+	CCONJ
ejpam-4316	204	7	2n+	2n+	NUM
ejpam-4316	204	8	2	2	NUM
ejpam-4316	204	9	m.	m.	NOUN
ejpam-4316	204	10	proof	proof	NOUN
ejpam-4316	204	11	.	.	PUNCT
ejpam-4316	205	1	let	let	VERB
ejpam-4316	205	2	g	g	NOUN
ejpam-4316	205	3	be	be	AUX
ejpam-4316	205	4	any	any	DET
ejpam-4316	205	5	connected	connected	ADJ
ejpam-4316	205	6	graph	graph	NOUN
ejpam-4316	205	7	of	of	ADP
ejpam-4316	205	8	order	order	NOUN
ejpam-4316	205	9	n	n	PRON
ejpam-4316	205	10	such	such	ADJ
ejpam-4316	205	11	that	that	SCONJ
ejpam-4316	205	12	any	any	DET
ejpam-4316	205	13	pair	pair	NOUN
ejpam-4316	205	14	of	of	ADP
ejpam-4316	205	15	adjacent	adjacent	ADJ
ejpam-4316	205	16	vertices	vertex	NOUN
ejpam-4316	205	17	has	have	VERB
ejpam-4316	205	18	no	no	DET
ejpam-4316	205	19	common	common	ADJ
ejpam-4316	205	20	neighbor	neighbor	NOUN
ejpam-4316	205	21	,	,	PUNCT
ejpam-4316	205	22	that	that	PRON
ejpam-4316	205	23	is	be	AUX
ejpam-4316	205	24	g	g	NOUN
ejpam-4316	205	25	is	be	AUX
ejpam-4316	205	26	a	a	DET
ejpam-4316	205	27	triangle	triangle	NOUN
ejpam-4316	205	28	free	free	ADJ
ejpam-4316	205	29	graph	graph	NOUN
ejpam-4316	205	30	.	.	PUNCT
ejpam-4316	206	1	denote	denote	VERB
ejpam-4316	206	2	the	the	DET
ejpam-4316	206	3	splitting	splitting	NOUN
ejpam-4316	206	4	graph	graph	NOUN
ejpam-4316	206	5	of	of	ADP
ejpam-4316	206	6	g	g	NOUN
ejpam-4316	206	7	by	by	ADP
ejpam-4316	206	8	γ	γ	PROPN
ejpam-4316	206	9	.	.	PROPN
ejpam-4316	206	10	then	then	ADV
ejpam-4316	206	11	we	we	PRON
ejpam-4316	206	12	can	can	AUX
ejpam-4316	206	13	describe	describe	VERB
ejpam-4316	206	14	the	the	DET
ejpam-4316	206	15	distance	distance	NOUN
ejpam-4316	206	16	matrix	matrix	NOUN
ejpam-4316	206	17	of	of	ADP
ejpam-4316	206	18	γ	γ	PROPN
ejpam-4316	206	19	as	as	ADP
ejpam-4316	206	20	a	a	DET
ejpam-4316	206	21	2x2	2x2	NUM
ejpam-4316	206	22	block	block	NOUN
ejpam-4316	206	23	matrix	matrix	NOUN
ejpam-4316	206	24	entries	entry	NOUN
ejpam-4316	206	25	that	that	PRON
ejpam-4316	206	26	depends	depend	VERB
ejpam-4316	206	27	on	on	ADP
ejpam-4316	206	28	the	the	DET
ejpam-4316	206	29	distance	distance	NOUN
ejpam-4316	206	30	matrix	matrix	NOUN
ejpam-4316	206	31	,	,	PUNCT
ejpam-4316	206	32	adjacency	adjacency	NOUN
ejpam-4316	206	33	matrix	matrix	NOUN
ejpam-4316	206	34	and	and	CCONJ
ejpam-4316	206	35	identity	identity	NOUN
ejpam-4316	206	36	matrix	matrix	NOUN
ejpam-4316	206	37	of	of	ADP
ejpam-4316	206	38	the	the	DET
ejpam-4316	206	39	graph	graph	NOUN
ejpam-4316	206	40	g	g	NOUN
ejpam-4316	206	41	by	by	ADP
ejpam-4316	206	42	d(γ	d(γ	NOUN
ejpam-4316	206	43	)	)	PUNCT
ejpam-4316	207	1	=	=	PUNCT
ejpam-4316	207	2	[	[	PUNCT
ejpam-4316	207	3	d(g	d(g	PROPN
ejpam-4316	207	4	)	)	PUNCT
ejpam-4316	207	5	d(g	d(g	PROPN
ejpam-4316	207	6	)	)	PUNCT
ejpam-4316	208	1	+	+	CCONJ
ejpam-4316	208	2	2	2	NUM
ejpam-4316	208	3	in	in	ADP
ejpam-4316	208	4	d(g	d(g	PROPN
ejpam-4316	208	5	)	)	PUNCT
ejpam-4316	208	6	+	+	CCONJ
ejpam-4316	208	7	2	2	NUM
ejpam-4316	208	8	in	in	ADP
ejpam-4316	208	9	d(g	d(g	PROPN
ejpam-4316	208	10	)	)	PUNCT
ejpam-4316	208	11	+	+	NUM
ejpam-4316	208	12	2a(g	2a(g	NUM
ejpam-4316	208	13	)	)	PUNCT
ejpam-4316	208	14	]	]	PUNCT
ejpam-4316	208	15	since	since	SCONJ
ejpam-4316	208	16	the	the	DET
ejpam-4316	208	17	wiener	wiener	NOUN
ejpam-4316	208	18	index	index	NOUN
ejpam-4316	208	19	of	of	ADP
ejpam-4316	208	20	γ	γ	PROPN
ejpam-4316	208	21	is	be	AUX
ejpam-4316	208	22	half	half	NOUN
ejpam-4316	208	23	of	of	ADP
ejpam-4316	208	24	the	the	DET
ejpam-4316	208	25	distance	distance	NOUN
ejpam-4316	208	26	matrix	matrix	NOUN
ejpam-4316	208	27	of	of	ADP
ejpam-4316	208	28	γ	γ	PROPN
ejpam-4316	208	29	then	then	ADV
ejpam-4316	208	30	we	we	PRON
ejpam-4316	208	31	have	have	VERB
ejpam-4316	208	32	the	the	DET
ejpam-4316	208	33	following	following	NOUN
ejpam-4316	208	34	:	:	PUNCT
ejpam-4316	209	1	w	w	X
ejpam-4316	209	2	(	(	PUNCT
ejpam-4316	209	3	γ	γ	NOUN
ejpam-4316	209	4	)	)	PUNCT
ejpam-4316	209	5	=	=	SYM
ejpam-4316	209	6	1	1	NUM
ejpam-4316	209	7	2	2	NUM
ejpam-4316	209	8	∑	∑	PUNCT
ejpam-4316	209	9	d(γ	d(γ	PROPN
ejpam-4316	209	10	)	)	PUNCT
ejpam-4316	209	11	=	=	SYM
ejpam-4316	209	12	1	1	NUM
ejpam-4316	209	13	2	2	NUM
ejpam-4316	209	14	(	(	PUNCT
ejpam-4316	209	15	∑	∑	NOUN
ejpam-4316	209	16	4d(g	4d(g	NUM
ejpam-4316	209	17	)	)	PUNCT
ejpam-4316	210	1	+	+	CCONJ
ejpam-4316	210	2	4	4	NUM
ejpam-4316	210	3	∑	∑	NOUN
ejpam-4316	210	4	in	in	ADP
ejpam-4316	210	5	+	+	PROPN
ejpam-4316	210	6	∑	∑	PROPN
ejpam-4316	210	7	2a(g	2a(g	NUM
ejpam-4316	210	8	)	)	PUNCT
ejpam-4316	210	9	)	)	PUNCT
ejpam-4316	211	1	=	=	SYM
ejpam-4316	211	2	4	4	NUM
ejpam-4316	211	3	(	(	PUNCT
ejpam-4316	211	4	1	1	NUM
ejpam-4316	211	5	2	2	NUM
ejpam-4316	211	6	∑	∑	PUNCT
ejpam-4316	211	7	d(g	d(g	PROPN
ejpam-4316	211	8	)	)	PUNCT
ejpam-4316	211	9	)	)	PUNCT
ejpam-4316	212	1	+	+	CCONJ
ejpam-4316	212	2	2	2	NUM
ejpam-4316	212	3	∑	∑	NOUN
ejpam-4316	212	4	in	in	ADP
ejpam-4316	212	5	+	+	NOUN
ejpam-4316	212	6	∑	∑	PUNCT
ejpam-4316	212	7	a(g	a(g	PROPN
ejpam-4316	212	8	)	)	PUNCT
ejpam-4316	212	9	=	=	SYM
ejpam-4316	212	10	4w	4w	NOUN
ejpam-4316	212	11	(	(	PUNCT
ejpam-4316	212	12	g	g	NOUN
ejpam-4316	212	13	)	)	PUNCT
ejpam-4316	212	14	+	+	CCONJ
ejpam-4316	212	15	2n+	2n+	NUM
ejpam-4316	212	16	∑	∑	PUNCT
ejpam-4316	212	17	a(g	a(g	PROPN
ejpam-4316	212	18	)	)	PUNCT
ejpam-4316	212	19	observe	observe	VERB
ejpam-4316	212	20	that	that	SCONJ
ejpam-4316	212	21	the	the	DET
ejpam-4316	212	22	sum	sum	NOUN
ejpam-4316	212	23	of	of	ADP
ejpam-4316	212	24	the	the	DET
ejpam-4316	212	25	entries	entry	NOUN
ejpam-4316	212	26	in	in	ADP
ejpam-4316	212	27	an	an	DET
ejpam-4316	212	28	adjacency	adjacency	NOUN
ejpam-4316	212	29	matrix	matrix	NOUN
ejpam-4316	212	30	is	be	AUX
ejpam-4316	212	31	twice	twice	DET
ejpam-4316	212	32	the	the	DET
ejpam-4316	212	33	number	number	NOUN
ejpam-4316	212	34	of	of	ADP
ejpam-4316	212	35	edges	edge	NOUN
ejpam-4316	212	36	m.	m.	NOUN
ejpam-4316	212	37	that	that	PRON
ejpam-4316	212	38	is	be	AUX
ejpam-4316	212	39	,	,	PUNCT
ejpam-4316	212	40	w	w	PROPN
ejpam-4316	212	41	(	(	PUNCT
ejpam-4316	212	42	γ	γ	NOUN
ejpam-4316	212	43	)	)	PUNCT
ejpam-4316	212	44	=	=	SYM
ejpam-4316	212	45	4w	4w	NOUN
ejpam-4316	212	46	(	(	PUNCT
ejpam-4316	212	47	g	g	NOUN
ejpam-4316	212	48	)	)	PUNCT
ejpam-4316	212	49	+	+	CCONJ
ejpam-4316	212	50	2n+	2n+	NUM
ejpam-4316	212	51	2	2	NUM
ejpam-4316	212	52	m.	m.	NOUN
ejpam-4316	212	53	we	we	PRON
ejpam-4316	212	54	note	note	VERB
ejpam-4316	212	55	that	that	SCONJ
ejpam-4316	212	56	the	the	DET
ejpam-4316	212	57	path	path	NOUN
ejpam-4316	212	58	pn	pn	PROPN
ejpam-4316	212	59	,	,	PUNCT
ejpam-4316	212	60	star	star	PROPN
ejpam-4316	212	61	graph	graph	PROPN
ejpam-4316	212	62	sn	sn	PROPN
ejpam-4316	212	63	,	,	PUNCT
ejpam-4316	212	64	and	and	CCONJ
ejpam-4316	212	65	cycle	cycle	NOUN
ejpam-4316	212	66	cn	cn	PROPN
ejpam-4316	212	67	,	,	PUNCT
ejpam-4316	212	68	n	n	PROPN
ejpam-4316	212	69	>	>	X
ejpam-4316	212	70	3	3	NUM
ejpam-4316	212	71	,	,	PUNCT
ejpam-4316	212	72	are	be	AUX
ejpam-4316	212	73	triangle	triangle	NOUN
ejpam-4316	212	74	free	free	ADJ
ejpam-4316	212	75	graph	graph	NOUN
ejpam-4316	212	76	.	.	PUNCT
ejpam-4316	213	1	the	the	DET
ejpam-4316	213	2	following	follow	VERB
ejpam-4316	213	3	statements	statement	NOUN
ejpam-4316	213	4	follows	follow	VERB
ejpam-4316	213	5	easily	easily	ADV
ejpam-4316	213	6	.	.	PUNCT
ejpam-4316	214	1	corollary	corollary	ADJ
ejpam-4316	214	2	1	1	NUM
ejpam-4316	214	3	.	.	PUNCT
ejpam-4316	215	1	for	for	ADP
ejpam-4316	215	2	n	n	PROPN
ejpam-4316	215	3	>	>	X
ejpam-4316	215	4	3	3	NUM
ejpam-4316	215	5	,	,	PUNCT
ejpam-4316	215	6	the	the	DET
ejpam-4316	215	7	wiener	wiener	NOUN
ejpam-4316	215	8	index	index	NOUN
ejpam-4316	215	9	of	of	ADP
ejpam-4316	215	10	the	the	DET
ejpam-4316	215	11	v	v	NOUN
ejpam-4316	215	12	-splitting	-splitting	ADJ
ejpam-4316	215	13	graph	graph	NOUN
ejpam-4316	215	14	of	of	ADP
ejpam-4316	215	15	g	g	NOUN
ejpam-4316	215	16	,	,	PUNCT
ejpam-4316	215	17	γ	γ	X
ejpam-4316	215	18	is	be	AUX
ejpam-4316	215	19	given	give	VERB
ejpam-4316	215	20	by	by	ADP
ejpam-4316	215	21	(	(	PUNCT
ejpam-4316	215	22	i	i	NOUN
ejpam-4316	215	23	)	)	PUNCT
ejpam-4316	215	24	w	w	PROPN
ejpam-4316	215	25	(	(	PUNCT
ejpam-4316	215	26	γ(pn	γ(pn	NOUN
ejpam-4316	215	27	,	,	PUNCT
ejpam-4316	215	28	v	v	NOUN
ejpam-4316	215	29	)	)	PUNCT
ejpam-4316	215	30	)	)	PUNCT
ejpam-4316	216	1	=	=	PUNCT
ejpam-4316	217	1	2n3	2n3	NUM
ejpam-4316	217	2	+	+	SYM
ejpam-4316	217	3	10n−6	10n−6	NUM
ejpam-4316	217	4	3	3	NUM
ejpam-4316	217	5	;	;	PUNCT
ejpam-4316	217	6	f.j.h	f.j.h	ADJ
ejpam-4316	217	7	.	.	PUNCT
ejpam-4316	218	1	campeña	campeña	NOUN
ejpam-4316	218	2	,	,	PUNCT
ejpam-4316	218	3	m.c.g	m.c.g	PROPN
ejpam-4316	218	4	.	.	PUNCT
ejpam-4316	218	5	egan	egan	PROPN
ejpam-4316	218	6	,	,	PUNCT
ejpam-4316	218	7	j.r.m	j.r.m	PROPN
ejpam-4316	218	8	.	.	PUNCT
ejpam-4316	219	1	antalan	antalan	PROPN
ejpam-4316	219	2	/	/	SYM
ejpam-4316	219	3	eur	eur	PROPN
ejpam-4316	219	4	.	.	PUNCT
ejpam-4316	220	1	j.	j.	PROPN
ejpam-4316	220	2	pure	pure	PROPN
ejpam-4316	220	3	appl	appl	PROPN
ejpam-4316	220	4	.	.	PROPN
ejpam-4316	220	5	math	math	PROPN
ejpam-4316	220	6	,	,	PUNCT
ejpam-4316	220	7	15	15	NUM
ejpam-4316	220	8	(	(	PUNCT
ejpam-4316	220	9	2	2	NUM
ejpam-4316	220	10	)	)	PUNCT
ejpam-4316	220	11	(	(	PUNCT
ejpam-4316	220	12	2022	2022	NUM
ejpam-4316	220	13	)	)	PUNCT
ejpam-4316	220	14	,	,	PUNCT
ejpam-4316	220	15	602	602	NUM
ejpam-4316	220	16	-	-	SYM
ejpam-4316	220	17	619	619	NUM
ejpam-4316	220	18	609	609	NUM
ejpam-4316	220	19	(	(	PUNCT
ejpam-4316	220	20	ii	ii	NOUN
ejpam-4316	220	21	)	)	PUNCT
ejpam-4316	220	22	w	w	PROPN
ejpam-4316	220	23	(	(	PUNCT
ejpam-4316	220	24	γ(sn	γ(sn	PROPN
ejpam-4316	220	25	,	,	PUNCT
ejpam-4316	220	26	v	v	NOUN
ejpam-4316	220	27	)	)	PUNCT
ejpam-4316	220	28	)	)	PUNCT
ejpam-4316	221	1	=	=	SYM
ejpam-4316	221	2	4n2	4n2	NUM
ejpam-4316	222	1	−	−	NOUN
ejpam-4316	222	2	4n+	4n+	NUM
ejpam-4316	222	3	2	2	NUM
ejpam-4316	222	4	;	;	PUNCT
ejpam-4316	222	5	(	(	PUNCT
ejpam-4316	222	6	iii	iii	X
ejpam-4316	222	7	)	)	PUNCT
ejpam-4316	222	8	w	w	PROPN
ejpam-4316	222	9	(	(	PUNCT
ejpam-4316	222	10	γ(cn	γ(cn	PROPN
ejpam-4316	222	11	,	,	PUNCT
ejpam-4316	222	12	v	v	NOUN
ejpam-4316	222	13	)	)	PUNCT
ejpam-4316	222	14	)	)	PUNCT
ejpam-4316	223	1	=	=	PRON
ejpam-4316	223	2	{	{	PUNCT
ejpam-4316	223	3	n3	n3	NOUN
ejpam-4316	223	4	+	+	PROPN
ejpam-4316	223	5	8n	8n	NOUN
ejpam-4316	223	6	2	2	NUM
ejpam-4316	223	7	n	n	NOUN
ejpam-4316	223	8	even	even	ADV
ejpam-4316	223	9	n3	n3	ADJ
ejpam-4316	223	10	+	+	PROPN
ejpam-4316	223	11	7n	7n	ADJ
ejpam-4316	223	12	2	2	NUM
ejpam-4316	223	13	n	n	PRON
ejpam-4316	223	14	odd	odd	ADJ
ejpam-4316	223	15	.	.	PUNCT
ejpam-4316	224	1	proof	proof	NOUN
ejpam-4316	224	2	.	.	PUNCT
ejpam-4316	225	1	for	for	ADP
ejpam-4316	225	2	(	(	PUNCT
ejpam-4316	225	3	i	i	NOUN
ejpam-4316	225	4	)	)	PUNCT
ejpam-4316	225	5	the	the	DET
ejpam-4316	225	6	result	result	NOUN
ejpam-4316	225	7	follows	follow	VERB
ejpam-4316	225	8	from	from	ADP
ejpam-4316	225	9	theorem	theorem	ADJ
ejpam-4316	225	10	1	1	NUM
ejpam-4316	225	11	and	and	CCONJ
ejpam-4316	225	12	theorem	theorem	VERB
ejpam-4316	225	13	8	8	NUM
ejpam-4316	225	14	,	,	PUNCT
ejpam-4316	225	15	and	and	CCONJ
ejpam-4316	225	16	for	for	ADP
ejpam-4316	225	17	(	(	PUNCT
ejpam-4316	225	18	ii	ii	NOUN
ejpam-4316	225	19	)	)	PUNCT
ejpam-4316	225	20	,	,	PUNCT
ejpam-4316	225	21	the	the	DET
ejpam-4316	225	22	result	result	NOUN
ejpam-4316	225	23	follows	follow	VERB
ejpam-4316	225	24	from	from	ADP
ejpam-4316	225	25	theorem	theorem	ADJ
ejpam-4316	225	26	4	4	NUM
ejpam-4316	225	27	and	and	CCONJ
ejpam-4316	225	28	theorem	theorem	VERB
ejpam-4316	225	29	8	8	NUM
ejpam-4316	225	30	while	while	SCONJ
ejpam-4316	225	31	the	the	DET
ejpam-4316	225	32	result	result	NOUN
ejpam-4316	225	33	for	for	ADP
ejpam-4316	225	34	(	(	PUNCT
ejpam-4316	225	35	iii	iii	NOUN
ejpam-4316	225	36	)	)	PUNCT
ejpam-4316	225	37	follows	follow	VERB
ejpam-4316	225	38	from	from	ADP
ejpam-4316	225	39	theorem	theorem	ADJ
ejpam-4316	225	40	2	2	NUM
ejpam-4316	225	41	and	and	CCONJ
ejpam-4316	225	42	theorem	theorem	VERB
ejpam-4316	225	43	8	8	NUM
ejpam-4316	225	44	.	.	PUNCT
ejpam-4316	226	1	theorem	theorem	VERB
ejpam-4316	226	2	9	9	NUM
ejpam-4316	226	3	.	.	PUNCT
ejpam-4316	227	1	for	for	ADP
ejpam-4316	227	2	a	a	DET
ejpam-4316	227	3	connected	connected	ADJ
ejpam-4316	227	4	graph	graph	NOUN
ejpam-4316	227	5	g	g	PROPN
ejpam-4316	227	6	=	=	PUNCT
ejpam-4316	227	7	(	(	PUNCT
ejpam-4316	227	8	v	v	NOUN
ejpam-4316	227	9	,	,	PUNCT
ejpam-4316	227	10	e	e	NOUN
ejpam-4316	227	11	)	)	PUNCT
ejpam-4316	227	12	on	on	ADP
ejpam-4316	227	13	n	n	PRON
ejpam-4316	227	14	≥	≥	NUM
ejpam-4316	227	15	2	2	NUM
ejpam-4316	227	16	vertices	vertex	NOUN
ejpam-4316	227	17	and	and	CCONJ
ejpam-4316	227	18	m	m	PRON
ejpam-4316	227	19	≥	≥	NOUN
ejpam-4316	227	20	1	1	NUM
ejpam-4316	227	21	edges	edge	VERB
ejpam-4316	227	22	such	such	ADJ
ejpam-4316	227	23	that	that	SCONJ
ejpam-4316	227	24	any	any	DET
ejpam-4316	227	25	pair	pair	NOUN
ejpam-4316	227	26	of	of	ADP
ejpam-4316	227	27	adjacent	adjacent	ADJ
ejpam-4316	227	28	vertices	vertex	NOUN
ejpam-4316	227	29	have	have	VERB
ejpam-4316	227	30	at	at	ADV
ejpam-4316	227	31	least	least	ADV
ejpam-4316	227	32	one	one	NUM
ejpam-4316	227	33	common	common	ADJ
ejpam-4316	227	34	neighbor	neighbor	NOUN
ejpam-4316	227	35	and	and	CCONJ
ejpam-4316	227	36	v	v	NOUN
ejpam-4316	227	37	=	=	SYM
ejpam-4316	227	38	s	s	PROPN
ejpam-4316	227	39	,	,	PUNCT
ejpam-4316	227	40	the	the	DET
ejpam-4316	227	41	splitting	splitting	NOUN
ejpam-4316	227	42	graph	graph	NOUN
ejpam-4316	227	43	of	of	ADP
ejpam-4316	227	44	g	g	NOUN
ejpam-4316	227	45	,	,	PUNCT
ejpam-4316	227	46	say	say	VERB
ejpam-4316	227	47	γ	γ	X
ejpam-4316	227	48	=	=	SYM
ejpam-4316	227	49	γ(g	γ(g	PROPN
ejpam-4316	227	50	)	)	PUNCT
ejpam-4316	227	51	has	have	VERB
ejpam-4316	227	52	wiener	wiener	NOUN
ejpam-4316	227	53	index	index	NOUN
ejpam-4316	227	54	given	give	VERB
ejpam-4316	227	55	by	by	ADP
ejpam-4316	227	56	w	w	PROPN
ejpam-4316	227	57	(	(	PUNCT
ejpam-4316	227	58	γ	γ	NOUN
ejpam-4316	227	59	)	)	PUNCT
ejpam-4316	228	1	=	=	SYM
ejpam-4316	228	2	4w	4w	NOUN
ejpam-4316	228	3	(	(	PUNCT
ejpam-4316	228	4	g	g	NOUN
ejpam-4316	228	5	)	)	PUNCT
ejpam-4316	228	6	+	+	CCONJ
ejpam-4316	228	7	2n+m	2n+m	NUM
ejpam-4316	228	8	.	.	PUNCT
ejpam-4316	229	1	proof	proof	NOUN
ejpam-4316	229	2	.	.	PUNCT
ejpam-4316	230	1	then	then	ADV
ejpam-4316	230	2	distance	distance	NOUN
ejpam-4316	230	3	matrix	matrix	NOUN
ejpam-4316	230	4	of	of	ADP
ejpam-4316	230	5	γ	γ	PROPN
ejpam-4316	230	6	as	as	ADP
ejpam-4316	230	7	a	a	DET
ejpam-4316	230	8	2×	2×	NUM
ejpam-4316	230	9	2	2	NUM
ejpam-4316	230	10	block	block	NOUN
ejpam-4316	230	11	matrix	matrix	NOUN
ejpam-4316	230	12	entries	entry	NOUN
ejpam-4316	230	13	that	that	PRON
ejpam-4316	230	14	depends	depend	VERB
ejpam-4316	230	15	on	on	ADP
ejpam-4316	230	16	the	the	DET
ejpam-4316	230	17	distance	distance	NOUN
ejpam-4316	230	18	,	,	PUNCT
ejpam-4316	230	19	adjacency	adjacency	NOUN
ejpam-4316	230	20	and	and	CCONJ
ejpam-4316	230	21	identity	identity	NOUN
ejpam-4316	230	22	matrices	matrix	NOUN
ejpam-4316	230	23	of	of	ADP
ejpam-4316	230	24	the	the	DET
ejpam-4316	230	25	graph	graph	NOUN
ejpam-4316	230	26	g	g	NOUN
ejpam-4316	230	27	by	by	ADP
ejpam-4316	230	28	d(γ	d(γ	NOUN
ejpam-4316	230	29	)	)	PUNCT
ejpam-4316	230	30	=	=	PUNCT
ejpam-4316	231	1	[	[	PUNCT
ejpam-4316	231	2	d(g	d(g	PROPN
ejpam-4316	231	3	)	)	PUNCT
ejpam-4316	231	4	d(g	d(g	PROPN
ejpam-4316	231	5	)	)	PUNCT
ejpam-4316	232	1	+	+	CCONJ
ejpam-4316	232	2	2	2	NUM
ejpam-4316	232	3	in	in	ADP
ejpam-4316	232	4	d(g	d(g	PROPN
ejpam-4316	232	5	)	)	PUNCT
ejpam-4316	232	6	+	+	CCONJ
ejpam-4316	232	7	2	2	NUM
ejpam-4316	232	8	in	in	ADP
ejpam-4316	232	9	d(g	d(g	PROPN
ejpam-4316	232	10	)	)	PUNCT
ejpam-4316	233	1	+	+	NOUN
ejpam-4316	233	2	a(g	a(g	PROPN
ejpam-4316	233	3	)	)	PUNCT
ejpam-4316	233	4	]	]	PUNCT
ejpam-4316	233	5	where	where	SCONJ
ejpam-4316	233	6	d(g	d(g	NOUN
ejpam-4316	233	7	)	)	PUNCT
ejpam-4316	233	8	and	and	CCONJ
ejpam-4316	233	9	a(g	a(g	PROPN
ejpam-4316	233	10	)	)	PUNCT
ejpam-4316	233	11	are	be	AUX
ejpam-4316	233	12	the	the	DET
ejpam-4316	233	13	distance	distance	NOUN
ejpam-4316	233	14	,	,	PUNCT
ejpam-4316	233	15	adjacency	adjacency	NOUN
ejpam-4316	233	16	matrices	matrix	NOUN
ejpam-4316	233	17	of	of	ADP
ejpam-4316	233	18	the	the	DET
ejpam-4316	233	19	graph	graph	NOUN
ejpam-4316	233	20	g	g	NOUN
ejpam-4316	233	21	and	and	CCONJ
ejpam-4316	233	22	in	in	ADP
ejpam-4316	233	23	is	be	AUX
ejpam-4316	233	24	the	the	DET
ejpam-4316	233	25	identity	identity	NOUN
ejpam-4316	233	26	matrix	matrix	NOUN
ejpam-4316	233	27	of	of	ADP
ejpam-4316	233	28	size	size	NOUN
ejpam-4316	233	29	n.	n.	NOUN
ejpam-4316	233	30	notice	notice	VERB
ejpam-4316	233	31	that	that	SCONJ
ejpam-4316	233	32	we	we	PRON
ejpam-4316	233	33	can	can	AUX
ejpam-4316	233	34	express	express	VERB
ejpam-4316	233	35	the	the	DET
ejpam-4316	233	36	wiener	wiener	NOUN
ejpam-4316	233	37	index	index	NOUN
ejpam-4316	233	38	of	of	ADP
ejpam-4316	233	39	γ	γ	PROPN
ejpam-4316	233	40	using	use	VERB
ejpam-4316	233	41	the	the	DET
ejpam-4316	233	42	distance	distance	NOUN
ejpam-4316	233	43	matrix	matrix	NOUN
ejpam-4316	233	44	of	of	ADP
ejpam-4316	233	45	γ	γ	PROPN
ejpam-4316	233	46	then	then	ADV
ejpam-4316	233	47	have	have	AUX
ejpam-4316	233	48	the	the	DET
ejpam-4316	233	49	notation	notation	NOUN
ejpam-4316	233	50	:	:	PUNCT
ejpam-4316	233	51	w	w	X
ejpam-4316	233	52	(	(	PUNCT
ejpam-4316	233	53	γ	γ	NOUN
ejpam-4316	233	54	)	)	PUNCT
ejpam-4316	233	55	=	=	SYM
ejpam-4316	234	1	1	1	NUM
ejpam-4316	234	2	2	2	NUM
ejpam-4316	234	3	∑	∑	PUNCT
ejpam-4316	234	4	d(γ	d(γ	PROPN
ejpam-4316	234	5	)	)	PUNCT
ejpam-4316	234	6	=	=	SYM
ejpam-4316	234	7	1	1	NUM
ejpam-4316	234	8	2	2	NUM
ejpam-4316	234	9	(	(	PUNCT
ejpam-4316	234	10	∑	∑	NOUN
ejpam-4316	234	11	4d(g	4d(g	NUM
ejpam-4316	234	12	)	)	PUNCT
ejpam-4316	234	13	+	+	CCONJ
ejpam-4316	234	14	4	4	NUM
ejpam-4316	234	15	∑	∑	NOUN
ejpam-4316	234	16	in	in	ADP
ejpam-4316	234	17	+	+	NOUN
ejpam-4316	234	18	∑	∑	PUNCT
ejpam-4316	234	19	a(g	a(g	PROPN
ejpam-4316	234	20	)	)	PUNCT
ejpam-4316	234	21	)	)	PUNCT
ejpam-4316	235	1	=	=	SYM
ejpam-4316	235	2	4	4	NUM
ejpam-4316	235	3	(	(	PUNCT
ejpam-4316	235	4	1	1	NUM
ejpam-4316	235	5	2	2	NUM
ejpam-4316	235	6	∑	∑	PUNCT
ejpam-4316	235	7	d(g	d(g	PROPN
ejpam-4316	235	8	)	)	PUNCT
ejpam-4316	235	9	)	)	PUNCT
ejpam-4316	236	1	+	+	CCONJ
ejpam-4316	236	2	2	2	NUM
ejpam-4316	236	3	∑	∑	NOUN
ejpam-4316	236	4	in	in	ADP
ejpam-4316	236	5	+	+	NOUN
ejpam-4316	236	6	1	1	NUM
ejpam-4316	236	7	2	2	NUM
ejpam-4316	236	8	∑	∑	PUNCT
ejpam-4316	236	9	a(g	a(g	PROPN
ejpam-4316	236	10	)	)	PUNCT
ejpam-4316	236	11	=	=	SYM
ejpam-4316	236	12	4w	4w	NOUN
ejpam-4316	236	13	(	(	PUNCT
ejpam-4316	236	14	g	g	NOUN
ejpam-4316	236	15	)	)	PUNCT
ejpam-4316	236	16	+	+	CCONJ
ejpam-4316	236	17	2n+	2n+	NUM
ejpam-4316	236	18	1	1	NUM
ejpam-4316	236	19	2	2	NUM
ejpam-4316	236	20	∑	∑	PUNCT
ejpam-4316	236	21	a(g	a(g	NOUN
ejpam-4316	236	22	)	)	PUNCT
ejpam-4316	236	23	note	note	VERB
ejpam-4316	236	24	that	that	SCONJ
ejpam-4316	236	25	the	the	DET
ejpam-4316	236	26	sum	sum	NOUN
ejpam-4316	236	27	of	of	ADP
ejpam-4316	236	28	the	the	DET
ejpam-4316	236	29	entries	entry	NOUN
ejpam-4316	236	30	in	in	ADP
ejpam-4316	236	31	an	an	DET
ejpam-4316	236	32	adjacency	adjacency	NOUN
ejpam-4316	236	33	matrix	matrix	NOUN
ejpam-4316	236	34	is	be	AUX
ejpam-4316	236	35	twice	twice	DET
ejpam-4316	236	36	the	the	DET
ejpam-4316	236	37	number	number	NOUN
ejpam-4316	236	38	of	of	ADP
ejpam-4316	236	39	edges	edge	NOUN
ejpam-4316	236	40	m.	m.	NOUN
ejpam-4316	236	41	thus	thus	ADV
ejpam-4316	236	42	we	we	PRON
ejpam-4316	236	43	have	have	VERB
ejpam-4316	236	44	w	w	PROPN
ejpam-4316	236	45	(	(	PUNCT
ejpam-4316	236	46	γ	γ	NOUN
ejpam-4316	236	47	)	)	PUNCT
ejpam-4316	236	48	=	=	SYM
ejpam-4316	236	49	4w	4w	NOUN
ejpam-4316	236	50	(	(	PUNCT
ejpam-4316	236	51	g	g	NOUN
ejpam-4316	236	52	)	)	PUNCT
ejpam-4316	236	53	+	+	CCONJ
ejpam-4316	236	54	2n+	2n+	NUM
ejpam-4316	236	55	1	1	NUM
ejpam-4316	236	56	2(2	2(2	NUM
ejpam-4316	236	57	m	m	NOUN
ejpam-4316	236	58	)	)	PUNCT
ejpam-4316	237	1	=	=	SYM
ejpam-4316	237	2	4w	4w	NOUN
ejpam-4316	237	3	(	(	PUNCT
ejpam-4316	237	4	g	g	NOUN
ejpam-4316	237	5	)	)	PUNCT
ejpam-4316	237	6	+	+	CCONJ
ejpam-4316	237	7	2n+m	2n+m	NUM
ejpam-4316	237	8	.	.	PUNCT
ejpam-4316	238	1	corollary	corollary	ADJ
ejpam-4316	238	2	2	2	NUM
ejpam-4316	238	3	.	.	PUNCT
ejpam-4316	239	1	for	for	ADP
ejpam-4316	239	2	n	n	PROPN
ejpam-4316	239	3	>	>	X
ejpam-4316	239	4	3	3	NUM
ejpam-4316	239	5	,	,	PUNCT
ejpam-4316	239	6	the	the	DET
ejpam-4316	239	7	wiener	wiener	NOUN
ejpam-4316	239	8	index	index	NOUN
ejpam-4316	239	9	of	of	ADP
ejpam-4316	239	10	the	the	DET
ejpam-4316	239	11	v	v	NOUN
ejpam-4316	239	12	-splitting	-splitting	ADJ
ejpam-4316	239	13	graph	graph	NOUN
ejpam-4316	239	14	of	of	ADP
ejpam-4316	239	15	g	g	NOUN
ejpam-4316	239	16	,	,	PUNCT
ejpam-4316	239	17	γ	γ	X
ejpam-4316	239	18	is	be	AUX
ejpam-4316	239	19	given	give	VERB
ejpam-4316	239	20	by	by	ADP
ejpam-4316	239	21	(	(	PUNCT
ejpam-4316	239	22	i	i	NOUN
ejpam-4316	239	23	)	)	PUNCT
ejpam-4316	239	24	w	w	PROPN
ejpam-4316	239	25	(	(	PUNCT
ejpam-4316	239	26	γ(kn	γ(kn	PROPN
ejpam-4316	239	27	,	,	PUNCT
ejpam-4316	239	28	v	v	NOUN
ejpam-4316	239	29	)	)	PUNCT
ejpam-4316	239	30	)	)	PUNCT
ejpam-4316	240	1	=	=	PUNCT
ejpam-4316	241	1	5n2−n	5n2−n	NUM
ejpam-4316	241	2	2	2	NUM
ejpam-4316	241	3	;	;	PUNCT
ejpam-4316	241	4	(	(	PUNCT
ejpam-4316	241	5	ii	ii	NOUN
ejpam-4316	241	6	)	)	PUNCT
ejpam-4316	241	7	w	w	PROPN
ejpam-4316	241	8	(	(	PUNCT
ejpam-4316	241	9	γ(wn	γ(wn	NOUN
ejpam-4316	241	10	,	,	PUNCT
ejpam-4316	241	11	v	v	NOUN
ejpam-4316	241	12	)	)	PUNCT
ejpam-4316	241	13	)	)	PUNCT
ejpam-4316	242	1	=	=	PRON
ejpam-4316	242	2	4n2	4n2	NUM
ejpam-4316	243	1	−	−	X
ejpam-4316	243	2	8n+	8n+	NUM
ejpam-4316	243	3	6	6	NUM
ejpam-4316	243	4	.	.	PUNCT
ejpam-4316	244	1	proof	proof	NOUN
ejpam-4316	244	2	.	.	PUNCT
ejpam-4316	245	1	for	for	ADP
ejpam-4316	245	2	(	(	PUNCT
ejpam-4316	245	3	i	i	NOUN
ejpam-4316	245	4	)	)	PUNCT
ejpam-4316	245	5	,	,	PUNCT
ejpam-4316	245	6	the	the	DET
ejpam-4316	245	7	result	result	NOUN
ejpam-4316	245	8	follows	follow	VERB
ejpam-4316	245	9	from	from	ADP
ejpam-4316	245	10	theorem	theorem	ADJ
ejpam-4316	245	11	3	3	NUM
ejpam-4316	245	12	and	and	CCONJ
ejpam-4316	245	13	theorem	theorem	VERB
ejpam-4316	245	14	9	9	NUM
ejpam-4316	245	15	,	,	PUNCT
ejpam-4316	245	16	while	while	SCONJ
ejpam-4316	245	17	for	for	ADP
ejpam-4316	245	18	(	(	PUNCT
ejpam-4316	245	19	ii	ii	NOUN
ejpam-4316	245	20	)	)	PUNCT
ejpam-4316	245	21	,	,	PUNCT
ejpam-4316	245	22	the	the	DET
ejpam-4316	245	23	results	result	NOUN
ejpam-4316	245	24	are	be	AUX
ejpam-4316	245	25	immediate	immediate	ADJ
ejpam-4316	245	26	from	from	ADP
ejpam-4316	245	27	theorem	theorem	ADJ
ejpam-4316	245	28	5	5	NUM
ejpam-4316	245	29	and	and	CCONJ
ejpam-4316	245	30	theorem	theorem	VERB
ejpam-4316	245	31	9	9	NUM
ejpam-4316	245	32	.	.	PUNCT
ejpam-4316	246	1	the	the	DET
ejpam-4316	246	2	following	follow	VERB
ejpam-4316	246	3	observations	observation	NOUN
ejpam-4316	246	4	can	can	AUX
ejpam-4316	246	5	be	be	AUX
ejpam-4316	246	6	easily	easily	ADV
ejpam-4316	246	7	verified	verify	VERB
ejpam-4316	246	8	from	from	ADP
ejpam-4316	246	9	the	the	DET
ejpam-4316	246	10	definition	definition	NOUN
ejpam-4316	246	11	of	of	ADP
ejpam-4316	246	12	the	the	DET
ejpam-4316	246	13	s	s	NOUN
ejpam-4316	246	14	-	-	PUNCT
ejpam-4316	246	15	splitting	splitting	NOUN
ejpam-4316	246	16	graph	graph	NOUN
ejpam-4316	246	17	of	of	ADP
ejpam-4316	246	18	g.	g.	PROPN
ejpam-4316	246	19	•	•	ADV
ejpam-4316	247	1	if	if	SCONJ
ejpam-4316	247	2	g	g	PROPN
ejpam-4316	247	3	is	be	AUX
ejpam-4316	247	4	either	either	CCONJ
ejpam-4316	247	5	a	a	DET
ejpam-4316	247	6	complete	complete	ADJ
ejpam-4316	247	7	graph	graph	NOUN
ejpam-4316	247	8	kn	kn	PROPN
ejpam-4316	247	9	or	or	CCONJ
ejpam-4316	247	10	a	a	DET
ejpam-4316	247	11	cycle	cycle	NOUN
ejpam-4316	247	12	graph	graph	NOUN
ejpam-4316	247	13	cn	cn	PROPN
ejpam-4316	247	14	,	,	PUNCT
ejpam-4316	247	15	then	then	ADV
ejpam-4316	247	16	for	for	ADP
ejpam-4316	247	17	any	any	DET
ejpam-4316	247	18	x	x	NOUN
ejpam-4316	247	19	,	,	PUNCT
ejpam-4316	247	20	y	y	PROPN
ejpam-4316	247	21	∈	∈	PROPN
ejpam-4316	247	22	v	v	NOUN
ejpam-4316	247	23	(	(	PUNCT
ejpam-4316	247	24	g	g	NOUN
ejpam-4316	247	25	)	)	PUNCT
ejpam-4316	247	26	we	we	PRON
ejpam-4316	247	27	have	have	VERB
ejpam-4316	247	28	γ(g	γ(g	PROPN
ejpam-4316	247	29	,	,	PUNCT
ejpam-4316	247	30	{	{	PUNCT
ejpam-4316	247	31	x	x	NOUN
ejpam-4316	247	32	}	}	PUNCT
ejpam-4316	247	33	)	)	PUNCT
ejpam-4316	247	34	∼=	∼=	PROPN
ejpam-4316	247	35	γ(g	γ(g	PROPN
ejpam-4316	247	36	,	,	PUNCT
ejpam-4316	247	37	{	{	PUNCT
ejpam-4316	247	38	y	y	NOUN
ejpam-4316	247	39	}	}	PUNCT
ejpam-4316	247	40	)	)	PUNCT
ejpam-4316	247	41	.	.	PUNCT
ejpam-4316	248	1	f.j.h	f.j.h	ADJ
ejpam-4316	248	2	.	.	PUNCT
ejpam-4316	249	1	campeña	campeña	NOUN
ejpam-4316	249	2	,	,	PUNCT
ejpam-4316	249	3	m.c.g	m.c.g	PROPN
ejpam-4316	249	4	.	.	PUNCT
ejpam-4316	249	5	egan	egan	PROPN
ejpam-4316	249	6	,	,	PUNCT
ejpam-4316	249	7	j.r.m	j.r.m	PROPN
ejpam-4316	249	8	.	.	PUNCT
ejpam-4316	250	1	antalan	antalan	PROPN
ejpam-4316	250	2	/	/	SYM
ejpam-4316	250	3	eur	eur	PROPN
ejpam-4316	250	4	.	.	PUNCT
ejpam-4316	251	1	j.	j.	PROPN
ejpam-4316	251	2	pure	pure	PROPN
ejpam-4316	251	3	appl	appl	PROPN
ejpam-4316	251	4	.	.	PROPN
ejpam-4316	251	5	math	math	PROPN
ejpam-4316	251	6	,	,	PUNCT
ejpam-4316	251	7	15	15	NUM
ejpam-4316	251	8	(	(	PUNCT
ejpam-4316	251	9	2	2	NUM
ejpam-4316	251	10	)	)	PUNCT
ejpam-4316	251	11	(	(	PUNCT
ejpam-4316	251	12	2022	2022	NUM
ejpam-4316	251	13	)	)	PUNCT
ejpam-4316	251	14	,	,	PUNCT
ejpam-4316	251	15	602	602	NUM
ejpam-4316	251	16	-	-	SYM
ejpam-4316	251	17	619	619	NUM
ejpam-4316	251	18	610	610	NUM
ejpam-4316	251	19	•	•	NOUN
ejpam-4316	251	20	let	let	VERB
ejpam-4316	251	21	g	g	NOUN
ejpam-4316	251	22	be	be	AUX
ejpam-4316	251	23	a	a	DET
ejpam-4316	251	24	complete	complete	ADJ
ejpam-4316	251	25	graph	graph	NOUN
ejpam-4316	251	26	kn	kn	PROPN
ejpam-4316	251	27	and	and	CCONJ
ejpam-4316	251	28	n	n	PRON
ejpam-4316	251	29	≥	≥	NOUN
ejpam-4316	251	30	3	3	NUM
ejpam-4316	251	31	.	.	PUNCT
ejpam-4316	252	1	then	then	ADV
ejpam-4316	252	2	the	the	DET
ejpam-4316	252	3	graphs	graphs	PROPN
ejpam-4316	252	4	γ(g	γ(g	PROPN
ejpam-4316	252	5	,	,	PUNCT
ejpam-4316	252	6	s1	s1	PROPN
ejpam-4316	252	7	)	)	PUNCT
ejpam-4316	252	8	and	and	CCONJ
ejpam-4316	252	9	γ(g	γ(g	PROPN
ejpam-4316	252	10	,	,	PUNCT
ejpam-4316	252	11	s2	s2	PROPN
ejpam-4316	252	12	)	)	PUNCT
ejpam-4316	252	13	are	be	AUX
ejpam-4316	252	14	isomorphic	isomorphic	ADJ
ejpam-4316	252	15	for	for	ADP
ejpam-4316	252	16	any	any	DET
ejpam-4316	252	17	s1	s1	NOUN
ejpam-4316	252	18	,	,	PUNCT
ejpam-4316	252	19	s2	s2	X
ejpam-4316	252	20	⊂	⊂	X
ejpam-4316	252	21	v	v	X
ejpam-4316	252	22	(	(	PUNCT
ejpam-4316	252	23	g	g	NOUN
ejpam-4316	252	24	)	)	PUNCT
ejpam-4316	252	25	such	such	ADJ
ejpam-4316	252	26	that	that	DET
ejpam-4316	252	27	|s1|	|s1|	NOUN
ejpam-4316	252	28	=	=	SYM
ejpam-4316	252	29	|s2|	|s2|	NOUN
ejpam-4316	252	30	.	.	PUNCT
ejpam-4316	253	1	we	we	PRON
ejpam-4316	253	2	now	now	ADV
ejpam-4316	253	3	determine	determine	VERB
ejpam-4316	253	4	the	the	DET
ejpam-4316	253	5	wiener	wiener	NOUN
ejpam-4316	253	6	index	index	NOUN
ejpam-4316	253	7	of	of	ADP
ejpam-4316	253	8	γ(g	γ(g	PROPN
ejpam-4316	253	9	,	,	PUNCT
ejpam-4316	253	10	s	s	PART
ejpam-4316	253	11	)	)	PUNCT
ejpam-4316	253	12	where	where	SCONJ
ejpam-4316	253	13	s	s	X
ejpam-4316	253	14	6=	6=	PROPN
ejpam-4316	253	15	v	v	NOUN
ejpam-4316	253	16	for	for	ADP
ejpam-4316	253	17	some	some	DET
ejpam-4316	253	18	families	family	NOUN
ejpam-4316	253	19	of	of	ADP
ejpam-4316	253	20	graphs	graph	NOUN
ejpam-4316	253	21	.	.	PUNCT
ejpam-4316	254	1	the	the	DET
ejpam-4316	254	2	graphs	graph	NOUN
ejpam-4316	254	3	included	include	VERB
ejpam-4316	254	4	are	be	AUX
ejpam-4316	254	5	complete	complete	ADJ
ejpam-4316	254	6	graphs	graph	NOUN
ejpam-4316	254	7	,	,	PUNCT
ejpam-4316	254	8	complete	complete	ADJ
ejpam-4316	254	9	bipartite	bipartite	NOUN
ejpam-4316	254	10	graphs	graph	NOUN
ejpam-4316	254	11	,	,	PUNCT
ejpam-4316	254	12	cycle	cycle	NOUN
ejpam-4316	254	13	graphs	graph	NOUN
ejpam-4316	254	14	,	,	PUNCT
ejpam-4316	254	15	path	path	NOUN
ejpam-4316	254	16	graphs	graph	NOUN
ejpam-4316	254	17	,	,	PUNCT
ejpam-4316	254	18	star	star	NOUN
ejpam-4316	254	19	graphs	graph	NOUN
ejpam-4316	254	20	and	and	CCONJ
ejpam-4316	254	21	wheel	wheel	NOUN
ejpam-4316	254	22	graphs	graph	NOUN
ejpam-4316	254	23	.	.	PUNCT
ejpam-4316	255	1	the	the	DET
ejpam-4316	255	2	following	follow	VERB
ejpam-4316	255	3	lemma	lemma	PROPN
ejpam-4316	255	4	follows	follow	VERB
ejpam-4316	255	5	directly	directly	ADV
ejpam-4316	255	6	from	from	ADP
ejpam-4316	255	7	the	the	DET
ejpam-4316	255	8	definition	definition	NOUN
ejpam-4316	255	9	of	of	ADP
ejpam-4316	255	10	an	an	DET
ejpam-4316	255	11	s	s	NOUN
ejpam-4316	255	12	-	-	PUNCT
ejpam-4316	255	13	splitting	splitting	NOUN
ejpam-4316	255	14	of	of	ADP
ejpam-4316	255	15	g.	g.	PROPN
ejpam-4316	255	16	lemma	lemma	PROPN
ejpam-4316	255	17	4	4	X
ejpam-4316	255	18	.	.	PUNCT
ejpam-4316	256	1	let	let	VERB
ejpam-4316	256	2	g	g	PROPN
ejpam-4316	256	3	=	=	PROPN
ejpam-4316	256	4	km	km	PROPN
ejpam-4316	256	5	,	,	PUNCT
ejpam-4316	256	6	n	n	CCONJ
ejpam-4316	256	7	with	with	ADP
ejpam-4316	256	8	vertex	vertex	NOUN
ejpam-4316	256	9	partition	partition	NOUN
ejpam-4316	256	10	v	v	NOUN
ejpam-4316	256	11	=	=	SYM
ejpam-4316	256	12	v1	v1	NOUN
ejpam-4316	256	13	∪	∪	NOUN
ejpam-4316	256	14	v2	v2	NOUN
ejpam-4316	256	15	.	.	PUNCT
ejpam-4316	257	1	suppose	suppose	VERB
ejpam-4316	257	2	s	s	VERB
ejpam-4316	257	3	⊆	⊆	NUM
ejpam-4316	257	4	v1	v1	NOUN
ejpam-4316	257	5	,	,	PUNCT
ejpam-4316	257	6	where	where	SCONJ
ejpam-4316	257	7	|s|	|s|	VERB
ejpam-4316	257	8	=	=	SYM
ejpam-4316	257	9	p	p	PROPN
ejpam-4316	257	10	then	then	PROPN
ejpam-4316	257	11	γ(g	γ(g	PROPN
ejpam-4316	257	12	,	,	PUNCT
ejpam-4316	257	13	s	s	PART
ejpam-4316	257	14	)	)	PUNCT
ejpam-4316	257	15	∼=	∼=	PROPN
ejpam-4316	257	16	km+p	km+p	NOUN
ejpam-4316	257	17	,	,	PUNCT
ejpam-4316	257	18	n.	n.	PROPN
ejpam-4316	257	19	theorem	theorem	VERB
ejpam-4316	257	20	10	10	NUM
ejpam-4316	257	21	.	.	PUNCT
ejpam-4316	258	1	let	let	VERB
ejpam-4316	258	2	g	g	PROPN
ejpam-4316	258	3	=	=	PROPN
ejpam-4316	258	4	kn	kn	PROPN
ejpam-4316	258	5	,	,	PUNCT
ejpam-4316	258	6	for	for	ADP
ejpam-4316	258	7	n	n	NUM
ejpam-4316	258	8	≥	≥	NOUN
ejpam-4316	258	9	3	3	NUM
ejpam-4316	258	10	and	and	CCONJ
ejpam-4316	258	11	let	let	VERB
ejpam-4316	258	12	s	s	PRON
ejpam-4316	258	13	⊂	⊂	NOUN
ejpam-4316	258	14	v	v	X
ejpam-4316	258	15	(	(	PUNCT
ejpam-4316	258	16	kn	kn	PROPN
ejpam-4316	258	17	)	)	PUNCT
ejpam-4316	258	18	such	such	ADJ
ejpam-4316	258	19	that	that	SCONJ
ejpam-4316	258	20	|s|	|s|	PROPN
ejpam-4316	258	21	=	=	SYM
ejpam-4316	258	22	r	r	NOUN
ejpam-4316	258	23	where	where	SCONJ
ejpam-4316	258	24	1	1	NUM
ejpam-4316	258	25	≤	≤	NOUN
ejpam-4316	258	26	r	r	NOUN
ejpam-4316	258	27	≤	≤	NUM
ejpam-4316	258	28	n−	n−	NOUN
ejpam-4316	258	29	1	1	NUM
ejpam-4316	258	30	.	.	PUNCT
ejpam-4316	259	1	then	then	ADV
ejpam-4316	259	2	the	the	DET
ejpam-4316	259	3	wiener	wiener	NOUN
ejpam-4316	259	4	index	index	NOUN
ejpam-4316	259	5	of	of	ADP
ejpam-4316	259	6	the	the	DET
ejpam-4316	259	7	splitting	splitting	NOUN
ejpam-4316	259	8	graph	graph	NOUN
ejpam-4316	259	9	of	of	ADP
ejpam-4316	259	10	kn	kn	PROPN
ejpam-4316	259	11	is	be	AUX
ejpam-4316	259	12	given	give	VERB
ejpam-4316	259	13	by	by	ADP
ejpam-4316	259	14	w	w	PROPN
ejpam-4316	259	15	(	(	PUNCT
ejpam-4316	259	16	γ(kn	γ(kn	PROPN
ejpam-4316	259	17	,	,	PUNCT
ejpam-4316	259	18	s	s	NOUN
ejpam-4316	259	19	)	)	PUNCT
ejpam-4316	259	20	)	)	PUNCT
ejpam-4316	260	1	=	=	PUNCT
ejpam-4316	261	1	n2−n+2r2	n2−n+2r2	X
ejpam-4316	261	2	+	+	ADJ
ejpam-4316	261	3	2nr	2nr	ADJ
ejpam-4316	261	4	2	2	NUM
ejpam-4316	261	5	.	.	PUNCT
ejpam-4316	262	1	proof	proof	NOUN
ejpam-4316	262	2	.	.	PUNCT
ejpam-4316	263	1	let	let	VERB
ejpam-4316	263	2	v	v	X
ejpam-4316	263	3	(	(	PUNCT
ejpam-4316	263	4	kn	kn	PROPN
ejpam-4316	263	5	)	)	PUNCT
ejpam-4316	263	6	=	=	PRON
ejpam-4316	264	1	{	{	PUNCT
ejpam-4316	264	2	x1	x1	PROPN
ejpam-4316	264	3	,	,	PUNCT
ejpam-4316	264	4	x2	x2	PROPN
ejpam-4316	264	5	,	,	PUNCT
ejpam-4316	264	6	.	.	PUNCT
ejpam-4316	264	7	.	.	PUNCT
ejpam-4316	264	8	.	.	PUNCT
ejpam-4316	265	1	,	,	PUNCT
ejpam-4316	265	2	xn	xn	PROPN
ejpam-4316	265	3	}	}	PUNCT
ejpam-4316	265	4	.	.	PUNCT
ejpam-4316	266	1	without	without	ADP
ejpam-4316	266	2	loss	loss	NOUN
ejpam-4316	266	3	of	of	ADP
ejpam-4316	266	4	generality	generality	NOUN
ejpam-4316	266	5	,	,	PUNCT
ejpam-4316	266	6	suppose	suppose	VERB
ejpam-4316	266	7	s	s	VERB
ejpam-4316	266	8	=	=	PUNCT
ejpam-4316	266	9	{	{	PUNCT
ejpam-4316	266	10	x1	x1	PROPN
ejpam-4316	266	11	,	,	PUNCT
ejpam-4316	266	12	x2	x2	PROPN
ejpam-4316	266	13	,	,	PUNCT
ejpam-4316	266	14	.	.	PUNCT
ejpam-4316	266	15	.	.	PUNCT
ejpam-4316	267	1	.	.	PUNCT
ejpam-4316	268	1	,	,	PUNCT
ejpam-4316	268	2	xr	xr	PROPN
ejpam-4316	268	3	}	}	PUNCT
ejpam-4316	268	4	.	.	PUNCT
ejpam-4316	269	1	we	we	PRON
ejpam-4316	269	2	denote	denote	VERB
ejpam-4316	269	3	the	the	DET
ejpam-4316	269	4	ordering	ordering	NOUN
ejpam-4316	269	5	of	of	ADP
ejpam-4316	269	6	the	the	DET
ejpam-4316	269	7	vertices	vertex	NOUN
ejpam-4316	269	8	of	of	ADP
ejpam-4316	269	9	the	the	DET
ejpam-4316	269	10	graph	graph	NOUN
ejpam-4316	269	11	γ	γ	X
ejpam-4316	269	12	=	=	SYM
ejpam-4316	269	13	γ(kn	γ(kn	PROPN
ejpam-4316	269	14	,	,	PUNCT
ejpam-4316	269	15	s	s	AUX
ejpam-4316	269	16	)	)	PUNCT
ejpam-4316	269	17	by	by	ADP
ejpam-4316	269	18	x1	x1	PROPN
ejpam-4316	269	19	,	,	PUNCT
ejpam-4316	269	20	x2	x2	PROPN
ejpam-4316	269	21	,	,	PUNCT
ejpam-4316	269	22	.	.	PUNCT
ejpam-4316	269	23	.	.	PUNCT
ejpam-4316	270	1	.	.	PUNCT
ejpam-4316	271	1	,	,	PUNCT
ejpam-4316	271	2	xn	xn	PROPN
ejpam-4316	271	3	,	,	PUNCT
ejpam-4316	271	4	x	x	SYM
ejpam-4316	271	5	′	′	NUM
ejpam-4316	271	6	1	1	NUM
ejpam-4316	271	7	,	,	PUNCT
ejpam-4316	271	8	x	x	NOUN
ejpam-4316	271	9	′	′	NOUN
ejpam-4316	271	10	2	2	NUM
ejpam-4316	271	11	,	,	PUNCT
ejpam-4316	271	12	.	.	PUNCT
ejpam-4316	271	13	.	.	PUNCT
ejpam-4316	271	14	.	.	PUNCT
ejpam-4316	272	1	,	,	PUNCT
ejpam-4316	272	2	x	x	X
ejpam-4316	272	3	′	′	NUM
ejpam-4316	272	4	r.	r.	PROPN
ejpam-4316	272	5	then	then	ADV
ejpam-4316	272	6	we	we	PRON
ejpam-4316	272	7	can	can	AUX
ejpam-4316	272	8	write	write	VERB
ejpam-4316	272	9	the	the	DET
ejpam-4316	272	10	distance	distance	NOUN
ejpam-4316	272	11	matrix	matrix	NOUN
ejpam-4316	272	12	of	of	ADP
ejpam-4316	272	13	γ	γ	PROPN
ejpam-4316	272	14	as	as	ADP
ejpam-4316	272	15	a	a	DET
ejpam-4316	272	16	block	block	NOUN
ejpam-4316	272	17	matrix	matrix	NOUN
ejpam-4316	272	18	as	as	SCONJ
ejpam-4316	272	19	follows	follow	VERB
ejpam-4316	272	20	.	.	PUNCT
ejpam-4316	273	1	d(γ	d(γ	ADJ
ejpam-4316	273	2	)	)	PUNCT
ejpam-4316	273	3	=	=	SYM
ejpam-4316	273	4			NOUN
ejpam-4316	274	1	a(kr	a(kr	ADJ
ejpam-4316	274	2	)	)	PUNCT
ejpam-4316	275	1	+	+	CCONJ
ejpam-4316	275	2	2ir	2ir	ADJ
ejpam-4316	275	3	d(kn	d(kn	NOUN
ejpam-4316	275	4	)	)	PUNCT
ejpam-4316	275	5	jn−r×r	jn−r×r	NOUN
ejpam-4316	276	1	a(kr	a(kr	PROPN
ejpam-4316	276	2	)	)	PUNCT
ejpam-4316	277	1	+	+	CCONJ
ejpam-4316	277	2	2ir	2ir	ADJ
ejpam-4316	277	3	jr×n−r	jr×n−r	ADJ
ejpam-4316	277	4	2a(kr	2a(kr	NUM
ejpam-4316	277	5	)	)	PUNCT
ejpam-4316	277	6			NOUN
ejpam-4316	277	7	where	where	SCONJ
ejpam-4316	277	8	d(kn	d(kn	NOUN
ejpam-4316	277	9	)	)	PUNCT
ejpam-4316	277	10	,	,	PUNCT
ejpam-4316	277	11	a(kr	a(kr	PROPN
ejpam-4316	277	12	)	)	PUNCT
ejpam-4316	277	13	,	,	PUNCT
ejpam-4316	277	14	ir	ir	PROPN
ejpam-4316	277	15	,	,	PUNCT
ejpam-4316	277	16	jr×n−r	jr×n−r	PROPN
ejpam-4316	277	17	are	be	AUX
ejpam-4316	277	18	the	the	DET
ejpam-4316	277	19	distance	distance	NOUN
ejpam-4316	277	20	matrix	matrix	NOUN
ejpam-4316	277	21	of	of	ADP
ejpam-4316	277	22	kn	kn	PROPN
ejpam-4316	277	23	,	,	PUNCT
ejpam-4316	277	24	adjacency	adjacency	NOUN
ejpam-4316	277	25	matrix	matrix	NOUN
ejpam-4316	277	26	of	of	ADP
ejpam-4316	277	27	kr	kr	PROPN
ejpam-4316	277	28	,	,	PUNCT
ejpam-4316	277	29	identity	identity	NOUN
ejpam-4316	277	30	matrix	matrix	NOUN
ejpam-4316	277	31	of	of	ADP
ejpam-4316	277	32	size	size	NOUN
ejpam-4316	277	33	r	r	NOUN
ejpam-4316	277	34	,	,	PUNCT
ejpam-4316	277	35	and	and	CCONJ
ejpam-4316	277	36	the	the	DET
ejpam-4316	277	37	all	all	DET
ejpam-4316	277	38	one	one	NOUN
ejpam-4316	277	39	’s	’s	PART
ejpam-4316	277	40	matrix	matrix	NOUN
ejpam-4316	277	41	of	of	ADP
ejpam-4316	277	42	size	size	NOUN
ejpam-4316	277	43	r×	r×	NOUN
ejpam-4316	277	44	n−	n−	NOUN
ejpam-4316	277	45	r	r	NOUN
ejpam-4316	277	46	respectively	respectively	ADV
ejpam-4316	277	47	.	.	PUNCT
ejpam-4316	278	1	hence	hence	ADV
ejpam-4316	278	2	,	,	PUNCT
ejpam-4316	278	3	we	we	PRON
ejpam-4316	278	4	can	can	AUX
ejpam-4316	278	5	compute	compute	VERB
ejpam-4316	278	6	the	the	DET
ejpam-4316	278	7	wiener	wiener	NOUN
ejpam-4316	278	8	index	index	NOUN
ejpam-4316	278	9	by	by	ADP
ejpam-4316	278	10	w	w	PROPN
ejpam-4316	278	11	(	(	PUNCT
ejpam-4316	278	12	γ	γ	NOUN
ejpam-4316	278	13	)	)	PUNCT
ejpam-4316	278	14	=	=	SYM
ejpam-4316	279	1	1	1	NUM
ejpam-4316	279	2	2	2	NUM
ejpam-4316	279	3	∑	∑	PUNCT
ejpam-4316	279	4	d(γ	d(γ	PROPN
ejpam-4316	279	5	)	)	PUNCT
ejpam-4316	279	6	=	=	SYM
ejpam-4316	279	7	1	1	NUM
ejpam-4316	279	8	2	2	NUM
ejpam-4316	279	9	(	(	PUNCT
ejpam-4316	279	10	∑	∑	NOUN
ejpam-4316	279	11	d(kn	d(kn	NUM
ejpam-4316	279	12	)	)	PUNCT
ejpam-4316	279	13	+	+	CCONJ
ejpam-4316	279	14	4	4	NUM
ejpam-4316	279	15	∑	∑	PUNCT
ejpam-4316	279	16	a(kr	a(kr	ADJ
ejpam-4316	279	17	)	)	PUNCT
ejpam-4316	279	18	+	+	CCONJ
ejpam-4316	279	19	4	4	NUM
ejpam-4316	279	20	∑	∑	NOUN
ejpam-4316	279	21	ir	ir	PROPN
ejpam-4316	279	22	+	+	CCONJ
ejpam-4316	279	23	∑	∑	PUNCT
ejpam-4316	279	24	jn−r×r	jn−r×r	ADJ
ejpam-4316	279	25	+	+	CCONJ
ejpam-4316	279	26	∑	∑	ADV
ejpam-4316	279	27	jr×n−r	jr×n−r	ADJ
ejpam-4316	279	28	)	)	PUNCT
ejpam-4316	279	29	=	=	SYM
ejpam-4316	279	30	1	1	NUM
ejpam-4316	279	31	2	2	NUM
ejpam-4316	279	32	d(kn	d(kn	NUM
ejpam-4316	279	33	)	)	PUNCT
ejpam-4316	280	1	+	+	CCONJ
ejpam-4316	280	2	2	2	NUM
ejpam-4316	280	3	∑	∑	PUNCT
ejpam-4316	280	4	a(kr	a(kr	ADJ
ejpam-4316	280	5	)	)	PUNCT
ejpam-4316	280	6	+	+	CCONJ
ejpam-4316	280	7	2	2	NUM
ejpam-4316	280	8	∑	∑	PROPN
ejpam-4316	280	9	ir	ir	PROPN
ejpam-4316	280	10	+	+	NOUN
ejpam-4316	280	11	1	1	NUM
ejpam-4316	280	12	2	2	NUM
ejpam-4316	280	13	∑	∑	NOUN
ejpam-4316	280	14	jn−r×r	jn−r×r	ADJ
ejpam-4316	281	1	+	+	CCONJ
ejpam-4316	281	2	1	1	NUM
ejpam-4316	281	3	2	2	NUM
ejpam-4316	281	4	∑	∑	NOUN
ejpam-4316	281	5	jr×n−r	jr×n−r	NOUN
ejpam-4316	281	6	=	=	SYM
ejpam-4316	281	7	w	w	PROPN
ejpam-4316	281	8	(	(	PUNCT
ejpam-4316	281	9	kn	kn	PROPN
ejpam-4316	281	10	)	)	PUNCT
ejpam-4316	281	11	+	+	CCONJ
ejpam-4316	281	12	2	2	NUM
ejpam-4316	281	13	(	(	PUNCT
ejpam-4316	281	14	2|e(kr)|	2|e(kr)|	NUM
ejpam-4316	281	15	)	)	PUNCT
ejpam-4316	281	16	+	+	CCONJ
ejpam-4316	281	17	2	2	NUM
ejpam-4316	281	18	∑	∑	PROPN
ejpam-4316	281	19	ir	ir	PROPN
ejpam-4316	281	20	+	+	NOUN
ejpam-4316	281	21	1	1	NUM
ejpam-4316	281	22	2	2	NUM
ejpam-4316	281	23	∑	∑	NOUN
ejpam-4316	281	24	jn−r×r	jn−r×r	ADJ
ejpam-4316	282	1	+	+	CCONJ
ejpam-4316	282	2	1	1	NUM
ejpam-4316	282	3	2	2	NUM
ejpam-4316	282	4	∑	∑	NOUN
ejpam-4316	282	5	jr×n−r	jr×n−r	NOUN
ejpam-4316	282	6	=	=	PUNCT
ejpam-4316	282	7	n(n−	n(n−	NOUN
ejpam-4316	282	8	1	1	NUM
ejpam-4316	282	9	)	)	PUNCT
ejpam-4316	282	10	2	2	NUM
ejpam-4316	283	1	+	+	CCONJ
ejpam-4316	283	2	2r(r	2r(r	NOUN
ejpam-4316	283	3	−	−	NOUN
ejpam-4316	283	4	1	1	NUM
ejpam-4316	283	5	)	)	PUNCT
ejpam-4316	284	1	+	+	SYM
ejpam-4316	284	2	2r	2r	NUM
ejpam-4316	284	3	+	+	CCONJ
ejpam-4316	284	4	1	1	NUM
ejpam-4316	284	5	2	2	NUM
ejpam-4316	284	6	(	(	PUNCT
ejpam-4316	284	7	n−	n−	NOUN
ejpam-4316	284	8	r)r	r)r	VERB
ejpam-4316	284	9	+	+	CCONJ
ejpam-4316	284	10	1	1	NUM
ejpam-4316	284	11	2	2	NUM
ejpam-4316	284	12	(	(	PUNCT
ejpam-4316	284	13	n−	n−	NOUN
ejpam-4316	284	14	r)r	r)r	PUNCT
ejpam-4316	284	15	=	=	PUNCT
ejpam-4316	284	16	n(n−	n(n−	VERB
ejpam-4316	284	17	1	1	NUM
ejpam-4316	284	18	)	)	PUNCT
ejpam-4316	284	19	2	2	NUM
ejpam-4316	284	20	+	+	CCONJ
ejpam-4316	284	21	2r2	2r2	NUM
ejpam-4316	284	22	−	−	NUM
ejpam-4316	284	23	2r	2r	NUM
ejpam-4316	285	1	+	+	NUM
ejpam-4316	285	2	2r	2r	NUM
ejpam-4316	285	3	+	+	CCONJ
ejpam-4316	285	4	r(n−	r(n−	NOUN
ejpam-4316	285	5	r	r	NOUN
ejpam-4316	285	6	)	)	PUNCT
ejpam-4316	285	7	=	=	SYM
ejpam-4316	285	8	n2	n2	NOUN
ejpam-4316	285	9	−	−	PROPN
ejpam-4316	285	10	n+	n+	NUM
ejpam-4316	285	11	2r2	2r2	NUM
ejpam-4316	286	1	+	+	CCONJ
ejpam-4316	286	2	2nr	2nr	ADJ
ejpam-4316	286	3	2	2	NUM
ejpam-4316	286	4	.	.	PUNCT
ejpam-4316	286	5	theorem	theorem	NOUN
ejpam-4316	286	6	11	11	NUM
ejpam-4316	286	7	.	.	PUNCT
ejpam-4316	287	1	let	let	VERB
ejpam-4316	287	2	n	n	PRON
ejpam-4316	287	3	>	>	X
ejpam-4316	287	4	3	3	NUM
ejpam-4316	287	5	,	,	PUNCT
ejpam-4316	287	6	and	and	CCONJ
ejpam-4316	287	7	s	s	AUX
ejpam-4316	287	8	=	=	PUNCT
ejpam-4316	287	9	{	{	PUNCT
ejpam-4316	287	10	x	x	NOUN
ejpam-4316	287	11	}	}	PUNCT
ejpam-4316	287	12	such	such	ADJ
ejpam-4316	287	13	that	that	SCONJ
ejpam-4316	287	14	x	x	SYM
ejpam-4316	287	15	∈	∈	NOUN
ejpam-4316	287	16	v	v	X
ejpam-4316	287	17	(	(	PUNCT
ejpam-4316	287	18	cn	cn	PROPN
ejpam-4316	287	19	)	)	PUNCT
ejpam-4316	287	20	.	.	PUNCT
ejpam-4316	288	1	then	then	ADV
ejpam-4316	288	2	the	the	DET
ejpam-4316	288	3	wiener	wiener	NOUN
ejpam-4316	288	4	index	index	NOUN
ejpam-4316	288	5	of	of	ADP
ejpam-4316	288	6	the	the	DET
ejpam-4316	288	7	s	s	NOUN
ejpam-4316	288	8	-	-	PUNCT
ejpam-4316	288	9	splitting	splitting	NOUN
ejpam-4316	288	10	graph	graph	NOUN
ejpam-4316	288	11	of	of	ADP
ejpam-4316	288	12	cn	cn	PROPN
ejpam-4316	288	13	is	be	AUX
ejpam-4316	288	14	given	give	VERB
ejpam-4316	288	15	by	by	ADP
ejpam-4316	288	16	f.j.h	f.j.h	ADJ
ejpam-4316	288	17	.	.	PUNCT
ejpam-4316	289	1	campeña	campeña	NOUN
ejpam-4316	289	2	,	,	PUNCT
ejpam-4316	289	3	m.c.g	m.c.g	PROPN
ejpam-4316	289	4	.	.	PUNCT
ejpam-4316	289	5	egan	egan	PROPN
ejpam-4316	289	6	,	,	PUNCT
ejpam-4316	289	7	j.r.m	j.r.m	PROPN
ejpam-4316	289	8	.	.	PUNCT
ejpam-4316	290	1	antalan	antalan	PROPN
ejpam-4316	290	2	/	/	SYM
ejpam-4316	290	3	eur	eur	PROPN
ejpam-4316	290	4	.	.	PUNCT
ejpam-4316	291	1	j.	j.	PROPN
ejpam-4316	291	2	pure	pure	PROPN
ejpam-4316	291	3	appl	appl	PROPN
ejpam-4316	291	4	.	.	PROPN
ejpam-4316	291	5	math	math	PROPN
ejpam-4316	291	6	,	,	PUNCT
ejpam-4316	291	7	15	15	NUM
ejpam-4316	291	8	(	(	PUNCT
ejpam-4316	291	9	2	2	NUM
ejpam-4316	291	10	)	)	PUNCT
ejpam-4316	291	11	(	(	PUNCT
ejpam-4316	291	12	2022	2022	NUM
ejpam-4316	291	13	)	)	PUNCT
ejpam-4316	291	14	,	,	PUNCT
ejpam-4316	291	15	602	602	NUM
ejpam-4316	291	16	-	-	SYM
ejpam-4316	291	17	619	619	NUM
ejpam-4316	291	18	611	611	NUM
ejpam-4316	291	19	(	(	PUNCT
ejpam-4316	291	20	i	i	NOUN
ejpam-4316	291	21	)	)	PUNCT
ejpam-4316	291	22	w	w	PROPN
ejpam-4316	291	23	(	(	PUNCT
ejpam-4316	291	24	γ(cn	γ(cn	PROPN
ejpam-4316	291	25	,	,	PUNCT
ejpam-4316	291	26	s	s	PART
ejpam-4316	291	27	)	)	PUNCT
ejpam-4316	291	28	)	)	PUNCT
ejpam-4316	292	1	=	=	SYM
ejpam-4316	292	2	n(n−1)(n+1	n(n−1)(n+1	ADJ
ejpam-4316	292	3	)	)	PUNCT
ejpam-4316	292	4	8	8	NUM
ejpam-4316	293	1	+	+	CCONJ
ejpam-4316	293	2	k2	k2	X
ejpam-4316	293	3	+	+	CCONJ
ejpam-4316	293	4	k	k	PROPN
ejpam-4316	293	5	+	+	CCONJ
ejpam-4316	293	6	2	2	NUM
ejpam-4316	293	7	if	if	SCONJ
ejpam-4316	293	8	n	n	NOUN
ejpam-4316	293	9	is	be	AUX
ejpam-4316	293	10	odd	odd	ADJ
ejpam-4316	293	11	;	;	PUNCT
ejpam-4316	293	12	(	(	PUNCT
ejpam-4316	293	13	ii	ii	NOUN
ejpam-4316	293	14	)	)	PUNCT
ejpam-4316	293	15	w	w	PROPN
ejpam-4316	293	16	(	(	PUNCT
ejpam-4316	293	17	γ(cn	γ(cn	PROPN
ejpam-4316	293	18	,	,	PUNCT
ejpam-4316	293	19	s	s	PART
ejpam-4316	293	20	)	)	PUNCT
ejpam-4316	293	21	)	)	PUNCT
ejpam-4316	293	22	=	=	SYM
ejpam-4316	293	23	n3	n3	VERB
ejpam-4316	293	24	8	8	NUM
ejpam-4316	293	25	+	+	SYM
ejpam-4316	293	26	k2	k2	NOUN
ejpam-4316	293	27	+	+	CCONJ
ejpam-4316	293	28	2	2	NUM
ejpam-4316	293	29	if	if	SCONJ
ejpam-4316	293	30	n	n	PRON
ejpam-4316	293	31	is	be	AUX
ejpam-4316	293	32	even	even	ADV
ejpam-4316	293	33	.	.	PUNCT
ejpam-4316	294	1	proof	proof	NOUN
ejpam-4316	294	2	.	.	PUNCT
ejpam-4316	295	1	suppose	suppose	VERB
ejpam-4316	295	2	n	n	PROPN
ejpam-4316	295	3	=	=	SYM
ejpam-4316	295	4	2k	2k	PROPN
ejpam-4316	295	5	+	+	CCONJ
ejpam-4316	295	6	1	1	X
ejpam-4316	295	7	.	.	X
ejpam-4316	296	1	let	let	VERB
ejpam-4316	296	2	v	v	X
ejpam-4316	296	3	(	(	PUNCT
ejpam-4316	296	4	cn	cn	PROPN
ejpam-4316	296	5	)	)	PUNCT
ejpam-4316	296	6	=	=	PRON
ejpam-4316	296	7	{	{	PUNCT
ejpam-4316	296	8	x1	x1	PROPN
ejpam-4316	296	9	,	,	PUNCT
ejpam-4316	296	10	x2	x2	PROPN
ejpam-4316	296	11	,	,	PUNCT
ejpam-4316	296	12	.	.	PUNCT
ejpam-4316	296	13	.	.	PUNCT
ejpam-4316	297	1	.	.	PUNCT
ejpam-4316	298	1	,	,	PUNCT
ejpam-4316	298	2	xn	xn	PROPN
ejpam-4316	298	3	}	}	PUNCT
ejpam-4316	298	4	.	.	PUNCT
ejpam-4316	299	1	without	without	ADP
ejpam-4316	299	2	loss	loss	NOUN
ejpam-4316	299	3	of	of	ADP
ejpam-4316	299	4	generality	generality	NOUN
ejpam-4316	299	5	,	,	PUNCT
ejpam-4316	299	6	suppose	suppose	VERB
ejpam-4316	299	7	s	s	VERB
ejpam-4316	299	8	=	=	PUNCT
ejpam-4316	299	9	{	{	PUNCT
ejpam-4316	299	10	x1	x1	PROPN
ejpam-4316	299	11	}	}	PUNCT
ejpam-4316	299	12	.	.	PUNCT
ejpam-4316	300	1	for	for	ADP
ejpam-4316	300	2	some	some	DET
ejpam-4316	300	3	ordering	ordering	NOUN
ejpam-4316	300	4	of	of	ADP
ejpam-4316	300	5	the	the	DET
ejpam-4316	300	6	vertices	vertex	NOUN
ejpam-4316	300	7	of	of	ADP
ejpam-4316	300	8	γ	γ	PROPN
ejpam-4316	300	9	say	say	VERB
ejpam-4316	300	10	,	,	PUNCT
ejpam-4316	300	11	x1	x1	PROPN
ejpam-4316	300	12	,	,	PUNCT
ejpam-4316	300	13	x2	x2	PROPN
ejpam-4316	300	14	,	,	PUNCT
ejpam-4316	300	15	xn	xn	PROPN
ejpam-4316	300	16	,	,	PUNCT
ejpam-4316	300	17	x3	x3	ADJ
ejpam-4316	300	18	,	,	PUNCT
ejpam-4316	300	19	xn−1	xn−1	PROPN
ejpam-4316	300	20	,	,	PUNCT
ejpam-4316	300	21	.	.	PUNCT
ejpam-4316	300	22	.	.	PUNCT
ejpam-4316	300	23	.	.	PUNCT
ejpam-4316	301	1	,	,	PUNCT
ejpam-4316	301	2	xk+1	xk+1	PROPN
ejpam-4316	301	3	,	,	PUNCT
ejpam-4316	301	4	xk+2	xk+2	NUM
ejpam-4316	301	5	,	,	PUNCT
ejpam-4316	301	6	x	x	NOUN
ejpam-4316	301	7	′	′	NUM
ejpam-4316	301	8	1	1	NUM
ejpam-4316	301	9	,	,	PUNCT
ejpam-4316	301	10	the	the	DET
ejpam-4316	301	11	distance	distance	NOUN
ejpam-4316	301	12	matrix	matrix	NOUN
ejpam-4316	301	13	of	of	ADP
ejpam-4316	301	14	d(γ	d(γ	PROPN
ejpam-4316	301	15	)	)	PUNCT
ejpam-4316	301	16	can	can	AUX
ejpam-4316	301	17	describe	describe	VERB
ejpam-4316	301	18	as	as	ADP
ejpam-4316	301	19	a	a	DET
ejpam-4316	301	20	bloc	bloc	NOUN
ejpam-4316	301	21	matrix	matrix	NOUN
ejpam-4316	301	22	given	give	VERB
ejpam-4316	301	23	by	by	ADP
ejpam-4316	301	24	d(γ	d(γ	PROPN
ejpam-4316	301	25	)	)	PUNCT
ejpam-4316	301	26	=	=	PUNCT
ejpam-4316	302	1	[	[	PUNCT
ejpam-4316	302	2	d(cn	d(cn	NOUN
ejpam-4316	302	3	)	)	PUNCT
ejpam-4316	302	4	a	a	PRON
ejpam-4316	302	5	at	at	ADP
ejpam-4316	302	6	0	0	NUM
ejpam-4316	302	7	]	]	PUNCT
ejpam-4316	302	8	where	where	SCONJ
ejpam-4316	302	9	d(cn	d(cn	NOUN
ejpam-4316	302	10	)	)	PUNCT
ejpam-4316	302	11	is	be	AUX
ejpam-4316	302	12	the	the	DET
ejpam-4316	302	13	distance	distance	NOUN
ejpam-4316	302	14	matrix	matrix	NOUN
ejpam-4316	302	15	of	of	ADP
ejpam-4316	302	16	cn	cn	PROPN
ejpam-4316	302	17	and	and	CCONJ
ejpam-4316	302	18	at	at	ADP
ejpam-4316	302	19	is	be	AUX
ejpam-4316	302	20	the	the	DET
ejpam-4316	302	21	1×n	1×n	NUM
ejpam-4316	302	22	matrix	matrix	NOUN
ejpam-4316	302	23	[	[	X
ejpam-4316	302	24	2	2	NUM
ejpam-4316	302	25	,	,	PUNCT
ejpam-4316	302	26	1	1	NUM
ejpam-4316	302	27	,	,	PUNCT
ejpam-4316	302	28	1	1	NUM
ejpam-4316	302	29	,	,	PUNCT
ejpam-4316	302	30	2	2	NUM
ejpam-4316	302	31	,	,	PUNCT
ejpam-4316	302	32	2	2	NUM
ejpam-4316	302	33	,	,	PUNCT
ejpam-4316	302	34	3	3	NUM
ejpam-4316	302	35	,	,	PUNCT
ejpam-4316	302	36	3	3	NUM
ejpam-4316	302	37	,	,	PUNCT
ejpam-4316	302	38	.	.	PUNCT
ejpam-4316	302	39	.	.	PUNCT
ejpam-4316	303	1	.	.	PUNCT
ejpam-4316	304	1	,	,	PUNCT
ejpam-4316	304	2	k	k	X
ejpam-4316	304	3	,	,	PUNCT
ejpam-4316	304	4	k	k	X
ejpam-4316	304	5	]	]	X
ejpam-4316	304	6	.	.	PUNCT
ejpam-4316	305	1	thus	thus	ADV
ejpam-4316	305	2	we	we	PRON
ejpam-4316	305	3	have	have	VERB
ejpam-4316	305	4	,	,	PUNCT
ejpam-4316	305	5	w	w	PROPN
ejpam-4316	305	6	(	(	PUNCT
ejpam-4316	305	7	γ	γ	NOUN
ejpam-4316	305	8	)	)	PUNCT
ejpam-4316	305	9	=	=	SYM
ejpam-4316	306	1	w	w	PROPN
ejpam-4316	306	2	(	(	PUNCT
ejpam-4316	306	3	cn	cn	PROPN
ejpam-4316	306	4	)	)	PUNCT
ejpam-4316	306	5	+	+	CCONJ
ejpam-4316	306	6	2	2	NUM
ejpam-4316	306	7	+	+	SYM
ejpam-4316	306	8	2	2	NUM
ejpam-4316	306	9	k∑	k∑	NOUN
ejpam-4316	306	10	i=1	i=1	PROPN
ejpam-4316	307	1	i	i	PRON
ejpam-4316	307	2	=	=	PUNCT
ejpam-4316	307	3	n(n−	n(n−	VERB
ejpam-4316	307	4	1)(n+	1)(n+	NUM
ejpam-4316	307	5	1	1	NUM
ejpam-4316	307	6	)	)	PUNCT
ejpam-4316	307	7	8	8	NUM
ejpam-4316	308	1	+	+	CCONJ
ejpam-4316	308	2	2	2	NUM
ejpam-4316	308	3	+	+	NUM
ejpam-4316	308	4	2	2	NUM
ejpam-4316	308	5	(	(	PUNCT
ejpam-4316	308	6	k(k	k(k	X
ejpam-4316	308	7	+	+	NOUN
ejpam-4316	308	8	1	1	NUM
ejpam-4316	308	9	)	)	PUNCT
ejpam-4316	308	10	2	2	NUM
ejpam-4316	308	11	)	)	PUNCT
ejpam-4316	309	1	=	=	PRON
ejpam-4316	309	2	n(n−	n(n−	VERB
ejpam-4316	309	3	1)(n+	1)(n+	NUM
ejpam-4316	309	4	1	1	NUM
ejpam-4316	309	5	)	)	PUNCT
ejpam-4316	309	6	8	8	NUM
ejpam-4316	309	7	+	+	CCONJ
ejpam-4316	309	8	2	2	NUM
ejpam-4316	309	9	+	+	CCONJ
ejpam-4316	309	10	k(k	k(k	ADJ
ejpam-4316	309	11	+	+	NOUN
ejpam-4316	309	12	1	1	X
ejpam-4316	309	13	)	)	PUNCT
ejpam-4316	309	14	=	=	VERB
ejpam-4316	309	15	n(n−	n(n−	VERB
ejpam-4316	309	16	1)(n+	1)(n+	NUM
ejpam-4316	309	17	1	1	NUM
ejpam-4316	309	18	)	)	PUNCT
ejpam-4316	309	19	8	8	NUM
ejpam-4316	310	1	+	+	SYM
ejpam-4316	310	2	k2	k2	X
ejpam-4316	310	3	+	+	CCONJ
ejpam-4316	310	4	k	k	PROPN
ejpam-4316	310	5	+	+	PROPN
ejpam-4316	310	6	2	2	X
ejpam-4316	310	7	.	.	PUNCT
ejpam-4316	310	8	now	now	ADV
ejpam-4316	310	9	suppose	suppose	VERB
ejpam-4316	310	10	n	n	PROPN
ejpam-4316	310	11	=	=	SYM
ejpam-4316	310	12	2k	2k	NUM
ejpam-4316	310	13	,	,	PUNCT
ejpam-4316	310	14	given	give	VERB
ejpam-4316	310	15	the	the	DET
ejpam-4316	310	16	ordering	ordering	NOUN
ejpam-4316	310	17	of	of	ADP
ejpam-4316	310	18	the	the	DET
ejpam-4316	310	19	vertices	vertex	NOUN
ejpam-4316	310	20	of	of	ADP
ejpam-4316	310	21	γ	γ	NOUN
ejpam-4316	310	22	by	by	ADP
ejpam-4316	310	23	x1	x1	PROPN
ejpam-4316	310	24	,	,	PUNCT
ejpam-4316	310	25	x2	x2	PROPN
ejpam-4316	310	26	,	,	PUNCT
ejpam-4316	310	27	xn	xn	PROPN
ejpam-4316	310	28	,	,	PUNCT
ejpam-4316	310	29	x3	x3	ADJ
ejpam-4316	310	30	,	,	PUNCT
ejpam-4316	310	31	xn−1	xn−1	PROPN
ejpam-4316	310	32	,	,	PUNCT
ejpam-4316	310	33	.	.	PUNCT
ejpam-4316	310	34	.	.	PUNCT
ejpam-4316	311	1	.	.	PUNCT
ejpam-4316	312	1	,	,	PUNCT
ejpam-4316	312	2	xk−1	xk−1	PROPN
ejpam-4316	312	3	,	,	PUNCT
ejpam-4316	312	4	xk+1	xk+1	PROPN
ejpam-4316	312	5	,	,	PUNCT
ejpam-4316	312	6	xk	xk	PROPN
ejpam-4316	312	7	,	,	PUNCT
ejpam-4316	312	8	x	x	NOUN
ejpam-4316	312	9	′	′	NOUN
ejpam-4316	312	10	1	1	NUM
ejpam-4316	313	1	where	where	SCONJ
ejpam-4316	313	2	n	n	NOUN
ejpam-4316	313	3	=	=	SYM
ejpam-4316	313	4	2k	2k	NUM
ejpam-4316	313	5	.	.	PUNCT
ejpam-4316	314	1	then	then	ADV
ejpam-4316	314	2	we	we	PRON
ejpam-4316	314	3	can	can	AUX
ejpam-4316	314	4	write	write	VERB
ejpam-4316	314	5	the	the	DET
ejpam-4316	314	6	distance	distance	NOUN
ejpam-4316	314	7	matrix	matrix	NOUN
ejpam-4316	314	8	of	of	ADP
ejpam-4316	314	9	γ	γ	X
ejpam-4316	314	10	by	by	ADP
ejpam-4316	314	11	d(γ	d(γ	PROPN
ejpam-4316	314	12	)	)	PUNCT
ejpam-4316	314	13	=	=	PUNCT
ejpam-4316	315	1	[	[	PUNCT
ejpam-4316	315	2	d(cn	d(cn	NOUN
ejpam-4316	315	3	)	)	PUNCT
ejpam-4316	315	4	a	a	PRON
ejpam-4316	315	5	at	at	ADP
ejpam-4316	315	6	0	0	NUM
ejpam-4316	315	7	]	]	PUNCT
ejpam-4316	315	8	where	where	SCONJ
ejpam-4316	315	9	d(cn	d(cn	NOUN
ejpam-4316	315	10	)	)	PUNCT
ejpam-4316	315	11	is	be	AUX
ejpam-4316	315	12	the	the	DET
ejpam-4316	315	13	distance	distance	NOUN
ejpam-4316	315	14	matrix	matrix	NOUN
ejpam-4316	315	15	of	of	ADP
ejpam-4316	315	16	cn	cn	PROPN
ejpam-4316	315	17	and	and	CCONJ
ejpam-4316	315	18	at	at	ADP
ejpam-4316	315	19	is	be	AUX
ejpam-4316	315	20	the	the	DET
ejpam-4316	315	21	1×	1×	NUM
ejpam-4316	315	22	n	n	NOUN
ejpam-4316	315	23	matrix	matrix	NOUN
ejpam-4316	315	24	[	[	X
ejpam-4316	315	25	2	2	NUM
ejpam-4316	315	26	,	,	PUNCT
ejpam-4316	315	27	1	1	NUM
ejpam-4316	315	28	,	,	PUNCT
ejpam-4316	315	29	1	1	NUM
ejpam-4316	315	30	,	,	PUNCT
ejpam-4316	315	31	2	2	NUM
ejpam-4316	315	32	,	,	PUNCT
ejpam-4316	315	33	2	2	NUM
ejpam-4316	315	34	,	,	PUNCT
ejpam-4316	315	35	.	.	PUNCT
ejpam-4316	315	36	.	.	PUNCT
ejpam-4316	316	1	.	.	PUNCT
ejpam-4316	317	1	,	,	PUNCT
ejpam-4316	318	1	k	k	PROPN
ejpam-4316	319	1	−	−	PROPN
ejpam-4316	319	2	1	1	NUM
ejpam-4316	319	3	,	,	PUNCT
ejpam-4316	319	4	k	k	PROPN
ejpam-4316	319	5	−	−	PROPN
ejpam-4316	319	6	1	1	NUM
ejpam-4316	319	7	,	,	PUNCT
ejpam-4316	319	8	k	k	NOUN
ejpam-4316	319	9	]	]	X
ejpam-4316	319	10	.	.	PUNCT
ejpam-4316	320	1	computing	compute	VERB
ejpam-4316	320	2	for	for	ADP
ejpam-4316	320	3	the	the	DET
ejpam-4316	320	4	wiener	wiener	NOUN
ejpam-4316	320	5	index	index	NOUN
ejpam-4316	320	6	of	of	ADP
ejpam-4316	320	7	the	the	DET
ejpam-4316	320	8	graph	graph	NOUN
ejpam-4316	320	9	γ(cn	γ(cn	PROPN
ejpam-4316	320	10	,	,	PUNCT
ejpam-4316	320	11	s	s	PART
ejpam-4316	320	12	)	)	PUNCT
ejpam-4316	320	13	,	,	PUNCT
ejpam-4316	320	14	we	we	PRON
ejpam-4316	320	15	have	have	VERB
ejpam-4316	320	16	:	:	PUNCT
ejpam-4316	320	17	w	w	X
ejpam-4316	320	18	(	(	PUNCT
ejpam-4316	320	19	γ	γ	NOUN
ejpam-4316	320	20	)	)	PUNCT
ejpam-4316	320	21	=	=	SYM
ejpam-4316	321	1	w	w	PROPN
ejpam-4316	321	2	(	(	PUNCT
ejpam-4316	321	3	cn	cn	PROPN
ejpam-4316	321	4	)	)	PUNCT
ejpam-4316	321	5	+	+	CCONJ
ejpam-4316	321	6	2	2	NUM
ejpam-4316	321	7	+	+	SYM
ejpam-4316	321	8	2	2	NUM
ejpam-4316	321	9	k−1∑	k−1∑	PROPN
ejpam-4316	321	10	i=1	i=1	PROPN
ejpam-4316	321	11	i+	i+	ADJ
ejpam-4316	321	12	k	k	NOUN
ejpam-4316	321	13	=	=	SYM
ejpam-4316	321	14	n3	n3	NOUN
ejpam-4316	321	15	8	8	NUM
ejpam-4316	321	16	+	+	CCONJ
ejpam-4316	321	17	2	2	NUM
ejpam-4316	321	18	+	+	NUM
ejpam-4316	321	19	2	2	NUM
ejpam-4316	321	20	(	(	PUNCT
ejpam-4316	321	21	k(k	k(k	ADJ
ejpam-4316	321	22	−	−	PROPN
ejpam-4316	321	23	1	1	NUM
ejpam-4316	321	24	)	)	PUNCT
ejpam-4316	321	25	2	2	NUM
ejpam-4316	321	26	)	)	PUNCT
ejpam-4316	322	1	+	+	CCONJ
ejpam-4316	322	2	k	k	X
ejpam-4316	322	3	=	=	SYM
ejpam-4316	322	4	n3	n3	NOUN
ejpam-4316	322	5	8	8	NUM
ejpam-4316	322	6	+	+	CCONJ
ejpam-4316	322	7	2	2	NUM
ejpam-4316	322	8	+	+	NUM
ejpam-4316	322	9	2	2	NUM
ejpam-4316	322	10	(	(	PUNCT
ejpam-4316	322	11	k(k	k(k	ADJ
ejpam-4316	322	12	−	−	PROPN
ejpam-4316	322	13	1	1	NUM
ejpam-4316	322	14	)	)	PUNCT
ejpam-4316	322	15	2	2	NUM
ejpam-4316	322	16	)	)	PUNCT
ejpam-4316	323	1	+	+	CCONJ
ejpam-4316	323	2	k	k	X
ejpam-4316	323	3	=	=	SYM
ejpam-4316	323	4	n3	n3	ADJ
ejpam-4316	323	5	8	8	NUM
ejpam-4316	323	6	+	+	SYM
ejpam-4316	323	7	k2	k2	NOUN
ejpam-4316	323	8	+	+	CCONJ
ejpam-4316	323	9	2	2	NUM
ejpam-4316	323	10	.	.	X
ejpam-4316	323	11	theorem	theorem	NOUN
ejpam-4316	323	12	12	12	NUM
ejpam-4316	323	13	.	.	PUNCT
ejpam-4316	324	1	let	let	VERB
ejpam-4316	324	2	g	g	PRON
ejpam-4316	324	3	be	be	AUX
ejpam-4316	324	4	a	a	DET
ejpam-4316	324	5	path	path	NOUN
ejpam-4316	324	6	graph	graph	NOUN
ejpam-4316	324	7	and	and	CCONJ
ejpam-4316	324	8	s	s	VERB
ejpam-4316	324	9	⊂	⊂	PROPN
ejpam-4316	324	10	v	v	X
ejpam-4316	324	11	(	(	PUNCT
ejpam-4316	324	12	pn	pn	NOUN
ejpam-4316	324	13	)	)	PUNCT
ejpam-4316	324	14	=	=	PRON
ejpam-4316	325	1	{	{	PUNCT
ejpam-4316	325	2	x1	x1	PROPN
ejpam-4316	325	3	,	,	PUNCT
ejpam-4316	325	4	x2	x2	PROPN
ejpam-4316	325	5	,	,	PUNCT
ejpam-4316	325	6	.	.	PUNCT
ejpam-4316	325	7	.	.	PUNCT
ejpam-4316	325	8	.	.	PUNCT
ejpam-4316	326	1	,	,	PUNCT
ejpam-4316	326	2	xn	xn	X
ejpam-4316	326	3	}	}	PUNCT
ejpam-4316	327	1	where	where	SCONJ
ejpam-4316	327	2	n	n	PRON
ejpam-4316	327	3	≥	≥	NOUN
ejpam-4316	327	4	2	2	NUM
ejpam-4316	327	5	.	.	PUNCT
ejpam-4316	327	6	then	then	ADV
ejpam-4316	327	7	(	(	PUNCT
ejpam-4316	327	8	i	i	NOUN
ejpam-4316	327	9	)	)	PUNCT
ejpam-4316	327	10	if	if	SCONJ
ejpam-4316	327	11	s	s	VERB
ejpam-4316	327	12	=	=	PUNCT
ejpam-4316	327	13	{	{	PUNCT
ejpam-4316	327	14	x1	x1	PROPN
ejpam-4316	327	15	}	}	PUNCT
ejpam-4316	327	16	or	or	CCONJ
ejpam-4316	327	17	s	s	NOUN
ejpam-4316	327	18	=	=	X
ejpam-4316	327	19	{	{	PUNCT
ejpam-4316	327	20	xn	xn	NUM
ejpam-4316	327	21	}	}	PUNCT
ejpam-4316	327	22	,	,	PUNCT
ejpam-4316	327	23	then	then	ADV
ejpam-4316	327	24	w	w	PROPN
ejpam-4316	327	25	(	(	PUNCT
ejpam-4316	327	26	γ(pn	γ(pn	X
ejpam-4316	327	27	,	,	PUNCT
ejpam-4316	327	28	s	s	NOUN
ejpam-4316	327	29	)	)	PUNCT
ejpam-4316	327	30	)	)	PUNCT
ejpam-4316	327	31	=	=	SYM
ejpam-4316	327	32	n3	n3	VERB
ejpam-4316	327	33	+	+	PROPN
ejpam-4316	327	34	3n2−4n+12	3n2−4n+12	NUM
ejpam-4316	327	35	6	6	NUM
ejpam-4316	327	36	;	;	PUNCT
ejpam-4316	327	37	(	(	PUNCT
ejpam-4316	327	38	ii	ii	NOUN
ejpam-4316	327	39	)	)	PUNCT
ejpam-4316	327	40	if	if	SCONJ
ejpam-4316	327	41	s	s	VERB
ejpam-4316	327	42	=	=	X
ejpam-4316	327	43	{	{	PUNCT
ejpam-4316	327	44	xi	xi	ADP
ejpam-4316	327	45	}	}	PUNCT
ejpam-4316	327	46	such	such	ADJ
ejpam-4316	327	47	that	that	SCONJ
ejpam-4316	327	48	2	2	NUM
ejpam-4316	327	49	≤	≤	NUM
ejpam-4316	327	50	i	i	PRON
ejpam-4316	327	51	≤	≤	ADJ
ejpam-4316	327	52	n−	n−	NOUN
ejpam-4316	327	53	1	1	NUM
ejpam-4316	327	54	,	,	PUNCT
ejpam-4316	327	55	then	then	ADV
ejpam-4316	327	56	w	w	PROPN
ejpam-4316	327	57	(	(	PUNCT
ejpam-4316	327	58	γ(pn	γ(pn	X
ejpam-4316	327	59	,	,	PUNCT
ejpam-4316	327	60	s	s	NOUN
ejpam-4316	327	61	)	)	PUNCT
ejpam-4316	327	62	)	)	PUNCT
ejpam-4316	328	1	=	=	PUNCT
ejpam-4316	328	2	n3	n3	PROPN
ejpam-4316	328	3	+	+	PROPN
ejpam-4316	328	4	3n2	3n2	PROPN
ejpam-4316	328	5	+	+	ADJ
ejpam-4316	328	6	2n+6i2−6in−6i+12	2n+6i2−6in−6i+12	PROPN
ejpam-4316	328	7	6	6	NUM
ejpam-4316	328	8	.	.	PUNCT
ejpam-4316	329	1	f.j.h	f.j.h	ADJ
ejpam-4316	329	2	.	.	PUNCT
ejpam-4316	330	1	campeña	campeña	NOUN
ejpam-4316	330	2	,	,	PUNCT
ejpam-4316	330	3	m.c.g	m.c.g	PROPN
ejpam-4316	330	4	.	.	PUNCT
ejpam-4316	330	5	egan	egan	PROPN
ejpam-4316	330	6	,	,	PUNCT
ejpam-4316	330	7	j.r.m	j.r.m	PROPN
ejpam-4316	330	8	.	.	PUNCT
ejpam-4316	331	1	antalan	antalan	PROPN
ejpam-4316	331	2	/	/	SYM
ejpam-4316	331	3	eur	eur	PROPN
ejpam-4316	331	4	.	.	PUNCT
ejpam-4316	332	1	j.	j.	PROPN
ejpam-4316	332	2	pure	pure	PROPN
ejpam-4316	332	3	appl	appl	PROPN
ejpam-4316	332	4	.	.	PROPN
ejpam-4316	332	5	math	math	PROPN
ejpam-4316	332	6	,	,	PUNCT
ejpam-4316	332	7	15	15	NUM
ejpam-4316	332	8	(	(	PUNCT
ejpam-4316	332	9	2	2	NUM
ejpam-4316	332	10	)	)	PUNCT
ejpam-4316	332	11	(	(	PUNCT
ejpam-4316	332	12	2022	2022	NUM
ejpam-4316	332	13	)	)	PUNCT
ejpam-4316	332	14	,	,	PUNCT
ejpam-4316	332	15	602	602	NUM
ejpam-4316	332	16	-	-	SYM
ejpam-4316	332	17	619	619	NUM
ejpam-4316	332	18	612	612	NUM
ejpam-4316	332	19	proof	proof	NOUN
ejpam-4316	332	20	.	.	PUNCT
ejpam-4316	333	1	let	let	VERB
ejpam-4316	333	2	s	s	PRON
ejpam-4316	333	3	=	=	PUNCT
ejpam-4316	333	4	{	{	PUNCT
ejpam-4316	333	5	x1	x1	PROPN
ejpam-4316	333	6	}	}	PUNCT
ejpam-4316	333	7	.	.	PUNCT
ejpam-4316	334	1	given	give	VERB
ejpam-4316	334	2	the	the	DET
ejpam-4316	334	3	ordering	ordering	NOUN
ejpam-4316	334	4	of	of	ADP
ejpam-4316	334	5	the	the	DET
ejpam-4316	334	6	vertices	vertex	NOUN
ejpam-4316	334	7	x1	x1	PROPN
ejpam-4316	334	8	,	,	PUNCT
ejpam-4316	334	9	x2	x2	PROPN
ejpam-4316	334	10	,	,	PUNCT
ejpam-4316	334	11	.	.	PUNCT
ejpam-4316	334	12	.	.	PUNCT
ejpam-4316	334	13	.	.	PUNCT
ejpam-4316	335	1	,	,	PUNCT
ejpam-4316	335	2	xn	xn	PROPN
ejpam-4316	335	3	,	,	PUNCT
ejpam-4316	335	4	x	x	X
ejpam-4316	335	5	′	′	NOUN
ejpam-4316	336	1	1	1	NUM
ejpam-4316	336	2	.	.	PUNCT
ejpam-4316	337	1	we	we	PRON
ejpam-4316	337	2	have	have	VERB
ejpam-4316	337	3	the	the	DET
ejpam-4316	337	4	distance	distance	NOUN
ejpam-4316	337	5	matrix	matrix	NOUN
ejpam-4316	337	6	for	for	ADP
ejpam-4316	337	7	the	the	DET
ejpam-4316	337	8	graph	graph	NOUN
ejpam-4316	337	9	γ(s	γ(s	PROPN
ejpam-4316	337	10	,	,	PUNCT
ejpam-4316	337	11	pn	pn	NOUN
ejpam-4316	337	12	)	)	PUNCT
ejpam-4316	337	13	as	as	SCONJ
ejpam-4316	337	14	follows	follow	VERB
ejpam-4316	337	15	.	.	PUNCT
ejpam-4316	338	1	d(γ	d(γ	ADJ
ejpam-4316	338	2	)	)	PUNCT
ejpam-4316	339	1	=	=	PUNCT
ejpam-4316	339	2	[	[	PUNCT
ejpam-4316	339	3	d(pn	d(pn	PROPN
ejpam-4316	339	4	)	)	PUNCT
ejpam-4316	339	5	a	a	PRON
ejpam-4316	339	6	at	at	ADP
ejpam-4316	339	7	0	0	NUM
ejpam-4316	339	8	]	]	PUNCT
ejpam-4316	339	9	where	where	SCONJ
ejpam-4316	339	10	d(pn	d(pn	NOUN
ejpam-4316	339	11	)	)	PUNCT
ejpam-4316	339	12	is	be	AUX
ejpam-4316	339	13	the	the	DET
ejpam-4316	339	14	distance	distance	NOUN
ejpam-4316	339	15	matrix	matrix	NOUN
ejpam-4316	339	16	of	of	ADP
ejpam-4316	339	17	pn	pn	PROPN
ejpam-4316	339	18	and	and	CCONJ
ejpam-4316	339	19	at	at	ADP
ejpam-4316	339	20	is	be	AUX
ejpam-4316	339	21	the	the	DET
ejpam-4316	339	22	1	1	NUM
ejpam-4316	339	23	×	×	NOUN
ejpam-4316	339	24	n	n	PRON
ejpam-4316	339	25	matrix	matrix	NOUN
ejpam-4316	339	26	[	[	X
ejpam-4316	339	27	2	2	NUM
ejpam-4316	339	28	,	,	PUNCT
ejpam-4316	339	29	1	1	NUM
ejpam-4316	339	30	,	,	PUNCT
ejpam-4316	339	31	2	2	NUM
ejpam-4316	339	32	,	,	PUNCT
ejpam-4316	339	33	.	.	PUNCT
ejpam-4316	339	34	.	.	PUNCT
ejpam-4316	340	1	.	.	PUNCT
ejpam-4316	341	1	,	,	PUNCT
ejpam-4316	342	1	n	n	CCONJ
ejpam-4316	342	2	−	−	PROPN
ejpam-4316	342	3	1	1	NUM
ejpam-4316	342	4	]	]	PUNCT
ejpam-4316	342	5	.	.	PUNCT
ejpam-4316	343	1	from	from	ADP
ejpam-4316	343	2	this	this	PRON
ejpam-4316	343	3	,	,	PUNCT
ejpam-4316	343	4	we	we	PRON
ejpam-4316	343	5	can	can	AUX
ejpam-4316	343	6	now	now	ADV
ejpam-4316	343	7	compute	compute	VERB
ejpam-4316	343	8	the	the	DET
ejpam-4316	343	9	wiener	wiener	NOUN
ejpam-4316	343	10	index	index	NOUN
ejpam-4316	343	11	of	of	ADP
ejpam-4316	343	12	γ(pn	γ(pn	NOUN
ejpam-4316	343	13	,	,	PUNCT
ejpam-4316	343	14	s	s	NOUN
ejpam-4316	343	15	)	)	PUNCT
ejpam-4316	343	16	as	as	SCONJ
ejpam-4316	343	17	follows	follow	VERB
ejpam-4316	343	18	w	w	PROPN
ejpam-4316	343	19	(	(	PUNCT
ejpam-4316	343	20	γ	γ	NOUN
ejpam-4316	343	21	)	)	PUNCT
ejpam-4316	343	22	=	=	SYM
ejpam-4316	344	1	w	w	PROPN
ejpam-4316	344	2	(	(	PUNCT
ejpam-4316	344	3	pn	pn	NOUN
ejpam-4316	344	4	)	)	PUNCT
ejpam-4316	344	5	+	+	CCONJ
ejpam-4316	344	6	2	2	NUM
ejpam-4316	344	7	+	+	NUM
ejpam-4316	344	8	n−1∑	n−1∑	NUM
ejpam-4316	344	9	i=1	i=1	PROPN
ejpam-4316	345	1	i	i	NOUN
ejpam-4316	345	2	=	=	PUNCT
ejpam-4316	345	3	n(n2	n(n2	NOUN
ejpam-4316	345	4	−	−	PROPN
ejpam-4316	345	5	1	1	NUM
ejpam-4316	345	6	)	)	PUNCT
ejpam-4316	345	7	6	6	NUM
ejpam-4316	346	1	+	+	SYM
ejpam-4316	346	2	2	2	NUM
ejpam-4316	346	3	+	+	NUM
ejpam-4316	346	4	n(n−	n(n−	NOUN
ejpam-4316	346	5	1	1	NUM
ejpam-4316	346	6	)	)	PUNCT
ejpam-4316	346	7	2	2	NUM
ejpam-4316	346	8	=	=	SYM
ejpam-4316	346	9	n3	n3	NOUN
ejpam-4316	346	10	+	+	CCONJ
ejpam-4316	346	11	3n2	3n2	NUM
ejpam-4316	346	12	−	−	NOUN
ejpam-4316	346	13	4n+	4n+	NUM
ejpam-4316	346	14	12	12	NUM
ejpam-4316	346	15	6	6	NUM
ejpam-4316	346	16	.	.	PUNCT
ejpam-4316	347	1	moreover	moreover	ADV
ejpam-4316	347	2	,	,	PUNCT
ejpam-4316	347	3	suppose	suppose	VERB
ejpam-4316	347	4	s	s	VERB
ejpam-4316	347	5	=	=	X
ejpam-4316	347	6	{	{	PUNCT
ejpam-4316	347	7	xi	xi	ADP
ejpam-4316	347	8	}	}	PUNCT
ejpam-4316	347	9	where	where	SCONJ
ejpam-4316	347	10	2	2	NUM
ejpam-4316	347	11	≤	≤	NUM
ejpam-4316	347	12	i	i	PRON
ejpam-4316	347	13	≤	≤	NOUN
ejpam-4316	347	14	n	n	CCONJ
ejpam-4316	347	15	−	−	PROPN
ejpam-4316	347	16	1	1	NUM
ejpam-4316	347	17	.	.	PUNCT
ejpam-4316	348	1	now	now	ADV
ejpam-4316	348	2	,	,	PUNCT
ejpam-4316	348	3	we	we	PRON
ejpam-4316	348	4	consider	consider	VERB
ejpam-4316	348	5	the	the	DET
ejpam-4316	348	6	ordering	ordering	NOUN
ejpam-4316	348	7	of	of	ADP
ejpam-4316	348	8	the	the	DET
ejpam-4316	348	9	vertices	vertex	NOUN
ejpam-4316	348	10	x1	x1	PROPN
ejpam-4316	348	11	,	,	PUNCT
ejpam-4316	348	12	x2	x2	PROPN
ejpam-4316	348	13	,	,	PUNCT
ejpam-4316	348	14	.	.	PUNCT
ejpam-4316	348	15	.	.	PUNCT
ejpam-4316	349	1	.	.	PUNCT
ejpam-4316	350	1	,	,	PUNCT
ejpam-4316	350	2	xn	xn	PROPN
ejpam-4316	350	3	,	,	PUNCT
ejpam-4316	350	4	x	x	NOUN
ejpam-4316	350	5	′	′	NUM
ejpam-4316	351	1	i	i	PRON
ejpam-4316	351	2	of	of	ADP
ejpam-4316	351	3	γ	γ	PROPN
ejpam-4316	351	4	.	.	PUNCT
ejpam-4316	352	1	so	so	ADV
ejpam-4316	352	2	,	,	PUNCT
ejpam-4316	352	3	the	the	DET
ejpam-4316	352	4	distance	distance	NOUN
ejpam-4316	352	5	matrix	matrix	NOUN
ejpam-4316	352	6	of	of	ADP
ejpam-4316	352	7	the	the	DET
ejpam-4316	352	8	graph	graph	NOUN
ejpam-4316	352	9	γ(pn	γ(pn	NOUN
ejpam-4316	352	10	,	,	PUNCT
ejpam-4316	352	11	s	s	PART
ejpam-4316	352	12	)	)	PUNCT
ejpam-4316	352	13	is	be	AUX
ejpam-4316	352	14	given	give	VERB
ejpam-4316	352	15	by	by	ADP
ejpam-4316	352	16	d(γ	d(γ	NOUN
ejpam-4316	352	17	)	)	PUNCT
ejpam-4316	352	18	=	=	PUNCT
ejpam-4316	352	19	[	[	PUNCT
ejpam-4316	352	20	d(pn	d(pn	PROPN
ejpam-4316	352	21	)	)	PUNCT
ejpam-4316	352	22	a	a	PRON
ejpam-4316	352	23	at	at	ADP
ejpam-4316	352	24	0	0	NUM
ejpam-4316	352	25	]	]	PUNCT
ejpam-4316	352	26	where	where	SCONJ
ejpam-4316	352	27	d(pn	d(pn	NOUN
ejpam-4316	352	28	)	)	PUNCT
ejpam-4316	352	29	is	be	AUX
ejpam-4316	352	30	the	the	DET
ejpam-4316	352	31	distance	distance	NOUN
ejpam-4316	352	32	matrix	matrix	NOUN
ejpam-4316	352	33	of	of	ADP
ejpam-4316	352	34	pn	pn	PROPN
ejpam-4316	352	35	and	and	CCONJ
ejpam-4316	352	36	at	at	ADP
ejpam-4316	352	37	is	be	AUX
ejpam-4316	352	38	the	the	DET
ejpam-4316	352	39	1×n	1×n	NUM
ejpam-4316	352	40	matrix	matrix	NOUN
ejpam-4316	352	41	[	[	X
ejpam-4316	352	42	i−1	i−1	PROPN
ejpam-4316	352	43	,	,	PUNCT
ejpam-4316	352	44	i−2	i−2	PROPN
ejpam-4316	352	45	,	,	PUNCT
ejpam-4316	352	46	.	.	PUNCT
ejpam-4316	352	47	.	.	PUNCT
ejpam-4316	352	48	.	.	PUNCT
ejpam-4316	353	1	,	,	PUNCT
ejpam-4316	353	2	2	2	NUM
ejpam-4316	353	3	,	,	PUNCT
ejpam-4316	353	4	1	1	NUM
ejpam-4316	353	5	,	,	PUNCT
ejpam-4316	353	6	2	2	NUM
ejpam-4316	353	7	,	,	PUNCT
ejpam-4316	353	8	.	.	PUNCT
ejpam-4316	353	9	.	.	PUNCT
ejpam-4316	353	10	.	.	PUNCT
ejpam-4316	354	1	,	,	PUNCT
ejpam-4316	354	2	n−	n−	NOUN
ejpam-4316	354	3	i	i	PRON
ejpam-4316	354	4	]	]	X
ejpam-4316	354	5	.	.	PUNCT
ejpam-4316	355	1	from	from	ADP
ejpam-4316	355	2	this	this	PRON
ejpam-4316	355	3	,	,	PUNCT
ejpam-4316	355	4	we	we	PRON
ejpam-4316	355	5	now	now	ADV
ejpam-4316	355	6	have	have	VERB
ejpam-4316	355	7	w	w	PROPN
ejpam-4316	355	8	(	(	PUNCT
ejpam-4316	355	9	γ	γ	NOUN
ejpam-4316	355	10	)	)	PUNCT
ejpam-4316	355	11	=	=	SYM
ejpam-4316	355	12	w	w	PROPN
ejpam-4316	355	13	(	(	PUNCT
ejpam-4316	355	14	pn	pn	NOUN
ejpam-4316	355	15	)	)	PUNCT
ejpam-4316	355	16	+	+	CCONJ
ejpam-4316	355	17	2	2	NUM
ejpam-4316	355	18	+	+	NUM
ejpam-4316	355	19	i−1∑	i−1∑	NOUN
ejpam-4316	355	20	j=1	j=1	PROPN
ejpam-4316	355	21	j	j	PROPN
ejpam-4316	356	1	+	+	CCONJ
ejpam-4316	356	2	n−1∑	n−1∑	PROPN
ejpam-4316	356	3	j=1	j=1	ADJ
ejpam-4316	356	4	j	j	PROPN
ejpam-4316	357	1	=	=	SYM
ejpam-4316	357	2	w	w	PROPN
ejpam-4316	357	3	(	(	PUNCT
ejpam-4316	357	4	pn	pn	NOUN
ejpam-4316	357	5	)	)	PUNCT
ejpam-4316	357	6	+	+	CCONJ
ejpam-4316	357	7	2	2	NUM
ejpam-4316	357	8	+	+	NUM
ejpam-4316	357	9	i2	i2	NOUN
ejpam-4316	357	10	−	−	NOUN
ejpam-4316	357	11	1	1	NUM
ejpam-4316	357	12	2	2	NUM
ejpam-4316	357	13	+	+	CCONJ
ejpam-4316	357	14	n2	n2	ADJ
ejpam-4316	357	15	+	+	CCONJ
ejpam-4316	357	16	i2	i2	PROPN
ejpam-4316	357	17	−	−	PROPN
ejpam-4316	357	18	2in+	2in+	NUM
ejpam-4316	357	19	n−	n−	PROPN
ejpam-4316	357	20	i	i	NOUN
ejpam-4316	357	21	2	2	NUM
ejpam-4316	357	22	=	=	NOUN
ejpam-4316	357	23	n(n2	n(n2	NOUN
ejpam-4316	357	24	−	−	NOUN
ejpam-4316	357	25	1	1	NUM
ejpam-4316	357	26	)	)	PUNCT
ejpam-4316	357	27	6	6	NUM
ejpam-4316	357	28	+	+	SYM
ejpam-4316	357	29	2	2	NUM
ejpam-4316	357	30	+	+	NUM
ejpam-4316	357	31	i2	i2	NOUN
ejpam-4316	357	32	−	−	NOUN
ejpam-4316	357	33	1	1	NUM
ejpam-4316	357	34	2	2	NUM
ejpam-4316	357	35	+	+	CCONJ
ejpam-4316	357	36	n2	n2	ADJ
ejpam-4316	357	37	+	+	CCONJ
ejpam-4316	357	38	i2	i2	PROPN
ejpam-4316	357	39	−	−	PROPN
ejpam-4316	357	40	2in+	2in+	NUM
ejpam-4316	357	41	n−	n−	PROPN
ejpam-4316	357	42	i	i	NOUN
ejpam-4316	357	43	2	2	X
ejpam-4316	357	44	=	=	SYM
ejpam-4316	357	45	n3	n3	NOUN
ejpam-4316	357	46	+	+	CCONJ
ejpam-4316	357	47	3n2	3n2	NUM
ejpam-4316	357	48	+	+	NUM
ejpam-4316	357	49	2n+	2n+	NUM
ejpam-4316	357	50	6i2	6i2	NUM
ejpam-4316	357	51	−	−	NUM
ejpam-4316	357	52	6in−	6in−	NUM
ejpam-4316	357	53	6i+	6i+	NUM
ejpam-4316	357	54	12	12	NUM
ejpam-4316	357	55	6	6	NUM
ejpam-4316	357	56	.	.	PUNCT
ejpam-4316	358	1	theorem	theorem	VERB
ejpam-4316	358	2	13	13	NUM
ejpam-4316	358	3	.	.	PUNCT
ejpam-4316	359	1	let	let	VERB
ejpam-4316	359	2	g	g	NOUN
ejpam-4316	359	3	be	be	AUX
ejpam-4316	359	4	the	the	DET
ejpam-4316	359	5	complete	complete	ADJ
ejpam-4316	359	6	bipartite	bipartite	PROPN
ejpam-4316	359	7	graph	graph	NOUN
ejpam-4316	359	8	km	km	PROPN
ejpam-4316	359	9	,	,	PUNCT
ejpam-4316	359	10	n	n	CCONJ
ejpam-4316	359	11	with	with	ADP
ejpam-4316	359	12	vertex	vertex	NOUN
ejpam-4316	359	13	partition	partition	NOUN
ejpam-4316	359	14	v	v	NOUN
ejpam-4316	359	15	=	=	X
ejpam-4316	359	16	v1∪v2	v1∪v2	ADP
ejpam-4316	359	17	such	such	ADJ
ejpam-4316	359	18	that	that	DET
ejpam-4316	359	19	|v1|	|v1|	NOUN
ejpam-4316	359	20	=	=	NOUN
ejpam-4316	359	21	m	m	NOUN
ejpam-4316	359	22	and	and	CCONJ
ejpam-4316	359	23	|v2|	|v2|	NOUN
ejpam-4316	359	24	=	=	SYM
ejpam-4316	359	25	n	n	PROPN
ejpam-4316	359	26	and	and	CCONJ
ejpam-4316	359	27	s	s	X
ejpam-4316	359	28	⊂	⊂	PROPN
ejpam-4316	359	29	vk	vk	PROPN
ejpam-4316	359	30	.	.	PUNCT
ejpam-4316	360	1	then	then	ADV
ejpam-4316	360	2	the	the	DET
ejpam-4316	360	3	wiener	wiener	NOUN
ejpam-4316	360	4	index	index	NOUN
ejpam-4316	360	5	of	of	ADP
ejpam-4316	360	6	γ	γ	PROPN
ejpam-4316	360	7	=	=	SYM
ejpam-4316	360	8	γ(km	γ(km	PROPN
ejpam-4316	360	9	,	,	PUNCT
ejpam-4316	360	10	n	n	CCONJ
ejpam-4316	360	11	,	,	PUNCT
ejpam-4316	360	12	s	s	AUX
ejpam-4316	360	13	)	)	PUNCT
ejpam-4316	360	14	is	be	AUX
ejpam-4316	360	15	given	give	VERB
ejpam-4316	360	16	by	by	ADP
ejpam-4316	360	17	w	w	PROPN
ejpam-4316	360	18	(	(	PUNCT
ejpam-4316	360	19	γ	γ	NOUN
ejpam-4316	360	20	)	)	PUNCT
ejpam-4316	360	21	=	=	PROPN
ejpam-4316	360	22	m2	m2	PROPN
ejpam-4316	360	23	+	+	CCONJ
ejpam-4316	360	24	n2	n2	PROPN
ejpam-4316	360	25	+	+	CCONJ
ejpam-4316	360	26	i2	i2	PROPN
ejpam-4316	360	27	+	+	CCONJ
ejpam-4316	360	28	j2	j2	PROPN
ejpam-4316	360	29	−m−	−m−	PROPN
ejpam-4316	360	30	n−	n−	PROPN
ejpam-4316	360	31	i−	i−	PROPN
ejpam-4316	360	32	j	j	PROPN
ejpam-4316	361	1	+	+	PROPN
ejpam-4316	361	2	mn+	mn+	NOUN
ejpam-4316	361	3	ni+mj	ni+mj	ADP
ejpam-4316	361	4	+	+	NOUN
ejpam-4316	361	5	2mi+	2mi+	NUM
ejpam-4316	361	6	2nj	2nj	NOUN
ejpam-4316	362	1	+	+	X
ejpam-4316	362	2	3ij	3ij	ADJ
ejpam-4316	362	3	where	where	SCONJ
ejpam-4316	362	4	|s	|s	PROPN
ejpam-4316	362	5	∩	∩	NOUN
ejpam-4316	362	6	v1|	v1|	NOUN
ejpam-4316	363	1	=	=	PUNCT
ejpam-4316	363	2	i	i	PROPN
ejpam-4316	363	3	and	and	CCONJ
ejpam-4316	363	4	|s	|s	PROPN
ejpam-4316	363	5	∩	∩	ADJ
ejpam-4316	363	6	v2|	v2|	X
ejpam-4316	363	7	=	=	SYM
ejpam-4316	363	8	j.	j.	PROPN
ejpam-4316	363	9	f.j.h	f.j.h	PROPN
ejpam-4316	363	10	.	.	PUNCT
ejpam-4316	364	1	campeña	campeña	PROPN
ejpam-4316	364	2	,	,	PUNCT
ejpam-4316	364	3	m.c.g	m.c.g	PROPN
ejpam-4316	364	4	.	.	PUNCT
ejpam-4316	364	5	egan	egan	PROPN
ejpam-4316	364	6	,	,	PUNCT
ejpam-4316	364	7	j.r.m	j.r.m	PROPN
ejpam-4316	364	8	.	.	PUNCT
ejpam-4316	365	1	antalan	antalan	PROPN
ejpam-4316	365	2	/	/	SYM
ejpam-4316	365	3	eur	eur	PROPN
ejpam-4316	365	4	.	.	PUNCT
ejpam-4316	366	1	j.	j.	PROPN
ejpam-4316	366	2	pure	pure	PROPN
ejpam-4316	366	3	appl	appl	PROPN
ejpam-4316	366	4	.	.	PROPN
ejpam-4316	366	5	math	math	PROPN
ejpam-4316	366	6	,	,	PUNCT
ejpam-4316	366	7	15	15	NUM
ejpam-4316	366	8	(	(	PUNCT
ejpam-4316	366	9	2	2	NUM
ejpam-4316	366	10	)	)	PUNCT
ejpam-4316	366	11	(	(	PUNCT
ejpam-4316	366	12	2022	2022	NUM
ejpam-4316	366	13	)	)	PUNCT
ejpam-4316	366	14	,	,	PUNCT
ejpam-4316	366	15	602	602	NUM
ejpam-4316	366	16	-	-	SYM
ejpam-4316	366	17	619	619	NUM
ejpam-4316	366	18	613	613	NUM
ejpam-4316	366	19	proof	proof	NOUN
ejpam-4316	366	20	.	.	PUNCT
ejpam-4316	367	1	let	let	VERB
ejpam-4316	367	2	v	v	VERB
ejpam-4316	367	3	=	=	SYM
ejpam-4316	367	4	{	{	PUNCT
ejpam-4316	367	5	x1	x1	PROPN
ejpam-4316	367	6	,	,	PUNCT
ejpam-4316	367	7	x2	x2	PROPN
ejpam-4316	367	8	,	,	PUNCT
ejpam-4316	367	9	.	.	PUNCT
ejpam-4316	367	10	.	.	PUNCT
ejpam-4316	368	1	.	.	PUNCT
ejpam-4316	369	1	,	,	PUNCT
ejpam-4316	369	2	xm	xm	PROPN
ejpam-4316	369	3	,	,	PUNCT
ejpam-4316	369	4	y1	y1	PROPN
ejpam-4316	369	5	,	,	PUNCT
ejpam-4316	369	6	y2	y2	PROPN
ejpam-4316	369	7	,	,	PUNCT
ejpam-4316	369	8	.	.	PUNCT
ejpam-4316	369	9	.	.	PUNCT
ejpam-4316	369	10	.	.	PUNCT
ejpam-4316	370	1	,	,	PUNCT
ejpam-4316	370	2	yn	yn	PRON
ejpam-4316	370	3	}	}	PUNCT
ejpam-4316	370	4	be	be	VERB
ejpam-4316	370	5	the	the	DET
ejpam-4316	370	6	vertex	vertex	NOUN
ejpam-4316	370	7	set	set	NOUN
ejpam-4316	370	8	of	of	ADP
ejpam-4316	370	9	km	km	PROPN
ejpam-4316	370	10	,	,	PUNCT
ejpam-4316	370	11	n.	n.	NOUN
ejpam-4316	370	12	without	without	ADP
ejpam-4316	370	13	loss	loss	NOUN
ejpam-4316	370	14	of	of	ADP
ejpam-4316	370	15	generality	generality	NOUN
ejpam-4316	370	16	,	,	PUNCT
ejpam-4316	370	17	suppose	suppose	VERB
ejpam-4316	370	18	s	s	VERB
ejpam-4316	370	19	=	=	PUNCT
ejpam-4316	370	20	{	{	PUNCT
ejpam-4316	370	21	x1	x1	PROPN
ejpam-4316	370	22	,	,	PUNCT
ejpam-4316	370	23	x2	x2	PROPN
ejpam-4316	370	24	,	,	PUNCT
ejpam-4316	370	25	.	.	PUNCT
ejpam-4316	370	26	.	.	PUNCT
ejpam-4316	371	1	.	.	PUNCT
ejpam-4316	372	1	,	,	PUNCT
ejpam-4316	372	2	xi	xi	PROPN
ejpam-4316	372	3	,	,	PUNCT
ejpam-4316	372	4	y1	y1	PROPN
ejpam-4316	372	5	,	,	PUNCT
ejpam-4316	372	6	y2	y2	PROPN
ejpam-4316	372	7	,	,	PUNCT
ejpam-4316	372	8	.	.	PUNCT
ejpam-4316	372	9	.	.	PUNCT
ejpam-4316	373	1	.	.	PUNCT
ejpam-4316	374	1	,	,	PUNCT
ejpam-4316	374	2	yj	yj	PROPN
ejpam-4316	374	3	}	}	PUNCT
ejpam-4316	374	4	.	.	PUNCT
ejpam-4316	375	1	now	now	ADV
ejpam-4316	375	2	,	,	PUNCT
ejpam-4316	375	3	consider	consider	VERB
ejpam-4316	375	4	the	the	DET
ejpam-4316	375	5	vertex	vertex	NOUN
ejpam-4316	375	6	set	set	NOUN
ejpam-4316	375	7	of	of	ADP
ejpam-4316	375	8	γ	γ	PROPN
ejpam-4316	375	9	=	=	SYM
ejpam-4316	375	10	γ(km	γ(km	PROPN
ejpam-4316	375	11	,	,	PUNCT
ejpam-4316	375	12	n	n	CCONJ
ejpam-4316	375	13	,	,	PUNCT
ejpam-4316	375	14	s	s	X
ejpam-4316	375	15	)	)	PUNCT
ejpam-4316	375	16	say	say	INTJ
ejpam-4316	375	17	,	,	PUNCT
ejpam-4316	375	18	{	{	PUNCT
ejpam-4316	375	19	x1	x1	PROPN
ejpam-4316	375	20	,	,	PUNCT
ejpam-4316	375	21	.	.	PUNCT
ejpam-4316	375	22	.	.	PUNCT
ejpam-4316	376	1	.	.	PUNCT
ejpam-4316	377	1	,	,	PUNCT
ejpam-4316	377	2	xm	xm	PROPN
ejpam-4316	377	3	,	,	PUNCT
ejpam-4316	377	4	y1	y1	PROPN
ejpam-4316	377	5	,	,	PUNCT
ejpam-4316	377	6	.	.	PUNCT
ejpam-4316	377	7	.	.	PUNCT
ejpam-4316	378	1	.	.	PUNCT
ejpam-4316	379	1	,	,	PUNCT
ejpam-4316	379	2	yn	yn	INTJ
ejpam-4316	379	3	,	,	PUNCT
ejpam-4316	379	4	x	x	NOUN
ejpam-4316	379	5	′	′	NUM
ejpam-4316	379	6	1	1	NUM
ejpam-4316	379	7	,	,	PUNCT
ejpam-4316	379	8	.	.	PUNCT
ejpam-4316	379	9	.	.	PUNCT
ejpam-4316	379	10	.	.	PUNCT
ejpam-4316	380	1	,	,	PUNCT
ejpam-4316	380	2	x	x	X
ejpam-4316	381	1	′	′	NUM
ejpam-4316	381	2	i	i	PRON
ejpam-4316	381	3	,	,	PUNCT
ejpam-4316	381	4	y	y	PROPN
ejpam-4316	381	5	′	′	NUM
ejpam-4316	381	6	1	1	NUM
ejpam-4316	381	7	,	,	PUNCT
ejpam-4316	381	8	.	.	PUNCT
ejpam-4316	381	9	.	.	PUNCT
ejpam-4316	381	10	.	.	PUNCT
ejpam-4316	382	1	,	,	PUNCT
ejpam-4316	382	2	y	y	PROPN
ejpam-4316	382	3	′	′	NUM
ejpam-4316	382	4	j	j	NOUN
ejpam-4316	382	5	}	}	PUNCT
ejpam-4316	382	6	.	.	PUNCT
ejpam-4316	383	1	the	the	DET
ejpam-4316	383	2	distance	distance	NOUN
ejpam-4316	383	3	matrix	matrix	NOUN
ejpam-4316	383	4	for	for	ADP
ejpam-4316	383	5	the	the	DET
ejpam-4316	383	6	s	s	NOUN
ejpam-4316	383	7	-	-	PUNCT
ejpam-4316	383	8	splitting	splitting	NOUN
ejpam-4316	383	9	of	of	ADP
ejpam-4316	383	10	km	km	PROPN
ejpam-4316	383	11	,	,	PUNCT
ejpam-4316	383	12	n	n	PRON
ejpam-4316	383	13	can	can	AUX
ejpam-4316	383	14	be	be	AUX
ejpam-4316	383	15	written	write	VERB
ejpam-4316	383	16	as	as	ADP
ejpam-4316	383	17	d(γ	d(γ	PROPN
ejpam-4316	383	18	)	)	PUNCT
ejpam-4316	383	19	=	=	SYM
ejpam-4316	383	20			NOUN
ejpam-4316	383	21	2jm	2jm	NOUN
ejpam-4316	383	22	−	−	NOUN
ejpam-4316	383	23	2im	2im	ADJ
ejpam-4316	383	24	jm×n	jm×n	PROPN
ejpam-4316	383	25	2jm×i	2jm×i	NUM
ejpam-4316	383	26	jm×j	jm×j	ADJ
ejpam-4316	383	27	jn×m	jn×m	NOUN
ejpam-4316	383	28	2jn	2jn	NOUN
ejpam-4316	383	29	−	−	PROPN
ejpam-4316	383	30	2	2	NUM
ejpam-4316	383	31	in	in	ADP
ejpam-4316	383	32	jn×i	jn×i	ADJ
ejpam-4316	383	33	2jn×j	2jn×j	NUM
ejpam-4316	383	34	2ji×m	2ji×m	PROPN
ejpam-4316	383	35	ji×n	ji×n	PROPN
ejpam-4316	383	36	2ji	2ji	NOUN
ejpam-4316	384	1	−	−	PROPN
ejpam-4316	384	2	2ii	2ii	ADJ
ejpam-4316	384	3	3ji×j	3ji×j	PROPN
ejpam-4316	384	4	jj×m	jj×m	NOUN
ejpam-4316	384	5	2jj×n	2jj×n	NOUN
ejpam-4316	384	6	3jj×i	3jj×i	NUM
ejpam-4316	384	7	2jj	2jj	NOUN
ejpam-4316	384	8	−	−	NOUN
ejpam-4316	384	9	2ij	2ij	ADJ
ejpam-4316	384	10			NOUN
ejpam-4316	384	11	notice	notice	NOUN
ejpam-4316	384	12	that	that	SCONJ
ejpam-4316	384	13	from	from	ADP
ejpam-4316	384	14	the	the	DET
ejpam-4316	384	15	distance	distance	NOUN
ejpam-4316	384	16	matrix	matrix	NOUN
ejpam-4316	384	17	,	,	PUNCT
ejpam-4316	384	18	the	the	DET
ejpam-4316	384	19	wiener	wiener	NOUN
ejpam-4316	384	20	index	index	NOUN
ejpam-4316	384	21	of	of	ADP
ejpam-4316	384	22	γ	γ	PROPN
ejpam-4316	384	23	is	be	AUX
ejpam-4316	384	24	the	the	DET
ejpam-4316	384	25	sum	sum	NOUN
ejpam-4316	384	26	of	of	ADP
ejpam-4316	384	27	∑	∑	PROPN
ejpam-4316	384	28	jm	jm	PROPN
ejpam-4316	384	29	−	−	PROPN
ejpam-4316	384	30	im,∑	im,∑	PRON
ejpam-4316	384	31	jn	jn	PROPN
ejpam-4316	384	32	−	−	PROPN
ejpam-4316	384	33	in	in	ADP
ejpam-4316	384	34	,	,	PUNCT
ejpam-4316	384	35	∑	∑	PROPN
ejpam-4316	384	36	ji	ji	PROPN
ejpam-4316	384	37	−	−	PROPN
ejpam-4316	384	38	ii	ii	PROPN
ejpam-4316	384	39	,	,	PUNCT
ejpam-4316	384	40	∑	∑	PROPN
ejpam-4316	384	41	jj	jj	PROPN
ejpam-4316	384	42	−	−	PROPN
ejpam-4316	384	43	ij	ij	INTJ
ejpam-4316	384	44	,	,	PUNCT
ejpam-4316	384	45	∑	∑	ADV
ejpam-4316	384	46	jm×n	jm×n	PROPN
ejpam-4316	384	47	,	,	PUNCT
ejpam-4316	384	48	∑	∑	ADV
ejpam-4316	384	49	jn×i	jn×i	ADJ
ejpam-4316	384	50	,	,	PUNCT
ejpam-4316	384	51	∑	∑	ADV
ejpam-4316	384	52	jm×j	jm×j	PROPN
ejpam-4316	384	53	,	,	PUNCT
ejpam-4316	384	54	3	3	NUM
ejpam-4316	384	55	∑	∑	PROPN
ejpam-4316	384	56	ji×j	ji×j	PROPN
ejpam-4316	384	57	,	,	PUNCT
ejpam-4316	384	58	2	2	NUM
ejpam-4316	384	59	∑	∑	PROPN
ejpam-4316	384	60	jm×i	jm×i	PROPN
ejpam-4316	384	61	,	,	PUNCT
ejpam-4316	384	62	and	and	CCONJ
ejpam-4316	384	63	2	2	NUM
ejpam-4316	384	64	∑	∑	ADV
ejpam-4316	384	65	jn×j	jn×j	PROPN
ejpam-4316	384	66	.	.	PUNCT
ejpam-4316	385	1	thus	thus	ADV
ejpam-4316	385	2	,	,	PUNCT
ejpam-4316	385	3	the	the	DET
ejpam-4316	385	4	result	result	NOUN
ejpam-4316	385	5	follows	follow	VERB
ejpam-4316	385	6	.	.	PUNCT
ejpam-4316	386	1	3.3	3.3	NUM
ejpam-4316	386	2	.	.	PUNCT
ejpam-4316	387	1	harary	harary	PROPN
ejpam-4316	387	2	index	index	NOUN
ejpam-4316	387	3	of	of	ADP
ejpam-4316	387	4	γ(g	γ(g	PROPN
ejpam-4316	387	5	,	,	PUNCT
ejpam-4316	387	6	v	v	NOUN
ejpam-4316	387	7	)	)	PUNCT
ejpam-4316	387	8	another	another	DET
ejpam-4316	387	9	well	well	ADV
ejpam-4316	387	10	-	-	PUNCT
ejpam-4316	387	11	known	know	VERB
ejpam-4316	387	12	topological	topological	ADJ
ejpam-4316	387	13	index	index	NOUN
ejpam-4316	387	14	of	of	ADP
ejpam-4316	387	15	a	a	DET
ejpam-4316	387	16	graph	graph	NOUN
ejpam-4316	387	17	studied	study	VERB
ejpam-4316	387	18	by	by	ADP
ejpam-4316	387	19	plavšić	plavšić	PROPN
ejpam-4316	387	20	et	et	PROPN
ejpam-4316	387	21	al	al	PROPN
ejpam-4316	387	22	.	.	PUNCT
ejpam-4316	388	1	[	[	X
ejpam-4316	388	2	17	17	NUM
ejpam-4316	388	3	]	]	PUNCT
ejpam-4316	388	4	and	and	CCONJ
ejpam-4316	388	5	by	by	ADP
ejpam-4316	388	6	ivanciuc	ivanciuc	PROPN
ejpam-4316	388	7	et	et	PROPN
ejpam-4316	388	8	al	al	PROPN
ejpam-4316	388	9	.	.	PUNCT
ejpam-4316	389	1	[	[	X
ejpam-4316	389	2	11	11	NUM
ejpam-4316	389	3	]	]	PUNCT
ejpam-4316	389	4	is	be	AUX
ejpam-4316	389	5	hararay	hararay	ADJ
ejpam-4316	389	6	index	index	NOUN
ejpam-4316	389	7	.	.	PUNCT
ejpam-4316	390	1	we	we	PRON
ejpam-4316	390	2	recall	recall	VERB
ejpam-4316	390	3	the	the	DET
ejpam-4316	390	4	harary	harary	PROPN
ejpam-4316	390	5	index	index	NOUN
ejpam-4316	390	6	of	of	ADP
ejpam-4316	390	7	the	the	DET
ejpam-4316	390	8	graph	graph	NOUN
ejpam-4316	390	9	g	g	NOUN
ejpam-4316	390	10	and	and	CCONJ
ejpam-4316	390	11	is	be	AUX
ejpam-4316	390	12	defined	define	VERB
ejpam-4316	390	13	as	as	SCONJ
ejpam-4316	390	14	follows	follow	VERB
ejpam-4316	390	15	.	.	PUNCT
ejpam-4316	391	1	h(g	h(g	NOUN
ejpam-4316	391	2	)	)	PUNCT
ejpam-4316	392	1	=	=	PUNCT
ejpam-4316	392	2	∑	∑	PUNCT
ejpam-4316	392	3	{	{	PUNCT
ejpam-4316	392	4	vi	vi	PROPN
ejpam-4316	392	5	,	,	PUNCT
ejpam-4316	392	6	vj}⊆v	vj}⊆v	NOUN
ejpam-4316	392	7	(	(	PUNCT
ejpam-4316	392	8	g	g	NOUN
ejpam-4316	392	9	)	)	PUNCT
ejpam-4316	392	10	1	1	NUM
ejpam-4316	392	11	dg(vi	dg(vi	NOUN
ejpam-4316	392	12	,	,	PUNCT
ejpam-4316	392	13	vj	vj	INTJ
ejpam-4316	392	14	)	)	PUNCT
ejpam-4316	392	15	=	=	SYM
ejpam-4316	392	16	1	1	NUM
ejpam-4316	392	17	2	2	NUM
ejpam-4316	392	18	n∑	n∑	NOUN
ejpam-4316	392	19	i=1	i=1	PROPN
ejpam-4316	392	20	n∑	n∑	PROPN
ejpam-4316	393	1	j=1	j=1	NOUN
ejpam-4316	393	2	1	1	NUM
ejpam-4316	393	3	dg(vi	dg(vi	NOUN
ejpam-4316	393	4	,	,	PUNCT
ejpam-4316	393	5	vj	vj	PROPN
ejpam-4316	393	6	)	)	PUNCT
ejpam-4316	393	7	.	.	PUNCT
ejpam-4316	394	1	the	the	DET
ejpam-4316	394	2	harary	harary	PROPN
ejpam-4316	394	3	index	index	NOUN
ejpam-4316	394	4	of	of	ADP
ejpam-4316	394	5	γ	γ	PROPN
ejpam-4316	394	6	=	=	SYM
ejpam-4316	394	7	γ(g	γ(g	PROPN
ejpam-4316	394	8	,	,	PUNCT
ejpam-4316	394	9	s	s	PART
ejpam-4316	394	10	)	)	PUNCT
ejpam-4316	394	11	can	can	AUX
ejpam-4316	394	12	be	be	AUX
ejpam-4316	394	13	computed	compute	VERB
ejpam-4316	394	14	using	use	VERB
ejpam-4316	394	15	the	the	DET
ejpam-4316	394	16	distance	distance	NOUN
ejpam-4316	394	17	matrix	matrix	NOUN
ejpam-4316	394	18	of	of	ADP
ejpam-4316	394	19	γ	γ	PRON
ejpam-4316	394	20	viewed	view	VERB
ejpam-4316	394	21	as	as	ADP
ejpam-4316	394	22	a	a	DET
ejpam-4316	394	23	block	block	NOUN
ejpam-4316	394	24	matrix	matrix	NOUN
ejpam-4316	394	25	similar	similar	ADJ
ejpam-4316	394	26	to	to	ADP
ejpam-4316	394	27	the	the	DET
ejpam-4316	394	28	computation	computation	NOUN
ejpam-4316	394	29	of	of	ADP
ejpam-4316	394	30	the	the	DET
ejpam-4316	394	31	wiener	wiener	NOUN
ejpam-4316	394	32	index	index	NOUN
ejpam-4316	394	33	of	of	ADP
ejpam-4316	394	34	γ	γ	PROPN
ejpam-4316	394	35	.	.	PUNCT
ejpam-4316	395	1	in	in	ADP
ejpam-4316	395	2	order	order	NOUN
ejpam-4316	395	3	to	to	PART
ejpam-4316	395	4	compute	compute	VERB
ejpam-4316	395	5	the	the	DET
ejpam-4316	395	6	harary	harary	PROPN
ejpam-4316	395	7	index	index	NOUN
ejpam-4316	395	8	of	of	ADP
ejpam-4316	395	9	the	the	DET
ejpam-4316	395	10	s	s	NOUN
ejpam-4316	395	11	-	-	PUNCT
ejpam-4316	395	12	splitting	splitting	NOUN
ejpam-4316	395	13	graph	graph	NOUN
ejpam-4316	395	14	of	of	ADP
ejpam-4316	395	15	g	g	NOUN
ejpam-4316	395	16	,	,	PUNCT
ejpam-4316	395	17	we	we	PRON
ejpam-4316	395	18	consider	consider	VERB
ejpam-4316	395	19	a	a	DET
ejpam-4316	395	20	matrix	matrix	NOUN
ejpam-4316	395	21	whose	whose	DET
ejpam-4316	395	22	entries	entry	NOUN
ejpam-4316	395	23	are	be	AUX
ejpam-4316	395	24	the	the	DET
ejpam-4316	395	25	reciprocals	reciprocal	NOUN
ejpam-4316	395	26	of	of	ADP
ejpam-4316	395	27	the	the	DET
ejpam-4316	395	28	nonzero	nonzero	ADJ
ejpam-4316	395	29	entries	entry	NOUN
ejpam-4316	395	30	of	of	ADP
ejpam-4316	395	31	its	its	PRON
ejpam-4316	395	32	distance	distance	NOUN
ejpam-4316	395	33	matrix	matrix	NOUN
ejpam-4316	395	34	.	.	PUNCT
ejpam-4316	396	1	for	for	ADP
ejpam-4316	396	2	any	any	DET
ejpam-4316	396	3	matrix	matrix	NOUN
ejpam-4316	396	4	a	a	PRON
ejpam-4316	396	5	,	,	PUNCT
ejpam-4316	396	6	we	we	PRON
ejpam-4316	396	7	let	let	VERB
ejpam-4316	396	8	a	a	PRON
ejpam-4316	396	9	be	be	AUX
ejpam-4316	396	10	the	the	DET
ejpam-4316	396	11	matrix	matrix	NOUN
ejpam-4316	396	12	whose	whose	DET
ejpam-4316	396	13	entries	entry	NOUN
ejpam-4316	396	14	are	be	AUX
ejpam-4316	396	15	the	the	DET
ejpam-4316	396	16	reciprocals	reciprocal	NOUN
ejpam-4316	396	17	of	of	ADP
ejpam-4316	396	18	the	the	DET
ejpam-4316	396	19	non	non	ADJ
ejpam-4316	396	20	zero	zero	NUM
ejpam-4316	396	21	entries	entry	NOUN
ejpam-4316	396	22	in	in	ADP
ejpam-4316	396	23	a	a	PRON
ejpam-4316	396	24	and	and	CCONJ
ejpam-4316	396	25	∑	∑	ADV
ejpam-4316	396	26	a	a	DET
ejpam-4316	396	27	be	be	AUX
ejpam-4316	396	28	the	the	DET
ejpam-4316	396	29	sum	sum	NOUN
ejpam-4316	396	30	of	of	ADP
ejpam-4316	396	31	the	the	DET
ejpam-4316	396	32	reciprocals	reciprocal	NOUN
ejpam-4316	396	33	of	of	ADP
ejpam-4316	396	34	the	the	DET
ejpam-4316	396	35	nonzero	nonzero	PROPN
ejpam-4316	396	36	entries	entry	NOUN
ejpam-4316	396	37	in	in	ADP
ejpam-4316	396	38	a	a	PRON
ejpam-4316	396	39	,	,	PUNCT
ejpam-4316	396	40	that	that	ADV
ejpam-4316	396	41	is	is	ADV
ejpam-4316	396	42	,	,	PUNCT
ejpam-4316	396	43	if	if	SCONJ
ejpam-4316	396	44	a	a	PRON
ejpam-4316	396	45	=	=	X
ejpam-4316	397	1	[	[	X
ejpam-4316	397	2	aij	aij	X
ejpam-4316	397	3	]	]	PUNCT
ejpam-4316	397	4	,	,	PUNCT
ejpam-4316	397	5	then	then	ADV
ejpam-4316	397	6	a	a	PRON
ejpam-4316	397	7	=	=	PUNCT
ejpam-4316	398	1	[	[	X
ejpam-4316	398	2	aij	aij	X
ejpam-4316	398	3	]	]	PUNCT
ejpam-4316	398	4	where	where	SCONJ
ejpam-4316	398	5	aij	aij	PROPN
ejpam-4316	398	6	=	=	SYM
ejpam-4316	398	7	1	1	NUM
ejpam-4316	398	8	aij	aij	PROPN
ejpam-4316	398	9	if	if	SCONJ
ejpam-4316	398	10	aij	aij	PROPN
ejpam-4316	398	11	6=	6=	SYM
ejpam-4316	398	12	0	0	NUM
ejpam-4316	398	13	and	and	CCONJ
ejpam-4316	398	14	0	0	NUM
ejpam-4316	398	15	otherwise	otherwise	ADV
ejpam-4316	398	16	.	.	PUNCT
ejpam-4316	399	1	if	if	SCONJ
ejpam-4316	399	2	the	the	DET
ejpam-4316	399	3	entries	entry	NOUN
ejpam-4316	399	4	in	in	ADP
ejpam-4316	399	5	a	a	DET
ejpam-4316	399	6	are	be	AUX
ejpam-4316	399	7	0	0	NUM
ejpam-4316	399	8	or	or	CCONJ
ejpam-4316	399	9	1	1	NUM
ejpam-4316	399	10	,	,	PUNCT
ejpam-4316	399	11	then	then	ADV
ejpam-4316	399	12	∑	∑	PUNCT
ejpam-4316	399	13	a	a	DET
ejpam-4316	399	14	=	=	X
ejpam-4316	399	15	∑	∑	PUNCT
ejpam-4316	399	16	a.	a.	NOUN
ejpam-4316	399	17	additionally	additionally	ADV
ejpam-4316	399	18	,	,	PUNCT
ejpam-4316	399	19	for	for	ADP
ejpam-4316	399	20	any	any	DET
ejpam-4316	399	21	nonzero	nonzero	NOUN
ejpam-4316	399	22	c	c	NOUN
ejpam-4316	399	23	,	,	PUNCT
ejpam-4316	399	24	we	we	PRON
ejpam-4316	399	25	have	have	VERB
ejpam-4316	399	26	∑	∑	PROPN
ejpam-4316	399	27	ca	ca	NOUN
ejpam-4316	399	28	=	=	SYM
ejpam-4316	399	29	c	c	X
ejpam-4316	399	30	∑	∑	PUNCT
ejpam-4316	399	31	a.	a.	NOUN
ejpam-4316	399	32	we	we	PRON
ejpam-4316	399	33	will	will	AUX
ejpam-4316	399	34	use	use	VERB
ejpam-4316	399	35	the	the	DET
ejpam-4316	399	36	following	follow	VERB
ejpam-4316	399	37	lemma	lemma	PROPN
ejpam-4316	399	38	in	in	ADP
ejpam-4316	399	39	order	order	NOUN
ejpam-4316	399	40	to	to	PART
ejpam-4316	399	41	compute	compute	VERB
ejpam-4316	399	42	for	for	ADP
ejpam-4316	399	43	the	the	DET
ejpam-4316	399	44	harary	harary	PROPN
ejpam-4316	399	45	index	index	NOUN
ejpam-4316	399	46	of	of	ADP
ejpam-4316	399	47	γ(g	γ(g	PROPN
ejpam-4316	399	48	,	,	PUNCT
ejpam-4316	399	49	s	s	PART
ejpam-4316	399	50	)	)	PUNCT
ejpam-4316	399	51	.	.	PUNCT
ejpam-4316	400	1	lemma	lemma	PROPN
ejpam-4316	400	2	5	5	X
ejpam-4316	400	3	.	.	PUNCT
ejpam-4316	401	1	let	let	VERB
ejpam-4316	401	2	a	a	PRON
ejpam-4316	401	3	=	=	PUNCT
ejpam-4316	402	1	[	[	X
ejpam-4316	402	2	aij	aij	X
ejpam-4316	402	3	]	]	X
ejpam-4316	402	4	,	,	PUNCT
ejpam-4316	402	5	b	b	X
ejpam-4316	402	6	=	=	PUNCT
ejpam-4316	403	1	[	[	X
ejpam-4316	403	2	bij	bij	NOUN
ejpam-4316	403	3	]	]	PUNCT
ejpam-4316	403	4	be	be	AUX
ejpam-4316	403	5	n×	n×	PROPN
ejpam-4316	403	6	n	n	PRON
ejpam-4316	403	7	square	square	ADJ
ejpam-4316	403	8	matrices	matrix	NOUN
ejpam-4316	403	9	with	with	ADP
ejpam-4316	403	10	real	real	ADJ
ejpam-4316	403	11	entries	entry	NOUN
ejpam-4316	403	12	such	such	ADJ
ejpam-4316	403	13	that	that	SCONJ
ejpam-4316	403	14	at	at	ADV
ejpam-4316	403	15	least	least	ADJ
ejpam-4316	403	16	one	one	NUM
ejpam-4316	403	17	of	of	ADP
ejpam-4316	403	18	aij	aij	PROPN
ejpam-4316	403	19	or	or	CCONJ
ejpam-4316	403	20	bij	bij	NOUN
ejpam-4316	403	21	is	be	AUX
ejpam-4316	403	22	zero	zero	NUM
ejpam-4316	403	23	for	for	ADP
ejpam-4316	403	24	all	all	PRON
ejpam-4316	403	25	0	0	NUM
ejpam-4316	403	26	≤	≤	NOUN
ejpam-4316	404	1	i	i	PRON
ejpam-4316	404	2	,	,	PUNCT
ejpam-4316	404	3	j	j	PROPN
ejpam-4316	404	4	≤	≤	PROPN
ejpam-4316	404	5	n	n	CCONJ
ejpam-4316	404	6	,	,	PUNCT
ejpam-4316	404	7	then∑	then∑	VERB
ejpam-4316	404	8	a+b	a+b	NUM
ejpam-4316	404	9	=	=	SYM
ejpam-4316	404	10	∑	∑	PUNCT
ejpam-4316	404	11	a+	a+	PUNCT
ejpam-4316	404	12	∑	∑	PROPN
ejpam-4316	404	13	b.	b.	PROPN
ejpam-4316	404	14	proposition	proposition	PROPN
ejpam-4316	404	15	1	1	NUM
ejpam-4316	404	16	.	.	PUNCT
ejpam-4316	405	1	let	let	VERB
ejpam-4316	405	2	d	d	X
ejpam-4316	405	3	,	,	PUNCT
ejpam-4316	405	4	a	a	DET
ejpam-4316	405	5	be	be	AUX
ejpam-4316	405	6	the	the	DET
ejpam-4316	405	7	distance	distance	NOUN
ejpam-4316	405	8	matrix	matrix	NOUN
ejpam-4316	405	9	and	and	CCONJ
ejpam-4316	405	10	adjacency	adjacency	NOUN
ejpam-4316	405	11	matrix	matrix	NOUN
ejpam-4316	405	12	of	of	ADP
ejpam-4316	405	13	a	a	DET
ejpam-4316	405	14	graph	graph	NOUN
ejpam-4316	405	15	g	g	NOUN
ejpam-4316	405	16	on	on	ADP
ejpam-4316	405	17	n	n	PRON
ejpam-4316	405	18	vertices	vertex	NOUN
ejpam-4316	406	1	and	and	CCONJ
ejpam-4316	406	2	i	i	PRON
ejpam-4316	406	3	be	be	VERB
ejpam-4316	406	4	the	the	DET
ejpam-4316	406	5	identity	identity	NOUN
ejpam-4316	406	6	matrix	matrix	NOUN
ejpam-4316	406	7	of	of	ADP
ejpam-4316	406	8	size	size	NOUN
ejpam-4316	406	9	n.	n.	PROPN
ejpam-4316	406	10	let	let	VERB
ejpam-4316	406	11	c	c	NOUN
ejpam-4316	406	12	any	any	DET
ejpam-4316	406	13	nonzero	nonzero	ADJ
ejpam-4316	406	14	real	real	ADJ
ejpam-4316	406	15	number	number	NOUN
ejpam-4316	406	16	.	.	PUNCT
ejpam-4316	407	1	(	(	PUNCT
ejpam-4316	407	2	i	i	NOUN
ejpam-4316	407	3	)	)	PUNCT
ejpam-4316	407	4	∑	∑	ADP
ejpam-4316	407	5	ca	ca	NOUN
ejpam-4316	407	6	=	=	SYM
ejpam-4316	407	7	1	1	NUM
ejpam-4316	407	8	c	c	X
ejpam-4316	407	9	∑	∑	PROPN
ejpam-4316	407	10	a	a	DET
ejpam-4316	407	11	(	(	PUNCT
ejpam-4316	407	12	ii	ii	NOUN
ejpam-4316	407	13	)	)	PUNCT
ejpam-4316	407	14	∑	∑	PUNCT
ejpam-4316	408	1	d	d	PROPN
ejpam-4316	409	1	+	+	X
ejpam-4316	409	2	ca	ca	NOUN
ejpam-4316	409	3	=	=	SYM
ejpam-4316	409	4	∑	∑	PUNCT
ejpam-4316	409	5	d	d	X
ejpam-4316	409	6	−a+	−a+	X
ejpam-4316	409	7	∑	∑	PUNCT
ejpam-4316	409	8	(	(	PUNCT
ejpam-4316	409	9	c+	c+	VERB
ejpam-4316	409	10	1)a	1)a	NUM
ejpam-4316	409	11	f.j.h	f.j.h	ADJ
ejpam-4316	409	12	.	.	PUNCT
ejpam-4316	410	1	campeña	campeña	NOUN
ejpam-4316	410	2	,	,	PUNCT
ejpam-4316	410	3	m.c.g	m.c.g	PROPN
ejpam-4316	410	4	.	.	PUNCT
ejpam-4316	410	5	egan	egan	PROPN
ejpam-4316	410	6	,	,	PUNCT
ejpam-4316	410	7	j.r.m	j.r.m	PROPN
ejpam-4316	410	8	.	.	PUNCT
ejpam-4316	411	1	antalan	antalan	PROPN
ejpam-4316	411	2	/	/	SYM
ejpam-4316	411	3	eur	eur	PROPN
ejpam-4316	411	4	.	.	PUNCT
ejpam-4316	412	1	j.	j.	PROPN
ejpam-4316	412	2	pure	pure	PROPN
ejpam-4316	412	3	appl	appl	PROPN
ejpam-4316	412	4	.	.	PROPN
ejpam-4316	412	5	math	math	PROPN
ejpam-4316	412	6	,	,	PUNCT
ejpam-4316	412	7	15	15	NUM
ejpam-4316	412	8	(	(	PUNCT
ejpam-4316	412	9	2	2	NUM
ejpam-4316	412	10	)	)	PUNCT
ejpam-4316	412	11	(	(	PUNCT
ejpam-4316	412	12	2022	2022	NUM
ejpam-4316	412	13	)	)	PUNCT
ejpam-4316	412	14	,	,	PUNCT
ejpam-4316	412	15	602	602	NUM
ejpam-4316	412	16	-	-	SYM
ejpam-4316	412	17	619	619	NUM
ejpam-4316	412	18	614	614	NUM
ejpam-4316	412	19	(	(	PUNCT
ejpam-4316	412	20	iii	iii	NOUN
ejpam-4316	412	21	)	)	PUNCT
ejpam-4316	412	22	∑	∑	PUNCT
ejpam-4316	413	1	d	d	PROPN
ejpam-4316	413	2	+	+	CCONJ
ejpam-4316	413	3	ci	ci	NOUN
ejpam-4316	413	4	=	=	PUNCT
ejpam-4316	413	5	∑	∑	PUNCT
ejpam-4316	413	6	d	d	PROPN
ejpam-4316	413	7	+	+	CCONJ
ejpam-4316	413	8	∑	∑	PROPN
ejpam-4316	413	9	ci	ci	NOUN
ejpam-4316	413	10	proof	proof	NOUN
ejpam-4316	413	11	.	.	PUNCT
ejpam-4316	414	1	let	let	VERB
ejpam-4316	414	2	d	d	NOUN
ejpam-4316	415	1	=	=	PUNCT
ejpam-4316	416	1	[	[	X
ejpam-4316	416	2	dij	dij	X
ejpam-4316	416	3	]	]	X
ejpam-4316	416	4	,	,	PUNCT
ejpam-4316	416	5	a	a	PRON
ejpam-4316	416	6	=	=	X
ejpam-4316	417	1	[	[	X
ejpam-4316	417	2	aij	aij	X
ejpam-4316	417	3	]	]	PUNCT
ejpam-4316	417	4	.	.	PUNCT
ejpam-4316	418	1	for	for	ADP
ejpam-4316	418	2	(	(	PUNCT
ejpam-4316	418	3	i	i	NOUN
ejpam-4316	418	4	)	)	PUNCT
ejpam-4316	418	5	:	:	PUNCT
ejpam-4316	418	6	note	note	VERB
ejpam-4316	418	7	that	that	SCONJ
ejpam-4316	418	8	since	since	SCONJ
ejpam-4316	418	9	aij	aij	PROPN
ejpam-4316	418	10	is	be	AUX
ejpam-4316	418	11	either	either	CCONJ
ejpam-4316	418	12	0	0	NUM
ejpam-4316	418	13	or	or	CCONJ
ejpam-4316	418	14	1	1	NUM
ejpam-4316	418	15	,	,	PUNCT
ejpam-4316	418	16	for	for	ADP
ejpam-4316	418	17	0	0	NUM
ejpam-4316	418	18	≤	≤	NOUN
ejpam-4316	418	19	i	i	PRON
ejpam-4316	418	20	,	,	PUNCT
ejpam-4316	418	21	j	j	PROPN
ejpam-4316	418	22	≤	≤	PROPN
ejpam-4316	418	23	n	n	CCONJ
ejpam-4316	418	24	,	,	PUNCT
ejpam-4316	418	25	then	then	ADV
ejpam-4316	418	26	we	we	PRON
ejpam-4316	418	27	have∑	have∑	VERB
ejpam-4316	418	28	ca	can	AUX
ejpam-4316	418	29	=	=	SYM
ejpam-4316	418	30	∑	∑	PROPN
ejpam-4316	418	31	1	1	NUM
ejpam-4316	418	32	caij	caij	NOUN
ejpam-4316	418	33	=	=	SYM
ejpam-4316	418	34	1	1	NUM
ejpam-4316	418	35	c	c	NOUN
ejpam-4316	418	36	∑	∑	PROPN
ejpam-4316	418	37	1	1	NUM
ejpam-4316	418	38	aij	aij	X
ejpam-4316	418	39	=	=	SYM
ejpam-4316	418	40	1	1	NUM
ejpam-4316	418	41	c	c	NOUN
ejpam-4316	418	42	∑	∑	PUNCT
ejpam-4316	418	43	aij	aij	PROPN
ejpam-4316	418	44	=	=	SYM
ejpam-4316	418	45	1	1	NUM
ejpam-4316	418	46	c	c	X
ejpam-4316	418	47	∑	∑	PUNCT
ejpam-4316	418	48	a	a	PRON
ejpam-4316	418	49	where	where	SCONJ
ejpam-4316	418	50	the	the	DET
ejpam-4316	418	51	summation	summation	NOUN
ejpam-4316	418	52	runs	run	VERB
ejpam-4316	418	53	over	over	ADP
ejpam-4316	418	54	all	all	DET
ejpam-4316	418	55	non	non	ADJ
ejpam-4316	418	56	-	-	ADJ
ejpam-4316	418	57	zero	zero	NUM
ejpam-4316	418	58	aij	aij	PROPN
ejpam-4316	418	59	.	.	PUNCT
ejpam-4316	419	1	for	for	ADP
ejpam-4316	419	2	(	(	PUNCT
ejpam-4316	419	3	ii	ii	NOUN
ejpam-4316	419	4	)	)	PUNCT
ejpam-4316	419	5	:	:	PUNCT
ejpam-4316	419	6	we	we	PRON
ejpam-4316	419	7	note	note	VERB
ejpam-4316	419	8	that	that	SCONJ
ejpam-4316	419	9	dij	dij	NOUN
ejpam-4316	419	10	=	=	PUNCT
ejpam-4316	419	11	aij	aij	PROPN
ejpam-4316	419	12	=	=	SYM
ejpam-4316	419	13	1	1	NUM
ejpam-4316	419	14	whenever	whenever	SCONJ
ejpam-4316	419	15	vertex	vertex	NOUN
ejpam-4316	419	16	i	i	PRON
ejpam-4316	419	17	is	be	AUX
ejpam-4316	419	18	adjacent	adjacent	ADJ
ejpam-4316	419	19	to	to	PART
ejpam-4316	419	20	vertex	vertex	PROPN
ejpam-4316	419	21	j.	j.	PROPN
ejpam-4316	419	22	note	note	VERB
ejpam-4316	419	23	that	that	SCONJ
ejpam-4316	419	24	the	the	DET
ejpam-4316	419	25	diagonal	diagonal	ADJ
ejpam-4316	419	26	entries	entry	NOUN
ejpam-4316	419	27	of	of	ADP
ejpam-4316	419	28	d	d	PROPN
ejpam-4316	419	29	−	−	PROPN
ejpam-4316	419	30	a	a	PRON
ejpam-4316	419	31	and	and	CCONJ
ejpam-4316	419	32	and	and	CCONJ
ejpam-4316	419	33	(	(	PUNCT
ejpam-4316	419	34	c+	c+	X
ejpam-4316	419	35	1)a	1)a	NUM
ejpam-4316	419	36	are	be	AUX
ejpam-4316	419	37	all	all	PRON
ejpam-4316	419	38	zero	zero	NUM
ejpam-4316	419	39	.	.	PUNCT
ejpam-4316	420	1	moreover	moreover	ADV
ejpam-4316	420	2	,	,	PUNCT
ejpam-4316	420	3	the	the	DET
ejpam-4316	420	4	ij	ij	NOUN
ejpam-4316	420	5	-	-	NOUN
ejpam-4316	420	6	entry	entry	NOUN
ejpam-4316	420	7	of	of	ADP
ejpam-4316	420	8	d	d	NOUN
ejpam-4316	420	9	−	−	PROPN
ejpam-4316	420	10	a	a	PRON
ejpam-4316	420	11	is	be	AUX
ejpam-4316	420	12	zero	zero	NUM
ejpam-4316	420	13	whenever	whenever	SCONJ
ejpam-4316	420	14	vertex	vertex	NOUN
ejpam-4316	420	15	i	i	PRON
ejpam-4316	420	16	is	be	AUX
ejpam-4316	420	17	adjacent	adjacent	ADJ
ejpam-4316	420	18	to	to	PART
ejpam-4316	420	19	vertex	vertex	VERB
ejpam-4316	420	20	j	j	PROPN
ejpam-4316	420	21	and	and	CCONJ
ejpam-4316	420	22	greater	great	ADJ
ejpam-4316	420	23	than	than	ADP
ejpam-4316	420	24	0	0	NUM
ejpam-4316	420	25	whenever	whenever	SCONJ
ejpam-4316	420	26	vertex	vertex	NOUN
ejpam-4316	421	1	i	i	PRON
ejpam-4316	421	2	is	be	AUX
ejpam-4316	421	3	not	not	PART
ejpam-4316	421	4	adjacent	adjacent	ADJ
ejpam-4316	421	5	to	to	PART
ejpam-4316	421	6	vertex	vertex	VERB
ejpam-4316	421	7	j.	j.	PROPN
ejpam-4316	421	8	furthermore	furthermore	ADV
ejpam-4316	421	9	,	,	PUNCT
ejpam-4316	421	10	the	the	DET
ejpam-4316	421	11	ij	ij	NOUN
ejpam-4316	421	12	-	-	NOUN
ejpam-4316	421	13	entry	entry	NOUN
ejpam-4316	421	14	in	in	ADP
ejpam-4316	421	15	the	the	DET
ejpam-4316	421	16	matrix	matrix	NOUN
ejpam-4316	421	17	(	(	PUNCT
ejpam-4316	421	18	c	c	X
ejpam-4316	421	19	+	+	SYM
ejpam-4316	421	20	1)a	1)a	PROPN
ejpam-4316	421	21	is	be	AUX
ejpam-4316	421	22	zero	zero	NUM
ejpam-4316	421	23	whenever	whenever	SCONJ
ejpam-4316	421	24	vertex	vertex	NOUN
ejpam-4316	421	25	i	i	PRON
ejpam-4316	421	26	is	be	AUX
ejpam-4316	421	27	not	not	PART
ejpam-4316	421	28	adjacent	adjacent	ADJ
ejpam-4316	421	29	to	to	PART
ejpam-4316	421	30	vertex	vertex	VERB
ejpam-4316	421	31	j	j	PROPN
ejpam-4316	421	32	and	and	CCONJ
ejpam-4316	421	33	(	(	PUNCT
ejpam-4316	421	34	c	c	NOUN
ejpam-4316	421	35	+	+	NOUN
ejpam-4316	421	36	1	1	X
ejpam-4316	421	37	)	)	PUNCT
ejpam-4316	421	38	whenever	whenever	SCONJ
ejpam-4316	421	39	vertex	vertex	NOUN
ejpam-4316	421	40	i	i	PRON
ejpam-4316	421	41	is	be	AUX
ejpam-4316	421	42	adjacent	adjacent	ADJ
ejpam-4316	421	43	to	to	PART
ejpam-4316	421	44	vertex	vertex	VERB
ejpam-4316	421	45	j.	j.	PROPN
ejpam-4316	421	46	since	since	SCONJ
ejpam-4316	421	47	d	d	PROPN
ejpam-4316	422	1	+	+	X
ejpam-4316	422	2	ca	ca	NOUN
ejpam-4316	422	3	=	=	SYM
ejpam-4316	422	4	(	(	PUNCT
ejpam-4316	422	5	d	d	NOUN
ejpam-4316	422	6	−	−	PROPN
ejpam-4316	422	7	a	a	X
ejpam-4316	422	8	)	)	PUNCT
ejpam-4316	422	9	+	+	CCONJ
ejpam-4316	422	10	(	(	PUNCT
ejpam-4316	422	11	c	c	X
ejpam-4316	422	12	+	+	SYM
ejpam-4316	422	13	1)a	1)a	NUM
ejpam-4316	422	14	and	and	CCONJ
ejpam-4316	422	15	by	by	ADP
ejpam-4316	422	16	lemma	lemma	PROPN
ejpam-4316	422	17	5	5	NUM
ejpam-4316	422	18	,	,	PUNCT
ejpam-4316	422	19	we	we	PRON
ejpam-4316	422	20	have∑	have∑	VERB
ejpam-4316	423	1	d	d	NOUN
ejpam-4316	423	2	+	+	X
ejpam-4316	423	3	ca	ca	NOUN
ejpam-4316	423	4	=	=	SYM
ejpam-4316	423	5	∑	∑	PUNCT
ejpam-4316	423	6	d	d	X
ejpam-4316	423	7	−a+	−a+	X
ejpam-4316	423	8	∑	∑	PUNCT
ejpam-4316	423	9	(	(	PUNCT
ejpam-4316	423	10	c+	c+	VERB
ejpam-4316	423	11	1)a	1)a	NUM
ejpam-4316	423	12	.	.	PUNCT
ejpam-4316	424	1	for	for	ADP
ejpam-4316	424	2	(	(	PUNCT
ejpam-4316	424	3	iii	iii	NOUN
ejpam-4316	424	4	):	):	PUNCT
ejpam-4316	424	5	from	from	ADP
ejpam-4316	424	6	the	the	DET
ejpam-4316	424	7	definition	definition	NOUN
ejpam-4316	424	8	of	of	ADP
ejpam-4316	424	9	d	d	NOUN
ejpam-4316	424	10	the	the	DET
ejpam-4316	424	11	entries	entry	NOUN
ejpam-4316	424	12	in	in	ADP
ejpam-4316	424	13	the	the	DET
ejpam-4316	424	14	main	main	ADJ
ejpam-4316	424	15	diagonal	diagonal	NOUN
ejpam-4316	424	16	are	be	AUX
ejpam-4316	424	17	all	all	PRON
ejpam-4316	424	18	zero	zero	NUM
ejpam-4316	424	19	and	and	CCONJ
ejpam-4316	424	20	that	that	SCONJ
ejpam-4316	424	21	the	the	DET
ejpam-4316	424	22	entries	entry	NOUN
ejpam-4316	424	23	outside	outside	ADP
ejpam-4316	424	24	the	the	DET
ejpam-4316	424	25	main	main	ADJ
ejpam-4316	424	26	diagonal	diagonal	NOUN
ejpam-4316	424	27	of	of	ADP
ejpam-4316	424	28	(	(	PUNCT
ejpam-4316	424	29	c+1)i	c+1)i	NOUN
ejpam-4316	424	30	are	be	AUX
ejpam-4316	424	31	all	all	DET
ejpam-4316	424	32	zero	zero	NUM
ejpam-4316	424	33	.	.	PUNCT
ejpam-4316	425	1	thus	thus	ADV
ejpam-4316	425	2	,	,	PUNCT
ejpam-4316	425	3	by	by	ADP
ejpam-4316	425	4	lemma	lemma	PROPN
ejpam-4316	425	5	5	5	NUM
ejpam-4316	425	6	,	,	PUNCT
ejpam-4316	425	7	the	the	DET
ejpam-4316	425	8	statement	statement	NOUN
ejpam-4316	425	9	follows	follow	VERB
ejpam-4316	425	10	.	.	PUNCT
ejpam-4316	426	1	theorem	theorem	ADJ
ejpam-4316	426	2	14	14	NUM
ejpam-4316	426	3	.	.	PUNCT
ejpam-4316	427	1	suppose	suppose	VERB
ejpam-4316	427	2	g	g	PROPN
ejpam-4316	427	3	=	=	SYM
ejpam-4316	427	4	(	(	PUNCT
ejpam-4316	427	5	v	v	NOUN
ejpam-4316	427	6	,	,	PUNCT
ejpam-4316	427	7	e	e	NOUN
ejpam-4316	427	8	)	)	PUNCT
ejpam-4316	427	9	is	be	AUX
ejpam-4316	427	10	a	a	DET
ejpam-4316	427	11	connected	connected	ADJ
ejpam-4316	427	12	triangle	triangle	NOUN
ejpam-4316	427	13	free	free	ADJ
ejpam-4316	427	14	graph	graph	NOUN
ejpam-4316	427	15	on	on	ADP
ejpam-4316	427	16	n	n	DET
ejpam-4316	427	17	vertices	vertex	NOUN
ejpam-4316	427	18	and	and	CCONJ
ejpam-4316	427	19	m	m	PRON
ejpam-4316	427	20	edges	edge	NOUN
ejpam-4316	427	21	,	,	PUNCT
ejpam-4316	427	22	then	then	ADV
ejpam-4316	427	23	the	the	DET
ejpam-4316	427	24	harary	harary	PROPN
ejpam-4316	427	25	index	index	NOUN
ejpam-4316	427	26	of	of	ADP
ejpam-4316	427	27	γ(g	γ(g	PROPN
ejpam-4316	427	28	,	,	PUNCT
ejpam-4316	427	29	v	v	NOUN
ejpam-4316	427	30	)	)	PUNCT
ejpam-4316	427	31	is	be	AUX
ejpam-4316	427	32	given	give	VERB
ejpam-4316	427	33	by	by	ADP
ejpam-4316	427	34	h(γ	h(γ	NOUN
ejpam-4316	427	35	)	)	PUNCT
ejpam-4316	427	36	=	=	SYM
ejpam-4316	427	37	4h(g	4h(g	NOUN
ejpam-4316	427	38	)	)	PUNCT
ejpam-4316	428	1	+	+	CCONJ
ejpam-4316	428	2	n	n	CCONJ
ejpam-4316	428	3	2	2	NUM
ejpam-4316	428	4	−	−	NUM
ejpam-4316	428	5	2	2	NUM
ejpam-4316	428	6	3	3	NUM
ejpam-4316	428	7	m.	m.	NOUN
ejpam-4316	428	8	proof	proof	NOUN
ejpam-4316	428	9	.	.	PUNCT
ejpam-4316	429	1	let	let	VERB
ejpam-4316	429	2	g	g	NOUN
ejpam-4316	429	3	be	be	AUX
ejpam-4316	429	4	any	any	DET
ejpam-4316	429	5	connected	connected	ADJ
ejpam-4316	429	6	graph	graph	NOUN
ejpam-4316	429	7	of	of	ADP
ejpam-4316	429	8	order	order	NOUN
ejpam-4316	429	9	n	n	NOUN
ejpam-4316	429	10	and	and	CCONJ
ejpam-4316	429	11	m	m	VERB
ejpam-4316	429	12	edges	edge	VERB
ejpam-4316	429	13	such	such	ADJ
ejpam-4316	429	14	that	that	SCONJ
ejpam-4316	429	15	any	any	DET
ejpam-4316	429	16	pair	pair	NOUN
ejpam-4316	429	17	of	of	ADP
ejpam-4316	429	18	adjacent	adjacent	ADJ
ejpam-4316	429	19	vertices	vertex	NOUN
ejpam-4316	429	20	has	have	VERB
ejpam-4316	429	21	no	no	DET
ejpam-4316	429	22	common	common	ADJ
ejpam-4316	429	23	neighbor	neighbor	NOUN
ejpam-4316	429	24	,	,	PUNCT
ejpam-4316	429	25	that	that	PRON
ejpam-4316	429	26	is	be	AUX
ejpam-4316	429	27	g	g	NOUN
ejpam-4316	429	28	is	be	AUX
ejpam-4316	429	29	a	a	DET
ejpam-4316	429	30	triangle	triangle	NOUN
ejpam-4316	429	31	free	free	ADJ
ejpam-4316	429	32	graph	graph	NOUN
ejpam-4316	429	33	.	.	PUNCT
ejpam-4316	430	1	denote	denote	VERB
ejpam-4316	430	2	the	the	DET
ejpam-4316	430	3	splitting	splitting	NOUN
ejpam-4316	430	4	graph	graph	NOUN
ejpam-4316	430	5	of	of	ADP
ejpam-4316	430	6	g	g	NOUN
ejpam-4316	430	7	by	by	ADP
ejpam-4316	430	8	γ	γ	PROPN
ejpam-4316	430	9	.	.	PUNCT
ejpam-4316	431	1	the	the	DET
ejpam-4316	431	2	distance	distance	NOUN
ejpam-4316	431	3	matrix	matrix	NOUN
ejpam-4316	431	4	of	of	ADP
ejpam-4316	431	5	γ	γ	X
ejpam-4316	431	6	can	can	AUX
ejpam-4316	431	7	be	be	AUX
ejpam-4316	431	8	written	write	VERB
ejpam-4316	431	9	as	as	ADP
ejpam-4316	431	10	a	a	DET
ejpam-4316	431	11	2×2	2×2	NUM
ejpam-4316	431	12	block	block	NOUN
ejpam-4316	431	13	matrix	matrix	NOUN
ejpam-4316	431	14	given	give	VERB
ejpam-4316	431	15	by	by	ADP
ejpam-4316	431	16	d(γ	d(γ	PROPN
ejpam-4316	431	17	)	)	PUNCT
ejpam-4316	431	18	=	=	PUNCT
ejpam-4316	432	1	[	[	PUNCT
ejpam-4316	432	2	d(g	d(g	PROPN
ejpam-4316	432	3	)	)	PUNCT
ejpam-4316	432	4	d(g	d(g	PROPN
ejpam-4316	432	5	)	)	PUNCT
ejpam-4316	433	1	+	+	CCONJ
ejpam-4316	433	2	2	2	NUM
ejpam-4316	433	3	in	in	ADP
ejpam-4316	433	4	d(g	d(g	PROPN
ejpam-4316	433	5	)	)	PUNCT
ejpam-4316	433	6	+	+	CCONJ
ejpam-4316	433	7	2	2	NUM
ejpam-4316	433	8	in	in	ADP
ejpam-4316	433	9	d(g	d(g	PROPN
ejpam-4316	433	10	)	)	PUNCT
ejpam-4316	433	11	+	+	NUM
ejpam-4316	433	12	2a(g	2a(g	NUM
ejpam-4316	433	13	)	)	PUNCT
ejpam-4316	433	14	]	]	PUNCT
ejpam-4316	434	1	where	where	SCONJ
ejpam-4316	434	2	d(g	d(g	NOUN
ejpam-4316	434	3	)	)	PUNCT
ejpam-4316	434	4	and	and	CCONJ
ejpam-4316	434	5	a(g	a(g	PROPN
ejpam-4316	434	6	)	)	PUNCT
ejpam-4316	434	7	are	be	AUX
ejpam-4316	434	8	the	the	DET
ejpam-4316	434	9	distance	distance	NOUN
ejpam-4316	434	10	matrix	matrix	NOUN
ejpam-4316	434	11	,	,	PUNCT
ejpam-4316	434	12	adjacency	adjacency	NOUN
ejpam-4316	434	13	matrix	matrix	NOUN
ejpam-4316	434	14	of	of	ADP
ejpam-4316	434	15	the	the	DET
ejpam-4316	434	16	graph	graph	NOUN
ejpam-4316	434	17	g	g	NOUN
ejpam-4316	434	18	and	and	CCONJ
ejpam-4316	434	19	in	in	ADP
ejpam-4316	434	20	is	be	AUX
ejpam-4316	434	21	the	the	DET
ejpam-4316	434	22	identity	identity	NOUN
ejpam-4316	434	23	matrix	matrix	NOUN
ejpam-4316	434	24	of	of	ADP
ejpam-4316	434	25	size	size	NOUN
ejpam-4316	434	26	n.	n.	NOUN
ejpam-4316	434	27	since	since	SCONJ
ejpam-4316	434	28	the	the	DET
ejpam-4316	434	29	harary	harary	PROPN
ejpam-4316	434	30	index	index	NOUN
ejpam-4316	434	31	of	of	ADP
ejpam-4316	434	32	γ	γ	PROPN
ejpam-4316	434	33	is	be	AUX
ejpam-4316	434	34	half	half	DET
ejpam-4316	434	35	the	the	DET
ejpam-4316	434	36	sum	sum	NOUN
ejpam-4316	434	37	of	of	ADP
ejpam-4316	434	38	the	the	DET
ejpam-4316	434	39	entries	entry	NOUN
ejpam-4316	434	40	in	in	ADP
ejpam-4316	434	41	d(γ	d(γ	PROPN
ejpam-4316	434	42	)	)	PUNCT
ejpam-4316	434	43	,	,	PUNCT
ejpam-4316	434	44	then	then	ADV
ejpam-4316	434	45	we	we	PRON
ejpam-4316	434	46	have	have	VERB
ejpam-4316	434	47	the	the	DET
ejpam-4316	434	48	following	follow	VERB
ejpam-4316	434	49	computations	computation	NOUN
ejpam-4316	434	50	:	:	PUNCT
ejpam-4316	434	51	h(γ	h(γ	NOUN
ejpam-4316	434	52	)	)	PUNCT
ejpam-4316	434	53	=	=	SYM
ejpam-4316	435	1	1	1	NUM
ejpam-4316	435	2	2	2	NUM
ejpam-4316	435	3	∑	∑	PUNCT
ejpam-4316	435	4	d(γ	d(γ	PROPN
ejpam-4316	435	5	)	)	PUNCT
ejpam-4316	435	6	=	=	SYM
ejpam-4316	435	7	1	1	NUM
ejpam-4316	435	8	2	2	NUM
ejpam-4316	435	9	(	(	PUNCT
ejpam-4316	435	10	∑	∑	PUNCT
ejpam-4316	435	11	d(g	d(g	PROPN
ejpam-4316	435	12	)	)	PUNCT
ejpam-4316	435	13	+	+	CCONJ
ejpam-4316	435	14	∑	∑	PROPN
ejpam-4316	435	15	d(g	d(g	PROPN
ejpam-4316	435	16	)	)	PUNCT
ejpam-4316	435	17	+	+	CCONJ
ejpam-4316	435	18	2	2	NUM
ejpam-4316	435	19	in	in	ADP
ejpam-4316	435	20	+	+	NUM
ejpam-4316	435	21	∑	∑	PROPN
ejpam-4316	435	22	d(g	d(g	PROPN
ejpam-4316	435	23	)	)	PUNCT
ejpam-4316	435	24	+	+	CCONJ
ejpam-4316	435	25	2	2	NUM
ejpam-4316	435	26	in	in	ADP
ejpam-4316	435	27	+	+	NUM
ejpam-4316	435	28	∑	∑	PROPN
ejpam-4316	435	29	d(g	d(g	PROPN
ejpam-4316	435	30	)	)	PUNCT
ejpam-4316	435	31	+	+	NOUN
ejpam-4316	435	32	2a(g	2a(g	NUM
ejpam-4316	435	33	)	)	PUNCT
ejpam-4316	435	34	)	)	PUNCT
ejpam-4316	436	1	=	=	SYM
ejpam-4316	436	2	1	1	NUM
ejpam-4316	436	3	2	2	NUM
ejpam-4316	436	4	(	(	PUNCT
ejpam-4316	436	5	∑	∑	PUNCT
ejpam-4316	436	6	d(g	d(g	PROPN
ejpam-4316	436	7	)	)	PUNCT
ejpam-4316	437	1	+	+	CCONJ
ejpam-4316	437	2	∑	∑	PROPN
ejpam-4316	437	3	d(g	d(g	PROPN
ejpam-4316	437	4	)	)	PUNCT
ejpam-4316	437	5	+	+	CCONJ
ejpam-4316	437	6	∑	∑	PROPN
ejpam-4316	437	7	2	2	NUM
ejpam-4316	437	8	in	in	ADP
ejpam-4316	437	9	+	+	NUM
ejpam-4316	437	10	∑	∑	PROPN
ejpam-4316	437	11	d(g	d(g	PROPN
ejpam-4316	437	12	)	)	PUNCT
ejpam-4316	438	1	+	+	CCONJ
ejpam-4316	438	2	∑	∑	PROPN
ejpam-4316	438	3	2	2	NUM
ejpam-4316	438	4	in	in	ADP
ejpam-4316	438	5	+	+	NOUN
ejpam-4316	438	6	∑	∑	NOUN
ejpam-4316	438	7	d(g)−a(g	d(g)−a(g	NOUN
ejpam-4316	438	8	)	)	PUNCT
ejpam-4316	438	9	+	+	CCONJ
ejpam-4316	438	10	∑	∑	PROPN
ejpam-4316	438	11	3a(g	3a(g	NUM
ejpam-4316	438	12	)	)	PUNCT
ejpam-4316	438	13	)	)	PUNCT
ejpam-4316	439	1	=	=	SYM
ejpam-4316	440	1	1	1	NUM
ejpam-4316	440	2	2	2	NUM
ejpam-4316	440	3	(	(	PUNCT
ejpam-4316	440	4	4	4	NUM
ejpam-4316	440	5	∑	∑	PUNCT
ejpam-4316	440	6	d(g	d(g	PROPN
ejpam-4316	440	7	)	)	PUNCT
ejpam-4316	440	8	+	+	CCONJ
ejpam-4316	440	9	2	2	NUM
ejpam-4316	440	10	∑	∑	SYM
ejpam-4316	440	11	2	2	NUM
ejpam-4316	440	12	in	in	ADP
ejpam-4316	440	13	+	+	NUM
ejpam-4316	440	14	∑	∑	PROPN
ejpam-4316	440	15	3a(g)−	3a(g)−	NUM
ejpam-4316	440	16	∑	∑	PUNCT
ejpam-4316	440	17	a(g	a(g	PROPN
ejpam-4316	440	18	)	)	PUNCT
ejpam-4316	440	19	)	)	PUNCT
ejpam-4316	440	20	f.j.h	f.j.h	ADJ
ejpam-4316	440	21	.	.	PUNCT
ejpam-4316	441	1	campeña	campeña	NOUN
ejpam-4316	441	2	,	,	PUNCT
ejpam-4316	441	3	m.c.g	m.c.g	PROPN
ejpam-4316	441	4	.	.	PUNCT
ejpam-4316	441	5	egan	egan	PROPN
ejpam-4316	441	6	,	,	PUNCT
ejpam-4316	441	7	j.r.m	j.r.m	PROPN
ejpam-4316	441	8	.	.	PUNCT
ejpam-4316	442	1	antalan	antalan	PROPN
ejpam-4316	442	2	/	/	SYM
ejpam-4316	442	3	eur	eur	PROPN
ejpam-4316	442	4	.	.	PUNCT
ejpam-4316	443	1	j.	j.	PROPN
ejpam-4316	443	2	pure	pure	PROPN
ejpam-4316	443	3	appl	appl	PROPN
ejpam-4316	443	4	.	.	PROPN
ejpam-4316	443	5	math	math	PROPN
ejpam-4316	443	6	,	,	PUNCT
ejpam-4316	443	7	15	15	NUM
ejpam-4316	443	8	(	(	PUNCT
ejpam-4316	443	9	2	2	NUM
ejpam-4316	443	10	)	)	PUNCT
ejpam-4316	443	11	(	(	PUNCT
ejpam-4316	443	12	2022	2022	NUM
ejpam-4316	443	13	)	)	PUNCT
ejpam-4316	443	14	,	,	PUNCT
ejpam-4316	443	15	602	602	NUM
ejpam-4316	443	16	-	-	SYM
ejpam-4316	443	17	619	619	NUM
ejpam-4316	443	18	615	615	NUM
ejpam-4316	443	19	=	=	SYM
ejpam-4316	443	20	4	4	NUM
ejpam-4316	443	21	(	(	PUNCT
ejpam-4316	443	22	1	1	NUM
ejpam-4316	443	23	2	2	NUM
ejpam-4316	443	24	∑	∑	PUNCT
ejpam-4316	443	25	d(g	d(g	PROPN
ejpam-4316	443	26	)	)	PUNCT
ejpam-4316	443	27	)	)	PUNCT
ejpam-4316	444	1	+	+	CCONJ
ejpam-4316	444	2	∑	∑	PUNCT
ejpam-4316	444	3	2	2	NUM
ejpam-4316	444	4	in	in	ADP
ejpam-4316	444	5	+	+	NOUN
ejpam-4316	444	6	1	1	NUM
ejpam-4316	444	7	2	2	NUM
ejpam-4316	444	8	∑	∑	SYM
ejpam-4316	444	9	3a(g)−	3a(g)−	NUM
ejpam-4316	444	10	1	1	NUM
ejpam-4316	444	11	2	2	NUM
ejpam-4316	444	12	∑	∑	PUNCT
ejpam-4316	444	13	a(g	a(g	PROPN
ejpam-4316	444	14	)	)	PUNCT
ejpam-4316	444	15	=	=	SYM
ejpam-4316	444	16	4h(g	4h(g	PROPN
ejpam-4316	444	17	)	)	PUNCT
ejpam-4316	445	1	+	+	CCONJ
ejpam-4316	445	2	n	n	CCONJ
ejpam-4316	445	3	2	2	NUM
ejpam-4316	445	4	+	+	CCONJ
ejpam-4316	445	5	1	1	NUM
ejpam-4316	445	6	2	2	NUM
ejpam-4316	445	7	∑	∑	SYM
ejpam-4316	445	8	3a(g)−	3a(g)−	NUM
ejpam-4316	445	9	1	1	NUM
ejpam-4316	445	10	2	2	NUM
ejpam-4316	445	11	∑	∑	PUNCT
ejpam-4316	445	12	a(g	a(g	PROPN
ejpam-4316	445	13	)	)	PUNCT
ejpam-4316	445	14	observe	observe	VERB
ejpam-4316	445	15	that	that	SCONJ
ejpam-4316	445	16	the	the	DET
ejpam-4316	445	17	sum	sum	NOUN
ejpam-4316	445	18	of	of	ADP
ejpam-4316	445	19	the	the	DET
ejpam-4316	445	20	entries	entry	NOUN
ejpam-4316	445	21	in	in	ADP
ejpam-4316	445	22	an	an	DET
ejpam-4316	445	23	adjacency	adjacency	NOUN
ejpam-4316	445	24	matrix	matrix	NOUN
ejpam-4316	445	25	is	be	AUX
ejpam-4316	445	26	twice	twice	DET
ejpam-4316	445	27	the	the	DET
ejpam-4316	445	28	number	number	NOUN
ejpam-4316	445	29	of	of	ADP
ejpam-4316	445	30	edges	edge	NOUN
ejpam-4316	445	31	m.	m.	NOUN
ejpam-4316	445	32	that	that	PRON
ejpam-4316	445	33	is	be	AUX
ejpam-4316	445	34	,	,	PUNCT
ejpam-4316	445	35	h(γ	h(γ	PROPN
ejpam-4316	445	36	)	)	PUNCT
ejpam-4316	445	37	=	=	SYM
ejpam-4316	445	38	4h(g	4h(g	NOUN
ejpam-4316	445	39	)	)	PUNCT
ejpam-4316	446	1	+	+	CCONJ
ejpam-4316	446	2	n	n	CCONJ
ejpam-4316	446	3	2	2	NUM
ejpam-4316	446	4	+	+	CCONJ
ejpam-4316	446	5	1	1	NUM
ejpam-4316	446	6	2	2	NUM
ejpam-4316	446	7	(	(	PUNCT
ejpam-4316	446	8	2	2	NUM
ejpam-4316	446	9	m	m	NOUN
ejpam-4316	446	10	3	3	NUM
ejpam-4316	446	11	)	)	PUNCT
ejpam-4316	446	12	−	−	NOUN
ejpam-4316	446	13	1	1	NUM
ejpam-4316	446	14	2	2	NUM
ejpam-4316	446	15	(	(	PUNCT
ejpam-4316	446	16	2	2	NUM
ejpam-4316	446	17	m	m	NOUN
ejpam-4316	446	18	)	)	PUNCT
ejpam-4316	446	19	=	=	SYM
ejpam-4316	446	20	4h(g	4h(g	NOUN
ejpam-4316	446	21	)	)	PUNCT
ejpam-4316	447	1	+	+	CCONJ
ejpam-4316	447	2	n	n	CCONJ
ejpam-4316	447	3	2	2	NUM
ejpam-4316	447	4	+	+	CCONJ
ejpam-4316	447	5	m	m	PROPN
ejpam-4316	447	6	3	3	NUM
ejpam-4316	447	7	−m	−m	NOUN
ejpam-4316	447	8	=	=	SYM
ejpam-4316	447	9	4h(g	4h(g	PROPN
ejpam-4316	447	10	)	)	PUNCT
ejpam-4316	448	1	+	+	CCONJ
ejpam-4316	448	2	n	n	CCONJ
ejpam-4316	448	3	2	2	NUM
ejpam-4316	448	4	−	−	NUM
ejpam-4316	448	5	2	2	NUM
ejpam-4316	448	6	m	m	NOUN
ejpam-4316	448	7	3	3	NUM
ejpam-4316	448	8	corollary	corollary	NOUN
ejpam-4316	448	9	3	3	NUM
ejpam-4316	448	10	.	.	PUNCT
ejpam-4316	449	1	let	let	VERB
ejpam-4316	449	2	g	g	PRON
ejpam-4316	449	3	be	be	AUX
ejpam-4316	449	4	a	a	DET
ejpam-4316	449	5	cycle	cycle	NOUN
ejpam-4316	449	6	graph	graph	NOUN
ejpam-4316	449	7	cn	cn	PROPN
ejpam-4316	449	8	.	.	PUNCT
ejpam-4316	450	1	then	then	ADV
ejpam-4316	450	2	the	the	DET
ejpam-4316	450	3	v	v	ADJ
ejpam-4316	450	4	-splitting	-splitting	ADJ
ejpam-4316	450	5	graph	graph	NOUN
ejpam-4316	450	6	of	of	ADP
ejpam-4316	450	7	cn	cn	PROPN
ejpam-4316	450	8	has	have	VERB
ejpam-4316	450	9	a	a	DET
ejpam-4316	450	10	harary	harary	ADJ
ejpam-4316	450	11	index	index	NOUN
ejpam-4316	450	12	given	give	VERB
ejpam-4316	450	13	by	by	ADP
ejpam-4316	450	14	h(γ	h(γ	NOUN
ejpam-4316	450	15	)	)	PUNCT
ejpam-4316	450	16	=	=	SYM
ejpam-4316	450	17	2	2	NUM
ejpam-4316	450	18	(	(	PUNCT
ejpam-4316	450	19	1	1	NUM
ejpam-4316	450	20	+	+	CCONJ
ejpam-4316	450	21	(	(	PUNCT
ejpam-4316	450	22	−	−	PROPN
ejpam-4316	450	23	1	1	NUM
ejpam-4316	450	24	)	)	PUNCT
ejpam-4316	450	25	n	n	CCONJ
ejpam-4316	450	26	)	)	PUNCT
ejpam-4316	450	27	+	+	CCONJ
ejpam-4316	451	1	n	n	CCONJ
ejpam-4316	451	2	(	(	PUNCT
ejpam-4316	451	3	4hbn−1	4hbn−1	NUM
ejpam-4316	451	4	2	2	NUM
ejpam-4316	451	5	c	c	NOUN
ejpam-4316	451	6	−	−	PROPN
ejpam-4316	451	7	1	1	NUM
ejpam-4316	451	8	6	6	NUM
ejpam-4316	451	9	)	)	PUNCT
ejpam-4316	451	10	.	.	PUNCT
ejpam-4316	452	1	corollary	corollary	ADJ
ejpam-4316	452	2	4	4	NUM
ejpam-4316	452	3	.	.	PUNCT
ejpam-4316	453	1	let	let	VERB
ejpam-4316	453	2	g	g	PRON
ejpam-4316	453	3	be	be	AUX
ejpam-4316	453	4	a	a	DET
ejpam-4316	453	5	path	path	NOUN
ejpam-4316	453	6	graph	graph	NOUN
ejpam-4316	453	7	pn	pn	PROPN
ejpam-4316	453	8	.	.	PROPN
ejpam-4316	454	1	then	then	ADV
ejpam-4316	454	2	the	the	DET
ejpam-4316	454	3	harary	harary	PROPN
ejpam-4316	454	4	index	index	NOUN
ejpam-4316	454	5	of	of	ADP
ejpam-4316	454	6	v	v	NUM
ejpam-4316	454	7	-splitting	-splitte	VERB
ejpam-4316	454	8	graph	graph	NOUN
ejpam-4316	454	9	of	of	ADP
ejpam-4316	454	10	pn	pn	PROPN
ejpam-4316	454	11	is	be	AUX
ejpam-4316	454	12	given	give	VERB
ejpam-4316	454	13	by	by	ADP
ejpam-4316	454	14	h(γ	h(γ	NOUN
ejpam-4316	454	15	)	)	PUNCT
ejpam-4316	454	16	=	=	SYM
ejpam-4316	455	1	n	n	CCONJ
ejpam-4316	455	2	(	(	PUNCT
ejpam-4316	455	3	4hn	4hn	ADJ
ejpam-4316	455	4	−	−	PROPN
ejpam-4316	455	5	25	25	NUM
ejpam-4316	455	6	6	6	NUM
ejpam-4316	455	7	)	)	PUNCT
ejpam-4316	456	1	+	+	CCONJ
ejpam-4316	456	2	2	2	NUM
ejpam-4316	456	3	3	3	NUM
ejpam-4316	456	4	.	.	PUNCT
ejpam-4316	457	1	corollary	corollary	ADJ
ejpam-4316	457	2	5	5	NUM
ejpam-4316	457	3	.	.	PUNCT
ejpam-4316	458	1	let	let	VERB
ejpam-4316	458	2	g	g	PRON
ejpam-4316	458	3	be	be	AUX
ejpam-4316	458	4	a	a	DET
ejpam-4316	458	5	star	star	NOUN
ejpam-4316	458	6	graph	graph	NOUN
ejpam-4316	458	7	sn	sn	PROPN
ejpam-4316	458	8	.	.	PUNCT
ejpam-4316	459	1	then	then	ADV
ejpam-4316	459	2	the	the	DET
ejpam-4316	459	3	v	v	ADJ
ejpam-4316	459	4	-splitting	-splitting	ADJ
ejpam-4316	459	5	graph	graph	NOUN
ejpam-4316	459	6	of	of	ADP
ejpam-4316	459	7	sn	sn	PROPN
ejpam-4316	459	8	has	have	VERB
ejpam-4316	459	9	a	a	DET
ejpam-4316	459	10	harary	harary	ADJ
ejpam-4316	459	11	index	index	NOUN
ejpam-4316	459	12	given	give	VERB
ejpam-4316	459	13	by	by	ADP
ejpam-4316	459	14	h(γ	h(γ	NOUN
ejpam-4316	459	15	)	)	PUNCT
ejpam-4316	459	16	=	=	SYM
ejpam-4316	459	17	1	1	NUM
ejpam-4316	459	18	6	6	NUM
ejpam-4316	459	19	(	(	PUNCT
ejpam-4316	459	20	6n2	6n2	NUM
ejpam-4316	460	1	+	+	CCONJ
ejpam-4316	461	1	5n−	5n−	NUM
ejpam-4316	461	2	8	8	NUM
ejpam-4316	461	3	)	)	PUNCT
ejpam-4316	461	4	.	.	PUNCT
ejpam-4316	462	1	theorem	theorem	ADJ
ejpam-4316	462	2	15	15	NUM
ejpam-4316	462	3	.	.	PUNCT
ejpam-4316	463	1	suppose	suppose	VERB
ejpam-4316	463	2	g	g	PROPN
ejpam-4316	463	3	=	=	SYM
ejpam-4316	463	4	(	(	PUNCT
ejpam-4316	463	5	v	v	NOUN
ejpam-4316	463	6	,	,	PUNCT
ejpam-4316	463	7	e	e	NOUN
ejpam-4316	463	8	)	)	PUNCT
ejpam-4316	463	9	is	be	AUX
ejpam-4316	463	10	a	a	DET
ejpam-4316	463	11	connected	connected	ADJ
ejpam-4316	463	12	graph	graph	NOUN
ejpam-4316	463	13	on	on	ADP
ejpam-4316	463	14	n	n	PRON
ejpam-4316	463	15	≥	≥	NUM
ejpam-4316	463	16	2	2	NUM
ejpam-4316	463	17	vertices	vertex	NOUN
ejpam-4316	463	18	and	and	CCONJ
ejpam-4316	463	19	m	m	PRON
ejpam-4316	463	20	≥	≥	NOUN
ejpam-4316	463	21	1	1	NUM
ejpam-4316	463	22	edges	edge	VERB
ejpam-4316	463	23	such	such	ADJ
ejpam-4316	463	24	that	that	SCONJ
ejpam-4316	463	25	every	every	DET
ejpam-4316	463	26	pair	pair	NOUN
ejpam-4316	463	27	of	of	ADP
ejpam-4316	463	28	adjacent	adjacent	ADJ
ejpam-4316	463	29	vertices	vertex	NOUN
ejpam-4316	463	30	have	have	VERB
ejpam-4316	463	31	a	a	DET
ejpam-4316	463	32	common	common	ADJ
ejpam-4316	463	33	neighbor	neighbor	NOUN
ejpam-4316	463	34	,	,	PUNCT
ejpam-4316	463	35	then	then	ADV
ejpam-4316	463	36	the	the	DET
ejpam-4316	463	37	harary	harary	PROPN
ejpam-4316	463	38	index	index	NOUN
ejpam-4316	463	39	of	of	ADP
ejpam-4316	463	40	γ(g	γ(g	PROPN
ejpam-4316	463	41	,	,	PUNCT
ejpam-4316	463	42	v	v	NOUN
ejpam-4316	463	43	)	)	PUNCT
ejpam-4316	463	44	is	be	AUX
ejpam-4316	463	45	given	give	VERB
ejpam-4316	463	46	by	by	ADP
ejpam-4316	463	47	h(γ	h(γ	NOUN
ejpam-4316	463	48	)	)	PUNCT
ejpam-4316	463	49	=	=	SYM
ejpam-4316	463	50	4h(g	4h(g	NOUN
ejpam-4316	463	51	)	)	PUNCT
ejpam-4316	464	1	+	+	CCONJ
ejpam-4316	464	2	n−m	n−m	PROPN
ejpam-4316	464	3	2	2	NUM
ejpam-4316	464	4	.	.	PUNCT
ejpam-4316	465	1	proof	proof	NOUN
ejpam-4316	465	2	.	.	PUNCT
ejpam-4316	466	1	let	let	VERB
ejpam-4316	466	2	g	g	PRON
ejpam-4316	466	3	be	be	AUX
ejpam-4316	466	4	a	a	DET
ejpam-4316	466	5	connected	connected	ADJ
ejpam-4316	466	6	graph	graph	NOUN
ejpam-4316	466	7	of	of	ADP
ejpam-4316	466	8	order	order	NOUN
ejpam-4316	466	9	n	n	NOUN
ejpam-4316	466	10	and	and	CCONJ
ejpam-4316	466	11	m	m	VERB
ejpam-4316	466	12	edges	edge	VERB
ejpam-4316	466	13	such	such	ADJ
ejpam-4316	466	14	that	that	SCONJ
ejpam-4316	466	15	any	any	DET
ejpam-4316	466	16	pair	pair	NOUN
ejpam-4316	466	17	of	of	ADP
ejpam-4316	466	18	adjacent	adjacent	ADJ
ejpam-4316	466	19	vertices	vertex	NOUN
ejpam-4316	466	20	has	have	VERB
ejpam-4316	466	21	at	at	ADV
ejpam-4316	466	22	least	least	ADJ
ejpam-4316	466	23	common	common	ADJ
ejpam-4316	466	24	neighbor	neighbor	NOUN
ejpam-4316	466	25	and	and	CCONJ
ejpam-4316	466	26	let	let	VERB
ejpam-4316	466	27	γ	γ	NOUN
ejpam-4316	466	28	be	be	AUX
ejpam-4316	466	29	the	the	DET
ejpam-4316	466	30	splitting	splitting	NOUN
ejpam-4316	466	31	graph	graph	NOUN
ejpam-4316	466	32	of	of	ADP
ejpam-4316	466	33	g.	g.	PROPN
ejpam-4316	466	34	this	this	PRON
ejpam-4316	466	35	implies	imply	VERB
ejpam-4316	466	36	that	that	SCONJ
ejpam-4316	466	37	the	the	DET
ejpam-4316	466	38	distance	distance	NOUN
ejpam-4316	466	39	matrix	matrix	NOUN
ejpam-4316	466	40	of	of	ADP
ejpam-4316	466	41	γ	γ	X
ejpam-4316	466	42	can	can	AUX
ejpam-4316	466	43	be	be	AUX
ejpam-4316	466	44	written	write	VERB
ejpam-4316	466	45	as	as	ADP
ejpam-4316	466	46	a	a	DET
ejpam-4316	466	47	2×	2×	NUM
ejpam-4316	466	48	2	2	NUM
ejpam-4316	466	49	block	block	NOUN
ejpam-4316	466	50	matrix	matrix	NOUN
ejpam-4316	466	51	given	give	VERB
ejpam-4316	466	52	by	by	ADP
ejpam-4316	466	53	d(γ	d(γ	PROPN
ejpam-4316	466	54	)	)	PUNCT
ejpam-4316	466	55	=	=	PUNCT
ejpam-4316	466	56	[	[	PUNCT
ejpam-4316	466	57	d(g	d(g	PROPN
ejpam-4316	466	58	)	)	PUNCT
ejpam-4316	466	59	d(g	d(g	PROPN
ejpam-4316	466	60	)	)	PUNCT
ejpam-4316	467	1	+	+	CCONJ
ejpam-4316	467	2	2	2	NUM
ejpam-4316	467	3	in	in	ADP
ejpam-4316	467	4	d(g	d(g	PROPN
ejpam-4316	467	5	)	)	PUNCT
ejpam-4316	467	6	+	+	CCONJ
ejpam-4316	467	7	2	2	NUM
ejpam-4316	467	8	in	in	ADP
ejpam-4316	467	9	d(g	d(g	PROPN
ejpam-4316	467	10	)	)	PUNCT
ejpam-4316	468	1	+	+	NOUN
ejpam-4316	468	2	a(g	a(g	PROPN
ejpam-4316	468	3	)	)	PUNCT
ejpam-4316	468	4	]	]	PUNCT
ejpam-4316	468	5	where	where	SCONJ
ejpam-4316	468	6	d(g	d(g	NOUN
ejpam-4316	468	7	)	)	PUNCT
ejpam-4316	468	8	and	and	CCONJ
ejpam-4316	468	9	a(g	a(g	PROPN
ejpam-4316	468	10	)	)	PUNCT
ejpam-4316	468	11	are	be	AUX
ejpam-4316	468	12	the	the	DET
ejpam-4316	468	13	distance	distance	NOUN
ejpam-4316	468	14	matrix	matrix	NOUN
ejpam-4316	468	15	,	,	PUNCT
ejpam-4316	468	16	adjacency	adjacency	NOUN
ejpam-4316	468	17	matrix	matrix	NOUN
ejpam-4316	468	18	of	of	ADP
ejpam-4316	468	19	the	the	DET
ejpam-4316	468	20	graph	graph	NOUN
ejpam-4316	468	21	g	g	NOUN
ejpam-4316	468	22	and	and	CCONJ
ejpam-4316	468	23	in	in	ADP
ejpam-4316	468	24	is	be	AUX
ejpam-4316	468	25	the	the	DET
ejpam-4316	468	26	identity	identity	NOUN
ejpam-4316	468	27	matrix	matrix	NOUN
ejpam-4316	468	28	of	of	ADP
ejpam-4316	468	29	size	size	NOUN
ejpam-4316	468	30	n.	n.	NOUN
ejpam-4316	468	31	we	we	PRON
ejpam-4316	468	32	can	can	AUX
ejpam-4316	468	33	determine	determine	VERB
ejpam-4316	468	34	the	the	DET
ejpam-4316	468	35	harary	harary	PROPN
ejpam-4316	468	36	index	index	NOUN
ejpam-4316	468	37	of	of	ADP
ejpam-4316	468	38	γ	γ	PROPN
ejpam-4316	468	39	using	use	VERB
ejpam-4316	468	40	the	the	DET
ejpam-4316	468	41	distance	distance	NOUN
ejpam-4316	468	42	matrix	matrix	NOUN
ejpam-4316	468	43	of	of	ADP
ejpam-4316	468	44	γ	γ	PROPN
ejpam-4316	468	45	given	give	VERB
ejpam-4316	468	46	by	by	ADP
ejpam-4316	468	47	the	the	DET
ejpam-4316	468	48	following	following	NOUN
ejpam-4316	468	49	:	:	PUNCT
ejpam-4316	469	1	f.j.h	f.j.h	ADJ
ejpam-4316	469	2	.	.	PUNCT
ejpam-4316	470	1	campeña	campeña	NOUN
ejpam-4316	470	2	,	,	PUNCT
ejpam-4316	470	3	m.c.g	m.c.g	PROPN
ejpam-4316	470	4	.	.	PUNCT
ejpam-4316	470	5	egan	egan	PROPN
ejpam-4316	470	6	,	,	PUNCT
ejpam-4316	470	7	j.r.m	j.r.m	PROPN
ejpam-4316	470	8	.	.	PUNCT
ejpam-4316	471	1	antalan	antalan	PROPN
ejpam-4316	471	2	/	/	SYM
ejpam-4316	471	3	eur	eur	PROPN
ejpam-4316	471	4	.	.	PUNCT
ejpam-4316	472	1	j.	j.	PROPN
ejpam-4316	472	2	pure	pure	PROPN
ejpam-4316	472	3	appl	appl	PROPN
ejpam-4316	472	4	.	.	PROPN
ejpam-4316	472	5	math	math	PROPN
ejpam-4316	472	6	,	,	PUNCT
ejpam-4316	472	7	15	15	NUM
ejpam-4316	472	8	(	(	PUNCT
ejpam-4316	472	9	2	2	NUM
ejpam-4316	472	10	)	)	PUNCT
ejpam-4316	472	11	(	(	PUNCT
ejpam-4316	472	12	2022	2022	NUM
ejpam-4316	472	13	)	)	PUNCT
ejpam-4316	472	14	,	,	PUNCT
ejpam-4316	472	15	602	602	NUM
ejpam-4316	472	16	-	-	SYM
ejpam-4316	472	17	619	619	NUM
ejpam-4316	472	18	616	616	NUM
ejpam-4316	472	19	h(γ	h(γ	NOUN
ejpam-4316	472	20	)	)	PUNCT
ejpam-4316	472	21	=	=	SYM
ejpam-4316	473	1	1	1	NUM
ejpam-4316	473	2	2	2	NUM
ejpam-4316	473	3	∑	∑	PUNCT
ejpam-4316	473	4	d(γ	d(γ	PROPN
ejpam-4316	473	5	)	)	PUNCT
ejpam-4316	473	6	=	=	SYM
ejpam-4316	473	7	1	1	NUM
ejpam-4316	473	8	2	2	NUM
ejpam-4316	473	9	(	(	PUNCT
ejpam-4316	473	10	∑	∑	PUNCT
ejpam-4316	473	11	d(g	d(g	PROPN
ejpam-4316	473	12	)	)	PUNCT
ejpam-4316	473	13	+	+	CCONJ
ejpam-4316	473	14	∑	∑	PROPN
ejpam-4316	473	15	d(g	d(g	PROPN
ejpam-4316	473	16	)	)	PUNCT
ejpam-4316	473	17	+	+	CCONJ
ejpam-4316	473	18	2	2	NUM
ejpam-4316	473	19	in	in	ADP
ejpam-4316	473	20	+	+	NUM
ejpam-4316	473	21	∑	∑	PROPN
ejpam-4316	473	22	d(g	d(g	PROPN
ejpam-4316	473	23	)	)	PUNCT
ejpam-4316	473	24	+	+	CCONJ
ejpam-4316	473	25	2	2	NUM
ejpam-4316	473	26	in	in	ADP
ejpam-4316	473	27	+	+	NUM
ejpam-4316	473	28	∑	∑	PROPN
ejpam-4316	473	29	d(g	d(g	PROPN
ejpam-4316	473	30	)	)	PUNCT
ejpam-4316	473	31	+	+	NOUN
ejpam-4316	473	32	a(g	a(g	PROPN
ejpam-4316	473	33	)	)	PUNCT
ejpam-4316	473	34	)	)	PUNCT
ejpam-4316	474	1	=	=	SYM
ejpam-4316	474	2	1	1	NUM
ejpam-4316	474	3	2	2	NUM
ejpam-4316	474	4	(	(	PUNCT
ejpam-4316	474	5	∑	∑	PUNCT
ejpam-4316	474	6	d(g	d(g	PROPN
ejpam-4316	474	7	)	)	PUNCT
ejpam-4316	475	1	+	+	CCONJ
ejpam-4316	475	2	∑	∑	PROPN
ejpam-4316	475	3	d(g	d(g	PROPN
ejpam-4316	475	4	)	)	PUNCT
ejpam-4316	475	5	+	+	CCONJ
ejpam-4316	475	6	∑	∑	PROPN
ejpam-4316	475	7	2	2	NUM
ejpam-4316	475	8	in	in	ADP
ejpam-4316	475	9	+	+	NUM
ejpam-4316	475	10	∑	∑	PROPN
ejpam-4316	475	11	d(g	d(g	PROPN
ejpam-4316	475	12	)	)	PUNCT
ejpam-4316	476	1	+	+	CCONJ
ejpam-4316	476	2	∑	∑	PROPN
ejpam-4316	476	3	2	2	NUM
ejpam-4316	476	4	in	in	ADP
ejpam-4316	476	5	+	+	NOUN
ejpam-4316	476	6	∑	∑	NOUN
ejpam-4316	476	7	d(g)−a(g	d(g)−a(g	NOUN
ejpam-4316	476	8	)	)	PUNCT
ejpam-4316	476	9	+	+	CCONJ
ejpam-4316	476	10	∑	∑	PROPN
ejpam-4316	476	11	2a(g	2a(g	NUM
ejpam-4316	476	12	)	)	PUNCT
ejpam-4316	476	13	)	)	PUNCT
ejpam-4316	477	1	=	=	SYM
ejpam-4316	478	1	1	1	NUM
ejpam-4316	478	2	2	2	NUM
ejpam-4316	478	3	(	(	PUNCT
ejpam-4316	478	4	4	4	NUM
ejpam-4316	478	5	∑	∑	PUNCT
ejpam-4316	478	6	d(g	d(g	PROPN
ejpam-4316	478	7	)	)	PUNCT
ejpam-4316	478	8	+	+	CCONJ
ejpam-4316	478	9	2	2	NUM
ejpam-4316	478	10	∑	∑	SYM
ejpam-4316	478	11	2	2	NUM
ejpam-4316	478	12	in	in	ADP
ejpam-4316	478	13	+	+	NUM
ejpam-4316	478	14	∑	∑	PROPN
ejpam-4316	478	15	2a(g)−	2a(g)−	NUM
ejpam-4316	478	16	∑	∑	PUNCT
ejpam-4316	478	17	a(g	a(g	PROPN
ejpam-4316	478	18	)	)	PUNCT
ejpam-4316	478	19	)	)	PUNCT
ejpam-4316	479	1	=	=	SYM
ejpam-4316	479	2	4	4	NUM
ejpam-4316	479	3	(	(	PUNCT
ejpam-4316	479	4	1	1	NUM
ejpam-4316	479	5	2	2	NUM
ejpam-4316	479	6	∑	∑	PUNCT
ejpam-4316	479	7	d(g	d(g	PROPN
ejpam-4316	479	8	)	)	PUNCT
ejpam-4316	479	9	)	)	PUNCT
ejpam-4316	480	1	+	+	CCONJ
ejpam-4316	480	2	∑	∑	PUNCT
ejpam-4316	480	3	2	2	NUM
ejpam-4316	480	4	in	in	ADP
ejpam-4316	480	5	+	+	NOUN
ejpam-4316	480	6	1	1	NUM
ejpam-4316	480	7	2	2	NUM
ejpam-4316	480	8	∑	∑	SYM
ejpam-4316	480	9	2a(g)−	2a(g)−	NUM
ejpam-4316	480	10	1	1	NUM
ejpam-4316	480	11	2	2	NUM
ejpam-4316	480	12	∑	∑	PUNCT
ejpam-4316	480	13	a(g	a(g	PROPN
ejpam-4316	480	14	)	)	PUNCT
ejpam-4316	480	15	=	=	SYM
ejpam-4316	480	16	4h(g	4h(g	PROPN
ejpam-4316	480	17	)	)	PUNCT
ejpam-4316	481	1	+	+	CCONJ
ejpam-4316	481	2	n	n	CCONJ
ejpam-4316	481	3	2	2	NUM
ejpam-4316	481	4	+	+	CCONJ
ejpam-4316	481	5	1	1	NUM
ejpam-4316	481	6	2	2	NUM
ejpam-4316	481	7	∑	∑	SYM
ejpam-4316	481	8	2a(g)−	2a(g)−	NUM
ejpam-4316	481	9	1	1	NUM
ejpam-4316	481	10	2	2	NUM
ejpam-4316	481	11	∑	∑	PUNCT
ejpam-4316	481	12	a(g	a(g	NOUN
ejpam-4316	481	13	)	)	PUNCT
ejpam-4316	481	14	note	note	VERB
ejpam-4316	481	15	that	that	SCONJ
ejpam-4316	481	16	the	the	DET
ejpam-4316	481	17	sum	sum	NOUN
ejpam-4316	481	18	of	of	ADP
ejpam-4316	481	19	the	the	DET
ejpam-4316	481	20	entries	entry	NOUN
ejpam-4316	481	21	in	in	ADP
ejpam-4316	481	22	an	an	DET
ejpam-4316	481	23	adjacency	adjacency	NOUN
ejpam-4316	481	24	matrix	matrix	NOUN
ejpam-4316	481	25	is	be	AUX
ejpam-4316	481	26	twice	twice	DET
ejpam-4316	481	27	the	the	DET
ejpam-4316	481	28	number	number	NOUN
ejpam-4316	481	29	of	of	ADP
ejpam-4316	481	30	edges	edge	NOUN
ejpam-4316	481	31	m.	m.	NOUN
ejpam-4316	481	32	then	then	ADV
ejpam-4316	481	33	,	,	PUNCT
ejpam-4316	481	34	we	we	PRON
ejpam-4316	481	35	have	have	VERB
ejpam-4316	481	36	h(γ	h(γ	NOUN
ejpam-4316	481	37	)	)	PUNCT
ejpam-4316	481	38	=	=	SYM
ejpam-4316	481	39	4h(g	4h(g	NOUN
ejpam-4316	481	40	)	)	PUNCT
ejpam-4316	482	1	+	+	CCONJ
ejpam-4316	482	2	n	n	CCONJ
ejpam-4316	482	3	2	2	NUM
ejpam-4316	482	4	+	+	CCONJ
ejpam-4316	482	5	1	1	NUM
ejpam-4316	482	6	2	2	NUM
ejpam-4316	482	7	(	(	PUNCT
ejpam-4316	482	8	2	2	NUM
ejpam-4316	482	9	m	m	NOUN
ejpam-4316	482	10	2	2	NUM
ejpam-4316	482	11	)	)	PUNCT
ejpam-4316	482	12	−	−	NOUN
ejpam-4316	482	13	1	1	NUM
ejpam-4316	482	14	2	2	NUM
ejpam-4316	482	15	(	(	PUNCT
ejpam-4316	482	16	2	2	NUM
ejpam-4316	482	17	m	m	NOUN
ejpam-4316	482	18	)	)	PUNCT
ejpam-4316	482	19	=	=	SYM
ejpam-4316	482	20	4h(g	4h(g	NOUN
ejpam-4316	482	21	)	)	PUNCT
ejpam-4316	483	1	+	+	CCONJ
ejpam-4316	483	2	n	n	CCONJ
ejpam-4316	483	3	2	2	NUM
ejpam-4316	483	4	+	+	CCONJ
ejpam-4316	483	5	m	m	PROPN
ejpam-4316	483	6	2	2	NUM
ejpam-4316	483	7	−m	−m	NOUN
ejpam-4316	483	8	=	=	SYM
ejpam-4316	483	9	4h(g	4h(g	NOUN
ejpam-4316	483	10	)	)	PUNCT
ejpam-4316	484	1	+	+	CCONJ
ejpam-4316	484	2	n	n	PRON
ejpam-4316	484	3	2	2	NUM
ejpam-4316	484	4	−	−	NOUN
ejpam-4316	484	5	m	m	VERB
ejpam-4316	484	6	2	2	NUM
ejpam-4316	484	7	=	=	SYM
ejpam-4316	484	8	4h(g	4h(g	NOUN
ejpam-4316	484	9	)	)	PUNCT
ejpam-4316	485	1	+	+	CCONJ
ejpam-4316	485	2	n−m	n−m	PROPN
ejpam-4316	485	3	2	2	NUM
ejpam-4316	485	4	.	.	PUNCT
ejpam-4316	485	5	corollary	corollary	ADJ
ejpam-4316	485	6	6	6	NUM
ejpam-4316	485	7	.	.	PUNCT
ejpam-4316	486	1	let	let	VERB
ejpam-4316	486	2	g	g	PRON
ejpam-4316	486	3	be	be	AUX
ejpam-4316	486	4	a	a	DET
ejpam-4316	486	5	complete	complete	ADJ
ejpam-4316	486	6	graph	graph	NOUN
ejpam-4316	486	7	kn	kn	PROPN
ejpam-4316	486	8	.	.	PUNCT
ejpam-4316	487	1	then	then	ADV
ejpam-4316	487	2	the	the	DET
ejpam-4316	487	3	v	v	ADJ
ejpam-4316	487	4	-splitting	-splitting	ADJ
ejpam-4316	487	5	graph	graph	NOUN
ejpam-4316	487	6	of	of	ADP
ejpam-4316	487	7	kn	kn	PROPN
ejpam-4316	487	8	has	have	VERB
ejpam-4316	487	9	a	a	DET
ejpam-4316	487	10	harary	harary	ADJ
ejpam-4316	487	11	index	index	NOUN
ejpam-4316	487	12	given	give	VERB
ejpam-4316	487	13	by	by	ADP
ejpam-4316	487	14	h(γ	h(γ	NOUN
ejpam-4316	487	15	)	)	PUNCT
ejpam-4316	487	16	=	=	SYM
ejpam-4316	487	17	1	1	NUM
ejpam-4316	487	18	4	4	NUM
ejpam-4316	487	19	(	(	PUNCT
ejpam-4316	487	20	7n2	7n2	NUM
ejpam-4316	487	21	−	−	PROPN
ejpam-4316	487	22	5n	5n	NOUN
ejpam-4316	487	23	)	)	PUNCT
ejpam-4316	487	24	.	.	PUNCT
ejpam-4316	488	1	corollary	corollary	ADJ
ejpam-4316	488	2	7	7	NUM
ejpam-4316	488	3	.	.	PUNCT
ejpam-4316	489	1	let	let	VERB
ejpam-4316	489	2	g	g	NOUN
ejpam-4316	489	3	be	be	AUX
ejpam-4316	489	4	the	the	DET
ejpam-4316	489	5	wheel	wheel	NOUN
ejpam-4316	489	6	graph	graph	NOUN
ejpam-4316	489	7	wn	wn	PROPN
ejpam-4316	489	8	.	.	PUNCT
ejpam-4316	490	1	then	then	ADV
ejpam-4316	490	2	the	the	DET
ejpam-4316	490	3	splitting	splitting	NOUN
ejpam-4316	490	4	graph	graph	NOUN
ejpam-4316	490	5	γ(wn	γ(wn	NOUN
ejpam-4316	490	6	,	,	PUNCT
ejpam-4316	490	7	s	s	PART
ejpam-4316	490	8	)	)	PUNCT
ejpam-4316	490	9	has	have	VERB
ejpam-4316	490	10	a	a	DET
ejpam-4316	490	11	harary	harary	ADJ
ejpam-4316	490	12	index	index	NOUN
ejpam-4316	490	13	given	give	VERB
ejpam-4316	490	14	by	by	ADP
ejpam-4316	490	15	w	w	PROPN
ejpam-4316	490	16	(	(	PUNCT
ejpam-4316	490	17	γ	γ	NOUN
ejpam-4316	490	18	)	)	PUNCT
ejpam-4316	490	19	=	=	SYM
ejpam-4316	491	1	1	1	NUM
ejpam-4316	491	2	2(2n	2(2n	NUM
ejpam-4316	491	3	2	2	NUM
ejpam-4316	491	4	+	+	CCONJ
ejpam-4316	491	5	5n−	5n−	NUM
ejpam-4316	491	6	6	6	NUM
ejpam-4316	491	7	)	)	PUNCT
ejpam-4316	491	8	.	.	PUNCT
ejpam-4316	492	1	theorem	theorem	VERB
ejpam-4316	492	2	16	16	NUM
ejpam-4316	492	3	.	.	PUNCT
ejpam-4316	493	1	let	let	VERB
ejpam-4316	493	2	g	g	PRON
ejpam-4316	493	3	be	be	AUX
ejpam-4316	493	4	a	a	DET
ejpam-4316	493	5	complete	complete	ADJ
ejpam-4316	493	6	graph	graph	NOUN
ejpam-4316	493	7	for	for	ADP
ejpam-4316	493	8	n	n	X
ejpam-4316	493	9	≥	≥	NOUN
ejpam-4316	493	10	3	3	NUM
ejpam-4316	493	11	and	and	CCONJ
ejpam-4316	493	12	s	s	X
ejpam-4316	493	13	⊂	⊂	PROPN
ejpam-4316	493	14	v	v	X
ejpam-4316	493	15	(	(	PUNCT
ejpam-4316	493	16	kn	kn	PROPN
ejpam-4316	493	17	)	)	PUNCT
ejpam-4316	493	18	such	such	ADJ
ejpam-4316	493	19	that	that	SCONJ
ejpam-4316	493	20	|s|	|s|	PROPN
ejpam-4316	493	21	=	=	SYM
ejpam-4316	493	22	r	r	NOUN
ejpam-4316	493	23	where	where	SCONJ
ejpam-4316	493	24	1	1	NUM
ejpam-4316	493	25	≤	≤	NOUN
ejpam-4316	493	26	r	r	NOUN
ejpam-4316	493	27	≤	≤	NOUN
ejpam-4316	493	28	n	n	CCONJ
ejpam-4316	493	29	−	−	PROPN
ejpam-4316	493	30	1	1	NUM
ejpam-4316	493	31	.	.	PUNCT
ejpam-4316	494	1	then	then	ADV
ejpam-4316	494	2	the	the	DET
ejpam-4316	494	3	harary	harary	PROPN
ejpam-4316	494	4	index	index	NOUN
ejpam-4316	494	5	of	of	ADP
ejpam-4316	494	6	the	the	DET
ejpam-4316	494	7	splitting	splitting	NOUN
ejpam-4316	494	8	graph	graph	NOUN
ejpam-4316	494	9	of	of	ADP
ejpam-4316	494	10	kn	kn	PROPN
ejpam-4316	494	11	is	be	AUX
ejpam-4316	494	12	given	give	VERB
ejpam-4316	494	13	by	by	ADP
ejpam-4316	494	14	h(γ(kn	h(γ(kn	PROPN
ejpam-4316	494	15	,	,	PUNCT
ejpam-4316	494	16	s	s	NOUN
ejpam-4316	494	17	)	)	PUNCT
ejpam-4316	494	18	)	)	PUNCT
ejpam-4316	495	1	=	=	PUNCT
ejpam-4316	496	1	2n2−2n+r2−3r+4nr	2n2−2n+r2−3r+4nr	NUM
ejpam-4316	496	2	4	4	NUM
ejpam-4316	496	3	.	.	PUNCT
ejpam-4316	497	1	proof	proof	NOUN
ejpam-4316	497	2	.	.	PUNCT
ejpam-4316	498	1	let	let	VERB
ejpam-4316	498	2	v	v	X
ejpam-4316	498	3	(	(	PUNCT
ejpam-4316	498	4	kn	kn	PROPN
ejpam-4316	498	5	)	)	PUNCT
ejpam-4316	498	6	=	=	PRON
ejpam-4316	499	1	{	{	PUNCT
ejpam-4316	499	2	x1	x1	PROPN
ejpam-4316	499	3	,	,	PUNCT
ejpam-4316	499	4	x2	x2	PROPN
ejpam-4316	499	5	,	,	PUNCT
ejpam-4316	499	6	.	.	PUNCT
ejpam-4316	499	7	.	.	PUNCT
ejpam-4316	499	8	.	.	PUNCT
ejpam-4316	500	1	,	,	PUNCT
ejpam-4316	500	2	xn	xn	PROPN
ejpam-4316	500	3	}	}	PUNCT
ejpam-4316	500	4	.	.	PUNCT
ejpam-4316	501	1	without	without	ADP
ejpam-4316	501	2	loss	loss	NOUN
ejpam-4316	501	3	of	of	ADP
ejpam-4316	501	4	generality	generality	NOUN
ejpam-4316	501	5	,	,	PUNCT
ejpam-4316	501	6	suppose	suppose	VERB
ejpam-4316	501	7	s	s	VERB
ejpam-4316	501	8	=	=	PUNCT
ejpam-4316	501	9	{	{	PUNCT
ejpam-4316	501	10	x1	x1	PROPN
ejpam-4316	501	11	,	,	PUNCT
ejpam-4316	501	12	x2	x2	PROPN
ejpam-4316	501	13	,	,	PUNCT
ejpam-4316	501	14	.	.	PUNCT
ejpam-4316	501	15	.	.	PUNCT
ejpam-4316	502	1	.	.	PUNCT
ejpam-4316	503	1	,	,	PUNCT
ejpam-4316	503	2	xr	xr	PROPN
ejpam-4316	503	3	}	}	PUNCT
ejpam-4316	503	4	.	.	PUNCT
ejpam-4316	504	1	suppose	suppose	VERB
ejpam-4316	504	2	the	the	DET
ejpam-4316	504	3	ordering	ordering	NOUN
ejpam-4316	504	4	of	of	ADP
ejpam-4316	504	5	the	the	DET
ejpam-4316	504	6	vertices	vertex	NOUN
ejpam-4316	504	7	of	of	ADP
ejpam-4316	504	8	the	the	DET
ejpam-4316	504	9	graph	graph	NOUN
ejpam-4316	504	10	γ	γ	X
ejpam-4316	504	11	=	=	SYM
ejpam-4316	504	12	γ(kn	γ(kn	PROPN
ejpam-4316	504	13	,	,	PUNCT
ejpam-4316	504	14	s	s	PART
ejpam-4316	504	15	)	)	PUNCT
ejpam-4316	504	16	is	be	AUX
ejpam-4316	504	17	x1	x1	PROPN
ejpam-4316	504	18	,	,	PUNCT
ejpam-4316	504	19	x2	x2	PROPN
ejpam-4316	504	20	,	,	PUNCT
ejpam-4316	504	21	.	.	PUNCT
ejpam-4316	504	22	.	.	PUNCT
ejpam-4316	505	1	.	.	PUNCT
ejpam-4316	506	1	,	,	PUNCT
ejpam-4316	506	2	xn	xn	PROPN
ejpam-4316	506	3	,	,	PUNCT
ejpam-4316	506	4	x	x	SYM
ejpam-4316	506	5	′	′	NUM
ejpam-4316	506	6	1	1	NUM
ejpam-4316	506	7	,	,	PUNCT
ejpam-4316	506	8	x	x	NOUN
ejpam-4316	506	9	′	′	NOUN
ejpam-4316	506	10	2	2	NUM
ejpam-4316	506	11	,	,	PUNCT
ejpam-4316	506	12	.	.	PUNCT
ejpam-4316	506	13	.	.	PUNCT
ejpam-4316	506	14	.	.	PUNCT
ejpam-4316	507	1	,	,	PUNCT
ejpam-4316	507	2	x	x	X
ejpam-4316	507	3	′	′	NUM
ejpam-4316	507	4	r.	r.	PROPN
ejpam-4316	507	5	then	then	ADV
ejpam-4316	507	6	we	we	PRON
ejpam-4316	507	7	can	can	AUX
ejpam-4316	507	8	write	write	VERB
ejpam-4316	507	9	the	the	DET
ejpam-4316	507	10	distance	distance	NOUN
ejpam-4316	507	11	matrix	matrix	NOUN
ejpam-4316	507	12	of	of	ADP
ejpam-4316	507	13	γ	γ	PROPN
ejpam-4316	507	14	as	as	ADP
ejpam-4316	507	15	a	a	DET
ejpam-4316	507	16	block	block	NOUN
ejpam-4316	507	17	matrix	matrix	NOUN
ejpam-4316	507	18	as	as	SCONJ
ejpam-4316	507	19	follows	follow	VERB
ejpam-4316	507	20	.	.	PUNCT
ejpam-4316	508	1	d(γ	d(γ	ADJ
ejpam-4316	508	2	)	)	PUNCT
ejpam-4316	508	3	=	=	SYM
ejpam-4316	508	4			NOUN
ejpam-4316	509	1	a(kr	a(kr	ADJ
ejpam-4316	509	2	)	)	PUNCT
ejpam-4316	510	1	+	+	CCONJ
ejpam-4316	510	2	2ir	2ir	ADJ
ejpam-4316	510	3	d(kn	d(kn	NOUN
ejpam-4316	510	4	)	)	PUNCT
ejpam-4316	510	5	jn−r×r	jn−r×r	NOUN
ejpam-4316	511	1	a(kr	a(kr	PROPN
ejpam-4316	511	2	)	)	PUNCT
ejpam-4316	512	1	+	+	CCONJ
ejpam-4316	512	2	2ir	2ir	ADJ
ejpam-4316	512	3	jr×n−r	jr×n−r	ADJ
ejpam-4316	512	4	2a(kr	2a(kr	NUM
ejpam-4316	512	5	)	)	PUNCT
ejpam-4316	512	6			PROPN
ejpam-4316	512	7	f.j.h	f.j.h	NOUN
ejpam-4316	512	8	.	.	PUNCT
ejpam-4316	513	1	campeña	campeña	NOUN
ejpam-4316	513	2	,	,	PUNCT
ejpam-4316	513	3	m.c.g	m.c.g	PROPN
ejpam-4316	513	4	.	.	PUNCT
ejpam-4316	513	5	egan	egan	PROPN
ejpam-4316	513	6	,	,	PUNCT
ejpam-4316	513	7	j.r.m	j.r.m	PROPN
ejpam-4316	513	8	.	.	PUNCT
ejpam-4316	514	1	antalan	antalan	PROPN
ejpam-4316	514	2	/	/	SYM
ejpam-4316	514	3	eur	eur	PROPN
ejpam-4316	514	4	.	.	PUNCT
ejpam-4316	515	1	j.	j.	PROPN
ejpam-4316	515	2	pure	pure	PROPN
ejpam-4316	515	3	appl	appl	PROPN
ejpam-4316	515	4	.	.	PROPN
ejpam-4316	515	5	math	math	PROPN
ejpam-4316	515	6	,	,	PUNCT
ejpam-4316	515	7	15	15	NUM
ejpam-4316	515	8	(	(	PUNCT
ejpam-4316	515	9	2	2	NUM
ejpam-4316	515	10	)	)	PUNCT
ejpam-4316	515	11	(	(	PUNCT
ejpam-4316	515	12	2022	2022	NUM
ejpam-4316	515	13	)	)	PUNCT
ejpam-4316	515	14	,	,	PUNCT
ejpam-4316	515	15	602	602	NUM
ejpam-4316	515	16	-	-	SYM
ejpam-4316	515	17	619	619	NUM
ejpam-4316	515	18	617	617	NUM
ejpam-4316	515	19	where	where	SCONJ
ejpam-4316	515	20	d(kn	d(kn	NOUN
ejpam-4316	515	21	)	)	PUNCT
ejpam-4316	515	22	,	,	PUNCT
ejpam-4316	515	23	a(kr	a(kr	PROPN
ejpam-4316	515	24	)	)	PUNCT
ejpam-4316	515	25	,	,	PUNCT
ejpam-4316	515	26	ir	ir	PROPN
ejpam-4316	515	27	,	,	PUNCT
ejpam-4316	515	28	jr×n−r	jr×n−r	PROPN
ejpam-4316	515	29	are	be	AUX
ejpam-4316	515	30	the	the	DET
ejpam-4316	515	31	distance	distance	NOUN
ejpam-4316	515	32	matrix	matrix	NOUN
ejpam-4316	515	33	of	of	ADP
ejpam-4316	515	34	kn	kn	PROPN
ejpam-4316	515	35	,	,	PUNCT
ejpam-4316	515	36	adjacency	adjacency	NOUN
ejpam-4316	515	37	matrix	matrix	NOUN
ejpam-4316	515	38	of	of	ADP
ejpam-4316	515	39	kr	kr	PROPN
ejpam-4316	515	40	,	,	PUNCT
ejpam-4316	515	41	identity	identity	NOUN
ejpam-4316	515	42	matrix	matrix	NOUN
ejpam-4316	515	43	of	of	ADP
ejpam-4316	515	44	size	size	NOUN
ejpam-4316	515	45	r	r	NOUN
ejpam-4316	515	46	,	,	PUNCT
ejpam-4316	515	47	and	and	CCONJ
ejpam-4316	515	48	the	the	DET
ejpam-4316	515	49	all	all	DET
ejpam-4316	515	50	one	one	NOUN
ejpam-4316	515	51	’s	’s	PART
ejpam-4316	515	52	matrix	matrix	NOUN
ejpam-4316	515	53	of	of	ADP
ejpam-4316	515	54	size	size	NOUN
ejpam-4316	515	55	r×	r×	NOUN
ejpam-4316	515	56	n−	n−	NOUN
ejpam-4316	515	57	r	r	NOUN
ejpam-4316	515	58	respectively	respectively	ADV
ejpam-4316	515	59	.	.	PUNCT
ejpam-4316	516	1	hence	hence	ADV
ejpam-4316	516	2	,	,	PUNCT
ejpam-4316	516	3	we	we	PRON
ejpam-4316	516	4	can	can	AUX
ejpam-4316	516	5	compute	compute	VERB
ejpam-4316	516	6	the	the	DET
ejpam-4316	516	7	harary	harary	PROPN
ejpam-4316	516	8	index	index	NOUN
ejpam-4316	516	9	by	by	ADP
ejpam-4316	516	10	h(γ	h(γ	NOUN
ejpam-4316	516	11	)	)	PUNCT
ejpam-4316	516	12	=	=	SYM
ejpam-4316	517	1	1	1	NUM
ejpam-4316	517	2	2	2	NUM
ejpam-4316	517	3	∑	∑	PUNCT
ejpam-4316	517	4	d(γ	d(γ	PROPN
ejpam-4316	517	5	)	)	PUNCT
ejpam-4316	517	6	=	=	SYM
ejpam-4316	517	7	1	1	NUM
ejpam-4316	517	8	2	2	NUM
ejpam-4316	517	9	(	(	PUNCT
ejpam-4316	517	10	∑	∑	NOUN
ejpam-4316	517	11	d(kn	d(kn	NUM
ejpam-4316	517	12	)	)	PUNCT
ejpam-4316	517	13	+	+	CCONJ
ejpam-4316	517	14	2	2	NUM
ejpam-4316	517	15	∑	∑	PUNCT
ejpam-4316	517	16	a(kr	a(kr	ADJ
ejpam-4316	517	17	)	)	PUNCT
ejpam-4316	517	18	+	+	X
ejpam-4316	517	19	2ir	2ir	ADJ
ejpam-4316	517	20	+	+	CCONJ
ejpam-4316	517	21	∑	∑	PROPN
ejpam-4316	517	22	2a(kr	2a(kr	NUM
ejpam-4316	517	23	)	)	PUNCT
ejpam-4316	518	1	+	+	CCONJ
ejpam-4316	518	2	∑	∑	PUNCT
ejpam-4316	518	3	jn−r×r	jn−r×r	ADJ
ejpam-4316	518	4	+	+	CCONJ
ejpam-4316	518	5	∑	∑	ADV
ejpam-4316	518	6	jr×n−r	jr×n−r	ADJ
ejpam-4316	518	7	)	)	PUNCT
ejpam-4316	518	8	=	=	SYM
ejpam-4316	518	9	1	1	NUM
ejpam-4316	518	10	2	2	NUM
ejpam-4316	518	11	d(kn	d(kn	NUM
ejpam-4316	518	12	)	)	PUNCT
ejpam-4316	519	1	+	+	CCONJ
ejpam-4316	519	2	∑	∑	PUNCT
ejpam-4316	519	3	a(kr	a(kr	ADJ
ejpam-4316	519	4	)	)	PUNCT
ejpam-4316	520	1	+	+	X
ejpam-4316	520	2	2ir	2ir	ADJ
ejpam-4316	520	3	+	+	CCONJ
ejpam-4316	520	4	1	1	NUM
ejpam-4316	520	5	2	2	NUM
ejpam-4316	520	6	∑	∑	ADP
ejpam-4316	520	7	2a(kr	2a(kr	NUM
ejpam-4316	520	8	)	)	PUNCT
ejpam-4316	521	1	+	+	CCONJ
ejpam-4316	521	2	1	1	NUM
ejpam-4316	521	3	2	2	NUM
ejpam-4316	521	4	∑	∑	NOUN
ejpam-4316	521	5	jn−r×r	jn−r×r	ADJ
ejpam-4316	522	1	+	+	CCONJ
ejpam-4316	522	2	1	1	NUM
ejpam-4316	522	3	2	2	NUM
ejpam-4316	522	4	∑	∑	NOUN
ejpam-4316	522	5	jr×n−r	jr×n−r	NOUN
ejpam-4316	522	6	=	=	SYM
ejpam-4316	522	7	h(kn	h(kn	NOUN
ejpam-4316	522	8	)	)	PUNCT
ejpam-4316	523	1	+	+	CCONJ
ejpam-4316	523	2	∑	∑	PUNCT
ejpam-4316	523	3	a(kr	a(kr	ADJ
ejpam-4316	523	4	)	)	PUNCT
ejpam-4316	524	1	+	+	CCONJ
ejpam-4316	524	2	∑	∑	PROPN
ejpam-4316	524	3	2ir	2ir	ADJ
ejpam-4316	524	4	+	+	CCONJ
ejpam-4316	524	5	1	1	NUM
ejpam-4316	524	6	2	2	NUM
ejpam-4316	524	7	∑	∑	ADP
ejpam-4316	524	8	2a(kr	2a(kr	NUM
ejpam-4316	524	9	)	)	PUNCT
ejpam-4316	525	1	+	+	CCONJ
ejpam-4316	525	2	1	1	NUM
ejpam-4316	525	3	2	2	NUM
ejpam-4316	525	4	∑	∑	NOUN
ejpam-4316	525	5	jn−r×r	jn−r×r	ADJ
ejpam-4316	526	1	+	+	CCONJ
ejpam-4316	526	2	1	1	NUM
ejpam-4316	526	3	2	2	NUM
ejpam-4316	526	4	∑	∑	NOUN
ejpam-4316	526	5	jr×n−r	jr×n−r	NOUN
ejpam-4316	526	6	=	=	PUNCT
ejpam-4316	526	7	n(n−	n(n−	NOUN
ejpam-4316	526	8	1	1	NUM
ejpam-4316	526	9	)	)	PUNCT
ejpam-4316	526	10	2	2	NUM
ejpam-4316	527	1	+	+	CCONJ
ejpam-4316	527	2	2|e(kr)|+	2|e(kr)|+	NUM
ejpam-4316	527	3	r	r	NOUN
ejpam-4316	527	4	2	2	NUM
ejpam-4316	527	5	+	+	CCONJ
ejpam-4316	527	6	1	1	NUM
ejpam-4316	527	7	2	2	NUM
ejpam-4316	527	8	(	(	PUNCT
ejpam-4316	527	9	2|e(kr)|	2|e(kr)|	NOUN
ejpam-4316	527	10	2	2	NUM
ejpam-4316	527	11	)	)	PUNCT
ejpam-4316	527	12	+	+	CCONJ
ejpam-4316	527	13	1	1	NUM
ejpam-4316	527	14	2	2	NUM
ejpam-4316	527	15	(	(	PUNCT
ejpam-4316	527	16	n−	n−	NOUN
ejpam-4316	527	17	r)r	r)r	VERB
ejpam-4316	527	18	+	+	CCONJ
ejpam-4316	527	19	1	1	NUM
ejpam-4316	527	20	2	2	NUM
ejpam-4316	527	21	(	(	PUNCT
ejpam-4316	527	22	n−	n−	NOUN
ejpam-4316	527	23	r)r	r)r	PUNCT
ejpam-4316	527	24	=	=	PUNCT
ejpam-4316	527	25	n(n−	n(n−	VERB
ejpam-4316	527	26	1	1	NUM
ejpam-4316	527	27	)	)	PUNCT
ejpam-4316	527	28	2	2	NUM
ejpam-4316	528	1	+	+	CCONJ
ejpam-4316	528	2	2|e(kr)|+	2|e(kr)|+	NUM
ejpam-4316	528	3	r	r	NOUN
ejpam-4316	528	4	2	2	NUM
ejpam-4316	528	5	+	+	CCONJ
ejpam-4316	528	6	1	1	NUM
ejpam-4316	528	7	2	2	NUM
ejpam-4316	528	8	|e(kr)|+	|e(kr)|+	NOUN
ejpam-4316	528	9	r(n−	r(n−	NOUN
ejpam-4316	528	10	r	r	NOUN
ejpam-4316	528	11	)	)	PUNCT
ejpam-4316	528	12	=	=	PRON
ejpam-4316	528	13	n(n−	n(n−	ADJ
ejpam-4316	528	14	1	1	NUM
ejpam-4316	528	15	)	)	PUNCT
ejpam-4316	528	16	2	2	NUM
ejpam-4316	529	1	+	+	CCONJ
ejpam-4316	529	2	5	5	NUM
ejpam-4316	529	3	2	2	NUM
ejpam-4316	529	4	|e(kr)|+	|e(kr)|+	NOUN
ejpam-4316	529	5	r	r	NOUN
ejpam-4316	529	6	2	2	NUM
ejpam-4316	529	7	+	+	NUM
ejpam-4316	529	8	nr	nr	NOUN
ejpam-4316	529	9	−	−	NOUN
ejpam-4316	529	10	r2	r2	NOUN
ejpam-4316	529	11	=	=	PUNCT
ejpam-4316	529	12	n(n−	n(n−	PROPN
ejpam-4316	529	13	1	1	NUM
ejpam-4316	529	14	)	)	PUNCT
ejpam-4316	529	15	2	2	NUM
ejpam-4316	530	1	+	+	CCONJ
ejpam-4316	530	2	5	5	NUM
ejpam-4316	530	3	2	2	NUM
ejpam-4316	530	4	(	(	PUNCT
ejpam-4316	530	5	r(r	r(r	NOUN
ejpam-4316	530	6	−	−	PROPN
ejpam-4316	530	7	1	1	NUM
ejpam-4316	530	8	)	)	PUNCT
ejpam-4316	530	9	2	2	NUM
ejpam-4316	530	10	)	)	PUNCT
ejpam-4316	531	1	+	+	CCONJ
ejpam-4316	531	2	r	r	NOUN
ejpam-4316	531	3	2	2	NUM
ejpam-4316	531	4	+	+	NUM
ejpam-4316	531	5	nr	nr	NOUN
ejpam-4316	531	6	−	−	NOUN
ejpam-4316	531	7	r2	r2	NOUN
ejpam-4316	531	8	=	=	PUNCT
ejpam-4316	531	9	n(n−	n(n−	PROPN
ejpam-4316	531	10	1	1	NUM
ejpam-4316	531	11	)	)	PUNCT
ejpam-4316	531	12	2	2	NUM
ejpam-4316	532	1	+	+	NUM
ejpam-4316	532	2	5r2	5r2	NUM
ejpam-4316	532	3	−	−	NOUN
ejpam-4316	532	4	5r	5r	NOUN
ejpam-4316	532	5	4	4	NUM
ejpam-4316	533	1	+	+	CCONJ
ejpam-4316	533	2	r	r	NOUN
ejpam-4316	533	3	2	2	NUM
ejpam-4316	533	4	+	+	NUM
ejpam-4316	533	5	nr	nr	NOUN
ejpam-4316	533	6	−	−	NOUN
ejpam-4316	533	7	r2	r2	NOUN
ejpam-4316	533	8	=	=	NOUN
ejpam-4316	533	9	2n2	2n2	NUM
ejpam-4316	533	10	−	−	NUM
ejpam-4316	533	11	2n+	2n+	NUM
ejpam-4316	533	12	r2	r2	NOUN
ejpam-4316	533	13	−	−	PROPN
ejpam-4316	533	14	3r	3r	NOUN
ejpam-4316	533	15	+	+	CCONJ
ejpam-4316	533	16	4nr	4nr	NOUN
ejpam-4316	533	17	4	4	NUM
ejpam-4316	533	18	using	use	VERB
ejpam-4316	533	19	the	the	DET
ejpam-4316	533	20	distance	distance	NOUN
ejpam-4316	533	21	matrices	matrix	NOUN
ejpam-4316	533	22	of	of	ADP
ejpam-4316	533	23	the	the	DET
ejpam-4316	533	24	corresponding	corresponding	ADJ
ejpam-4316	533	25	s	s	NOUN
ejpam-4316	533	26	-	-	PUNCT
ejpam-4316	533	27	splitting	splitting	NOUN
ejpam-4316	533	28	graph	graph	NOUN
ejpam-4316	533	29	in	in	ADP
ejpam-4316	533	30	theorems	theorem	NOUN
ejpam-4316	533	31	11,12,and	11,12,and	NUM
ejpam-4316	533	32	13	13	NUM
ejpam-4316	533	33	respectively	respectively	ADV
ejpam-4316	533	34	and	and	CCONJ
ejpam-4316	533	35	the	the	DET
ejpam-4316	533	36	definition	definition	NOUN
ejpam-4316	533	37	of	of	ADP
ejpam-4316	533	38	the	the	DET
ejpam-4316	533	39	harary	harary	PROPN
ejpam-4316	533	40	index	index	NOUN
ejpam-4316	533	41	of	of	ADP
ejpam-4316	533	42	a	a	DET
ejpam-4316	533	43	graph	graph	NOUN
ejpam-4316	533	44	,	,	PUNCT
ejpam-4316	533	45	the	the	DET
ejpam-4316	533	46	following	follow	VERB
ejpam-4316	533	47	results	result	NOUN
ejpam-4316	533	48	hold	hold	VERB
ejpam-4316	533	49	.	.	PUNCT
ejpam-4316	534	1	theorem	theorem	NOUN
ejpam-4316	534	2	17	17	NUM
ejpam-4316	534	3	.	.	PUNCT
ejpam-4316	535	1	let	let	VERB
ejpam-4316	535	2	g	g	PRON
ejpam-4316	535	3	be	be	AUX
ejpam-4316	535	4	a	a	DET
ejpam-4316	535	5	cycle	cycle	NOUN
ejpam-4316	535	6	graph	graph	NOUN
ejpam-4316	535	7	,	,	PUNCT
ejpam-4316	535	8	and	and	CCONJ
ejpam-4316	535	9	s	s	VERB
ejpam-4316	535	10	=	=	PUNCT
ejpam-4316	535	11	{	{	PUNCT
ejpam-4316	535	12	x	x	NOUN
ejpam-4316	535	13	}	}	PUNCT
ejpam-4316	535	14	such	such	ADJ
ejpam-4316	535	15	that	that	SCONJ
ejpam-4316	535	16	x	x	SYM
ejpam-4316	535	17	∈	∈	NOUN
ejpam-4316	535	18	v	v	X
ejpam-4316	535	19	(	(	PUNCT
ejpam-4316	535	20	g	g	NOUN
ejpam-4316	535	21	)	)	PUNCT
ejpam-4316	535	22	.	.	PUNCT
ejpam-4316	536	1	then	then	ADV
ejpam-4316	536	2	(	(	PUNCT
ejpam-4316	536	3	i	i	NOUN
ejpam-4316	536	4	)	)	PUNCT
ejpam-4316	536	5	if	if	SCONJ
ejpam-4316	536	6	n	n	NOUN
ejpam-4316	536	7	=	=	SYM
ejpam-4316	536	8	2k	2k	NUM
ejpam-4316	536	9	+	+	CCONJ
ejpam-4316	536	10	1	1	NUM
ejpam-4316	536	11	,	,	PUNCT
ejpam-4316	536	12	then	then	ADV
ejpam-4316	536	13	h(γ(g	h(γ(g	PROPN
ejpam-4316	536	14	,	,	PUNCT
ejpam-4316	536	15	s	s	NOUN
ejpam-4316	536	16	)	)	PUNCT
ejpam-4316	536	17	)	)	PUNCT
ejpam-4316	536	18	=	=	SYM
ejpam-4316	536	19	1	1	NUM
ejpam-4316	536	20	2	2	NUM
ejpam-4316	536	21	(	(	PUNCT
ejpam-4316	536	22	2	2	NUM
ejpam-4316	536	23	+	+	CCONJ
ejpam-4316	536	24	(	(	PUNCT
ejpam-4316	536	25	−1)n	−1)n	PROPN
ejpam-4316	536	26	)	)	PUNCT
ejpam-4316	537	1	+	+	CCONJ
ejpam-4316	537	2	nhb(n−1)/2c	nhb(n−1)/2c	NOUN
ejpam-4316	537	3	+	+	CCONJ
ejpam-4316	537	4	2hk	2hk	NOUN
ejpam-4316	537	5	;	;	PUNCT
ejpam-4316	537	6	and	and	CCONJ
ejpam-4316	537	7	(	(	PUNCT
ejpam-4316	537	8	ii	ii	NOUN
ejpam-4316	537	9	)	)	PUNCT
ejpam-4316	537	10	if	if	SCONJ
ejpam-4316	537	11	n	n	NOUN
ejpam-4316	537	12	=	=	SYM
ejpam-4316	537	13	2k	2k	NUM
ejpam-4316	537	14	,	,	PUNCT
ejpam-4316	537	15	then	then	ADV
ejpam-4316	537	16	h(γ(g	h(γ(g	PROPN
ejpam-4316	537	17	,	,	PUNCT
ejpam-4316	537	18	s	s	NOUN
ejpam-4316	537	19	)	)	PUNCT
ejpam-4316	537	20	)	)	PUNCT
ejpam-4316	537	21	=	=	SYM
ejpam-4316	537	22	1	1	NUM
ejpam-4316	537	23	2	2	NUM
ejpam-4316	537	24	(	(	PUNCT
ejpam-4316	537	25	2	2	NUM
ejpam-4316	537	26	+	+	CCONJ
ejpam-4316	537	27	(	(	PUNCT
ejpam-4316	537	28	−1)n	−1)n	PROPN
ejpam-4316	537	29	)	)	PUNCT
ejpam-4316	537	30	+	+	CCONJ
ejpam-4316	537	31	nhb(n−1)/2c	nhb(n−1)/2c	PRON
ejpam-4316	537	32	+	+	NUM
ejpam-4316	537	33	2hk−1	2hk−1	NUM
ejpam-4316	537	34	+	+	CCONJ
ejpam-4316	537	35	1	1	NUM
ejpam-4316	537	36	k	k	X
ejpam-4316	537	37	.	.	PUNCT
ejpam-4316	538	1	theorem	theorem	PROPN
ejpam-4316	538	2	18	18	NUM
ejpam-4316	538	3	.	.	PUNCT
ejpam-4316	539	1	let	let	VERB
ejpam-4316	539	2	g	g	PRON
ejpam-4316	539	3	be	be	AUX
ejpam-4316	539	4	a	a	DET
ejpam-4316	539	5	path	path	NOUN
ejpam-4316	539	6	graph	graph	NOUN
ejpam-4316	539	7	and	and	CCONJ
ejpam-4316	539	8	s	s	VERB
ejpam-4316	539	9	⊂	⊂	PROPN
ejpam-4316	539	10	v	v	X
ejpam-4316	539	11	(	(	PUNCT
ejpam-4316	539	12	pn	pn	NOUN
ejpam-4316	539	13	)	)	PUNCT
ejpam-4316	539	14	=	=	PRON
ejpam-4316	539	15	{	{	PUNCT
ejpam-4316	539	16	x1	x1	PROPN
ejpam-4316	539	17	,	,	PUNCT
ejpam-4316	539	18	.	.	PUNCT
ejpam-4316	539	19	.	.	PUNCT
ejpam-4316	540	1	.	.	PUNCT
ejpam-4316	541	1	,	,	PUNCT
ejpam-4316	541	2	xn	xn	X
ejpam-4316	541	3	}	}	PUNCT
ejpam-4316	542	1	where	where	SCONJ
ejpam-4316	542	2	n	n	PRON
ejpam-4316	542	3	≥	≥	NOUN
ejpam-4316	542	4	2	2	NUM
ejpam-4316	542	5	.	.	PUNCT
ejpam-4316	542	6	then	then	ADV
ejpam-4316	542	7	(	(	PUNCT
ejpam-4316	542	8	i	i	NOUN
ejpam-4316	542	9	)	)	PUNCT
ejpam-4316	542	10	if	if	SCONJ
ejpam-4316	542	11	s	s	VERB
ejpam-4316	542	12	=	=	PUNCT
ejpam-4316	542	13	{	{	PUNCT
ejpam-4316	542	14	x1	x1	PROPN
ejpam-4316	542	15	}	}	PUNCT
ejpam-4316	542	16	or	or	CCONJ
ejpam-4316	542	17	s	s	NOUN
ejpam-4316	542	18	=	=	X
ejpam-4316	542	19	{	{	PUNCT
ejpam-4316	542	20	xn	xn	NUM
ejpam-4316	542	21	}	}	PUNCT
ejpam-4316	542	22	,	,	PUNCT
ejpam-4316	542	23	then	then	ADV
ejpam-4316	542	24	h(γ(pn	h(γ(pn	NUM
ejpam-4316	542	25	,	,	PUNCT
ejpam-4316	542	26	s	s	NOUN
ejpam-4316	542	27	)	)	PUNCT
ejpam-4316	542	28	)	)	PUNCT
ejpam-4316	542	29	=	=	PUNCT
ejpam-4316	542	30	(	(	PUNCT
ejpam-4316	542	31	n+	n+	NOUN
ejpam-4316	542	32	1)hn−1	1)hn−1	NUM
ejpam-4316	542	33	−	−	NOUN
ejpam-4316	542	34	n+	n+	NOUN
ejpam-4316	542	35	3	3	NUM
ejpam-4316	542	36	2	2	NUM
ejpam-4316	542	37	;	;	PUNCT
ejpam-4316	542	38	(	(	PUNCT
ejpam-4316	542	39	ii	ii	NOUN
ejpam-4316	542	40	)	)	PUNCT
ejpam-4316	542	41	if	if	SCONJ
ejpam-4316	542	42	s	s	VERB
ejpam-4316	542	43	=	=	X
ejpam-4316	542	44	{	{	PUNCT
ejpam-4316	542	45	xi	xi	ADP
ejpam-4316	542	46	}	}	PUNCT
ejpam-4316	542	47	such	such	ADJ
ejpam-4316	542	48	that	that	SCONJ
ejpam-4316	542	49	2	2	NUM
ejpam-4316	542	50	≤	≤	NUM
ejpam-4316	542	51	i	i	PRON
ejpam-4316	542	52	≤	≤	PROPN
ejpam-4316	543	1	n−1	n−1	PROPN
ejpam-4316	543	2	,	,	PUNCT
ejpam-4316	543	3	then	then	ADV
ejpam-4316	543	4	h(γ(pn	h(γ(pn	NUM
ejpam-4316	543	5	,	,	PUNCT
ejpam-4316	543	6	s	s	NOUN
ejpam-4316	543	7	)	)	PUNCT
ejpam-4316	543	8	)	)	PUNCT
ejpam-4316	544	1	=	=	SYM
ejpam-4316	544	2	n	n	CCONJ
ejpam-4316	544	3	(	(	PUNCT
ejpam-4316	544	4	hn−1	hn−1	PROPN
ejpam-4316	544	5	)	)	PUNCT
ejpam-4316	545	1	+	+	NOUN
ejpam-4316	545	2	hn−i+hi−1	hn−i+hi−1	NOUN
ejpam-4316	545	3	+	+	CCONJ
ejpam-4316	545	4	1	1	NUM
ejpam-4316	545	5	2	2	NUM
ejpam-4316	545	6	.	.	PUNCT
ejpam-4316	546	1	theorem	theorem	NOUN
ejpam-4316	546	2	19	19	NUM
ejpam-4316	546	3	.	.	PUNCT
ejpam-4316	547	1	let	let	VERB
ejpam-4316	547	2	g	g	NOUN
ejpam-4316	547	3	be	be	AUX
ejpam-4316	547	4	the	the	DET
ejpam-4316	547	5	complete	complete	ADJ
ejpam-4316	547	6	bipartite	bipartite	PROPN
ejpam-4316	547	7	graph	graph	NOUN
ejpam-4316	547	8	km	km	PROPN
ejpam-4316	547	9	,	,	PUNCT
ejpam-4316	547	10	n	n	CCONJ
ejpam-4316	547	11	with	with	ADP
ejpam-4316	547	12	vertex	vertex	NOUN
ejpam-4316	547	13	partition	partition	NOUN
ejpam-4316	547	14	v	v	NOUN
ejpam-4316	547	15	=	=	X
ejpam-4316	547	16	v1∪v2	v1∪v2	ADP
ejpam-4316	547	17	such	such	ADJ
ejpam-4316	547	18	that	that	DET
ejpam-4316	547	19	|v1|	|v1|	NOUN
ejpam-4316	547	20	=	=	NOUN
ejpam-4316	547	21	m	m	NOUN
ejpam-4316	547	22	and	and	CCONJ
ejpam-4316	547	23	|v2|	|v2|	ADV
ejpam-4316	548	1	=	=	PUNCT
ejpam-4316	548	2	n.	n.	NOUN
ejpam-4316	548	3	then	then	ADV
ejpam-4316	548	4	the	the	DET
ejpam-4316	548	5	harary	harary	PROPN
ejpam-4316	548	6	index	index	NOUN
ejpam-4316	548	7	of	of	ADP
ejpam-4316	548	8	γ	γ	PROPN
ejpam-4316	548	9	=	=	SYM
ejpam-4316	548	10	γ(km	γ(km	PROPN
ejpam-4316	548	11	,	,	PUNCT
ejpam-4316	548	12	n	n	CCONJ
ejpam-4316	548	13	,	,	PUNCT
ejpam-4316	548	14	s	s	AUX
ejpam-4316	548	15	)	)	PUNCT
ejpam-4316	548	16	is	be	AUX
ejpam-4316	548	17	given	give	VERB
ejpam-4316	548	18	by	by	ADP
ejpam-4316	548	19	h(γ	h(γ	NOUN
ejpam-4316	548	20	)	)	PUNCT
ejpam-4316	548	21	=	=	SYM
ejpam-4316	548	22	1	1	NUM
ejpam-4316	548	23	4	4	NUM
ejpam-4316	548	24	(	(	PUNCT
ejpam-4316	548	25	m2	m2	PROPN
ejpam-4316	548	26	+	+	CCONJ
ejpam-4316	548	27	n2	n2	PROPN
ejpam-4316	548	28	+	+	CCONJ
ejpam-4316	548	29	i2	i2	PROPN
ejpam-4316	548	30	+	+	CCONJ
ejpam-4316	548	31	j2	j2	PROPN
ejpam-4316	548	32	−m−	−m−	PROPN
ejpam-4316	548	33	n−	n−	PROPN
ejpam-4316	548	34	i−	i−	PROPN
ejpam-4316	548	35	j	j	PROPN
ejpam-4316	548	36	)	)	PUNCT
ejpam-4316	549	1	+	+	CCONJ
ejpam-4316	549	2	ij	ij	NOUN
ejpam-4316	549	3	3	3	NUM
ejpam-4316	549	4	+	+	CCONJ
ejpam-4316	549	5	mi	mi	PROPN
ejpam-4316	549	6	2	2	NUM
ejpam-4316	549	7	+	+	NUM
ejpam-4316	549	8	nj	nj	PROPN
ejpam-4316	549	9	2	2	NUM
ejpam-4316	549	10	+	+	NOUN
ejpam-4316	549	11	mn+mj	mn+mj	ADV
ejpam-4316	549	12	+	+	ADJ
ejpam-4316	549	13	ni	ni	PROPN
ejpam-4316	549	14	where	where	SCONJ
ejpam-4316	549	15	|s	|s	PROPN
ejpam-4316	549	16	∩	∩	NOUN
ejpam-4316	549	17	v1|	v1|	NOUN
ejpam-4316	549	18	=	=	PUNCT
ejpam-4316	550	1	i	i	PROPN
ejpam-4316	550	2	and	and	CCONJ
ejpam-4316	550	3	|s	|s	PROPN
ejpam-4316	550	4	∩	∩	ADJ
ejpam-4316	550	5	v2|	v2|	X
ejpam-4316	550	6	=	=	SYM
ejpam-4316	550	7	j.	j.	PROPN
ejpam-4316	550	8	references	reference	VERB
ejpam-4316	550	9	618	618	NUM
ejpam-4316	550	10	acknowledgements	acknowledgement	NOUN
ejpam-4316	550	11	the	the	DET
ejpam-4316	550	12	realization	realization	NOUN
ejpam-4316	550	13	of	of	ADP
ejpam-4316	550	14	this	this	DET
ejpam-4316	550	15	paper	paper	NOUN
ejpam-4316	550	16	and	and	CCONJ
ejpam-4316	550	17	the	the	DET
ejpam-4316	550	18	research	research	NOUN
ejpam-4316	550	19	behind	behind	ADP
ejpam-4316	550	20	it	it	PRON
ejpam-4316	550	21	would	would	AUX
ejpam-4316	550	22	not	not	PART
ejpam-4316	550	23	have	have	AUX
ejpam-4316	550	24	been	be	AUX
ejpam-4316	550	25	possible	possible	ADJ
ejpam-4316	550	26	without	without	ADP
ejpam-4316	550	27	the	the	DET
ejpam-4316	550	28	support	support	NOUN
ejpam-4316	550	29	of	of	ADP
ejpam-4316	550	30	the	the	DET
ejpam-4316	550	31	philippines	philippine	NOUN
ejpam-4316	550	32	’	'	PUNCT
ejpam-4316	550	33	department	department	NOUN
ejpam-4316	550	34	of	of	ADP
ejpam-4316	550	35	science	science	NOUN
ejpam-4316	550	36	and	and	CCONJ
ejpam-4316	550	37	technology	technology	NOUN
ejpam-4316	550	38	asthrdp	asthrdp	PROPN
ejpam-4316	550	39	,	,	PUNCT
ejpam-4316	550	40	central	central	ADJ
ejpam-4316	550	41	luzon	luzon	PROPN
ejpam-4316	550	42	state	state	PROPN
ejpam-4316	550	43	university	university	PROPN
ejpam-4316	550	44	,	,	PUNCT
ejpam-4316	550	45	and	and	CCONJ
ejpam-4316	550	46	de	de	ADP
ejpam-4316	550	47	la	la	X
ejpam-4316	550	48	salle	salle	PROPN
ejpam-4316	550	49	university	university	PROPN
ejpam-4316	550	50	.	.	PUNCT
ejpam-4316	551	1	the	the	DET
ejpam-4316	551	2	authors	author	NOUN
ejpam-4316	551	3	are	be	AUX
ejpam-4316	551	4	also	also	ADV
ejpam-4316	551	5	thankful	thankful	ADJ
ejpam-4316	551	6	to	to	ADP
ejpam-4316	551	7	the	the	DET
ejpam-4316	551	8	referees	referee	NOUN
ejpam-4316	551	9	for	for	ADP
ejpam-4316	551	10	their	their	PRON
ejpam-4316	551	11	valuable	valuable	ADJ
ejpam-4316	551	12	comments	comment	NOUN
ejpam-4316	551	13	and	and	CCONJ
ejpam-4316	551	14	suggestions	suggestion	NOUN
ejpam-4316	551	15	that	that	PRON
ejpam-4316	551	16	helped	help	VERB
ejpam-4316	551	17	improve	improve	VERB
ejpam-4316	551	18	the	the	DET
ejpam-4316	551	19	content	content	NOUN
ejpam-4316	551	20	and	and	CCONJ
ejpam-4316	551	21	presentation	presentation	NOUN
ejpam-4316	551	22	of	of	ADP
ejpam-4316	551	23	this	this	DET
ejpam-4316	551	24	paper	paper	NOUN
ejpam-4316	551	25	.	.	PUNCT
ejpam-4316	552	1	references	reference	NOUN
ejpam-4316	552	2	[	[	X
ejpam-4316	552	3	1	1	NUM
ejpam-4316	552	4	]	]	X
ejpam-4316	552	5	f.	f.	PROPN
ejpam-4316	552	6	abedin	abedin	PROPN
ejpam-4316	552	7	,	,	PUNCT
ejpam-4316	552	8	b.	b.	PROPN
ejpam-4316	552	9	roughton	roughton	PROPN
ejpam-4316	552	10	,	,	PUNCT
ejpam-4316	552	11	p.	p.	PROPN
ejpam-4316	552	12	spencer	spencer	PROPN
ejpam-4316	552	13	,	,	PUNCT
ejpam-4316	552	14	q.	q.	PROPN
ejpam-4316	552	15	ye	ye	PROPN
ejpam-4316	552	16	,	,	PUNCT
ejpam-4316	552	17	and	and	CCONJ
ejpam-4316	552	18	k.	k.	PROPN
ejpam-4316	552	19	camarda	camarda	PROPN
ejpam-4316	552	20	.	.	PUNCT
ejpam-4316	553	1	computational	computational	ADJ
ejpam-4316	553	2	molecular	molecular	ADJ
ejpam-4316	553	3	design	design	NOUN
ejpam-4316	553	4	of	of	ADP
ejpam-4316	553	5	water	water	NOUN
ejpam-4316	553	6	compatible	compatible	ADJ
ejpam-4316	553	7	dentin	dentin	NOUN
ejpam-4316	553	8	adhesive	adhesive	ADJ
ejpam-4316	553	9	system	system	NOUN
ejpam-4316	553	10	.	.	PUNCT
ejpam-4316	554	1	in	in	ADP
ejpam-4316	554	2	krist	krist	PROPN
ejpam-4316	554	3	v.	v.	PROPN
ejpam-4316	554	4	gernaey	gernaey	PROPN
ejpam-4316	554	5	,	,	PUNCT
ejpam-4316	554	6	jakob	jakob	PROPN
ejpam-4316	554	7	k.	k.	PROPN
ejpam-4316	554	8	huusom	huusom	PROPN
ejpam-4316	554	9	,	,	PUNCT
ejpam-4316	554	10	and	and	CCONJ
ejpam-4316	554	11	rafiqul	rafiqul	VERB
ejpam-4316	554	12	gani	gani	PROPN
ejpam-4316	554	13	,	,	PUNCT
ejpam-4316	554	14	editors	editor	NOUN
ejpam-4316	554	15	,	,	PUNCT
ejpam-4316	554	16	12th	12th	ADJ
ejpam-4316	554	17	international	international	ADJ
ejpam-4316	554	18	symposium	symposium	NOUN
ejpam-4316	554	19	on	on	ADP
ejpam-4316	554	20	process	process	NOUN
ejpam-4316	554	21	systems	system	NOUN
ejpam-4316	554	22	engineering	engineering	NOUN
ejpam-4316	554	23	and	and	CCONJ
ejpam-4316	554	24	25th	25th	ADJ
ejpam-4316	554	25	european	european	ADJ
ejpam-4316	554	26	symposium	symposium	NOUN
ejpam-4316	554	27	on	on	ADP
ejpam-4316	554	28	computer	computer	NOUN
ejpam-4316	554	29	aided	aid	VERB
ejpam-4316	554	30	process	process	NOUN
ejpam-4316	554	31	engineering	engineering	NOUN
ejpam-4316	554	32	,	,	PUNCT
ejpam-4316	554	33	volume	volume	NOUN
ejpam-4316	554	34	37	37	NUM
ejpam-4316	554	35	of	of	ADP
ejpam-4316	554	36	computer	computer	NOUN
ejpam-4316	554	37	aided	aid	VERB
ejpam-4316	554	38	chemical	chemical	NOUN
ejpam-4316	554	39	engineering	engineering	NOUN
ejpam-4316	554	40	,	,	PUNCT
ejpam-4316	554	41	pages	page	NOUN
ejpam-4316	554	42	2081–2086	2081–2086	NUM
ejpam-4316	554	43	.	.	PUNCT
ejpam-4316	555	1	elsevier	elsevier	NOUN
ejpam-4316	555	2	,	,	PUNCT
ejpam-4316	555	3	2015	2015	NUM
ejpam-4316	555	4	.	.	PUNCT
ejpam-4316	556	1	[	[	X
ejpam-4316	556	2	2	2	NUM
ejpam-4316	556	3	]	]	X
ejpam-4316	556	4	a.t	a.t	PROPN
ejpam-4316	556	5	.	.	PUNCT
ejpam-4316	556	6	balaban	balaban	PROPN
ejpam-4316	556	7	.	.	PUNCT
ejpam-4316	557	1	highly	highly	ADV
ejpam-4316	557	2	discriminating	discriminating	ADJ
ejpam-4316	557	3	distance	distance	NOUN
ejpam-4316	557	4	-	-	PUNCT
ejpam-4316	557	5	based	base	VERB
ejpam-4316	557	6	topological	topological	ADJ
ejpam-4316	557	7	index	index	NOUN
ejpam-4316	557	8	.	.	PUNCT
ejpam-4316	558	1	chemical	chemical	PROPN
ejpam-4316	558	2	physics	physics	PROPN
ejpam-4316	558	3	letters	letter	NOUN
ejpam-4316	558	4	,	,	PUNCT
ejpam-4316	558	5	89(5):399–404	89(5):399–404	PROPN
ejpam-4316	558	6	,	,	PUNCT
ejpam-4316	558	7	1982	1982	NUM
ejpam-4316	558	8	.	.	PUNCT
ejpam-4316	559	1	[	[	X
ejpam-4316	559	2	3	3	X
ejpam-4316	559	3	]	]	X
ejpam-4316	559	4	n.	n.	PROPN
ejpam-4316	559	5	de	de	PROPN
ejpam-4316	559	6	.	.	PUNCT
ejpam-4316	559	7	computing	compute	VERB
ejpam-4316	559	8	reformulated	reformulate	VERB
ejpam-4316	559	9	first	first	ADJ
ejpam-4316	559	10	zagreb	zagreb	PROPN
ejpam-4316	559	11	index	index	NOUN
ejpam-4316	559	12	of	of	ADP
ejpam-4316	559	13	some	some	DET
ejpam-4316	559	14	chemical	chemical	NOUN
ejpam-4316	559	15	graphs	graph	NOUN
ejpam-4316	559	16	as	as	ADP
ejpam-4316	559	17	an	an	DET
ejpam-4316	559	18	application	application	NOUN
ejpam-4316	559	19	of	of	ADP
ejpam-4316	559	20	generalized	generalized	ADJ
ejpam-4316	559	21	hierarchical	hierarchical	ADJ
ejpam-4316	559	22	product	product	NOUN
ejpam-4316	559	23	of	of	ADP
ejpam-4316	559	24	graphs	graph	NOUN
ejpam-4316	559	25	.	.	PUNCT
ejpam-4316	560	1	arxiv	arxiv	PROPN
ejpam-4316	560	2	preprint	preprint	VERB
ejpam-4316	560	3	arxiv:1704.05476	arxiv:1704.05476	ADP
ejpam-4316	560	4	,	,	PUNCT
ejpam-4316	560	5	2017	2017	NUM
ejpam-4316	560	6	.	.	PUNCT
ejpam-4316	561	1	[	[	X
ejpam-4316	561	2	4	4	NUM
ejpam-4316	561	3	]	]	X
ejpam-4316	561	4	r.	r.	PROPN
ejpam-4316	561	5	diestel	diestel	PROPN
ejpam-4316	561	6	.	.	PUNCT
ejpam-4316	562	1	graph	graph	NOUN
ejpam-4316	562	2	theory(5th	theory(5th	PROPN
ejpam-4316	562	3	edition	edition	NOUN
ejpam-4316	562	4	)	)	PUNCT
ejpam-4316	562	5	.	.	PUNCT
ejpam-4316	563	1	springer	springer	NOUN
ejpam-4316	563	2	-	-	PUNCT
ejpam-4316	563	3	verlag	verlag	PROPN
ejpam-4316	563	4	,	,	PUNCT
ejpam-4316	563	5	heildelberg	heildelberg	PROPN
ejpam-4316	563	6	,	,	PUNCT
ejpam-4316	563	7	new	new	PROPN
ejpam-4316	563	8	york	york	PROPN
ejpam-4316	563	9	.	.	PROPN
ejpam-4316	563	10	,	,	PUNCT
ejpam-4316	563	11	2017	2017	NUM
ejpam-4316	563	12	.	.	PUNCT
ejpam-4316	564	1	[	[	X
ejpam-4316	564	2	5	5	NUM
ejpam-4316	564	3	]	]	PUNCT
ejpam-4316	564	4	m.	m.	NOUN
ejpam-4316	564	5	eliasi	eliasi	PROPN
ejpam-4316	564	6	,	,	PUNCT
ejpam-4316	564	7	g.	g.	PROPN
ejpam-4316	564	8	raeisi	raeisi	PROPN
ejpam-4316	564	9	,	,	PUNCT
ejpam-4316	564	10	and	and	CCONJ
ejpam-4316	564	11	b.	b.	PROPN
ejpam-4316	564	12	taeri	taeri	PROPN
ejpam-4316	564	13	.	.	PUNCT
ejpam-4316	565	1	wiener	wiener	NOUN
ejpam-4316	565	2	index	index	NOUN
ejpam-4316	565	3	of	of	ADP
ejpam-4316	565	4	some	some	DET
ejpam-4316	565	5	graph	graph	NOUN
ejpam-4316	565	6	operations	operation	NOUN
ejpam-4316	565	7	.	.	PUNCT
ejpam-4316	566	1	discrete	discrete	ADJ
ejpam-4316	566	2	applied	applied	ADJ
ejpam-4316	566	3	mathematics	mathematic	NOUN
ejpam-4316	566	4	,	,	PUNCT
ejpam-4316	566	5	160(9):1333–1344	160(9):1333–1344	NUM
ejpam-4316	566	6	,	,	PUNCT
ejpam-4316	566	7	2012	2012	NUM
ejpam-4316	566	8	.	.	PUNCT
ejpam-4316	567	1	[	[	X
ejpam-4316	567	2	6	6	NUM
ejpam-4316	567	3	]	]	PUNCT
ejpam-4316	567	4	w.	w.	PROPN
ejpam-4316	567	5	gao	gao	PROPN
ejpam-4316	567	6	,	,	PUNCT
ejpam-4316	567	7	m.	m.	NOUN
ejpam-4316	567	8	asif	asif	NOUN
ejpam-4316	567	9	,	,	PUNCT
ejpam-4316	567	10	and	and	CCONJ
ejpam-4316	567	11	w.	w.	PROPN
ejpam-4316	567	12	nazeer	nazeer	PROPN
ejpam-4316	567	13	.	.	PUNCT
ejpam-4316	568	1	the	the	DET
ejpam-4316	568	2	study	study	NOUN
ejpam-4316	568	3	of	of	ADP
ejpam-4316	568	4	honey	honey	NOUN
ejpam-4316	568	5	comb	comb	NOUN
ejpam-4316	568	6	derived	derive	VERB
ejpam-4316	568	7	network	network	NOUN
ejpam-4316	568	8	via	via	ADP
ejpam-4316	568	9	topological	topological	ADJ
ejpam-4316	568	10	indices	index	NOUN
ejpam-4316	568	11	.	.	PUNCT
ejpam-4316	569	1	open	open	ADJ
ejpam-4316	569	2	j.	j.	PROPN
ejpam-4316	569	3	math	math	PROPN
ejpam-4316	569	4	.	.	PUNCT
ejpam-4316	570	1	anal	anal	ADJ
ejpam-4316	570	2	,	,	PUNCT
ejpam-4316	570	3	2(2):10–26	2(2):10–26	NUM
ejpam-4316	570	4	,	,	PUNCT
ejpam-4316	570	5	2018	2018	NUM
ejpam-4316	570	6	.	.	PUNCT
ejpam-4316	571	1	[	[	X
ejpam-4316	571	2	7	7	X
ejpam-4316	571	3	]	]	PUNCT
ejpam-4316	571	4	s.	s.	PROPN
ejpam-4316	571	5	goyal	goyal	PROPN
ejpam-4316	571	6	,	,	PUNCT
ejpam-4316	571	7	d.	d.	PROPN
ejpam-4316	571	8	jain	jain	PROPN
ejpam-4316	571	9	,	,	PUNCT
ejpam-4316	571	10	and	and	CCONJ
ejpam-4316	571	11	v.n	v.n	PROPN
ejpam-4316	571	12	.	.	PROPN
ejpam-4316	571	13	mishra	mishra	PROPN
ejpam-4316	571	14	.	.	PROPN
ejpam-4316	571	15	wiener	wiener	PROPN
ejpam-4316	571	16	index	index	NOUN
ejpam-4316	571	17	of	of	ADP
ejpam-4316	571	18	sum	sum	NOUN
ejpam-4316	571	19	of	of	ADP
ejpam-4316	571	20	shadowgraphs	shadowgraph	NOUN
ejpam-4316	571	21	.	.	PUNCT
ejpam-4316	572	1	discrete	discrete	ADJ
ejpam-4316	572	2	mathematics	mathematic	NOUN
ejpam-4316	572	3	,	,	PUNCT
ejpam-4316	572	4	algorithms	algorithm	NOUN
ejpam-4316	572	5	and	and	CCONJ
ejpam-4316	572	6	applications	application	NOUN
ejpam-4316	572	7	,	,	PUNCT
ejpam-4316	572	8	page	page	NOUN
ejpam-4316	572	9	2250068	2250068	NUM
ejpam-4316	572	10	,	,	PUNCT
ejpam-4316	572	11	2022	2022	NUM
ejpam-4316	572	12	.	.	PUNCT
ejpam-4316	573	1	[	[	X
ejpam-4316	573	2	8	8	NUM
ejpam-4316	573	3	]	]	PUNCT
ejpam-4316	573	4	a.	a.	NOUN
ejpam-4316	573	5	graovac	graovac	NOUN
ejpam-4316	573	6	and	and	CCONJ
ejpam-4316	573	7	t.	t.	PROPN
ejpam-4316	573	8	pisanski	pisanski	NOUN
ejpam-4316	573	9	.	.	PUNCT
ejpam-4316	574	1	on	on	ADP
ejpam-4316	574	2	the	the	DET
ejpam-4316	574	3	wiener	wiener	NOUN
ejpam-4316	574	4	index	index	NOUN
ejpam-4316	574	5	of	of	ADP
ejpam-4316	574	6	a	a	DET
ejpam-4316	574	7	graph	graph	NOUN
ejpam-4316	574	8	.	.	PUNCT
ejpam-4316	574	9	journal	journal	PROPN
ejpam-4316	574	10	of	of	ADP
ejpam-4316	574	11	mathematical	mathematical	ADJ
ejpam-4316	574	12	chemistry	chemistry	NOUN
ejpam-4316	574	13	,	,	PUNCT
ejpam-4316	574	14	8(1):53–62	8(1):53–62	NUM
ejpam-4316	574	15	,	,	PUNCT
ejpam-4316	574	16	1991	1991	NUM
ejpam-4316	574	17	.	.	PUNCT
ejpam-4316	575	1	[	[	X
ejpam-4316	575	2	9	9	NUM
ejpam-4316	575	3	]	]	PUNCT
ejpam-4316	575	4	f.	f.	PROPN
ejpam-4316	575	5	harary	harary	PROPN
ejpam-4316	575	6	.	.	PUNCT
ejpam-4316	576	1	graph	graph	NOUN
ejpam-4316	576	2	theory	theory	NOUN
ejpam-4316	576	3	.	.	PUNCT
ejpam-4316	577	1	addison	addison	PROPN
ejpam-4316	577	2	-	-	PUNCT
ejpam-4316	577	3	wesley	wesley	PROPN
ejpam-4316	577	4	publishing	publishing	PROPN
ejpam-4316	577	5	company	company	PROPN
ejpam-4316	577	6	,	,	PUNCT
ejpam-4316	577	7	inc	inc	PROPN
ejpam-4316	577	8	.	.	PROPN
ejpam-4316	577	9	,	,	PUNCT
ejpam-4316	577	10	1969	1969	NUM
ejpam-4316	577	11	.	.	PUNCT
ejpam-4316	578	1	[	[	X
ejpam-4316	578	2	10	10	NUM
ejpam-4316	578	3	]	]	X
ejpam-4316	578	4	s.m	s.m	PROPN
ejpam-4316	578	5	.	.	PROPN
ejpam-4316	578	6	hosamani	hosamani	PROPN
ejpam-4316	578	7	.	.	PUNCT
ejpam-4316	579	1	quantitative	quantitative	ADJ
ejpam-4316	579	2	structure	structure	NOUN
ejpam-4316	579	3	property	property	NOUN
ejpam-4316	579	4	analysis	analysis	NOUN
ejpam-4316	579	5	of	of	ADP
ejpam-4316	579	6	anti	anti	ADJ
ejpam-4316	579	7	-	-	ADJ
ejpam-4316	579	8	covid-19	covid-19	ADJ
ejpam-4316	579	9	drugs	drug	NOUN
ejpam-4316	579	10	.	.	PUNCT
ejpam-4316	580	1	arxiv	arxiv	PROPN
ejpam-4316	580	2	preprint	preprint	PROPN
ejpam-4316	580	3	arxiv:2008.07350	arxiv:2008.07350	PROPN
ejpam-4316	580	4	,	,	PUNCT
ejpam-4316	580	5	2020	2020	NUM
ejpam-4316	580	6	.	.	PUNCT
ejpam-4316	581	1	[	[	X
ejpam-4316	581	2	11	11	NUM
ejpam-4316	581	3	]	]	X
ejpam-4316	581	4	o.	o.	PROPN
ejpam-4316	581	5	ivanciuc	ivanciuc	PROPN
ejpam-4316	581	6	,	,	PUNCT
ejpam-4316	581	7	t.s	t.s	PROPN
ejpam-4316	581	8	.	.	PROPN
ejpam-4316	581	9	balaban	balaban	PROPN
ejpam-4316	581	10	,	,	PUNCT
ejpam-4316	581	11	and	and	CCONJ
ejpam-4316	581	12	a.t	a.t	PROPN
ejpam-4316	581	13	.	.	PROPN
ejpam-4316	581	14	balaban	balaban	PROPN
ejpam-4316	581	15	.	.	PUNCT
ejpam-4316	582	1	design	design	NOUN
ejpam-4316	582	2	of	of	ADP
ejpam-4316	582	3	topological	topological	ADJ
ejpam-4316	582	4	indices	index	NOUN
ejpam-4316	582	5	.	.	PUNCT
ejpam-4316	583	1	part	part	NOUN
ejpam-4316	583	2	4	4	NUM
ejpam-4316	583	3	.	.	PUNCT
ejpam-4316	583	4	reciprocal	reciprocal	ADJ
ejpam-4316	583	5	distance	distance	NOUN
ejpam-4316	583	6	matrix	matrix	NOUN
ejpam-4316	583	7	,	,	PUNCT
ejpam-4316	583	8	related	relate	VERB
ejpam-4316	583	9	local	local	ADJ
ejpam-4316	583	10	vertex	vertex	NOUN
ejpam-4316	583	11	invariants	invariant	NOUN
ejpam-4316	583	12	and	and	CCONJ
ejpam-4316	583	13	topological	topological	ADJ
ejpam-4316	583	14	indices	index	NOUN
ejpam-4316	583	15	.	.	PUNCT
ejpam-4316	584	1	journal	journal	NOUN
ejpam-4316	584	2	of	of	ADP
ejpam-4316	584	3	mathematical	mathematical	ADJ
ejpam-4316	584	4	chemistry	chemistry	NOUN
ejpam-4316	584	5	,	,	PUNCT
ejpam-4316	584	6	12(1):309–318	12(1):309–318	PROPN
ejpam-4316	584	7	,	,	PUNCT
ejpam-4316	584	8	1993	1993	NUM
ejpam-4316	584	9	.	.	PUNCT
ejpam-4316	585	1	references	reference	NOUN
ejpam-4316	585	2	619	619	NUM
ejpam-4316	586	1	[	[	X
ejpam-4316	586	2	12	12	NUM
ejpam-4316	586	3	]	]	X
ejpam-4316	586	4	m.h	m.h	PROPN
ejpam-4316	586	5	.	.	PROPN
ejpam-4316	586	6	khalifeh	khalifeh	PROPN
ejpam-4316	586	7	,	,	PUNCT
ejpam-4316	586	8	h.	h.	PROPN
ejpam-4316	586	9	yousefi	yousefi	PROPN
ejpam-4316	586	10	-	-	PUNCT
ejpam-4316	586	11	azari	azari	PROPN
ejpam-4316	586	12	,	,	PUNCT
ejpam-4316	586	13	and	and	CCONJ
ejpam-4316	586	14	a.r	a.r	PROPN
ejpam-4316	586	15	.	.	PROPN
ejpam-4316	586	16	ashrafi	ashrafi	PROPN
ejpam-4316	586	17	.	.	PUNCT
ejpam-4316	587	1	the	the	DET
ejpam-4316	587	2	hyper	hyper	ADJ
ejpam-4316	587	3	-	-	ADJ
ejpam-4316	587	4	wiener	wiener	NOUN
ejpam-4316	587	5	index	index	NOUN
ejpam-4316	587	6	of	of	ADP
ejpam-4316	587	7	graph	graph	NOUN
ejpam-4316	587	8	operations	operation	NOUN
ejpam-4316	587	9	.	.	PUNCT
ejpam-4316	588	1	computers	computer	NOUN
ejpam-4316	588	2	&	&	CCONJ
ejpam-4316	588	3	mathematics	mathematics	PROPN
ejpam-4316	588	4	with	with	ADP
ejpam-4316	588	5	applications	application	NOUN
ejpam-4316	588	6	,	,	PUNCT
ejpam-4316	588	7	56(5):1402–1407	56(5):1402–1407	NUM
ejpam-4316	588	8	,	,	PUNCT
ejpam-4316	588	9	2008	2008	NUM
ejpam-4316	588	10	.	.	PUNCT
ejpam-4316	589	1	[	[	X
ejpam-4316	589	2	13	13	NUM
ejpam-4316	589	3	]	]	PUNCT
ejpam-4316	589	4	s.	s.	PROPN
ejpam-4316	589	5	kwon	kwon	PROPN
ejpam-4316	589	6	,	,	PUNCT
ejpam-4316	589	7	h.	h.	PROPN
ejpam-4316	589	8	bae	bae	PROPN
ejpam-4316	589	9	,	,	PUNCT
ejpam-4316	589	10	j.	j.	PROPN
ejpam-4316	589	11	jo	jo	PROPN
ejpam-4316	589	12	,	,	PUNCT
ejpam-4316	589	13	and	and	CCONJ
ejpam-4316	589	14	s.	s.	PROPN
ejpam-4316	589	15	yoon	yoon	PROPN
ejpam-4316	589	16	.	.	PUNCT
ejpam-4316	590	1	comprehensive	comprehensive	PROPN
ejpam-4316	590	2	ensemble	ensemble	ADJ
ejpam-4316	590	3	in	in	ADP
ejpam-4316	590	4	qsar	qsar	NOUN
ejpam-4316	590	5	prediction	prediction	NOUN
ejpam-4316	590	6	for	for	ADP
ejpam-4316	590	7	drug	drug	NOUN
ejpam-4316	590	8	discovery	discovery	NOUN
ejpam-4316	590	9	.	.	PUNCT
ejpam-4316	591	1	bmc	bmc	ADJ
ejpam-4316	591	2	bioinformatics	bioinformatics	PROPN
ejpam-4316	591	3	,	,	PUNCT
ejpam-4316	591	4	20(1):1–12	20(1):1–12	NUM
ejpam-4316	591	5	,	,	PUNCT
ejpam-4316	591	6	2019	2019	NUM
ejpam-4316	591	7	.	.	PUNCT
ejpam-4316	592	1	[	[	X
ejpam-4316	592	2	14	14	NUM
ejpam-4316	592	3	]	]	PUNCT
ejpam-4316	592	4	i.	i.	NOUN
ejpam-4316	592	5	lukovits	lukovits	PROPN
ejpam-4316	592	6	and	and	CCONJ
ejpam-4316	592	7	w.	w.	PROPN
ejpam-4316	592	8	linert	linert	PROPN
ejpam-4316	592	9	.	.	PUNCT
ejpam-4316	593	1	a	a	DET
ejpam-4316	593	2	novel	novel	ADJ
ejpam-4316	593	3	definition	definition	NOUN
ejpam-4316	593	4	of	of	ADP
ejpam-4316	593	5	the	the	DET
ejpam-4316	593	6	hyper	hyper	ADJ
ejpam-4316	593	7	-	-	ADJ
ejpam-4316	593	8	wiener	wiener	NOUN
ejpam-4316	593	9	index	index	NOUN
ejpam-4316	593	10	for	for	ADP
ejpam-4316	593	11	cycles	cycle	NOUN
ejpam-4316	593	12	.	.	PUNCT
ejpam-4316	594	1	journal	journal	PROPN
ejpam-4316	594	2	of	of	ADP
ejpam-4316	594	3	chemical	chemical	ADJ
ejpam-4316	594	4	information	information	NOUN
ejpam-4316	594	5	and	and	CCONJ
ejpam-4316	594	6	computer	computer	NOUN
ejpam-4316	594	7	sciences	science	NOUN
ejpam-4316	594	8	,	,	PUNCT
ejpam-4316	594	9	34	34	NUM
ejpam-4316	594	10	,	,	PUNCT
ejpam-4316	594	11	1994	1994	NUM
ejpam-4316	594	12	.	.	PUNCT
ejpam-4316	595	1	[	[	X
ejpam-4316	595	2	15	15	NUM
ejpam-4316	595	3	]	]	X
ejpam-4316	595	4	s.	s.	PROPN
ejpam-4316	595	5	mondal	mondal	PROPN
ejpam-4316	595	6	,	,	PUNCT
ejpam-4316	595	7	n.	n.	PROPN
ejpam-4316	595	8	de	de	PROPN
ejpam-4316	595	9	,	,	PUNCT
ejpam-4316	595	10	and	and	CCONJ
ejpam-4316	595	11	a.	a.	NOUN
ejpam-4316	595	12	pal	pal	NOUN
ejpam-4316	595	13	.	.	PUNCT
ejpam-4316	596	1	topological	topological	ADJ
ejpam-4316	596	2	indices	index	NOUN
ejpam-4316	596	3	of	of	ADP
ejpam-4316	596	4	some	some	DET
ejpam-4316	596	5	chemical	chemical	NOUN
ejpam-4316	596	6	structures	structure	NOUN
ejpam-4316	596	7	applied	apply	VERB
ejpam-4316	596	8	for	for	ADP
ejpam-4316	596	9	the	the	DET
ejpam-4316	596	10	treatment	treatment	NOUN
ejpam-4316	596	11	of	of	ADP
ejpam-4316	596	12	covid-19	covid-19	PROPN
ejpam-4316	596	13	patients	patient	NOUN
ejpam-4316	596	14	.	.	PUNCT
ejpam-4316	597	1	polycyclic	polycyclic	ADJ
ejpam-4316	597	2	aromatic	aromatic	ADJ
ejpam-4316	597	3	compounds	compound	NOUN
ejpam-4316	597	4	,	,	PUNCT
ejpam-4316	597	5	pages	page	NOUN
ejpam-4316	597	6	1–15	1–15	NUM
ejpam-4316	597	7	,	,	PUNCT
ejpam-4316	597	8	2020	2020	NUM
ejpam-4316	597	9	.	.	PUNCT
ejpam-4316	598	1	[	[	X
ejpam-4316	598	2	16	16	NUM
ejpam-4316	598	3	]	]	X
ejpam-4316	598	4	e.	e.	PROPN
ejpam-4316	598	5	munarini	munarini	PROPN
ejpam-4316	598	6	,	,	PUNCT
ejpam-4316	598	7	c.p	c.p	PROPN
ejpam-4316	598	8	.	.	PROPN
ejpam-4316	598	9	cippo	cippo	PROPN
ejpam-4316	598	10	,	,	PUNCT
ejpam-4316	598	11	a.	a.	NOUN
ejpam-4316	598	12	scagliola	scagliola	PROPN
ejpam-4316	598	13	,	,	PUNCT
ejpam-4316	598	14	and	and	CCONJ
ejpam-4316	598	15	n.z	n.z	PROPN
ejpam-4316	598	16	.	.	PROPN
ejpam-4316	598	17	salvi	salvi	PROPN
ejpam-4316	598	18	.	.	PUNCT
ejpam-4316	599	1	double	double	ADJ
ejpam-4316	599	2	graphs	graph	NOUN
ejpam-4316	599	3	.	.	PUNCT
ejpam-4316	600	1	discrete	discrete	ADJ
ejpam-4316	600	2	mathematics	mathematic	NOUN
ejpam-4316	600	3	,	,	PUNCT
ejpam-4316	600	4	308:242–254	308:242–254	NUM
ejpam-4316	600	5	,	,	PUNCT
ejpam-4316	600	6	2	2	NUM
ejpam-4316	600	7	2008	2008	NUM
ejpam-4316	600	8	.	.	PUNCT
ejpam-4316	601	1	[	[	X
ejpam-4316	601	2	17	17	NUM
ejpam-4316	601	3	]	]	X
ejpam-4316	601	4	d.	d.	PROPN
ejpam-4316	601	5	plavšić	plavšić	PROPN
ejpam-4316	601	6	,	,	PUNCT
ejpam-4316	601	7	s.	s.	PROPN
ejpam-4316	601	8	nikolić	nikolić	PROPN
ejpam-4316	601	9	,	,	PUNCT
ejpam-4316	601	10	n.	n.	PROPN
ejpam-4316	601	11	trinajstić	trinajstić	PROPN
ejpam-4316	601	12	,	,	PUNCT
ejpam-4316	601	13	and	and	CCONJ
ejpam-4316	601	14	z.	z.	PROPN
ejpam-4316	601	15	mihalić	mihalić	NOUN
ejpam-4316	601	16	.	.	PUNCT
ejpam-4316	602	1	on	on	ADP
ejpam-4316	602	2	the	the	DET
ejpam-4316	602	3	harary	harary	PROPN
ejpam-4316	602	4	index	index	NOUN
ejpam-4316	602	5	for	for	ADP
ejpam-4316	602	6	the	the	DET
ejpam-4316	602	7	characterization	characterization	NOUN
ejpam-4316	602	8	of	of	ADP
ejpam-4316	602	9	chemical	chemical	NOUN
ejpam-4316	602	10	graphs	graph	NOUN
ejpam-4316	602	11	.	.	PUNCT
ejpam-4316	603	1	journal	journal	NOUN
ejpam-4316	603	2	of	of	ADP
ejpam-4316	603	3	mathematical	mathematical	ADJ
ejpam-4316	603	4	chemistry	chemistry	NOUN
ejpam-4316	603	5	,	,	PUNCT
ejpam-4316	603	6	12(1):235–250	12(1):235–250	NUM
ejpam-4316	603	7	,	,	PUNCT
ejpam-4316	603	8	1993	1993	NUM
ejpam-4316	603	9	.	.	PUNCT
ejpam-4316	604	1	[	[	X
ejpam-4316	604	2	18	18	NUM
ejpam-4316	604	3	]	]	X
ejpam-4316	604	4	d.h	d.h	PROPN
ejpam-4316	604	5	.	.	PROPN
ejpam-4316	604	6	rouvray	rouvray	PROPN
ejpam-4316	604	7	.	.	PUNCT
ejpam-4316	605	1	the	the	DET
ejpam-4316	605	2	search	search	NOUN
ejpam-4316	605	3	for	for	ADP
ejpam-4316	605	4	useful	useful	ADJ
ejpam-4316	605	5	topological	topological	ADJ
ejpam-4316	605	6	indices	index	NOUN
ejpam-4316	605	7	in	in	ADP
ejpam-4316	605	8	chemistry	chemistry	NOUN
ejpam-4316	605	9	:	:	PUNCT
ejpam-4316	605	10	topological	topological	ADJ
ejpam-4316	605	11	indices	index	NOUN
ejpam-4316	605	12	promise	promise	VERB
ejpam-4316	605	13	to	to	PART
ejpam-4316	605	14	have	have	VERB
ejpam-4316	605	15	far	far	ADV
ejpam-4316	605	16	-	-	PUNCT
ejpam-4316	605	17	reaching	reach	VERB
ejpam-4316	605	18	applications	application	NOUN
ejpam-4316	605	19	in	in	ADP
ejpam-4316	605	20	fields	field	NOUN
ejpam-4316	605	21	as	as	ADV
ejpam-4316	605	22	diverse	diverse	ADJ
ejpam-4316	605	23	as	as	ADP
ejpam-4316	605	24	bonding	bonding	NOUN
ejpam-4316	605	25	theory	theory	NOUN
ejpam-4316	605	26	,	,	PUNCT
ejpam-4316	605	27	cancer	cancer	NOUN
ejpam-4316	605	28	research	research	NOUN
ejpam-4316	605	29	,	,	PUNCT
ejpam-4316	605	30	and	and	CCONJ
ejpam-4316	605	31	drug	drug	NOUN
ejpam-4316	605	32	design	design	NOUN
ejpam-4316	605	33	.	.	PUNCT
ejpam-4316	606	1	american	american	PROPN
ejpam-4316	606	2	scientist	scientist	NOUN
ejpam-4316	606	3	,	,	PUNCT
ejpam-4316	606	4	61(6):729–735	61(6):729–735	NUM
ejpam-4316	606	5	,	,	PUNCT
ejpam-4316	606	6	1973	1973	NUM
ejpam-4316	606	7	.	.	PUNCT
ejpam-4316	607	1	[	[	X
ejpam-4316	607	2	19	19	NUM
ejpam-4316	607	3	]	]	X
ejpam-4316	607	4	e.	e.	PROPN
ejpam-4316	607	5	sampathkumar	sampathkumar	PROPN
ejpam-4316	607	6	and	and	CCONJ
ejpam-4316	607	7	h.b	h.b	PROPN
ejpam-4316	607	8	.	.	PROPN
ejpam-4316	607	9	walikar	walikar	PROPN
ejpam-4316	607	10	.	.	PUNCT
ejpam-4316	608	1	on	on	ADP
ejpam-4316	608	2	splitting	splitting	NOUN
ejpam-4316	608	3	graph	graph	NOUN
ejpam-4316	608	4	of	of	ADP
ejpam-4316	608	5	a	a	DET
ejpam-4316	608	6	graph	graph	NOUN
ejpam-4316	608	7	.	.	PUNCT
ejpam-4316	608	8	journal	journal	NOUN
ejpam-4316	608	9	of	of	ADP
ejpam-4316	608	10	the	the	DET
ejpam-4316	608	11	karnatak	karnatak	PROPN
ejpam-4316	608	12	university	university	PROPN
ejpam-4316	608	13	,	,	PUNCT
ejpam-4316	608	14	science	science	NOUN
ejpam-4316	608	15	.	.	PUNCT
ejpam-4316	608	16	,	,	PUNCT
ejpam-4316	608	17	25(13):13–16	25(13):13–16	NOUN
ejpam-4316	608	18	,	,	PUNCT
ejpam-4316	608	19	1980	1980	NUM
ejpam-4316	608	20	.	.	PUNCT
ejpam-4316	609	1	[	[	X
ejpam-4316	609	2	20	20	NUM
ejpam-4316	609	3	]	]	SYM
ejpam-4316	609	4	m.c	m.c	PROPN
ejpam-4316	609	5	.	.	PROPN
ejpam-4316	609	6	shanmukha	shanmukha	PROPN
ejpam-4316	609	7	,	,	PUNCT
ejpam-4316	609	8	n.s	n.s	PROPN
ejpam-4316	609	9	.	.	PROPN
ejpam-4316	609	10	basavarajappa	basavarajappa	PROPN
ejpam-4316	609	11	,	,	PUNCT
ejpam-4316	609	12	k.c	k.c	PROPN
ejpam-4316	609	13	.	.	PROPN
ejpam-4316	609	14	shilpa	shilpa	PROPN
ejpam-4316	609	15	,	,	PUNCT
ejpam-4316	609	16	and	and	CCONJ
ejpam-4316	609	17	a.	a.	PROPN
ejpam-4316	609	18	usha	usha	PROPN
ejpam-4316	609	19	.	.	PUNCT
ejpam-4316	609	20	degree	degree	NOUN
ejpam-4316	609	21	-	-	PUNCT
ejpam-4316	609	22	based	base	VERB
ejpam-4316	609	23	topological	topological	ADJ
ejpam-4316	609	24	indices	index	NOUN
ejpam-4316	609	25	on	on	ADP
ejpam-4316	609	26	anticancer	anticancer	NOUN
ejpam-4316	609	27	drugs	drug	NOUN
ejpam-4316	609	28	with	with	ADP
ejpam-4316	609	29	qspr	qspr	ADJ
ejpam-4316	609	30	analysis	analysis	NOUN
ejpam-4316	609	31	.	.	PUNCT
ejpam-4316	610	1	heliyon	heliyon	NOUN
ejpam-4316	610	2	,	,	PUNCT
ejpam-4316	610	3	6(6):e04235	6(6):e04235	NUM
ejpam-4316	610	4	,	,	PUNCT
ejpam-4316	610	5	2020	2020	NUM
ejpam-4316	610	6	.	.	PUNCT
ejpam-4316	611	1	[	[	X
ejpam-4316	611	2	21	21	NUM
ejpam-4316	611	3	]	]	X
ejpam-4316	611	4	d.	d.	PROPN
ejpam-4316	611	5	stevanović	stevanović	PROPN
ejpam-4316	611	6	.	.	PUNCT
ejpam-4316	612	1	hosoya	hosoya	PROPN
ejpam-4316	612	2	polynomial	polynomial	ADJ
ejpam-4316	612	3	of	of	ADP
ejpam-4316	612	4	composite	composite	ADJ
ejpam-4316	612	5	graphs	graph	NOUN
ejpam-4316	612	6	.	.	PUNCT
ejpam-4316	613	1	discrete	discrete	ADJ
ejpam-4316	613	2	mathematics	mathematic	NOUN
ejpam-4316	613	3	,	,	PUNCT
ejpam-4316	613	4	235(1):237–244	235(1):237–244	NUM
ejpam-4316	613	5	,	,	PUNCT
ejpam-4316	613	6	2001	2001	NUM
ejpam-4316	613	7	.	.	PUNCT
ejpam-4316	614	1	chech	chech	NOUN
ejpam-4316	614	2	and	and	CCONJ
ejpam-4316	614	3	slovak	slovak	ADJ
ejpam-4316	614	4	3	3	NUM
ejpam-4316	614	5	.	.	PUNCT
ejpam-4316	615	1	[	[	X
ejpam-4316	615	2	22	22	NUM
ejpam-4316	615	3	]	]	X
ejpam-4316	615	4	e.w	e.w	PROPN
ejpam-4316	615	5	.	.	PROPN
ejpam-4316	615	6	weisstein	weisstein	PROPN
ejpam-4316	615	7	.	.	PUNCT
ejpam-4316	616	1	wiener	wiener	NOUN
ejpam-4316	616	2	index	index	NOUN
ejpam-4316	616	3	–	–	PUNCT
ejpam-4316	616	4	from	from	ADP
ejpam-4316	616	5	wolfram	wolfram	PROPN
ejpam-4316	616	6	mathworld	mathworld	PROPN
ejpam-4316	616	7	.	.	PUNCT
ejpam-4316	617	1	https://mathworld.wolfram.com/wienerindex.html	https://mathworld.wolfram.com/wienerindex.html	PROPN
ejpam-4316	617	2	,	,	PUNCT
ejpam-4316	617	3	2008	2008	NUM
ejpam-4316	617	4	.	.	PUNCT
ejpam-4316	618	1	[	[	X
ejpam-4316	618	2	23	23	NUM
ejpam-4316	618	3	]	]	X
ejpam-4316	618	4	e.w	e.w	PROPN
ejpam-4316	618	5	.	.	PROPN
ejpam-4316	618	6	weisstein	weisstein	PROPN
ejpam-4316	618	7	.	.	PUNCT
ejpam-4316	619	1	harary	harary	PROPN
ejpam-4316	619	2	index	index	PROPN
ejpam-4316	619	3	–	–	PUNCT
ejpam-4316	619	4	from	from	ADP
ejpam-4316	619	5	wolfram	wolfram	PROPN
ejpam-4316	619	6	mathworld	mathworld	PROPN
ejpam-4316	619	7	.	.	PUNCT
ejpam-4316	620	1	https://mathworld.wolfram.com/hararyindex.html	https://mathworld.wolfram.com/hararyindex.html	NOUN
ejpam-4316	620	2	,	,	PUNCT
ejpam-4316	620	3	2009	2009	NUM
ejpam-4316	620	4	.	.	PUNCT
ejpam-4316	621	1	[	[	X
ejpam-4316	621	2	24	24	NUM
ejpam-4316	621	3	]	]	PUNCT
ejpam-4316	621	4	h.	h.	PROPN
ejpam-4316	621	5	wiener	wiener	PROPN
ejpam-4316	621	6	.	.	PUNCT
ejpam-4316	622	1	structural	structural	ADJ
ejpam-4316	622	2	determination	determination	NOUN
ejpam-4316	622	3	of	of	ADP
ejpam-4316	622	4	paraffin	paraffin	NOUN
ejpam-4316	622	5	boiling	boiling	NOUN
ejpam-4316	622	6	points	point	NOUN
ejpam-4316	622	7	.	.	PUNCT
ejpam-4316	623	1	journal	journal	NOUN
ejpam-4316	623	2	of	of	ADP
ejpam-4316	623	3	the	the	DET
ejpam-4316	623	4	american	american	PROPN
ejpam-4316	623	5	chemical	chemical	PROPN
ejpam-4316	623	6	society	society	PROPN
ejpam-4316	623	7	,	,	PUNCT
ejpam-4316	623	8	69(1):17–20	69(1):17–20	NUM
ejpam-4316	623	9	,	,	PUNCT
ejpam-4316	623	10	1947	1947	NUM
ejpam-4316	623	11	.	.	PUNCT
ejpam-4316	624	1	pmid	pmid	NOUN
ejpam-4316	624	2	:	:	PUNCT
ejpam-4316	624	3	20291038	20291038	NUM
ejpam-4316	624	4	.	.	PUNCT
ejpam-4316	625	1	[	[	X
ejpam-4316	625	2	25	25	NUM
ejpam-4316	625	3	]	]	X
ejpam-4316	625	4	y.n	y.n	PROPN
ejpam-4316	625	5	.	.	PROPN
ejpam-4316	625	6	yeh	yeh	PROPN
ejpam-4316	625	7	and	and	CCONJ
ejpam-4316	625	8	i.	i.	PROPN
ejpam-4316	625	9	gutman	gutman	PROPN
ejpam-4316	625	10	.	.	PUNCT
ejpam-4316	626	1	on	on	ADP
ejpam-4316	626	2	the	the	DET
ejpam-4316	626	3	sum	sum	NOUN
ejpam-4316	626	4	of	of	ADP
ejpam-4316	626	5	all	all	DET
ejpam-4316	626	6	distances	distance	NOUN
ejpam-4316	626	7	in	in	ADP
ejpam-4316	626	8	composite	composite	ADJ
ejpam-4316	626	9	graphs	graph	NOUN
ejpam-4316	626	10	.	.	PUNCT
ejpam-4316	627	1	discrete	discrete	ADJ
ejpam-4316	627	2	mathematics	mathematic	NOUN
ejpam-4316	627	3	,	,	PUNCT
ejpam-4316	627	4	135(1):359–365	135(1):359–365	NUM
ejpam-4316	627	5	,	,	PUNCT
ejpam-4316	627	6	1994	1994	NUM
ejpam-4316	627	7	.	.	PUNCT