id	sid	tid	token	lemma	pos
ejpam-3745	1	1	european	european	PROPN
ejpam-3745	1	2	journal	journal	PROPN
ejpam-3745	1	3	of	of	ADP
ejpam-3745	1	4	pure	pure	ADJ
ejpam-3745	1	5	and	and	CCONJ
ejpam-3745	1	6	applied	apply	VERB
ejpam-3745	1	7	mathematics	mathematic	NOUN
ejpam-3745	1	8	vol	vol	NOUN
ejpam-3745	1	9	.	.	PROPN
ejpam-3745	2	1	13	13	NUM
ejpam-3745	2	2	,	,	PUNCT
ejpam-3745	2	3	no	no	INTJ
ejpam-3745	2	4	.	.	NOUN
ejpam-3745	2	5	5	5	NUM
ejpam-3745	2	6	,	,	PUNCT
ejpam-3745	2	7	2020	2020	NUM
ejpam-3745	2	8	,	,	PUNCT
ejpam-3745	2	9	1231	1231	NUM
ejpam-3745	2	10	-	-	SYM
ejpam-3745	2	11	1240	1240	NUM
ejpam-3745	2	12	issn	issn	PROPN
ejpam-3745	2	13	1307	1307	NUM
ejpam-3745	2	14	-	-	SYM
ejpam-3745	2	15	5543	5543	NUM
ejpam-3745	2	16	–	–	PUNCT
ejpam-3745	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-3745	2	18	published	publish	VERB
ejpam-3745	2	19	by	by	ADP
ejpam-3745	2	20	new	new	PROPN
ejpam-3745	2	21	york	york	PROPN
ejpam-3745	2	22	business	business	PROPN
ejpam-3745	2	23	global	global	ADJ
ejpam-3745	2	24	special	special	ADJ
ejpam-3745	2	25	issue	issue	NOUN
ejpam-3745	2	26	dedicated	dedicate	VERB
ejpam-3745	2	27	to	to	ADP
ejpam-3745	2	28	professor	professor	NOUN
ejpam-3745	2	29	hari	hari	PROPN
ejpam-3745	2	30	m.	m.	PROPN
ejpam-3745	2	31	srivastava	srivastava	PROPN
ejpam-3745	2	32	on	on	ADP
ejpam-3745	2	33	the	the	DET
ejpam-3745	2	34	occasion	occasion	NOUN
ejpam-3745	2	35	of	of	ADP
ejpam-3745	2	36	his	his	PRON
ejpam-3745	2	37	80th	80th	ADJ
ejpam-3745	2	38	birthday	birthday	NOUN
ejpam-3745	2	39	on	on	ADP
ejpam-3745	2	40	the	the	DET
ejpam-3745	2	41	wiener	wiener	NOUN
ejpam-3745	2	42	index	index	NOUN
ejpam-3745	2	43	of	of	ADP
ejpam-3745	2	44	the	the	DET
ejpam-3745	2	45	dot	dot	NOUN
ejpam-3745	2	46	product	product	NOUN
ejpam-3745	2	47	graph	graph	NOUN
ejpam-3745	2	48	over	over	ADP
ejpam-3745	2	49	monogenic	monogenic	ADJ
ejpam-3745	2	50	semigroups	semigroup	NOUN
ejpam-3745	2	51	büşra	büşra	PROPN
ejpam-3745	2	52	aydın1	aydın1	PROPN
ejpam-3745	2	53	,	,	PUNCT
ejpam-3745	2	54	nihat	nihat	PROPN
ejpam-3745	2	55	akgüneş1,∗	akgüneş1,∗	PROPN
ejpam-3745	2	56	,	,	PUNCT
ejpam-3745	2	57	ismail	ismail	PROPN
ejpam-3745	2	58	naci	naci	PROPN
ejpam-3745	2	59	cangul2	cangul2	PROPN
ejpam-3745	2	60	1	1	NUM
ejpam-3745	2	61	department	department	NOUN
ejpam-3745	2	62	of	of	ADP
ejpam-3745	2	63	mathematics	mathematics	NOUN
ejpam-3745	2	64	-	-	PUNCT
ejpam-3745	2	65	computer	computer	NOUN
ejpam-3745	2	66	sciences	science	NOUN
ejpam-3745	2	67	,	,	PUNCT
ejpam-3745	2	68	necmettin	necmettin	PROPN
ejpam-3745	2	69	erbakan	erbakan	PROPN
ejpam-3745	2	70	university	university	PROPN
ejpam-3745	2	71	,	,	PUNCT
ejpam-3745	2	72	konya	konya	PROPN
ejpam-3745	2	73	,	,	PUNCT
ejpam-3745	2	74	turkey	turkey	PROPN
ejpam-3745	2	75	2	2	NUM
ejpam-3745	2	76	department	department	NOUN
ejpam-3745	2	77	of	of	ADP
ejpam-3745	2	78	mathematics	mathematics	PROPN
ejpam-3745	2	79	,	,	PUNCT
ejpam-3745	2	80	bursa	bursa	PROPN
ejpam-3745	2	81	uludag	uludag	PROPN
ejpam-3745	2	82	university	university	PROPN
ejpam-3745	2	83	,	,	PUNCT
ejpam-3745	2	84	bursa	bursa	NOUN
ejpam-3745	2	85	,	,	PUNCT
ejpam-3745	2	86	turkey	turkey	NOUN
ejpam-3745	2	87	abstract	abstract	NOUN
ejpam-3745	2	88	.	.	PUNCT
ejpam-3745	3	1	algebraic	algebraic	ADJ
ejpam-3745	3	2	study	study	NOUN
ejpam-3745	3	3	of	of	ADP
ejpam-3745	3	4	graphs	graph	NOUN
ejpam-3745	3	5	is	be	AUX
ejpam-3745	3	6	a	a	DET
ejpam-3745	3	7	relatively	relatively	ADV
ejpam-3745	3	8	recent	recent	ADJ
ejpam-3745	3	9	subject	subject	NOUN
ejpam-3745	3	10	which	which	PRON
ejpam-3745	3	11	arose	arise	VERB
ejpam-3745	3	12	in	in	ADP
ejpam-3745	3	13	two	two	NUM
ejpam-3745	3	14	main	main	ADJ
ejpam-3745	3	15	streams	stream	NOUN
ejpam-3745	3	16	:	:	PUNCT
ejpam-3745	3	17	one	one	NUM
ejpam-3745	3	18	is	be	AUX
ejpam-3745	3	19	named	name	VERB
ejpam-3745	3	20	as	as	ADP
ejpam-3745	3	21	the	the	DET
ejpam-3745	3	22	spectral	spectral	ADJ
ejpam-3745	3	23	graph	graph	NOUN
ejpam-3745	3	24	theory	theory	NOUN
ejpam-3745	3	25	and	and	CCONJ
ejpam-3745	3	26	the	the	DET
ejpam-3745	3	27	second	second	ADJ
ejpam-3745	3	28	one	one	NUM
ejpam-3745	3	29	deals	deal	NOUN
ejpam-3745	3	30	with	with	ADP
ejpam-3745	3	31	graphs	graph	NOUN
ejpam-3745	3	32	over	over	ADP
ejpam-3745	3	33	several	several	ADJ
ejpam-3745	3	34	algebraic	algebraic	ADJ
ejpam-3745	3	35	structures	structure	NOUN
ejpam-3745	3	36	.	.	PUNCT
ejpam-3745	4	1	topological	topological	ADJ
ejpam-3745	4	2	graph	graph	NOUN
ejpam-3745	4	3	indices	index	NOUN
ejpam-3745	4	4	are	be	AUX
ejpam-3745	4	5	widely	widely	ADV
ejpam-3745	4	6	-	-	PUNCT
ejpam-3745	4	7	used	use	VERB
ejpam-3745	4	8	tools	tool	NOUN
ejpam-3745	4	9	in	in	ADP
ejpam-3745	4	10	especially	especially	ADV
ejpam-3745	4	11	molecular	molecular	ADJ
ejpam-3745	4	12	graph	graph	NOUN
ejpam-3745	4	13	theory	theory	NOUN
ejpam-3745	4	14	and	and	CCONJ
ejpam-3745	4	15	mathematical	mathematical	ADJ
ejpam-3745	4	16	chemistry	chemistry	NOUN
ejpam-3745	4	17	due	due	ADP
ejpam-3745	4	18	to	to	ADP
ejpam-3745	4	19	their	their	PRON
ejpam-3745	4	20	time	time	NOUN
ejpam-3745	4	21	and	and	CCONJ
ejpam-3745	4	22	money	money	NOUN
ejpam-3745	4	23	saving	saving	NOUN
ejpam-3745	4	24	applications	application	NOUN
ejpam-3745	4	25	.	.	PUNCT
ejpam-3745	5	1	the	the	DET
ejpam-3745	5	2	wiener	wiener	NOUN
ejpam-3745	5	3	index	index	NOUN
ejpam-3745	5	4	is	be	AUX
ejpam-3745	5	5	one	one	NUM
ejpam-3745	5	6	of	of	ADP
ejpam-3745	5	7	these	these	DET
ejpam-3745	5	8	indices	index	NOUN
ejpam-3745	5	9	which	which	PRON
ejpam-3745	5	10	is	be	AUX
ejpam-3745	5	11	equal	equal	ADJ
ejpam-3745	5	12	to	to	ADP
ejpam-3745	5	13	the	the	DET
ejpam-3745	5	14	sum	sum	NOUN
ejpam-3745	5	15	of	of	ADP
ejpam-3745	5	16	distances	distance	NOUN
ejpam-3745	5	17	between	between	ADP
ejpam-3745	5	18	all	all	DET
ejpam-3745	5	19	pairs	pair	NOUN
ejpam-3745	5	20	of	of	ADP
ejpam-3745	5	21	vertices	vertex	NOUN
ejpam-3745	5	22	in	in	ADP
ejpam-3745	5	23	a	a	DET
ejpam-3745	5	24	connected	connected	ADJ
ejpam-3745	5	25	graph	graph	NOUN
ejpam-3745	5	26	.	.	PUNCT
ejpam-3745	6	1	the	the	DET
ejpam-3745	6	2	graph	graph	NOUN
ejpam-3745	6	3	over	over	ADP
ejpam-3745	6	4	the	the	DET
ejpam-3745	6	5	finite	finite	ADJ
ejpam-3745	6	6	dot	dot	NOUN
ejpam-3745	6	7	product	product	NOUN
ejpam-3745	6	8	of	of	ADP
ejpam-3745	6	9	monogenic	monogenic	ADJ
ejpam-3745	6	10	semigroups	semigroup	NOUN
ejpam-3745	6	11	has	have	AUX
ejpam-3745	6	12	recently	recently	ADV
ejpam-3745	6	13	been	be	AUX
ejpam-3745	6	14	defined	define	VERB
ejpam-3745	6	15	and	and	CCONJ
ejpam-3745	6	16	in	in	ADP
ejpam-3745	6	17	this	this	DET
ejpam-3745	6	18	paper	paper	NOUN
ejpam-3745	6	19	,	,	PUNCT
ejpam-3745	6	20	some	some	DET
ejpam-3745	6	21	results	result	NOUN
ejpam-3745	6	22	on	on	ADP
ejpam-3745	6	23	the	the	DET
ejpam-3745	6	24	wiener	wiener	NOUN
ejpam-3745	6	25	index	index	NOUN
ejpam-3745	6	26	of	of	ADP
ejpam-3745	6	27	the	the	DET
ejpam-3745	6	28	dot	dot	NOUN
ejpam-3745	6	29	product	product	NOUN
ejpam-3745	6	30	graph	graph	NOUN
ejpam-3745	6	31	over	over	ADP
ejpam-3745	6	32	monogenic	monogenic	ADJ
ejpam-3745	6	33	semigroups	semigroup	NOUN
ejpam-3745	6	34	are	be	AUX
ejpam-3745	6	35	given	give	VERB
ejpam-3745	6	36	.	.	PUNCT
ejpam-3745	7	1	2020	2020	NUM
ejpam-3745	7	2	mathematics	mathematic	NOUN
ejpam-3745	7	3	subject	subject	NOUN
ejpam-3745	7	4	classifications	classification	NOUN
ejpam-3745	7	5	:	:	PUNCT
ejpam-3745	7	6	05c12	05c12	NUM
ejpam-3745	7	7	,	,	PUNCT
ejpam-3745	7	8	05c25	05c25	X
ejpam-3745	7	9	key	key	ADJ
ejpam-3745	7	10	words	word	NOUN
ejpam-3745	7	11	and	and	CCONJ
ejpam-3745	7	12	phrases	phrase	NOUN
ejpam-3745	7	13	:	:	PUNCT
ejpam-3745	7	14	dot	dot	NOUN
ejpam-3745	7	15	product	product	NOUN
ejpam-3745	7	16	,	,	PUNCT
ejpam-3745	7	17	dot	dot	NOUN
ejpam-3745	7	18	product	product	NOUN
ejpam-3745	7	19	graph	graph	NOUN
ejpam-3745	7	20	,	,	PUNCT
ejpam-3745	7	21	wiener	wiener	NOUN
ejpam-3745	7	22	index	index	NOUN
ejpam-3745	7	23	,	,	PUNCT
ejpam-3745	7	24	topological	topological	ADJ
ejpam-3745	7	25	index	index	NOUN
ejpam-3745	7	26	,	,	PUNCT
ejpam-3745	7	27	monogenic	monogenic	ADJ
ejpam-3745	7	28	semigroup	semigroup	NOUN
ejpam-3745	7	29	1	1	NUM
ejpam-3745	7	30	.	.	PUNCT
ejpam-3745	7	31	introduction	introduction	NOUN
ejpam-3745	7	32	and	and	CCONJ
ejpam-3745	7	33	preliminaries	preliminary	NOUN
ejpam-3745	7	34	the	the	DET
ejpam-3745	7	35	connections	connection	NOUN
ejpam-3745	7	36	between	between	ADP
ejpam-3745	7	37	graph	graph	NOUN
ejpam-3745	7	38	theory	theory	NOUN
ejpam-3745	7	39	and	and	CCONJ
ejpam-3745	7	40	ring	ring	NOUN
ejpam-3745	7	41	theory	theory	NOUN
ejpam-3745	7	42	was	be	AUX
ejpam-3745	7	43	first	first	ADV
ejpam-3745	7	44	established	establish	VERB
ejpam-3745	7	45	in	in	ADP
ejpam-3745	7	46	1988	1988	NUM
ejpam-3745	7	47	by	by	ADP
ejpam-3745	7	48	beck	beck	NOUN
ejpam-3745	8	1	[	[	X
ejpam-3745	8	2	1	1	NUM
ejpam-3745	8	3	]	]	PUNCT
ejpam-3745	8	4	.	.	PUNCT
ejpam-3745	9	1	since	since	SCONJ
ejpam-3745	9	2	then	then	ADV
ejpam-3745	9	3	,	,	PUNCT
ejpam-3745	9	4	different	different	ADJ
ejpam-3745	9	5	types	type	NOUN
ejpam-3745	9	6	of	of	ADP
ejpam-3745	9	7	algebraic	algebraic	ADJ
ejpam-3745	9	8	graphs	graph	NOUN
ejpam-3745	9	9	have	have	AUX
ejpam-3745	9	10	been	be	AUX
ejpam-3745	9	11	introduced	introduce	VERB
ejpam-3745	9	12	and	and	CCONJ
ejpam-3745	9	13	studied	study	VERB
ejpam-3745	9	14	.	.	PUNCT
ejpam-3745	10	1	the	the	DET
ejpam-3745	10	2	most	most	ADV
ejpam-3745	10	3	well	well	ADV
ejpam-3745	10	4	-	-	PUNCT
ejpam-3745	10	5	known	know	VERB
ejpam-3745	10	6	example	example	NOUN
ejpam-3745	10	7	is	be	AUX
ejpam-3745	10	8	the	the	DET
ejpam-3745	10	9	zero	zero	NUM
ejpam-3745	10	10	divisor	divisor	NOUN
ejpam-3745	10	11	graphs	graph	NOUN
ejpam-3745	10	12	.	.	PUNCT
ejpam-3745	11	1	anderson	anderson	PROPN
ejpam-3745	11	2	and	and	CCONJ
ejpam-3745	11	3	livingston	livingston	PROPN
ejpam-3745	11	4	studied	study	VERB
ejpam-3745	11	5	the	the	DET
ejpam-3745	11	6	zero	zero	NUM
ejpam-3745	11	7	divisor	divisor	NOUN
ejpam-3745	11	8	graph	graph	NOUN
ejpam-3745	11	9	of	of	ADP
ejpam-3745	11	10	a	a	DET
ejpam-3745	11	11	commutative	commutative	ADJ
ejpam-3745	11	12	ring	ring	NOUN
ejpam-3745	11	13	in	in	ADP
ejpam-3745	11	14	[	[	X
ejpam-3745	11	15	2	2	NUM
ejpam-3745	11	16	]	]	PUNCT
ejpam-3745	11	17	.	.	PUNCT
ejpam-3745	12	1	similarly	similarly	ADV
ejpam-3745	12	2	,	,	PUNCT
ejpam-3745	12	3	zero	zero	NUM
ejpam-3745	12	4	divisor	divisor	NOUN
ejpam-3745	12	5	graphs	graph	NOUN
ejpam-3745	12	6	∗corresponding	∗corresponde	VERB
ejpam-3745	12	7	author	author	NOUN
ejpam-3745	12	8	.	.	PUNCT
ejpam-3745	13	1	doi	doi	NOUN
ejpam-3745	13	2	:	:	PUNCT
ejpam-3745	13	3	https://doi.org/10.29020/nybg.ejpam.v13i5.3745	https://doi.org/10.29020/nybg.ejpam.v13i5.3745	ADJ
ejpam-3745	13	4	email	email	NOUN
ejpam-3745	13	5	addresses	address	VERB
ejpam-3745	13	6	:	:	PUNCT
ejpam-3745	13	7	bsrcgn@gmail.com	bsrcgn@gmail.com	X
ejpam-3745	13	8	(	(	PUNCT
ejpam-3745	13	9	b.	b.	PROPN
ejpam-3745	13	10	aydın	aydın	PROPN
ejpam-3745	13	11	)	)	PUNCT
ejpam-3745	13	12	,	,	PUNCT
ejpam-3745	13	13	nakgunes@erbakan.edu.tr	nakgunes@erbakan.edu.tr	PROPN
ejpam-3745	13	14	(	(	PUNCT
ejpam-3745	13	15	n.	n.	PROPN
ejpam-3745	13	16	akgünes	akgünes	PROPN
ejpam-3745	13	17	)	)	PUNCT
ejpam-3745	13	18	,	,	PUNCT
ejpam-3745	13	19	cangul@uludag.edu.tr	cangul@uludag.edu.tr	NOUN
ejpam-3745	13	20	(	(	PUNCT
ejpam-3745	13	21	i.	i.	PROPN
ejpam-3745	13	22	n.	n.	PROPN
ejpam-3745	13	23	cangul	cangul	PROPN
ejpam-3745	13	24	)	)	PUNCT
ejpam-3745	13	25	https://www.ejpam.com	https://www.ejpam.com	NOUN
ejpam-3745	13	26	1231	1231	NUM
ejpam-3745	14	1	c	c	NOUN
ejpam-3745	14	2	©	©	NOUN
ejpam-3745	14	3	2020	2020	NUM
ejpam-3745	14	4	ejpam	ejpam	VERB
ejpam-3745	14	5	all	all	DET
ejpam-3745	14	6	rights	right	NOUN
ejpam-3745	14	7	reserved	reserve	VERB
ejpam-3745	14	8	.	.	PUNCT
ejpam-3745	15	1	b.	b.	PROPN
ejpam-3745	15	2	aydın	aydın	PROPN
ejpam-3745	15	3	,	,	PUNCT
ejpam-3745	15	4	n.	n.	PROPN
ejpam-3745	15	5	akgüneş	akgüneş	PROPN
ejpam-3745	15	6	,	,	PUNCT
ejpam-3745	15	7	i.	i.	PROPN
ejpam-3745	15	8	n.	n.	PROPN
ejpam-3745	15	9	cangul	cangul	PROPN
ejpam-3745	15	10	/	/	SYM
ejpam-3745	15	11	eur	eur	NOUN
ejpam-3745	15	12	.	.	PUNCT
ejpam-3745	16	1	j.	j.	PROPN
ejpam-3745	16	2	pure	pure	PROPN
ejpam-3745	16	3	appl	appl	PROPN
ejpam-3745	16	4	.	.	PROPN
ejpam-3745	16	5	math	math	PROPN
ejpam-3745	16	6	,	,	PUNCT
ejpam-3745	16	7	13	13	NUM
ejpam-3745	16	8	(	(	PUNCT
ejpam-3745	16	9	5	5	NUM
ejpam-3745	16	10	)	)	PUNCT
ejpam-3745	16	11	(	(	PUNCT
ejpam-3745	16	12	2020	2020	NUM
ejpam-3745	16	13	)	)	PUNCT
ejpam-3745	16	14	,	,	PUNCT
ejpam-3745	16	15	1231	1231	NUM
ejpam-3745	16	16	-	-	SYM
ejpam-3745	16	17	1240	1240	NUM
ejpam-3745	16	18	1232	1232	NUM
ejpam-3745	16	19	of	of	ADP
ejpam-3745	16	20	commutative	commutative	ADJ
ejpam-3745	16	21	semigroups	semigroup	NOUN
ejpam-3745	16	22	have	have	AUX
ejpam-3745	16	23	been	be	AUX
ejpam-3745	16	24	studied	study	VERB
ejpam-3745	16	25	in	in	ADP
ejpam-3745	16	26	[	[	X
ejpam-3745	16	27	3	3	NUM
ejpam-3745	16	28	]	]	PUNCT
ejpam-3745	16	29	,	,	PUNCT
ejpam-3745	16	30	[	[	X
ejpam-3745	16	31	5	5	NUM
ejpam-3745	16	32	]	]	PUNCT
ejpam-3745	16	33	and	and	CCONJ
ejpam-3745	16	34	[	[	X
ejpam-3745	16	35	4	4	NUM
ejpam-3745	16	36	]	]	PUNCT
ejpam-3745	16	37	.	.	PUNCT
ejpam-3745	17	1	the	the	DET
ejpam-3745	17	2	zero	zero	NUM
ejpam-3745	17	3	divisor	divisor	NOUN
ejpam-3745	17	4	graphs	graph	NOUN
ejpam-3745	17	5	have	have	AUX
ejpam-3745	17	6	been	be	AUX
ejpam-3745	17	7	studied	study	VERB
ejpam-3745	17	8	intensively	intensively	ADV
ejpam-3745	17	9	,	,	PUNCT
ejpam-3745	17	10	see	see	VERB
ejpam-3745	18	1	e.g.	e.g.	ADV
ejpam-3745	18	2	[	[	X
ejpam-3745	18	3	6	6	NUM
ejpam-3745	18	4	]	]	PUNCT
ejpam-3745	18	5	,	,	PUNCT
ejpam-3745	18	6	[	[	X
ejpam-3745	18	7	7	7	NUM
ejpam-3745	18	8	]	]	PUNCT
ejpam-3745	18	9	,	,	PUNCT
ejpam-3745	18	10	[	[	X
ejpam-3745	18	11	9	9	NUM
ejpam-3745	18	12	]	]	PUNCT
ejpam-3745	18	13	and	and	CCONJ
ejpam-3745	18	14	[	[	X
ejpam-3745	18	15	8	8	NUM
ejpam-3745	18	16	]	]	PUNCT
ejpam-3745	18	17	.	.	PUNCT
ejpam-3745	19	1	further	far	ADV
ejpam-3745	19	2	,	,	PUNCT
ejpam-3745	19	3	badawi	badawi	PROPN
ejpam-3745	19	4	has	have	AUX
ejpam-3745	19	5	also	also	ADV
ejpam-3745	19	6	studied	study	VERB
ejpam-3745	19	7	the	the	DET
ejpam-3745	19	8	dot	dot	NOUN
ejpam-3745	19	9	product	product	NOUN
ejpam-3745	19	10	graphs	graph	NOUN
ejpam-3745	19	11	of	of	ADP
ejpam-3745	19	12	commutative	commutative	ADJ
ejpam-3745	19	13	rings	ring	NOUN
ejpam-3745	19	14	in	in	ADP
ejpam-3745	19	15	[	[	X
ejpam-3745	19	16	10	10	NUM
ejpam-3745	19	17	]	]	PUNCT
ejpam-3745	19	18	.	.	PUNCT
ejpam-3745	20	1	akgüneş	akgüneş	PROPN
ejpam-3745	20	2	has	have	AUX
ejpam-3745	20	3	defined	define	VERB
ejpam-3745	20	4	the	the	DET
ejpam-3745	20	5	graph	graph	NOUN
ejpam-3745	20	6	of	of	ADP
ejpam-3745	20	7	monogenic	monogenic	ADJ
ejpam-3745	20	8	semigroups	semigroup	NOUN
ejpam-3745	20	9	in	in	ADP
ejpam-3745	20	10	[	[	X
ejpam-3745	20	11	11	11	NUM
ejpam-3745	20	12	]	]	PUNCT
ejpam-3745	20	13	in	in	ADP
ejpam-3745	20	14	a	a	DET
ejpam-3745	20	15	similar	similar	ADJ
ejpam-3745	20	16	manner	manner	NOUN
ejpam-3745	20	17	.	.	PUNCT
ejpam-3745	21	1	the	the	DET
ejpam-3745	21	2	dot	dot	NOUN
ejpam-3745	21	3	product	product	NOUN
ejpam-3745	21	4	graphs	graph	NOUN
ejpam-3745	21	5	of	of	ADP
ejpam-3745	21	6	monogenic	monogenic	ADJ
ejpam-3745	21	7	semigroups	semigroup	NOUN
ejpam-3745	21	8	have	have	AUX
ejpam-3745	21	9	been	be	AUX
ejpam-3745	21	10	studied	study	VERB
ejpam-3745	21	11	in	in	ADP
ejpam-3745	21	12	[	[	X
ejpam-3745	21	13	12	12	NUM
ejpam-3745	21	14	]	]	PUNCT
ejpam-3745	21	15	.	.	PUNCT
ejpam-3745	22	1	topological	topological	ADJ
ejpam-3745	22	2	graph	graph	NOUN
ejpam-3745	22	3	indices	index	NOUN
ejpam-3745	22	4	are	be	AUX
ejpam-3745	22	5	very	very	ADV
ejpam-3745	22	6	useful	useful	ADJ
ejpam-3745	22	7	tools	tool	NOUN
ejpam-3745	22	8	in	in	ADP
ejpam-3745	22	9	graph	graph	NOUN
ejpam-3745	22	10	theory	theory	NOUN
ejpam-3745	22	11	and	and	CCONJ
ejpam-3745	22	12	mathematical	mathematical	ADJ
ejpam-3745	22	13	chemistry	chemistry	NOUN
ejpam-3745	22	14	.	.	PUNCT
ejpam-3745	23	1	by	by	ADP
ejpam-3745	23	2	modelling	model	VERB
ejpam-3745	23	3	a	a	DET
ejpam-3745	23	4	chemical	chemical	ADJ
ejpam-3745	23	5	substance	substance	NOUN
ejpam-3745	23	6	with	with	ADP
ejpam-3745	23	7	a	a	DET
ejpam-3745	23	8	graph	graph	NOUN
ejpam-3745	23	9	,	,	PUNCT
ejpam-3745	23	10	we	we	PRON
ejpam-3745	23	11	can	can	AUX
ejpam-3745	23	12	apply	apply	VERB
ejpam-3745	23	13	these	these	DET
ejpam-3745	23	14	indices	index	NOUN
ejpam-3745	23	15	and	and	CCONJ
ejpam-3745	23	16	obtain	obtain	VERB
ejpam-3745	23	17	physico	physico	NOUN
ejpam-3745	23	18	-	-	PUNCT
ejpam-3745	23	19	chemical	chemical	NOUN
ejpam-3745	23	20	properties	property	NOUN
ejpam-3745	23	21	of	of	ADP
ejpam-3745	23	22	that	that	DET
ejpam-3745	23	23	substance	substance	NOUN
ejpam-3745	23	24	solely	solely	ADV
ejpam-3745	23	25	by	by	ADP
ejpam-3745	23	26	means	mean	NOUN
ejpam-3745	23	27	of	of	ADP
ejpam-3745	23	28	mathematical	mathematical	ADJ
ejpam-3745	23	29	calculations	calculation	NOUN
ejpam-3745	23	30	without	without	ADP
ejpam-3745	23	31	any	any	DET
ejpam-3745	23	32	experiments	experiment	NOUN
ejpam-3745	23	33	in	in	ADP
ejpam-3745	23	34	laboratory	laboratory	NOUN
ejpam-3745	23	35	.	.	PUNCT
ejpam-3745	24	1	the	the	DET
ejpam-3745	24	2	wiener	wiener	NOUN
ejpam-3745	24	3	index	index	NOUN
ejpam-3745	24	4	is	be	AUX
ejpam-3745	24	5	one	one	NUM
ejpam-3745	24	6	of	of	ADP
ejpam-3745	24	7	the	the	DET
ejpam-3745	24	8	significant	significant	ADJ
ejpam-3745	24	9	and	and	CCONJ
ejpam-3745	24	10	surely	surely	ADV
ejpam-3745	24	11	the	the	DET
ejpam-3745	24	12	oldest	old	ADJ
ejpam-3745	24	13	topological	topological	ADJ
ejpam-3745	24	14	indices	index	NOUN
ejpam-3745	24	15	used	use	VERB
ejpam-3745	24	16	in	in	ADP
ejpam-3745	24	17	mathematical	mathematical	ADJ
ejpam-3745	24	18	chemistry	chemistry	NOUN
ejpam-3745	24	19	.	.	PUNCT
ejpam-3745	25	1	it	it	PRON
ejpam-3745	25	2	was	be	AUX
ejpam-3745	25	3	introduced	introduce	VERB
ejpam-3745	25	4	in	in	ADP
ejpam-3745	25	5	1947	1947	NUM
ejpam-3745	25	6	by	by	ADP
ejpam-3745	25	7	wiener	wiener	NOUN
ejpam-3745	25	8	[	[	X
ejpam-3745	25	9	13	13	NUM
ejpam-3745	25	10	]	]	PUNCT
ejpam-3745	25	11	and	and	CCONJ
ejpam-3745	25	12	used	use	VERB
ejpam-3745	25	13	for	for	ADP
ejpam-3745	25	14	modelling	model	VERB
ejpam-3745	25	15	the	the	DET
ejpam-3745	25	16	shape	shape	NOUN
ejpam-3745	25	17	of	of	ADP
ejpam-3745	25	18	organic	organic	ADJ
ejpam-3745	25	19	molecules	molecule	NOUN
ejpam-3745	25	20	and	and	CCONJ
ejpam-3745	25	21	for	for	ADP
ejpam-3745	25	22	calculating	calculate	VERB
ejpam-3745	25	23	several	several	ADJ
ejpam-3745	25	24	of	of	ADP
ejpam-3745	25	25	their	their	PRON
ejpam-3745	25	26	physico	physico	NOUN
ejpam-3745	25	27	-	-	PUNCT
ejpam-3745	25	28	chemical	chemical	NOUN
ejpam-3745	25	29	properties	property	NOUN
ejpam-3745	25	30	,	,	PUNCT
ejpam-3745	25	31	in	in	ADP
ejpam-3745	25	32	particular	particular	ADJ
ejpam-3745	25	33	the	the	DET
ejpam-3745	25	34	boiling	boiling	NOUN
ejpam-3745	25	35	points	point	NOUN
ejpam-3745	25	36	of	of	ADP
ejpam-3745	25	37	alkane	alkane	NOUN
ejpam-3745	25	38	isomers	isomer	NOUN
ejpam-3745	25	39	.	.	PUNCT
ejpam-3745	26	1	mathematicians	mathematician	NOUN
ejpam-3745	26	2	are	be	AUX
ejpam-3745	26	3	interested	interested	ADJ
ejpam-3745	26	4	in	in	ADP
ejpam-3745	26	5	the	the	DET
ejpam-3745	26	6	wiener	wiener	NOUN
ejpam-3745	26	7	index	index	NOUN
ejpam-3745	26	8	as	as	ADV
ejpam-3745	26	9	much	much	ADV
ejpam-3745	26	10	as	as	ADP
ejpam-3745	26	11	chemists	chemist	NOUN
ejpam-3745	26	12	.	.	PUNCT
ejpam-3745	27	1	mathematical	mathematical	ADJ
ejpam-3745	27	2	research	research	NOUN
ejpam-3745	27	3	on	on	ADP
ejpam-3745	27	4	the	the	DET
ejpam-3745	27	5	wiener	wiener	NOUN
ejpam-3745	27	6	index	index	NOUN
ejpam-3745	27	7	was	be	AUX
ejpam-3745	27	8	started	start	VERB
ejpam-3745	27	9	in	in	ADP
ejpam-3745	27	10	1976	1976	NUM
ejpam-3745	27	11	in	in	ADP
ejpam-3745	27	12	[	[	X
ejpam-3745	27	13	14	14	NUM
ejpam-3745	27	14	]	]	PUNCT
ejpam-3745	27	15	and	and	CCONJ
ejpam-3745	27	16	since	since	SCONJ
ejpam-3745	27	17	then	then	ADV
ejpam-3745	27	18	,	,	PUNCT
ejpam-3745	27	19	this	this	DET
ejpam-3745	27	20	distance	distance	NOUN
ejpam-3745	27	21	-	-	PUNCT
ejpam-3745	27	22	based	base	VERB
ejpam-3745	27	23	quantity	quantity	NOUN
ejpam-3745	27	24	had	have	AUX
ejpam-3745	27	25	been	be	AUX
ejpam-3745	27	26	studied	study	VERB
ejpam-3745	27	27	in	in	ADP
ejpam-3745	27	28	[	[	X
ejpam-3745	27	29	16	16	NUM
ejpam-3745	27	30	]	]	PUNCT
ejpam-3745	27	31	,	,	PUNCT
ejpam-3745	28	1	[	[	X
ejpam-3745	28	2	17	17	NUM
ejpam-3745	28	3	]	]	PUNCT
ejpam-3745	28	4	and	and	CCONJ
ejpam-3745	28	5	[	[	X
ejpam-3745	28	6	15	15	NUM
ejpam-3745	28	7	]	]	PUNCT
ejpam-3745	28	8	.	.	PUNCT
ejpam-3745	29	1	now	now	ADV
ejpam-3745	29	2	let	let	VERB
ejpam-3745	29	3	us	we	PRON
ejpam-3745	29	4	recall	recall	VERB
ejpam-3745	29	5	the	the	DET
ejpam-3745	29	6	definitions	definition	NOUN
ejpam-3745	29	7	of	of	ADP
ejpam-3745	29	8	the	the	DET
ejpam-3745	29	9	wiener	wiener	NOUN
ejpam-3745	29	10	index	index	NOUN
ejpam-3745	29	11	and	and	CCONJ
ejpam-3745	29	12	monogenic	monogenic	ADJ
ejpam-3745	29	13	semigroups	semigroup	NOUN
ejpam-3745	29	14	:	:	PUNCT
ejpam-3745	29	15	the	the	DET
ejpam-3745	29	16	vertex	vertex	NOUN
ejpam-3745	29	17	set	set	NOUN
ejpam-3745	29	18	of	of	ADP
ejpam-3745	29	19	a	a	DET
ejpam-3745	29	20	graph	graph	NOUN
ejpam-3745	29	21	g	g	NOUN
ejpam-3745	29	22	is	be	AUX
ejpam-3745	29	23	denoted	denote	VERB
ejpam-3745	29	24	by	by	ADP
ejpam-3745	29	25	v	v	NOUN
ejpam-3745	29	26	(	(	PUNCT
ejpam-3745	29	27	g	g	NOUN
ejpam-3745	29	28	)	)	PUNCT
ejpam-3745	29	29	.	.	PUNCT
ejpam-3745	30	1	the	the	DET
ejpam-3745	30	2	distance	distance	NOUN
ejpam-3745	30	3	between	between	ADP
ejpam-3745	30	4	two	two	NUM
ejpam-3745	30	5	vertices	vertex	NOUN
ejpam-3745	30	6	u	u	NOUN
ejpam-3745	30	7	and	and	CCONJ
ejpam-3745	30	8	v	v	NOUN
ejpam-3745	30	9	in	in	ADP
ejpam-3745	30	10	v	v	NOUN
ejpam-3745	30	11	(	(	PUNCT
ejpam-3745	30	12	g	g	NOUN
ejpam-3745	30	13	)	)	PUNCT
ejpam-3745	30	14	is	be	AUX
ejpam-3745	30	15	denoted	denote	VERB
ejpam-3745	30	16	by	by	ADP
ejpam-3745	30	17	dg(u	dg(u	NOUN
ejpam-3745	30	18	,	,	PUNCT
ejpam-3745	30	19	v	v	NOUN
ejpam-3745	30	20	)	)	PUNCT
ejpam-3745	30	21	.	.	PUNCT
ejpam-3745	31	1	then	then	ADV
ejpam-3745	31	2	the	the	DET
ejpam-3745	31	3	wiener	wiener	NOUN
ejpam-3745	31	4	index	index	NOUN
ejpam-3745	31	5	w	w	PROPN
ejpam-3745	31	6	(	(	PUNCT
ejpam-3745	31	7	g	g	NOUN
ejpam-3745	31	8	)	)	PUNCT
ejpam-3745	31	9	of	of	ADP
ejpam-3745	31	10	g	g	PROPN
ejpam-3745	31	11	is	be	AUX
ejpam-3745	31	12	defined	define	VERB
ejpam-3745	31	13	by	by	ADP
ejpam-3745	31	14	w	w	PROPN
ejpam-3745	31	15	(	(	PUNCT
ejpam-3745	31	16	g	g	NOUN
ejpam-3745	31	17	)	)	PUNCT
ejpam-3745	31	18	=	=	PUNCT
ejpam-3745	32	1	∑	∑	PUNCT
ejpam-3745	32	2	{	{	PUNCT
ejpam-3745	32	3	u	u	NOUN
ejpam-3745	32	4	,	,	PUNCT
ejpam-3745	32	5	v}⊆v	v}⊆v	PROPN
ejpam-3745	32	6	(	(	PUNCT
ejpam-3745	32	7	g	g	NOUN
ejpam-3745	32	8	)	)	PUNCT
ejpam-3745	32	9	dg(u	dg(u	X
ejpam-3745	32	10	,	,	PUNCT
ejpam-3745	32	11	v	v	NOUN
ejpam-3745	32	12	)	)	PUNCT
ejpam-3745	32	13	.	.	PUNCT
ejpam-3745	33	1	let	let	VERB
ejpam-3745	33	2	sn	sn	PROPN
ejpam-3745	33	3	be	be	AUX
ejpam-3745	33	4	a	a	DET
ejpam-3745	33	5	finite	finite	ADJ
ejpam-3745	33	6	semigroup	semigroup	NOUN
ejpam-3745	33	7	of	of	ADP
ejpam-3745	33	8	order	order	NOUN
ejpam-3745	33	9	n.	n.	VERB
ejpam-3745	33	10	in	in	ADP
ejpam-3745	33	11	[	[	PUNCT
ejpam-3745	33	12	11	11	NUM
ejpam-3745	33	13	]	]	PUNCT
ejpam-3745	33	14	,	,	PUNCT
ejpam-3745	33	15	an	an	DET
ejpam-3745	33	16	undirected	undirected	ADJ
ejpam-3745	33	17	graph	graph	NOUN
ejpam-3745	33	18	denoted	denote	VERB
ejpam-3745	33	19	by	by	ADP
ejpam-3745	33	20	d(sn	d(sn	NOUN
ejpam-3745	33	21	)	)	PUNCT
ejpam-3745	33	22	=	=	SYM
ejpam-3745	33	23	(	(	PUNCT
ejpam-3745	33	24	v	v	NOUN
ejpam-3745	33	25	,	,	PUNCT
ejpam-3745	33	26	e	e	NOUN
ejpam-3745	33	27	)	)	PUNCT
ejpam-3745	33	28	was	be	AUX
ejpam-3745	33	29	defined	define	VERB
ejpam-3745	33	30	as	as	SCONJ
ejpam-3745	33	31	follows	follow	VERB
ejpam-3745	33	32	:	:	PUNCT
ejpam-3745	33	33	the	the	DET
ejpam-3745	33	34	vertex	vertex	NOUN
ejpam-3745	33	35	set	set	VERB
ejpam-3745	33	36	consists	consist	VERB
ejpam-3745	33	37	of	of	ADP
ejpam-3745	33	38	the	the	DET
ejpam-3745	33	39	non	non	ADJ
ejpam-3745	33	40	-	-	ADJ
ejpam-3745	33	41	zero	zero	NUM
ejpam-3745	33	42	elements	element	NOUN
ejpam-3745	33	43	of	of	ADP
ejpam-3745	33	44	sn	sn	PROPN
ejpam-3745	33	45	and	and	CCONJ
ejpam-3745	33	46	two	two	NUM
ejpam-3745	33	47	vertices	vertex	NOUN
ejpam-3745	33	48	x	x	PUNCT
ejpam-3745	33	49	and	and	CCONJ
ejpam-3745	33	50	y	y	PROPN
ejpam-3745	33	51	which	which	PRON
ejpam-3745	33	52	are	be	AUX
ejpam-3745	33	53	distinct	distinct	ADJ
ejpam-3745	33	54	non	non	ADJ
ejpam-3745	33	55	-	-	ADJ
ejpam-3745	33	56	zero	zero	NUM
ejpam-3745	33	57	elements	element	NOUN
ejpam-3745	33	58	in	in	ADP
ejpam-3745	33	59	sn	sn	PROPN
ejpam-3745	33	60	are	be	AUX
ejpam-3745	33	61	adjacent	adjacent	ADJ
ejpam-3745	33	62	if	if	SCONJ
ejpam-3745	34	1	and	and	CCONJ
ejpam-3745	34	2	only	only	ADV
ejpam-3745	34	3	if	if	SCONJ
ejpam-3745	34	4	xy	xy	PROPN
ejpam-3745	34	5	=	=	SYM
ejpam-3745	34	6	0sn	0sn	PROPN
ejpam-3745	34	7	.	.	PUNCT
ejpam-3745	35	1	hence	hence	ADV
ejpam-3745	35	2	sn	sn	PROPN
ejpam-3745	35	3	=	=	PUNCT
ejpam-3745	35	4	{	{	PUNCT
ejpam-3745	35	5	0	0	NUM
ejpam-3745	35	6	,	,	PUNCT
ejpam-3745	35	7	x	x	NOUN
ejpam-3745	35	8	,	,	PUNCT
ejpam-3745	35	9	x2	x2	PROPN
ejpam-3745	35	10	,	,	PUNCT
ejpam-3745	35	11	·	·	PUNCT
ejpam-3745	35	12	·	·	PUNCT
ejpam-3745	35	13	·	·	PUNCT
ejpam-3745	35	14	,	,	PUNCT
ejpam-3745	35	15	xn	xn	PROPN
ejpam-3745	35	16	}	}	PUNCT
ejpam-3745	35	17	where	where	SCONJ
ejpam-3745	35	18	xi	xi	PROPN
ejpam-3745	35	19	,	,	PUNCT
ejpam-3745	35	20	xj	xj	PROPN
ejpam-3745	35	21	∈	∈	PROPN
ejpam-3745	35	22	v	v	ADP
ejpam-3745	35	23	(	(	PUNCT
ejpam-3745	35	24	d(sn	d(sn	NOUN
ejpam-3745	35	25	)	)	PUNCT
ejpam-3745	35	26	)	)	PUNCT
ejpam-3745	35	27	are	be	AUX
ejpam-3745	35	28	adjacent	adjacent	ADJ
ejpam-3745	35	29	⇔	⇔	PROPN
ejpam-3745	35	30	xi	xi	PROPN
ejpam-3745	35	31	·	·	PUNCT
ejpam-3745	35	32	xj	xj	PROPN
ejpam-3745	36	1	=	=	PROPN
ejpam-3745	36	2	0sn	0sn	PROPN
ejpam-3745	36	3	⇔	⇔	PROPN
ejpam-3745	36	4	xi+j	xi+j	PROPN
ejpam-3745	36	5	=	=	PROPN
ejpam-3745	36	6	0sn	0sn	PROPN
ejpam-3745	36	7	⇔	⇔	PROPN
ejpam-3745	36	8	i	i	PROPN
ejpam-3745	37	1	+	+	X
ejpam-3745	37	2	j	j	PROPN
ejpam-3745	37	3	>	>	X
ejpam-3745	37	4	n	n	PROPN
ejpam-3745	37	5	(	(	PUNCT
ejpam-3745	37	6	1	1	NUM
ejpam-3745	37	7	≤	≤	NUM
ejpam-3745	37	8	i	i	PROPN
ejpam-3745	37	9	,	,	PUNCT
ejpam-3745	37	10	j	j	PROPN
ejpam-3745	37	11	≤	≤	PROPN
ejpam-3745	37	12	n	n	CCONJ
ejpam-3745	37	13	)	)	PUNCT
ejpam-3745	37	14	.	.	PUNCT
ejpam-3745	38	1	some	some	DET
ejpam-3745	38	2	various	various	ADJ
ejpam-3745	38	3	types	type	NOUN
ejpam-3745	38	4	of	of	ADP
ejpam-3745	38	5	monogenic	monogenic	ADJ
ejpam-3745	38	6	semigroups	semigroup	NOUN
ejpam-3745	38	7	including	include	VERB
ejpam-3745	38	8	the	the	DET
ejpam-3745	38	9	tensor	tensor	NOUN
ejpam-3745	38	10	,	,	PUNCT
ejpam-3745	38	11	lexicographic	lexicographic	ADJ
ejpam-3745	38	12	,	,	PUNCT
ejpam-3745	38	13	strong	strong	ADJ
ejpam-3745	38	14	and	and	CCONJ
ejpam-3745	38	15	disjunctive	disjunctive	ADJ
ejpam-3745	38	16	products	product	NOUN
ejpam-3745	38	17	were	be	AUX
ejpam-3745	38	18	studied	study	VERB
ejpam-3745	38	19	in	in	ADP
ejpam-3745	38	20	[	[	X
ejpam-3745	38	21	20	20	NUM
ejpam-3745	38	22	]	]	PUNCT
ejpam-3745	38	23	,	,	PUNCT
ejpam-3745	38	24	[	[	X
ejpam-3745	38	25	21	21	NUM
ejpam-3745	38	26	]	]	PUNCT
ejpam-3745	38	27	,	,	PUNCT
ejpam-3745	38	28	[	[	X
ejpam-3745	38	29	19	19	NUM
ejpam-3745	38	30	]	]	PUNCT
ejpam-3745	38	31	and	and	CCONJ
ejpam-3745	38	32	[	[	X
ejpam-3745	38	33	18	18	NUM
ejpam-3745	38	34	]	]	PUNCT
ejpam-3745	38	35	.	.	PUNCT
ejpam-3745	39	1	also	also	ADV
ejpam-3745	39	2	some	some	DET
ejpam-3745	39	3	topological	topological	ADJ
ejpam-3745	39	4	indices	index	NOUN
ejpam-3745	39	5	of	of	ADP
ejpam-3745	39	6	monogenic	monogenic	ADJ
ejpam-3745	39	7	semigroups	semigroup	NOUN
ejpam-3745	39	8	were	be	AUX
ejpam-3745	39	9	calculated	calculate	VERB
ejpam-3745	39	10	in	in	ADP
ejpam-3745	39	11	[	[	X
ejpam-3745	39	12	24	24	NUM
ejpam-3745	39	13	]	]	PUNCT
ejpam-3745	39	14	,	,	PUNCT
ejpam-3745	40	1	[	[	X
ejpam-3745	40	2	22	22	NUM
ejpam-3745	40	3	]	]	PUNCT
ejpam-3745	40	4	and	and	CCONJ
ejpam-3745	40	5	[	[	X
ejpam-3745	40	6	23	23	NUM
ejpam-3745	40	7	]	]	PUNCT
ejpam-3745	40	8	.	.	PUNCT
ejpam-3745	41	1	in	in	ADP
ejpam-3745	41	2	[	[	X
ejpam-3745	41	3	12	12	NUM
ejpam-3745	41	4	]	]	PUNCT
ejpam-3745	41	5	,	,	PUNCT
ejpam-3745	41	6	the	the	DET
ejpam-3745	41	7	dot	dot	NOUN
ejpam-3745	41	8	product	product	NOUN
ejpam-3745	41	9	graph	graph	NOUN
ejpam-3745	41	10	considered	consider	VERB
ejpam-3745	41	11	was	be	AUX
ejpam-3745	41	12	d(s	d(s	PROPN
ejpam-3745	41	13	)	)	PUNCT
ejpam-3745	41	14	where	where	SCONJ
ejpam-3745	41	15	s	s	NOUN
ejpam-3745	41	16	is	be	AUX
ejpam-3745	41	17	the	the	DET
ejpam-3745	41	18	cartesian	cartesian	ADJ
ejpam-3745	41	19	product	product	NOUN
ejpam-3745	41	20	of	of	ADP
ejpam-3745	41	21	k	k	PROPN
ejpam-3745	41	22	times	times	PROPN
ejpam-3745	41	23	sn	sn	PROPN
ejpam-3745	41	24	:	:	PUNCT
ejpam-3745	41	25	s	s	X
ejpam-3745	41	26	=	=	SYM
ejpam-3745	41	27	sn	sn	PROPN
ejpam-3745	41	28	×	×	PROPN
ejpam-3745	41	29	sn	sn	PROPN
ejpam-3745	41	30	×	×	NOUN
ejpam-3745	41	31	.	.	PUNCT
ejpam-3745	41	32	.	.	PUNCT
ejpam-3745	42	1	.×	.×	PROPN
ejpam-3745	42	2	sn	sn	PROPN
ejpam-3745	42	3	for	for	ADP
ejpam-3745	42	4	k	k	PROPN
ejpam-3745	42	5	times	times	PROPN
ejpam-3745	42	6	,	,	PUNCT
ejpam-3745	42	7	where	where	SCONJ
ejpam-3745	42	8	1	1	NUM
ejpam-3745	42	9	≤	≤	NUM
ejpam-3745	43	1	k	k	NOUN
ejpam-3745	43	2	<	<	X
ejpam-3745	43	3	∞.	∞.	PROPN
ejpam-3745	43	4	b.	b.	PROPN
ejpam-3745	43	5	aydın	aydın	PROPN
ejpam-3745	43	6	,	,	PUNCT
ejpam-3745	43	7	n.	n.	PROPN
ejpam-3745	43	8	akgüneş	akgüneş	PROPN
ejpam-3745	43	9	,	,	PUNCT
ejpam-3745	43	10	i.	i.	PROPN
ejpam-3745	43	11	n.	n.	PROPN
ejpam-3745	43	12	cangul	cangul	PROPN
ejpam-3745	43	13	/	/	SYM
ejpam-3745	43	14	eur	eur	NOUN
ejpam-3745	43	15	.	.	PUNCT
ejpam-3745	44	1	j.	j.	PROPN
ejpam-3745	44	2	pure	pure	PROPN
ejpam-3745	44	3	appl	appl	PROPN
ejpam-3745	44	4	.	.	PROPN
ejpam-3745	44	5	math	math	PROPN
ejpam-3745	44	6	,	,	PUNCT
ejpam-3745	44	7	13	13	NUM
ejpam-3745	44	8	(	(	PUNCT
ejpam-3745	44	9	5	5	NUM
ejpam-3745	44	10	)	)	PUNCT
ejpam-3745	44	11	(	(	PUNCT
ejpam-3745	44	12	2020	2020	NUM
ejpam-3745	44	13	)	)	PUNCT
ejpam-3745	44	14	,	,	PUNCT
ejpam-3745	44	15	1231	1231	NUM
ejpam-3745	44	16	-	-	SYM
ejpam-3745	44	17	1240	1240	NUM
ejpam-3745	44	18	1233	1233	NUM
ejpam-3745	44	19	let	let	VERB
ejpam-3745	44	20	two	two	NUM
ejpam-3745	44	21	nonzero	nonzero	ADJ
ejpam-3745	44	22	elements	element	NOUN
ejpam-3745	44	23	of	of	ADP
ejpam-3745	44	24	s	s	VERB
ejpam-3745	44	25	be	be	AUX
ejpam-3745	44	26	x	x	X
ejpam-3745	44	27	=	=	SYM
ejpam-3745	44	28	(	(	PUNCT
ejpam-3745	44	29	xi1	xi1	PROPN
ejpam-3745	44	30	,	,	PUNCT
ejpam-3745	44	31	xi2	xi2	PROPN
ejpam-3745	44	32	,	,	PUNCT
ejpam-3745	44	33	·	·	PUNCT
ejpam-3745	44	34	·	·	PUNCT
ejpam-3745	44	35	·	·	PUNCT
ejpam-3745	44	36	,	,	PUNCT
ejpam-3745	44	37	xik	xik	PROPN
ejpam-3745	44	38	)	)	PUNCT
ejpam-3745	44	39	and	and	CCONJ
ejpam-3745	44	40	y	y	PROPN
ejpam-3745	44	41	=	=	SYM
ejpam-3745	44	42	(	(	PUNCT
ejpam-3745	44	43	xj1	xj1	PROPN
ejpam-3745	44	44	,	,	PUNCT
ejpam-3745	44	45	xj2	xj2	X
ejpam-3745	44	46	,	,	PUNCT
ejpam-3745	44	47	·	·	PUNCT
ejpam-3745	44	48	·	·	PUNCT
ejpam-3745	44	49	·	·	PUNCT
ejpam-3745	44	50	,	,	PUNCT
ejpam-3745	44	51	xjk	xjk	PROPN
ejpam-3745	44	52	)	)	PUNCT
ejpam-3745	44	53	for	for	ADP
ejpam-3745	44	54	{	{	PUNCT
ejpam-3745	44	55	it}kt=1	it}kt=1	PROPN
ejpam-3745	44	56	,	,	PUNCT
ejpam-3745	44	57	{	{	PUNCT
ejpam-3745	44	58	jt}kt=1	jt}kt=1	ADV
ejpam-3745	44	59	∈	∈	PROPN
ejpam-3745	44	60	{	{	PUNCT
ejpam-3745	44	61	0	0	NUM
ejpam-3745	44	62	,	,	PUNCT
ejpam-3745	44	63	1	1	NUM
ejpam-3745	44	64	,	,	PUNCT
ejpam-3745	44	65	2	2	NUM
ejpam-3745	44	66	,	,	PUNCT
ejpam-3745	44	67	·	·	PUNCT
ejpam-3745	44	68	·	·	PUNCT
ejpam-3745	44	69	·	·	PUNCT
ejpam-3745	44	70	,	,	PUNCT
ejpam-3745	44	71	n	n	CCONJ
ejpam-3745	44	72	}	}	PUNCT
ejpam-3745	44	73	where	where	SCONJ
ejpam-3745	44	74	xit	xit	PROPN
ejpam-3745	44	75	=	=	PROPN
ejpam-3745	44	76	0sn	0sn	PROPN
ejpam-3745	45	1	if	if	SCONJ
ejpam-3745	45	2	and	and	CCONJ
ejpam-3745	45	3	only	only	ADV
ejpam-3745	45	4	if	if	SCONJ
ejpam-3745	45	5	it	it	PRON
ejpam-3745	45	6	=	=	NOUN
ejpam-3745	45	7	0	0	X
ejpam-3745	45	8	.	.	PUNCT
ejpam-3745	46	1	a	a	DET
ejpam-3745	46	2	more	more	ADV
ejpam-3745	46	3	explicit	explicit	ADJ
ejpam-3745	46	4	definition	definition	NOUN
ejpam-3745	46	5	of	of	ADP
ejpam-3745	46	6	the	the	DET
ejpam-3745	46	7	dot	dot	NOUN
ejpam-3745	46	8	product	product	NOUN
ejpam-3745	46	9	in	in	ADP
ejpam-3745	46	10	terms	term	NOUN
ejpam-3745	46	11	of	of	ADP
ejpam-3745	46	12	the	the	DET
ejpam-3745	46	13	elements	element	NOUN
ejpam-3745	46	14	of	of	ADP
ejpam-3745	46	15	s	s	NOUN
ejpam-3745	46	16	is	be	AUX
ejpam-3745	46	17	as	as	SCONJ
ejpam-3745	46	18	follows	follow	VERB
ejpam-3745	46	19	:	:	PUNCT
ejpam-3745	46	20	x	x	X
ejpam-3745	46	21	·	·	PUNCT
ejpam-3745	46	22	y	y	X
ejpam-3745	46	23	=	=	SYM
ejpam-3745	46	24	(	(	PUNCT
ejpam-3745	46	25	xi1	xi1	PROPN
ejpam-3745	46	26	,	,	PUNCT
ejpam-3745	46	27	xi2	xi2	PROPN
ejpam-3745	46	28	,	,	PUNCT
ejpam-3745	46	29	·	·	PUNCT
ejpam-3745	46	30	·	·	PUNCT
ejpam-3745	46	31	·	·	PUNCT
ejpam-3745	46	32	,	,	PUNCT
ejpam-3745	46	33	xik	xik	PROPN
ejpam-3745	46	34	)	)	PUNCT
ejpam-3745	46	35	·	·	PUNCT
ejpam-3745	47	1	(	(	PUNCT
ejpam-3745	47	2	xj1	xj1	PROPN
ejpam-3745	47	3	,	,	PUNCT
ejpam-3745	47	4	xj2	xj2	X
ejpam-3745	47	5	,	,	PUNCT
ejpam-3745	47	6	·	·	PUNCT
ejpam-3745	47	7	·	·	PUNCT
ejpam-3745	47	8	·	·	PUNCT
ejpam-3745	47	9	,	,	PUNCT
ejpam-3745	47	10	xjk	xjk	X
ejpam-3745	47	11	)	)	PUNCT
ejpam-3745	47	12	=	=	PUNCT
ejpam-3745	47	13	xi1	xi1	PROPN
ejpam-3745	47	14	·	·	PUNCT
ejpam-3745	47	15	xj1	xj1	PROPN
ejpam-3745	48	1	+	+	CCONJ
ejpam-3745	48	2	xi2	xi2	PROPN
ejpam-3745	48	3	·	·	PUNCT
ejpam-3745	48	4	xj2	xj2	X
ejpam-3745	48	5	+	+	CCONJ
ejpam-3745	48	6	·	·	PUNCT
ejpam-3745	48	7	·	·	PUNCT
ejpam-3745	48	8	·	·	PUNCT
ejpam-3745	49	1	+	+	NUM
ejpam-3745	49	2	xik	xik	X
ejpam-3745	49	3	·	·	PUNCT
ejpam-3745	49	4	xjk	xjk	X
ejpam-3745	50	1	=	=	PUNCT
ejpam-3745	50	2	xi1+j1	xi1+j1	PROPN
ejpam-3745	50	3	+	+	CCONJ
ejpam-3745	50	4	xi2+j2	xi2+j2	PROPN
ejpam-3745	50	5	+	+	CCONJ
ejpam-3745	50	6	·	·	PUNCT
ejpam-3745	50	7	·	·	PUNCT
ejpam-3745	50	8	·	·	PUNCT
ejpam-3745	51	1	+	+	CCONJ
ejpam-3745	51	2	xik+jk	xik+jk	PROPN
ejpam-3745	51	3	.	.	PUNCT
ejpam-3745	52	1	then	then	ADV
ejpam-3745	52	2	the	the	DET
ejpam-3745	52	3	dot	dot	NOUN
ejpam-3745	52	4	product	product	NOUN
ejpam-3745	52	5	graph	graph	NOUN
ejpam-3745	52	6	d(s	d(s	PROPN
ejpam-3745	52	7	)	)	PUNCT
ejpam-3745	52	8	can	can	AUX
ejpam-3745	52	9	be	be	AUX
ejpam-3745	52	10	defined	define	VERB
ejpam-3745	52	11	as	as	ADP
ejpam-3745	52	12	an	an	DET
ejpam-3745	52	13	(	(	PUNCT
ejpam-3745	52	14	undirected	undirected	ADJ
ejpam-3745	52	15	)	)	PUNCT
ejpam-3745	52	16	graph	graph	NOUN
ejpam-3745	52	17	with	with	ADP
ejpam-3745	52	18	vertices	vertex	NOUN
ejpam-3745	52	19	x	x	X
ejpam-3745	52	20	,	,	PUNCT
ejpam-3745	52	21	y	y	PROPN
ejpam-3745	52	22	∈	∈	PROPN
ejpam-3745	52	23	s∗	s∗	PROPN
ejpam-3745	52	24	=	=	SYM
ejpam-3745	52	25	s	s	PART
ejpam-3745	52	26	\	\	X
ejpam-3745	52	27	{	{	PUNCT
ejpam-3745	52	28	0s	0s	NOUN
ejpam-3745	52	29	}	}	PUNCT
ejpam-3745	52	30	such	such	ADJ
ejpam-3745	52	31	that	that	SCONJ
ejpam-3745	52	32	x	x	PROPN
ejpam-3745	52	33	and	and	CCONJ
ejpam-3745	52	34	y	y	PROPN
ejpam-3745	52	35	are	be	AUX
ejpam-3745	52	36	adjacent	adjacent	ADJ
ejpam-3745	53	1	iff	iff	PROPN
ejpam-3745	53	2	x	x	PROPN
ejpam-3745	53	3	·	·	PUNCT
ejpam-3745	53	4	y	y	PROPN
ejpam-3745	53	5	=	=	PUNCT
ejpam-3745	53	6	0sn	0sn	NOUN
ejpam-3745	54	1	and	and	CCONJ
ejpam-3745	54	2	this	this	PRON
ejpam-3745	54	3	is	be	AUX
ejpam-3745	54	4	denoted	denote	VERB
ejpam-3745	54	5	by	by	ADP
ejpam-3745	54	6	x	x	PUNCT
ejpam-3745	54	7	∼	∼	NOUN
ejpam-3745	54	8	y	y	NOUN
ejpam-3745	54	9	.	.	PUNCT
ejpam-3745	55	1	the	the	DET
ejpam-3745	55	2	following	following	ADJ
ejpam-3745	55	3	result	result	NOUN
ejpam-3745	55	4	will	will	AUX
ejpam-3745	55	5	be	be	AUX
ejpam-3745	55	6	used	use	VERB
ejpam-3745	55	7	in	in	ADP
ejpam-3745	55	8	the	the	DET
ejpam-3745	55	9	rest	rest	NOUN
ejpam-3745	55	10	of	of	ADP
ejpam-3745	55	11	the	the	DET
ejpam-3745	55	12	paper	paper	NOUN
ejpam-3745	55	13	:	:	PUNCT
ejpam-3745	55	14	lemma	lemma	PROPN
ejpam-3745	55	15	1	1	NUM
ejpam-3745	55	16	(	(	PUNCT
ejpam-3745	55	17	[	[	X
ejpam-3745	55	18	12	12	NUM
ejpam-3745	55	19	]	]	NUM
ejpam-3745	55	20	)	)	PUNCT
ejpam-3745	55	21	.	.	PUNCT
ejpam-3745	56	1	d(s	d(s	PROPN
ejpam-3745	56	2	)	)	PUNCT
ejpam-3745	56	3	is	be	AUX
ejpam-3745	56	4	always	always	ADV
ejpam-3745	56	5	connected	connect	VERB
ejpam-3745	56	6	and	and	CCONJ
ejpam-3745	56	7	its	its	PRON
ejpam-3745	56	8	diameter	diameter	NOUN
ejpam-3745	56	9	is	be	AUX
ejpam-3745	56	10	equal	equal	ADJ
ejpam-3745	56	11	to	to	ADP
ejpam-3745	56	12	2	2	NUM
ejpam-3745	56	13	,	,	PUNCT
ejpam-3745	56	14	that	that	PRON
ejpam-3745	56	15	is	be	AUX
ejpam-3745	56	16	diam(d(s	diam(d(s	PROPN
ejpam-3745	56	17	)	)	PUNCT
ejpam-3745	56	18	)	)	PUNCT
ejpam-3745	57	1	=	=	PUNCT
ejpam-3745	58	1	2	2	X
ejpam-3745	58	2	.	.	NOUN
ejpam-3745	58	3	2	2	NUM
ejpam-3745	58	4	.	.	X
ejpam-3745	58	5	main	main	ADJ
ejpam-3745	58	6	results	result	NOUN
ejpam-3745	58	7	let	let	VERB
ejpam-3745	58	8	n	n	PRON
ejpam-3745	58	9	∈	∈	PROPN
ejpam-3745	58	10	n	n	ADV
ejpam-3745	58	11	and	and	CCONJ
ejpam-3745	58	12	let	let	VERB
ejpam-3745	58	13	sn	sn	PROPN
ejpam-3745	58	14	=	=	PUNCT
ejpam-3745	58	15	{	{	PUNCT
ejpam-3745	58	16	0	0	NUM
ejpam-3745	58	17	,	,	PUNCT
ejpam-3745	58	18	x	x	NOUN
ejpam-3745	58	19	,	,	PUNCT
ejpam-3745	58	20	x2	x2	PROPN
ejpam-3745	58	21	,	,	PUNCT
ejpam-3745	58	22	·	·	PUNCT
ejpam-3745	58	23	·	·	PUNCT
ejpam-3745	58	24	·	·	PUNCT
ejpam-3745	58	25	,	,	PUNCT
ejpam-3745	58	26	xn	xn	PROPN
ejpam-3745	58	27	}	}	PUNCT
ejpam-3745	58	28	be	be	AUX
ejpam-3745	58	29	a	a	DET
ejpam-3745	58	30	non	non	ADJ
ejpam-3745	58	31	-	-	ADJ
ejpam-3745	58	32	empty	empty	ADJ
ejpam-3745	58	33	monogenic	monogenic	ADJ
ejpam-3745	58	34	semigroup	semigroup	NOUN
ejpam-3745	58	35	.	.	PUNCT
ejpam-3745	59	1	let	let	VERB
ejpam-3745	59	2	d(s	d(s	PROPN
ejpam-3745	59	3	)	)	PUNCT
ejpam-3745	59	4	be	be	AUX
ejpam-3745	59	5	the	the	DET
ejpam-3745	59	6	dot	dot	NOUN
ejpam-3745	59	7	product	product	NOUN
ejpam-3745	59	8	graph	graph	NOUN
ejpam-3745	59	9	where	where	SCONJ
ejpam-3745	59	10	s	s	VERB
ejpam-3745	59	11	=	=	PUNCT
ejpam-3745	59	12	sn	sn	PROPN
ejpam-3745	59	13	×	×	PROPN
ejpam-3745	59	14	sn	sn	PROPN
ejpam-3745	59	15	is	be	AUX
ejpam-3745	59	16	the	the	DET
ejpam-3745	59	17	cartesian	cartesian	ADJ
ejpam-3745	59	18	product	product	NOUN
ejpam-3745	59	19	of	of	ADP
ejpam-3745	59	20	two	two	NUM
ejpam-3745	59	21	sn	sn	NOUN
ejpam-3745	59	22	’s	’s	NOUN
ejpam-3745	59	23	.	.	PUNCT
ejpam-3745	60	1	recall	recall	VERB
ejpam-3745	60	2	that	that	SCONJ
ejpam-3745	60	3	its	its	PRON
ejpam-3745	60	4	vertices	vertex	NOUN
ejpam-3745	60	5	are	be	AUX
ejpam-3745	60	6	the	the	DET
ejpam-3745	60	7	non	non	ADJ
ejpam-3745	60	8	-	-	ADJ
ejpam-3745	60	9	zero	zero	NUM
ejpam-3745	60	10	elements	element	NOUN
ejpam-3745	60	11	in	in	ADP
ejpam-3745	60	12	s.	s.	PROPN
ejpam-3745	60	13	the	the	DET
ejpam-3745	60	14	following	following	ADJ
ejpam-3745	60	15	result	result	NOUN
ejpam-3745	60	16	is	be	AUX
ejpam-3745	60	17	clear	clear	ADJ
ejpam-3745	60	18	as	as	ADP
ejpam-3745	60	19	the	the	DET
ejpam-3745	60	20	diameter	diameter	NOUN
ejpam-3745	60	21	of	of	ADP
ejpam-3745	60	22	d(s	d(s	PROPN
ejpam-3745	60	23	)	)	PUNCT
ejpam-3745	60	24	is	be	AUX
ejpam-3745	60	25	equal	equal	ADJ
ejpam-3745	60	26	to	to	ADP
ejpam-3745	60	27	2	2	NUM
ejpam-3745	60	28	by	by	ADP
ejpam-3745	60	29	lemma	lemma	PROPN
ejpam-3745	60	30	1	1	NUM
ejpam-3745	60	31	:	:	PUNCT
ejpam-3745	60	32	lemma	lemma	PROPN
ejpam-3745	60	33	2	2	NUM
ejpam-3745	60	34	(	(	PUNCT
ejpam-3745	60	35	[	[	X
ejpam-3745	60	36	12	12	NUM
ejpam-3745	60	37	]	]	NUM
ejpam-3745	60	38	)	)	PUNCT
ejpam-3745	60	39	.	.	PUNCT
ejpam-3745	61	1	the	the	DET
ejpam-3745	61	2	distance	distance	NOUN
ejpam-3745	61	3	of	of	ADP
ejpam-3745	61	4	any	any	DET
ejpam-3745	61	5	two	two	NUM
ejpam-3745	61	6	vertices	vertex	NOUN
ejpam-3745	61	7	is	be	AUX
ejpam-3745	61	8	less	less	ADJ
ejpam-3745	61	9	than	than	ADP
ejpam-3745	61	10	or	or	CCONJ
ejpam-3745	61	11	equal	equal	ADJ
ejpam-3745	61	12	to	to	ADP
ejpam-3745	61	13	2	2	NUM
ejpam-3745	61	14	.	.	PUNCT
ejpam-3745	62	1	that	that	PRON
ejpam-3745	62	2	is	is	ADV
ejpam-3745	62	3	,	,	PUNCT
ejpam-3745	62	4	dd(s)(vi	dd(s)(vi	PROPN
ejpam-3745	62	5	,	,	PUNCT
ejpam-3745	62	6	vj	vj	NOUN
ejpam-3745	62	7	)	)	PUNCT
ejpam-3745	62	8	≤	≤	NOUN
ejpam-3745	62	9	2	2	NUM
ejpam-3745	62	10	where	where	SCONJ
ejpam-3745	62	11	i	i	PRON
ejpam-3745	62	12	,	,	PUNCT
ejpam-3745	62	13	j	j	PROPN
ejpam-3745	62	14	∈	∈	PROPN
ejpam-3745	62	15	n	n	CCONJ
ejpam-3745	62	16	,	,	PUNCT
ejpam-3745	62	17	vi	vi	PROPN
ejpam-3745	62	18	,	,	PUNCT
ejpam-3745	62	19	vj	vj	X
ejpam-3745	62	20	∈	∈	PROPN
ejpam-3745	62	21	v	v	PROPN
ejpam-3745	62	22	(	(	PUNCT
ejpam-3745	62	23	d(s	d(s	PROPN
ejpam-3745	62	24	)	)	PUNCT
ejpam-3745	62	25	)	)	PUNCT
ejpam-3745	62	26	.	.	PUNCT
ejpam-3745	63	1	theorem	theorem	NOUN
ejpam-3745	63	2	1	1	NUM
ejpam-3745	63	3	.	.	PUNCT
ejpam-3745	64	1	the	the	DET
ejpam-3745	64	2	wiener	wiener	NOUN
ejpam-3745	64	3	index	index	NOUN
ejpam-3745	64	4	of	of	ADP
ejpam-3745	64	5	the	the	DET
ejpam-3745	64	6	dot	dot	NOUN
ejpam-3745	64	7	product	product	NOUN
ejpam-3745	64	8	graph	graph	NOUN
ejpam-3745	64	9	over	over	ADP
ejpam-3745	64	10	a	a	DET
ejpam-3745	64	11	monogenic	monogenic	ADJ
ejpam-3745	64	12	semigroup	semigroup	NOUN
ejpam-3745	64	13	of	of	ADP
ejpam-3745	64	14	order	order	NOUN
ejpam-3745	64	15	n	n	X
ejpam-3745	64	16	is	be	AUX
ejpam-3745	64	17	that	that	PRON
ejpam-3745	64	18	w	w	PROPN
ejpam-3745	64	19	(	(	PUNCT
ejpam-3745	64	20	s	s	NOUN
ejpam-3745	64	21	)	)	PUNCT
ejpam-3745	64	22	=	=	SYM
ejpam-3745	64	23	1	1	NUM
ejpam-3745	64	24	2	2	NUM
ejpam-3745	64	25			NOUN
ejpam-3745	64	26	(	(	PUNCT
ejpam-3745	64	27	6n−	6n−	PROPN
ejpam-3745	64	28	2	2	NUM
ejpam-3745	64	29	)	)	PUNCT
ejpam-3745	64	30	(	(	PUNCT
ejpam-3745	64	31	n2	n2	NOUN
ejpam-3745	64	32	+	+	X
ejpam-3745	64	33	2n	2n	NUM
ejpam-3745	64	34	)	)	PUNCT
ejpam-3745	65	1	+	+	CCONJ
ejpam-3745	65	2	(	(	PUNCT
ejpam-3745	65	3	⌈	⌈	NUM
ejpam-3745	65	4	n	n	PRON
ejpam-3745	65	5	2	2	NUM
ejpam-3745	65	6	⌉	⌉	NOUN
ejpam-3745	65	7	+	+	X
ejpam-3745	65	8	1	1	NUM
ejpam-3745	65	9	)	)	SYM
ejpam-3745	65	10	2	2	NUM
ejpam-3745	65	11	−	−	PROPN
ejpam-3745	65	12	1−	1−	NUM
ejpam-3745	65	13	∑	∑	PUNCT
ejpam-3745	65	14	k	k	PROPN
ejpam-3745	65	15	,	,	PUNCT
ejpam-3745	65	16	t∈{0,1,	t∈{0,1,	PRON
ejpam-3745	65	17	...	...	PUNCT
ejpam-3745	65	18	,n−1	,n−1	PUNCT
ejpam-3745	65	19	}	}	PUNCT
ejpam-3745	66	1	[	[	X
ejpam-3745	66	2	2n−	2n−	NUM
ejpam-3745	66	3	k	k	NOUN
ejpam-3745	66	4	−	−	PROPN
ejpam-3745	66	5	t	t	PROPN
ejpam-3745	66	6	+	+	CCONJ
ejpam-3745	66	7	(	(	PUNCT
ejpam-3745	66	8	n−	n−	NOUN
ejpam-3745	66	9	k)(n−	k)(n−	PROPN
ejpam-3745	66	10	t	t	PROPN
ejpam-3745	66	11	)	)	PUNCT
ejpam-3745	66	12	]	]	PUNCT
ejpam-3745	67	1	−	−	PROPN
ejpam-3745	67	2	∑	∑	PROPN
ejpam-3745	67	3	k∈{0,1,	k∈{0,1,	PROPN
ejpam-3745	67	4	...	...	PUNCT
ejpam-3745	67	5	,n−1	,n−1	PUNCT
ejpam-3745	67	6	}	}	PUNCT
ejpam-3745	67	7	t	t	PROPN
ejpam-3745	67	8	=	=	SYM
ejpam-3745	67	9	n	n	X
ejpam-3745	67	10	[	[	X
ejpam-3745	67	11	(	(	PUNCT
ejpam-3745	67	12	n−	n−	NOUN
ejpam-3745	67	13	k)(n	k)(n	VERB
ejpam-3745	67	14	+	+	CCONJ
ejpam-3745	67	15	1	1	X
ejpam-3745	67	16	)	)	PUNCT
ejpam-3745	67	17	+	+	CCONJ
ejpam-3745	67	18	n]−	n]−	ADV
ejpam-3745	67	19	∑	∑	PUNCT
ejpam-3745	67	20	t∈{0,1,	t∈{0,1,	NOUN
ejpam-3745	67	21	...	...	PUNCT
ejpam-3745	67	22	,n−1	,n−1	PUNCT
ejpam-3745	67	23	}	}	PUNCT
ejpam-3745	67	24	k	k	X
ejpam-3745	67	25	=	=	NOUN
ejpam-3745	67	26	n	n	X
ejpam-3745	67	27	[	[	X
ejpam-3745	67	28	(	(	PUNCT
ejpam-3745	67	29	n−	n−	NOUN
ejpam-3745	67	30	t)(n	t)(n	X
ejpam-3745	67	31	+	+	CCONJ
ejpam-3745	67	32	1	1	X
ejpam-3745	67	33	)	)	PUNCT
ejpam-3745	67	34	+	+	NUM
ejpam-3745	67	35	n	n	CCONJ
ejpam-3745	67	36	]	]	X
ejpam-3745	67	37			VERB
ejpam-3745	67	38	.	.	PUNCT
ejpam-3745	68	1	proof	proof	NOUN
ejpam-3745	68	2	.	.	PUNCT
ejpam-3745	69	1	since	since	SCONJ
ejpam-3745	69	2	the	the	DET
ejpam-3745	69	3	diameter	diameter	NOUN
ejpam-3745	69	4	of	of	ADP
ejpam-3745	69	5	d(s	d(s	PROPN
ejpam-3745	69	6	)	)	PUNCT
ejpam-3745	69	7	is	be	AUX
ejpam-3745	69	8	equal	equal	ADJ
ejpam-3745	69	9	to	to	ADP
ejpam-3745	69	10	2	2	NUM
ejpam-3745	69	11	,	,	PUNCT
ejpam-3745	69	12	we	we	PRON
ejpam-3745	69	13	can	can	AUX
ejpam-3745	69	14	write	write	VERB
ejpam-3745	69	15	dd(s)(vi	dd(s)(vi	PROPN
ejpam-3745	69	16	,	,	PUNCT
ejpam-3745	69	17	vj	vj	ADJ
ejpam-3745	69	18	)	)	PUNCT
ejpam-3745	69	19	≤	≤	NUM
ejpam-3745	69	20	2	2	NUM
ejpam-3745	69	21	for	for	ADP
ejpam-3745	69	22	every	every	DET
ejpam-3745	69	23	pair	pair	NOUN
ejpam-3745	69	24	i	i	PRON
ejpam-3745	69	25	,	,	PUNCT
ejpam-3745	69	26	j	j	PROPN
ejpam-3745	69	27	∈	∈	PROPN
ejpam-3745	69	28	n	n	PROPN
ejpam-3745	69	29	and	and	CCONJ
ejpam-3745	69	30	vi	vi	NOUN
ejpam-3745	69	31	,	,	PUNCT
ejpam-3745	69	32	vj	vj	X
ejpam-3745	69	33	∈	∈	PROPN
ejpam-3745	69	34	v	v	PROPN
ejpam-3745	69	35	(	(	PUNCT
ejpam-3745	69	36	d(s	d(s	PROPN
ejpam-3745	69	37	)	)	PUNCT
ejpam-3745	69	38	)	)	PUNCT
ejpam-3745	69	39	.	.	PUNCT
ejpam-3745	70	1	hence	hence	ADV
ejpam-3745	70	2	the	the	DET
ejpam-3745	70	3	distance	distance	NOUN
ejpam-3745	70	4	of	of	ADP
ejpam-3745	70	5	any	any	DET
ejpam-3745	70	6	two	two	NUM
ejpam-3745	70	7	vertices	vertex	NOUN
ejpam-3745	70	8	is	be	AUX
ejpam-3745	70	9	1	1	NUM
ejpam-3745	70	10	or	or	CCONJ
ejpam-3745	70	11	2	2	NUM
ejpam-3745	70	12	.	.	PUNCT
ejpam-3745	71	1	consequently	consequently	ADV
ejpam-3745	71	2	the	the	DET
ejpam-3745	71	3	wiener	wiener	NOUN
ejpam-3745	71	4	index	index	NOUN
ejpam-3745	71	5	of	of	ADP
ejpam-3745	71	6	d(s	d(s	PROPN
ejpam-3745	71	7	)	)	PUNCT
ejpam-3745	71	8	is	be	AUX
ejpam-3745	71	9	as	as	SCONJ
ejpam-3745	71	10	follows	follow	VERB
ejpam-3745	71	11	:	:	PUNCT
ejpam-3745	71	12	w	w	X
ejpam-3745	71	13	(	(	PUNCT
ejpam-3745	71	14	d(s	d(s	PROPN
ejpam-3745	71	15	)	)	PUNCT
ejpam-3745	71	16	)	)	PUNCT
ejpam-3745	72	1	=	=	SYM
ejpam-3745	72	2	1	1	NUM
ejpam-3745	72	3	2	2	NUM
ejpam-3745	72	4	∑	∑	PUNCT
ejpam-3745	72	5	{	{	PUNCT
ejpam-3745	72	6	vi	vi	PROPN
ejpam-3745	72	7	,	,	PUNCT
ejpam-3745	72	8	vj}⊆v	vj}⊆v	NOUN
ejpam-3745	72	9	(	(	PUNCT
ejpam-3745	72	10	d(s	d(s	PROPN
ejpam-3745	72	11	)	)	PUNCT
ejpam-3745	72	12	)	)	PUNCT
ejpam-3745	73	1	dd(s)(vi	dd(s)(vi	PROPN
ejpam-3745	73	2	,	,	PUNCT
ejpam-3745	73	3	vj	vj	NOUN
ejpam-3745	73	4	)	)	PUNCT
ejpam-3745	73	5	.	.	PUNCT
ejpam-3745	74	1	b.	b.	PROPN
ejpam-3745	74	2	aydın	aydın	PROPN
ejpam-3745	74	3	,	,	PUNCT
ejpam-3745	74	4	n.	n.	PROPN
ejpam-3745	74	5	akgüneş	akgüneş	PROPN
ejpam-3745	74	6	,	,	PUNCT
ejpam-3745	74	7	i.	i.	PROPN
ejpam-3745	74	8	n.	n.	PROPN
ejpam-3745	74	9	cangul	cangul	PROPN
ejpam-3745	74	10	/	/	SYM
ejpam-3745	74	11	eur	eur	NOUN
ejpam-3745	74	12	.	.	PUNCT
ejpam-3745	75	1	j.	j.	PROPN
ejpam-3745	75	2	pure	pure	PROPN
ejpam-3745	75	3	appl	appl	PROPN
ejpam-3745	75	4	.	.	PROPN
ejpam-3745	75	5	math	math	PROPN
ejpam-3745	75	6	,	,	PUNCT
ejpam-3745	75	7	13	13	NUM
ejpam-3745	75	8	(	(	PUNCT
ejpam-3745	75	9	5	5	NUM
ejpam-3745	75	10	)	)	PUNCT
ejpam-3745	75	11	(	(	PUNCT
ejpam-3745	75	12	2020	2020	NUM
ejpam-3745	75	13	)	)	PUNCT
ejpam-3745	75	14	,	,	PUNCT
ejpam-3745	75	15	1231	1231	NUM
ejpam-3745	75	16	-	-	SYM
ejpam-3745	75	17	1240	1240	NUM
ejpam-3745	75	18	1234	1234	NUM
ejpam-3745	75	19	here	here	ADV
ejpam-3745	75	20	,	,	PUNCT
ejpam-3745	75	21	let	let	VERB
ejpam-3745	75	22	v1	v1	VERB
ejpam-3745	75	23	=	=	SYM
ejpam-3745	75	24	{	{	PUNCT
ejpam-3745	75	25	vi	vi	NOUN
ejpam-3745	75	26	:	:	PUNCT
ejpam-3745	75	27	dd(s)(vi	dd(s)(vi	PROPN
ejpam-3745	75	28	,	,	PUNCT
ejpam-3745	75	29	vj	vj	NOUN
ejpam-3745	75	30	)	)	PUNCT
ejpam-3745	75	31	=	=	SYM
ejpam-3745	75	32	1	1	NUM
ejpam-3745	75	33	,	,	PUNCT
ejpam-3745	75	34	i	i	PRON
ejpam-3745	75	35	,	,	PUNCT
ejpam-3745	75	36	j	j	PROPN
ejpam-3745	75	37	∈	∈	PROPN
ejpam-3745	75	38	n	n	CCONJ
ejpam-3745	75	39	,	,	PUNCT
ejpam-3745	75	40	vj	vj	PROPN
ejpam-3745	75	41	∈	∈	PROPN
ejpam-3745	75	42	v	v	PROPN
ejpam-3745	75	43	(	(	PUNCT
ejpam-3745	75	44	d(s	d(s	PROPN
ejpam-3745	75	45	)	)	PUNCT
ejpam-3745	75	46	)	)	PUNCT
ejpam-3745	75	47	}	}	PUNCT
ejpam-3745	75	48	and	and	CCONJ
ejpam-3745	75	49	v2	v2	NOUN
ejpam-3745	75	50	=	=	SYM
ejpam-3745	75	51	{	{	PUNCT
ejpam-3745	75	52	vi	vi	NOUN
ejpam-3745	75	53	:	:	PUNCT
ejpam-3745	75	54	dd(s)(vi	dd(s)(vi	PROPN
ejpam-3745	75	55	,	,	PUNCT
ejpam-3745	75	56	vj	vj	NOUN
ejpam-3745	75	57	)	)	PUNCT
ejpam-3745	75	58	=	=	SYM
ejpam-3745	75	59	2	2	NUM
ejpam-3745	75	60	,	,	PUNCT
ejpam-3745	75	61	i	i	PRON
ejpam-3745	75	62	,	,	PUNCT
ejpam-3745	75	63	j	j	PROPN
ejpam-3745	75	64	∈	∈	PROPN
ejpam-3745	75	65	n	n	CCONJ
ejpam-3745	75	66	,	,	PUNCT
ejpam-3745	75	67	vj	vj	PROPN
ejpam-3745	75	68	∈	∈	PROPN
ejpam-3745	75	69	v	v	PROPN
ejpam-3745	75	70	(	(	PUNCT
ejpam-3745	75	71	d(s	d(s	PROPN
ejpam-3745	75	72	)	)	PUNCT
ejpam-3745	75	73	)	)	PUNCT
ejpam-3745	75	74	}	}	PUNCT
ejpam-3745	75	75	.	.	PUNCT
ejpam-3745	76	1	then	then	ADV
ejpam-3745	76	2	the	the	DET
ejpam-3745	76	3	wiener	wiener	NOUN
ejpam-3745	76	4	index	index	NOUN
ejpam-3745	76	5	formula	formula	NOUN
ejpam-3745	76	6	becomes	become	VERB
ejpam-3745	76	7	w	w	ADP
ejpam-3745	76	8	(	(	PUNCT
ejpam-3745	76	9	d(s	d(s	PROPN
ejpam-3745	76	10	)	)	PUNCT
ejpam-3745	76	11	)	)	PUNCT
ejpam-3745	77	1	=	=	SYM
ejpam-3745	77	2	1	1	NUM
ejpam-3745	77	3	2	2	NUM
ejpam-3745	77	4	∑	∑	NOUN
ejpam-3745	77	5	v∈v	v∈v	NOUN
ejpam-3745	77	6	(	(	PUNCT
ejpam-3745	77	7	d(s	d(s	PROPN
ejpam-3745	77	8	)	)	PUNCT
ejpam-3745	77	9	)	)	PUNCT
ejpam-3745	78	1	[	[	X
ejpam-3745	78	2	1	1	NUM
ejpam-3745	78	3	·	·	PUNCT
ejpam-3745	78	4	|v1|+	|v1|+	PRON
ejpam-3745	78	5	2	2	NUM
ejpam-3745	78	6	·	·	SYM
ejpam-3745	78	7	|v2|	|v2|	NOUN
ejpam-3745	78	8	]	]	PUNCT
ejpam-3745	78	9	.	.	PUNCT
ejpam-3745	79	1	so	so	ADV
ejpam-3745	79	2	if	if	SCONJ
ejpam-3745	79	3	we	we	PRON
ejpam-3745	79	4	find	find	VERB
ejpam-3745	79	5	the	the	DET
ejpam-3745	79	6	cardinalities	cardinality	NOUN
ejpam-3745	79	7	of	of	ADP
ejpam-3745	79	8	the	the	DET
ejpam-3745	79	9	sets	set	NOUN
ejpam-3745	79	10	v1	v1	VERB
ejpam-3745	79	11	and	and	CCONJ
ejpam-3745	79	12	v2	v2	NOUN
ejpam-3745	79	13	,	,	PUNCT
ejpam-3745	79	14	the	the	DET
ejpam-3745	79	15	wiener	wiener	NOUN
ejpam-3745	79	16	index	index	NOUN
ejpam-3745	79	17	of	of	ADP
ejpam-3745	79	18	d(s	d(s	PROPN
ejpam-3745	79	19	)	)	PUNCT
ejpam-3745	79	20	will	will	AUX
ejpam-3745	79	21	be	be	AUX
ejpam-3745	79	22	calculated	calculate	VERB
ejpam-3745	79	23	.	.	PUNCT
ejpam-3745	80	1	since	since	SCONJ
ejpam-3745	80	2	the	the	DET
ejpam-3745	80	3	distance	distance	NOUN
ejpam-3745	80	4	of	of	ADP
ejpam-3745	80	5	any	any	DET
ejpam-3745	80	6	two	two	NUM
ejpam-3745	80	7	vertices	vertex	NOUN
ejpam-3745	80	8	in	in	ADP
ejpam-3745	80	9	d(s	d(s	PROPN
ejpam-3745	80	10	)	)	PUNCT
ejpam-3745	80	11	is	be	AUX
ejpam-3745	80	12	1	1	NUM
ejpam-3745	80	13	or	or	CCONJ
ejpam-3745	80	14	2	2	NUM
ejpam-3745	80	15	,	,	PUNCT
ejpam-3745	80	16	it	it	PRON
ejpam-3745	80	17	is	be	AUX
ejpam-3745	80	18	clear	clear	ADJ
ejpam-3745	80	19	that	that	SCONJ
ejpam-3745	80	20	|v2|	|v2|	NOUN
ejpam-3745	81	1	=	=	SYM
ejpam-3745	82	1	|v	|v	PROPN
ejpam-3745	83	1	|	|	ADV
ejpam-3745	83	2	−	−	PROPN
ejpam-3745	83	3	|v1|	|v1|	NOUN
ejpam-3745	83	4	.	.	PUNCT
ejpam-3745	84	1	then	then	ADV
ejpam-3745	84	2	w	w	PROPN
ejpam-3745	84	3	(	(	PUNCT
ejpam-3745	84	4	d(s	d(s	PROPN
ejpam-3745	84	5	)	)	PUNCT
ejpam-3745	84	6	)	)	PUNCT
ejpam-3745	85	1	=	=	SYM
ejpam-3745	85	2	1	1	NUM
ejpam-3745	85	3	2	2	NUM
ejpam-3745	85	4	∑	∑	NOUN
ejpam-3745	85	5	v∈v	v∈v	NOUN
ejpam-3745	85	6	(	(	PUNCT
ejpam-3745	85	7	d(s	d(s	PROPN
ejpam-3745	85	8	)	)	PUNCT
ejpam-3745	85	9	)	)	PUNCT
ejpam-3745	86	1	[	[	X
ejpam-3745	86	2	1	1	NUM
ejpam-3745	86	3	·	·	PUNCT
ejpam-3745	86	4	|v1|+	|v1|+	PRON
ejpam-3745	86	5	2	2	NUM
ejpam-3745	86	6	·	·	SYM
ejpam-3745	86	7	|v2|	|v2|	NOUN
ejpam-3745	86	8	]	]	PUNCT
ejpam-3745	87	1	=	=	SYM
ejpam-3745	88	1	1	1	NUM
ejpam-3745	88	2	2	2	NUM
ejpam-3745	88	3	∑	∑	NOUN
ejpam-3745	88	4	v∈v	v∈v	NOUN
ejpam-3745	88	5	(	(	PUNCT
ejpam-3745	88	6	d(s	d(s	PROPN
ejpam-3745	88	7	)	)	PUNCT
ejpam-3745	88	8	)	)	PUNCT
ejpam-3745	89	1	[	[	X
ejpam-3745	89	2	1	1	NUM
ejpam-3745	89	3	·	·	PUNCT
ejpam-3745	89	4	|v1|+	|v1|+	PRON
ejpam-3745	89	5	2	2	NUM
ejpam-3745	89	6	·	·	PUNCT
ejpam-3745	89	7	(	(	PUNCT
ejpam-3745	89	8	|v	|v	PROPN
ejpam-3745	89	9	|	|	ADV
ejpam-3745	89	10	−	−	PROPN
ejpam-3745	89	11	|v1|	|v1|	NOUN
ejpam-3745	89	12	)	)	PUNCT
ejpam-3745	89	13	]	]	PUNCT
ejpam-3745	89	14	=	=	SYM
ejpam-3745	89	15	1	1	NUM
ejpam-3745	89	16	2	2	NUM
ejpam-3745	89	17	∑	∑	NOUN
ejpam-3745	89	18	v∈v	v∈v	NOUN
ejpam-3745	89	19	(	(	PUNCT
ejpam-3745	89	20	d(s	d(s	PROPN
ejpam-3745	89	21	)	)	PUNCT
ejpam-3745	89	22	)	)	PUNCT
ejpam-3745	90	1	[	[	X
ejpam-3745	90	2	1	1	NUM
ejpam-3745	90	3	·	·	PUNCT
ejpam-3745	90	4	|v1|+	|v1|+	PRON
ejpam-3745	90	5	2	2	NUM
ejpam-3745	90	6	·	·	PUNCT
ejpam-3745	90	7	|v	|v	NOUN
ejpam-3745	90	8	|	|	ADV
ejpam-3745	90	9	−	−	PROPN
ejpam-3745	90	10	2	2	NUM
ejpam-3745	90	11	·	·	PUNCT
ejpam-3745	90	12	|v1|	|v1|	NOUN
ejpam-3745	90	13	]	]	X
ejpam-3745	90	14	=	=	SYM
ejpam-3745	90	15	1	1	NUM
ejpam-3745	90	16	2	2	NUM
ejpam-3745	90	17	∑	∑	NOUN
ejpam-3745	90	18	v∈v	v∈v	NOUN
ejpam-3745	90	19	(	(	PUNCT
ejpam-3745	90	20	d(s	d(s	PROPN
ejpam-3745	90	21	)	)	PUNCT
ejpam-3745	90	22	)	)	PUNCT
ejpam-3745	91	1	[	[	X
ejpam-3745	91	2	2	2	NUM
ejpam-3745	91	3	·	·	PUNCT
ejpam-3745	91	4	|v	|v	NOUN
ejpam-3745	91	5	|	|	ADV
ejpam-3745	91	6	−	−	PROPN
ejpam-3745	91	7	|v1|	|v1|	NOUN
ejpam-3745	91	8	]	]	PUNCT
ejpam-3745	91	9	and	and	CCONJ
ejpam-3745	91	10	therefore	therefore	ADV
ejpam-3745	91	11	finding	find	VERB
ejpam-3745	91	12	|v1|	|v1|	NOUN
ejpam-3745	91	13	will	will	AUX
ejpam-3745	91	14	be	be	AUX
ejpam-3745	91	15	enough	enough	ADJ
ejpam-3745	91	16	.	.	PUNCT
ejpam-3745	92	1	in	in	ADP
ejpam-3745	92	2	the	the	DET
ejpam-3745	92	3	next	next	ADJ
ejpam-3745	92	4	step	step	NOUN
ejpam-3745	92	5	,	,	PUNCT
ejpam-3745	92	6	let	let	VERB
ejpam-3745	92	7	us	we	PRON
ejpam-3745	92	8	determine	determine	VERB
ejpam-3745	92	9	the	the	DET
ejpam-3745	92	10	distance	distance	NOUN
ejpam-3745	92	11	of	of	ADP
ejpam-3745	92	12	each	each	DET
ejpam-3745	92	13	vertex	vertex	NOUN
ejpam-3745	92	14	to	to	ADP
ejpam-3745	92	15	other	other	ADJ
ejpam-3745	92	16	vertices	vertex	NOUN
ejpam-3745	92	17	.	.	PUNCT
ejpam-3745	93	1	if	if	SCONJ
ejpam-3745	93	2	we	we	PRON
ejpam-3745	93	3	can	can	AUX
ejpam-3745	93	4	determine	determine	VERB
ejpam-3745	93	5	how	how	SCONJ
ejpam-3745	93	6	many	many	ADJ
ejpam-3745	93	7	distances	distance	NOUN
ejpam-3745	93	8	are	be	AUX
ejpam-3745	93	9	1	1	NUM
ejpam-3745	93	10	,	,	PUNCT
ejpam-3745	93	11	it	it	PRON
ejpam-3745	93	12	means	mean	VERB
ejpam-3745	93	13	that	that	SCONJ
ejpam-3745	93	14	we	we	PRON
ejpam-3745	93	15	also	also	ADV
ejpam-3745	93	16	determined	determine	VERB
ejpam-3745	93	17	the	the	DET
ejpam-3745	93	18	number	number	NOUN
ejpam-3745	93	19	of	of	ADP
ejpam-3745	93	20	elements	element	NOUN
ejpam-3745	93	21	of	of	ADP
ejpam-3745	93	22	the	the	DET
ejpam-3745	93	23	set	set	NOUN
ejpam-3745	93	24	v1	v1	NOUN
ejpam-3745	93	25	.	.	PUNCT
ejpam-3745	94	1	any	any	DET
ejpam-3745	94	2	pair	pair	NOUN
ejpam-3745	94	3	of	of	ADP
ejpam-3745	94	4	two	two	NUM
ejpam-3745	94	5	non	non	ADJ
ejpam-3745	94	6	-	-	ADJ
ejpam-3745	94	7	zero	zero	NUM
ejpam-3745	94	8	elements	element	NOUN
ejpam-3745	94	9	of	of	ADP
ejpam-3745	94	10	s	s	PRON
ejpam-3745	94	11	will	will	AUX
ejpam-3745	94	12	be	be	AUX
ejpam-3745	94	13	denoted	denote	VERB
ejpam-3745	94	14	by	by	ADP
ejpam-3745	94	15	(	(	PUNCT
ejpam-3745	94	16	xn−k	xn−k	PROPN
ejpam-3745	94	17	,	,	PUNCT
ejpam-3745	94	18	xn−t	xn−t	PROPN
ejpam-3745	94	19	)	)	PUNCT
ejpam-3745	94	20	where	where	SCONJ
ejpam-3745	94	21	k	k	NOUN
ejpam-3745	94	22	,	,	PUNCT
ejpam-3745	94	23	t	t	PROPN
ejpam-3745	94	24	∈	∈	PROPN
ejpam-3745	94	25	{	{	PUNCT
ejpam-3745	94	26	0	0	NUM
ejpam-3745	94	27	,	,	PUNCT
ejpam-3745	94	28	1	1	NUM
ejpam-3745	94	29	,	,	PUNCT
ejpam-3745	94	30	2	2	NUM
ejpam-3745	94	31	,	,	PUNCT
ejpam-3745	94	32	·	·	PUNCT
ejpam-3745	94	33	·	·	PUNCT
ejpam-3745	94	34	·	·	PUNCT
ejpam-3745	94	35	,	,	PUNCT
ejpam-3745	94	36	n	n	CCONJ
ejpam-3745	94	37	}	}	PUNCT
ejpam-3745	94	38	.	.	PUNCT
ejpam-3745	95	1	as	as	ADP
ejpam-3745	95	2	a	a	DET
ejpam-3745	95	3	special	special	ADJ
ejpam-3745	95	4	case	case	NOUN
ejpam-3745	95	5	,	,	PUNCT
ejpam-3745	95	6	x0	x0	PROPN
ejpam-3745	95	7	=	=	PUNCT
ejpam-3745	95	8	0	0	NUM
ejpam-3745	95	9	is	be	AUX
ejpam-3745	95	10	assumed	assume	VERB
ejpam-3745	95	11	.	.	PUNCT
ejpam-3745	96	1	let	let	VERB
ejpam-3745	96	2	us	we	PRON
ejpam-3745	96	3	now	now	ADV
ejpam-3745	96	4	look	look	VERB
ejpam-3745	96	5	at	at	ADP
ejpam-3745	96	6	the	the	DET
ejpam-3745	96	7	three	three	NUM
ejpam-3745	96	8	cases	case	NOUN
ejpam-3745	96	9	where	where	SCONJ
ejpam-3745	96	10	k	k	NOUN
ejpam-3745	96	11	,	,	PUNCT
ejpam-3745	96	12	t	t	PROPN
ejpam-3745	96	13	∈	∈	PROPN
ejpam-3745	96	14	{	{	PUNCT
ejpam-3745	96	15	0	0	NUM
ejpam-3745	96	16	,	,	PUNCT
ejpam-3745	96	17	1	1	NUM
ejpam-3745	96	18	,	,	PUNCT
ejpam-3745	96	19	2	2	NUM
ejpam-3745	96	20	,	,	PUNCT
ejpam-3745	96	21	·	·	PUNCT
ejpam-3745	96	22	·	·	PUNCT
ejpam-3745	96	23	·	·	PUNCT
ejpam-3745	96	24	,	,	PUNCT
ejpam-3745	96	25	n−	n−	NOUN
ejpam-3745	96	26	1	1	NUM
ejpam-3745	96	27	}	}	PUNCT
ejpam-3745	96	28	or	or	CCONJ
ejpam-3745	96	29	k	k	NOUN
ejpam-3745	96	30	=	=	PUNCT
ejpam-3745	96	31	n	n	PROPN
ejpam-3745	96	32	or	or	CCONJ
ejpam-3745	96	33	t	t	NOUN
ejpam-3745	96	34	=	=	SYM
ejpam-3745	96	35	n	n	CCONJ
ejpam-3745	96	36	,	,	PUNCT
ejpam-3745	96	37	respectively	respectively	ADV
ejpam-3745	96	38	.	.	PUNCT
ejpam-3745	97	1	first	first	ADJ
ejpam-3745	97	2	case	case	NOUN
ejpam-3745	97	3	:	:	PUNCT
ejpam-3745	97	4	let	let	VERB
ejpam-3745	97	5	k	k	X
ejpam-3745	97	6	,	,	PUNCT
ejpam-3745	97	7	t	t	PROPN
ejpam-3745	97	8	∈	∈	PROPN
ejpam-3745	97	9	{	{	PUNCT
ejpam-3745	97	10	0	0	NUM
ejpam-3745	97	11	,	,	PUNCT
ejpam-3745	97	12	1	1	NUM
ejpam-3745	97	13	,	,	PUNCT
ejpam-3745	97	14	2	2	NUM
ejpam-3745	97	15	,	,	PUNCT
ejpam-3745	97	16	·	·	PUNCT
ejpam-3745	97	17	·	·	PUNCT
ejpam-3745	97	18	·	·	PUNCT
ejpam-3745	97	19	,	,	PUNCT
ejpam-3745	97	20	n	n	CCONJ
ejpam-3745	97	21	−	−	PROPN
ejpam-3745	97	22	1	1	NUM
ejpam-3745	97	23	}	}	PUNCT
ejpam-3745	97	24	.	.	PUNCT
ejpam-3745	98	1	there	there	PRON
ejpam-3745	98	2	are	be	VERB
ejpam-3745	98	3	(	(	PUNCT
ejpam-3745	98	4	n	n	CCONJ
ejpam-3745	98	5	−	−	PROPN
ejpam-3745	98	6	k)(n	k)(n	PROPN
ejpam-3745	98	7	−	−	PROPN
ejpam-3745	98	8	t	t	PROPN
ejpam-3745	98	9	)	)	PUNCT
ejpam-3745	98	10	+	+	NUM
ejpam-3745	98	11	2n	2n	NUM
ejpam-3745	98	12	−	−	NOUN
ejpam-3745	99	1	k	k	NOUN
ejpam-3745	99	2	−	−	PROPN
ejpam-3745	99	3	t	t	PROPN
ejpam-3745	99	4	vertices	vertice	VERB
ejpam-3745	99	5	where	where	SCONJ
ejpam-3745	99	6	the	the	DET
ejpam-3745	99	7	distance	distance	NOUN
ejpam-3745	99	8	of	of	ADP
ejpam-3745	99	9	the	the	DET
ejpam-3745	99	10	vertex	vertex	NOUN
ejpam-3745	99	11	(	(	PUNCT
ejpam-3745	99	12	xn−k	xn−k	PROPN
ejpam-3745	99	13	,	,	PUNCT
ejpam-3745	99	14	xn−t	xn−t	PROPN
ejpam-3745	99	15	)	)	PUNCT
ejpam-3745	99	16	to	to	ADP
ejpam-3745	99	17	another	another	DET
ejpam-3745	99	18	vertex	vertex	NOUN
ejpam-3745	99	19	(	(	PUNCT
ejpam-3745	99	20	xa	xa	PROPN
ejpam-3745	99	21	,	,	PUNCT
ejpam-3745	99	22	xb	xb	PROPN
ejpam-3745	99	23	)	)	PUNCT
ejpam-3745	99	24	in	in	ADP
ejpam-3745	99	25	v	v	NOUN
ejpam-3745	99	26	(	(	PUNCT
ejpam-3745	99	27	d(s	d(s	PROPN
ejpam-3745	99	28	)	)	PUNCT
ejpam-3745	99	29	)	)	PUNCT
ejpam-3745	99	30	is	be	AUX
ejpam-3745	99	31	1	1	NUM
ejpam-3745	99	32	.	.	PUNCT
ejpam-3745	100	1	indeed	indeed	ADV
ejpam-3745	100	2	,	,	PUNCT
ejpam-3745	100	3	any	any	DET
ejpam-3745	100	4	vertex	vertex	NOUN
ejpam-3745	100	5	x	x	X
ejpam-3745	100	6	=	=	SYM
ejpam-3745	100	7	(	(	PUNCT
ejpam-3745	100	8	xa	xa	PROPN
ejpam-3745	100	9	,	,	PUNCT
ejpam-3745	100	10	xb	xb	PROPN
ejpam-3745	100	11	)	)	PUNCT
ejpam-3745	100	12	in	in	ADP
ejpam-3745	100	13	v	v	NOUN
ejpam-3745	100	14	(	(	PUNCT
ejpam-3745	100	15	d(s	d(s	PROPN
ejpam-3745	100	16	)	)	PUNCT
ejpam-3745	100	17	)	)	PUNCT
ejpam-3745	100	18	is	be	AUX
ejpam-3745	100	19	adjacent	adjacent	ADJ
ejpam-3745	100	20	to	to	ADP
ejpam-3745	100	21	y	y	PROPN
ejpam-3745	100	22	=	=	SYM
ejpam-3745	100	23	(	(	PUNCT
ejpam-3745	100	24	xn−k	xn−k	PROPN
ejpam-3745	100	25	,	,	PUNCT
ejpam-3745	100	26	xn−t	xn−t	PROPN
ejpam-3745	100	27	)	)	PUNCT
ejpam-3745	100	28	for	for	ADP
ejpam-3745	100	29	k	k	PROPN
ejpam-3745	100	30	,	,	PUNCT
ejpam-3745	100	31	t	t	PROPN
ejpam-3745	100	32	∈	∈	PROPN
ejpam-3745	100	33	{	{	PUNCT
ejpam-3745	100	34	0	0	NUM
ejpam-3745	100	35	,	,	PUNCT
ejpam-3745	100	36	1	1	NUM
ejpam-3745	100	37	,	,	PUNCT
ejpam-3745	100	38	2	2	NUM
ejpam-3745	100	39	,	,	PUNCT
ejpam-3745	100	40	·	·	PUNCT
ejpam-3745	100	41	·	·	PUNCT
ejpam-3745	100	42	·	·	PUNCT
ejpam-3745	100	43	,	,	PUNCT
ejpam-3745	101	1	n	n	CCONJ
ejpam-3745	101	2	−	−	PROPN
ejpam-3745	101	3	1	1	NUM
ejpam-3745	101	4	}	}	PUNCT
ejpam-3745	101	5	if	if	SCONJ
ejpam-3745	101	6	x	x	X
ejpam-3745	101	7	·	·	PUNCT
ejpam-3745	101	8	y	y	SYM
ejpam-3745	101	9	=	=	SYM
ejpam-3745	101	10	0	0	NUM
ejpam-3745	101	11	,	,	PUNCT
ejpam-3745	101	12	so	so	ADV
ejpam-3745	101	13	xn−k+a	xn−k+a	PUNCT
ejpam-3745	102	1	+	+	PUNCT
ejpam-3745	102	2	xn−t+b	xn−t+b	PUNCT
ejpam-3745	102	3	=	=	SYM
ejpam-3745	102	4	0	0	PROPN
ejpam-3745	102	5	.	.	PUNCT
ejpam-3745	103	1	this	this	DET
ejpam-3745	103	2	equality	equality	NOUN
ejpam-3745	103	3	holds	hold	VERB
ejpam-3745	103	4	if	if	SCONJ
ejpam-3745	103	5	n−	n−	PROPN
ejpam-3745	103	6	k	k	PROPN
ejpam-3745	103	7	+	+	CCONJ
ejpam-3745	103	8	a	a	DET
ejpam-3745	103	9	>	>	X
ejpam-3745	103	10	n	n	NOUN
ejpam-3745	103	11	or	or	CCONJ
ejpam-3745	103	12	a	a	DET
ejpam-3745	103	13	=	=	X
ejpam-3745	103	14	0sn	0sn	NOUN
ejpam-3745	103	15	and	and	CCONJ
ejpam-3745	103	16	n−	n−	PROPN
ejpam-3745	103	17	t	t	PROPN
ejpam-3745	103	18	+	+	CCONJ
ejpam-3745	103	19	b	b	X
ejpam-3745	103	20	>	>	X
ejpam-3745	103	21	n	n	PROPN
ejpam-3745	103	22	or	or	CCONJ
ejpam-3745	103	23	a	a	DET
ejpam-3745	103	24	=	=	X
ejpam-3745	103	25	0sn	0sn	NOUN
ejpam-3745	103	26	.	.	PUNCT
ejpam-3745	104	1	alternatively	alternatively	ADV
ejpam-3745	104	2	,	,	PUNCT
ejpam-3745	104	3	all	all	DET
ejpam-3745	104	4	elements	element	NOUN
ejpam-3745	104	5	of	of	ADP
ejpam-3745	104	6	s	s	PRON
ejpam-3745	104	7	can	can	AUX
ejpam-3745	104	8	be	be	AUX
ejpam-3745	104	9	thought	think	VERB
ejpam-3745	104	10	to	to	PART
ejpam-3745	104	11	form	form	VERB
ejpam-3745	104	12	a	a	DET
ejpam-3745	104	13	matrix	matrix	NOUN
ejpam-3745	104	14	[	[	X
ejpam-3745	104	15	c](n+1)×(n+1	c](n+1)×(n+1	NOUN
ejpam-3745	104	16	)	)	PUNCT
ejpam-3745	104	17	for	for	ADP
ejpam-3745	104	18	n	n	DET
ejpam-3745	104	19	∈	∈	PROPN
ejpam-3745	104	20	n	n	CCONJ
ejpam-3745	104	21	,	,	PUNCT
ejpam-3745	104	22	in	in	ADP
ejpam-3745	104	23	[	[	X
ejpam-3745	104	24	12	12	NUM
ejpam-3745	104	25	]	]	X
ejpam-3745	104	26	:	:	PUNCT
ejpam-3745	104	27	b.	b.	PROPN
ejpam-3745	104	28	aydın	aydın	PROPN
ejpam-3745	104	29	,	,	PUNCT
ejpam-3745	104	30	n.	n.	PROPN
ejpam-3745	104	31	akgüneş	akgüneş	PROPN
ejpam-3745	104	32	,	,	PUNCT
ejpam-3745	104	33	i.	i.	PROPN
ejpam-3745	104	34	n.	n.	PROPN
ejpam-3745	104	35	cangul	cangul	PROPN
ejpam-3745	104	36	/	/	SYM
ejpam-3745	104	37	eur	eur	NOUN
ejpam-3745	104	38	.	.	PUNCT
ejpam-3745	105	1	j.	j.	PROPN
ejpam-3745	105	2	pure	pure	PROPN
ejpam-3745	105	3	appl	appl	PROPN
ejpam-3745	105	4	.	.	PROPN
ejpam-3745	105	5	math	math	PROPN
ejpam-3745	105	6	,	,	PUNCT
ejpam-3745	105	7	13	13	NUM
ejpam-3745	105	8	(	(	PUNCT
ejpam-3745	105	9	5	5	NUM
ejpam-3745	105	10	)	)	PUNCT
ejpam-3745	105	11	(	(	PUNCT
ejpam-3745	105	12	2020	2020	NUM
ejpam-3745	105	13	)	)	PUNCT
ejpam-3745	105	14	,	,	PUNCT
ejpam-3745	105	15	1231	1231	NUM
ejpam-3745	105	16	-	-	SYM
ejpam-3745	105	17	1240	1240	NUM
ejpam-3745	105	18	1235	1235	NUM
ejpam-3745	105	19	[	[	X
ejpam-3745	105	20	c](n+1)×(n+1	c](n+1)×(n+1	NOUN
ejpam-3745	105	21	)	)	PUNCT
ejpam-3745	106	1	=	=	VERB
ejpam-3745	106	2			NOUN
ejpam-3745	106	3	.	.	PUNCT
ejpam-3745	106	4	.	.	PUNCT
ejpam-3745	106	5	.	.	PUNCT
ejpam-3745	107	1	c0(t+1	c0(t+1	X
ejpam-3745	107	2	)	)	PUNCT
ejpam-3745	107	3	c0(t+2	c0(t+2	PROPN
ejpam-3745	107	4	)	)	PUNCT
ejpam-3745	107	5	.	.	PUNCT
ejpam-3745	107	6	.	.	PUNCT
ejpam-3745	107	7	.	.	PUNCT
ejpam-3745	108	1	c0(n−1	c0(n−1	X
ejpam-3745	108	2	)	)	PUNCT
ejpam-3745	108	3	c0n	c0n	NOUN
ejpam-3745	108	4	...	...	PUNCT
ejpam-3745	108	5	.	.	PUNCT
ejpam-3745	108	6	.	.	PUNCT
ejpam-3745	108	7	.	.	PUNCT
ejpam-3745	109	1	...	...	PUNCT
ejpam-3745	109	2	...	...	PUNCT
ejpam-3745	109	3	.	.	PUNCT
ejpam-3745	109	4	.	.	PUNCT
ejpam-3745	110	1	.	.	PUNCT
ejpam-3745	111	1	...	...	PUNCT
ejpam-3745	112	1	...	...	PUNCT
ejpam-3745	113	1	c(k+1)0	c(k+1)0	NOUN
ejpam-3745	113	2	.	.	PUNCT
ejpam-3745	113	3	.	.	PUNCT
ejpam-3745	113	4	.	.	PUNCT
ejpam-3745	114	1	c(k+1)(t+1	c(k+1)(t+1	PROPN
ejpam-3745	114	2	)	)	PUNCT
ejpam-3745	114	3	c(k+1)(t+2	c(k+1)(t+2	PROPN
ejpam-3745	114	4	)	)	PUNCT
ejpam-3745	114	5	.	.	PUNCT
ejpam-3745	114	6	.	.	PUNCT
ejpam-3745	114	7	.	.	PUNCT
ejpam-3745	115	1	c(k+1)(n−1	c(k+1)(n−1	X
ejpam-3745	115	2	)	)	PUNCT
ejpam-3745	115	3	c(k+1)n	c(k+1)n	PROPN
ejpam-3745	115	4	c(k+2)0	c(k+2)0	PROPN
ejpam-3745	115	5	.	.	PUNCT
ejpam-3745	115	6	.	.	PUNCT
ejpam-3745	115	7	.	.	PUNCT
ejpam-3745	116	1	c(k+2)(t+1	c(k+2)(t+1	PROPN
ejpam-3745	116	2	)	)	PUNCT
ejpam-3745	116	3	c(k+2)(t+2	c(k+2)(t+2	PROPN
ejpam-3745	116	4	)	)	PUNCT
ejpam-3745	116	5	.	.	PUNCT
ejpam-3745	116	6	.	.	PUNCT
ejpam-3745	116	7	.	.	PUNCT
ejpam-3745	117	1	c(k+2)(n−1	c(k+2)(n−1	X
ejpam-3745	117	2	)	)	PUNCT
ejpam-3745	117	3	c(k+2)n	c(k+2)n	NOUN
ejpam-3745	117	4	...	...	PUNCT
ejpam-3745	117	5	.	.	PUNCT
ejpam-3745	117	6	.	.	PUNCT
ejpam-3745	117	7	.	.	PUNCT
ejpam-3745	118	1	...	...	PUNCT
ejpam-3745	118	2	...	...	PUNCT
ejpam-3745	118	3	.	.	PUNCT
ejpam-3745	118	4	.	.	PUNCT
ejpam-3745	119	1	.	.	PUNCT
ejpam-3745	120	1	...	...	PUNCT
ejpam-3745	120	2	...	...	PUNCT
ejpam-3745	121	1	c(n−1)0	c(n−1)0	NOUN
ejpam-3745	121	2	.	.	PUNCT
ejpam-3745	121	3	.	.	PUNCT
ejpam-3745	121	4	.	.	PUNCT
ejpam-3745	122	1	c(n−1)(t+1	c(n−1)(t+1	X
ejpam-3745	122	2	)	)	PUNCT
ejpam-3745	122	3	c(n−1)(t+2	c(n−1)(t+2	PROPN
ejpam-3745	122	4	)	)	PUNCT
ejpam-3745	122	5	.	.	PUNCT
ejpam-3745	122	6	.	.	PUNCT
ejpam-3745	122	7	.	.	PUNCT
ejpam-3745	123	1	c(n−1)(n−1	c(n−1)(n−1	PUNCT
ejpam-3745	123	2	)	)	PUNCT
ejpam-3745	124	1	c(n−1)n	c(n−1)n	PROPN
ejpam-3745	124	2	cn0	cn0	PROPN
ejpam-3745	124	3	.	.	PUNCT
ejpam-3745	124	4	.	.	PUNCT
ejpam-3745	124	5	.	.	PUNCT
ejpam-3745	125	1	cn(t+1	cn(t+1	X
ejpam-3745	125	2	)	)	PUNCT
ejpam-3745	126	1	cn(t+2	cn(t+2	NOUN
ejpam-3745	126	2	)	)	PUNCT
ejpam-3745	126	3	.	.	PUNCT
ejpam-3745	127	1	.	.	PUNCT
ejpam-3745	127	2	.	.	PUNCT
ejpam-3745	128	1	cn(n−1	cn(n−1	ADJ
ejpam-3745	128	2	)	)	PUNCT
ejpam-3745	128	3	cnn	cnn	NOUN
ejpam-3745	128	4			NUM
ejpam-3745	128	5	.	.	PUNCT
ejpam-3745	129	1	for	for	ADP
ejpam-3745	129	2	xa	xa	PROPN
ejpam-3745	129	3	,	,	PUNCT
ejpam-3745	129	4	the	the	DET
ejpam-3745	129	5	values	value	NOUN
ejpam-3745	129	6	of	of	ADP
ejpam-3745	129	7	a	a	PRON
ejpam-3745	129	8	may	may	AUX
ejpam-3745	129	9	be	be	AUX
ejpam-3745	129	10	placed	place	VERB
ejpam-3745	129	11	in	in	ADP
ejpam-3745	129	12	the	the	DET
ejpam-3745	129	13	zero	zero	NUM
ejpam-3745	129	14	-	-	PUNCT
ejpam-3745	129	15	row	row	NOUN
ejpam-3745	129	16	and	and	CCONJ
ejpam-3745	129	17	also	also	ADV
ejpam-3745	129	18	in	in	ADP
ejpam-3745	129	19	the	the	DET
ejpam-3745	129	20	rows	row	NOUN
ejpam-3745	129	21	(	(	PUNCT
ejpam-3745	129	22	k	k	NOUN
ejpam-3745	129	23	+	+	PROPN
ejpam-3745	129	24	1	1	NUM
ejpam-3745	129	25	)	)	PUNCT
ejpam-3745	129	26	to	to	PART
ejpam-3745	129	27	n.	n.	VERB
ejpam-3745	129	28	for	for	ADP
ejpam-3745	129	29	xb	xb	PROPN
ejpam-3745	129	30	,	,	PUNCT
ejpam-3745	129	31	the	the	DET
ejpam-3745	129	32	values	value	NOUN
ejpam-3745	129	33	of	of	ADP
ejpam-3745	129	34	b	b	NOUN
ejpam-3745	129	35	may	may	AUX
ejpam-3745	129	36	be	be	AUX
ejpam-3745	129	37	placed	place	VERB
ejpam-3745	129	38	in	in	ADP
ejpam-3745	129	39	the	the	DET
ejpam-3745	129	40	zero	zero	NUM
ejpam-3745	129	41	-	-	PUNCT
ejpam-3745	129	42	column	column	NOUN
ejpam-3745	129	43	and	and	CCONJ
ejpam-3745	129	44	also	also	ADV
ejpam-3745	129	45	in	in	ADP
ejpam-3745	129	46	the	the	DET
ejpam-3745	129	47	columns	column	NOUN
ejpam-3745	129	48	(	(	PUNCT
ejpam-3745	129	49	t+1	t+1	NOUN
ejpam-3745	129	50	)	)	PUNCT
ejpam-3745	129	51	to	to	PART
ejpam-3745	129	52	n.	n.	VERB
ejpam-3745	129	53	let	let	VERB
ejpam-3745	129	54	us	we	PRON
ejpam-3745	129	55	find	find	VERB
ejpam-3745	129	56	out	out	ADP
ejpam-3745	129	57	the	the	DET
ejpam-3745	129	58	number	number	NOUN
ejpam-3745	129	59	of	of	ADP
ejpam-3745	129	60	vertices	vertex	NOUN
ejpam-3745	129	61	at	at	ADP
ejpam-3745	129	62	their	their	PRON
ejpam-3745	129	63	intersection	intersection	NOUN
ejpam-3745	129	64	:	:	PUNCT
ejpam-3745	129	65	(	(	PUNCT
ejpam-3745	129	66	n−	n−	NOUN
ejpam-3745	129	67	(	(	PUNCT
ejpam-3745	129	68	k	k	PROPN
ejpam-3745	129	69	+	+	PROPN
ejpam-3745	129	70	1	1	X
ejpam-3745	129	71	)	)	PUNCT
ejpam-3745	129	72	+	+	CCONJ
ejpam-3745	129	73	1)+(n−	1)+(n−	NUM
ejpam-3745	129	74	(	(	PUNCT
ejpam-3745	129	75	t	t	NOUN
ejpam-3745	129	76	+	+	NOUN
ejpam-3745	129	77	1	1	NUM
ejpam-3745	129	78	)	)	PUNCT
ejpam-3745	129	79	+	+	NUM
ejpam-3745	130	1	1)+	1)+	NUM
ejpam-3745	130	2	(	(	PUNCT
ejpam-3745	130	3	n−	n−	NOUN
ejpam-3745	130	4	(	(	PUNCT
ejpam-3745	130	5	k	k	PROPN
ejpam-3745	130	6	+	+	PROPN
ejpam-3745	130	7	1	1	X
ejpam-3745	130	8	)	)	PUNCT
ejpam-3745	130	9	+	+	CCONJ
ejpam-3745	130	10	1	1	X
ejpam-3745	130	11	)	)	PUNCT
ejpam-3745	130	12	(	(	PUNCT
ejpam-3745	130	13	n−	n−	NOUN
ejpam-3745	130	14	(	(	PUNCT
ejpam-3745	130	15	t	t	NOUN
ejpam-3745	130	16	+	+	CCONJ
ejpam-3745	130	17	1	1	NUM
ejpam-3745	130	18	)	)	PUNCT
ejpam-3745	130	19	+	+	CCONJ
ejpam-3745	130	20	1	1	X
ejpam-3745	130	21	)	)	PUNCT
ejpam-3745	130	22	=	=	SYM
ejpam-3745	130	23	2n−k−t+(n−	2n−k−t+(n−	NUM
ejpam-3745	130	24	k	k	NOUN
ejpam-3745	130	25	)	)	PUNCT
ejpam-3745	130	26	(	(	PUNCT
ejpam-3745	130	27	n−	n−	NOUN
ejpam-3745	130	28	t	t	PROPN
ejpam-3745	130	29	)	)	PUNCT
ejpam-3745	130	30	=	=	PUNCT
ejpam-3745	130	31	2n−k−t+(n−	2n−k−t+(n−	NUM
ejpam-3745	130	32	k	k	NOUN
ejpam-3745	130	33	)	)	PUNCT
ejpam-3745	130	34	(	(	PUNCT
ejpam-3745	130	35	n−	n−	NOUN
ejpam-3745	130	36	t	t	PROPN
ejpam-3745	130	37	)	)	PUNCT
ejpam-3745	130	38	vertex	vertex	NOUN
ejpam-3745	130	39	pairs	pair	NOUN
ejpam-3745	130	40	have	have	AUX
ejpam-3745	130	41	distance	distance	NOUN
ejpam-3745	130	42	1	1	NUM
ejpam-3745	130	43	.	.	PUNCT
ejpam-3745	131	1	second	second	ADJ
ejpam-3745	131	2	case	case	NOUN
ejpam-3745	131	3	:	:	PUNCT
ejpam-3745	131	4	let	let	VERB
ejpam-3745	131	5	k	k	PROPN
ejpam-3745	131	6	=	=	PUNCT
ejpam-3745	131	7	n.	n.	PROPN
ejpam-3745	131	8	here	here	ADV
ejpam-3745	131	9	d((x0	d((x0	PROPN
ejpam-3745	131	10	,	,	PUNCT
ejpam-3745	131	11	xn−t	xn−t	PROPN
ejpam-3745	131	12	)	)	PUNCT
ejpam-3745	131	13	,	,	PUNCT
ejpam-3745	131	14	(	(	PUNCT
ejpam-3745	131	15	xa	xa	PROPN
ejpam-3745	131	16	,	,	PUNCT
ejpam-3745	131	17	xb	xb	PROPN
ejpam-3745	131	18	)	)	PUNCT
ejpam-3745	131	19	)	)	PUNCT
ejpam-3745	132	1	=	=	PUNCT
ejpam-3745	132	2	d((0	d((0	PROPN
ejpam-3745	132	3	,	,	PUNCT
ejpam-3745	132	4	xn−t	xn−t	ADJ
ejpam-3745	132	5	)	)	PUNCT
ejpam-3745	132	6	,	,	PUNCT
ejpam-3745	132	7	(	(	PUNCT
ejpam-3745	132	8	xa	xa	PROPN
ejpam-3745	132	9	,	,	PUNCT
ejpam-3745	132	10	xb	xb	PROPN
ejpam-3745	132	11	)	)	PUNCT
ejpam-3745	132	12	)	)	PUNCT
ejpam-3745	133	1	=	=	SYM
ejpam-3745	133	2	1	1	NUM
ejpam-3745	133	3	so	so	ADV
ejpam-3745	133	4	there	there	PRON
ejpam-3745	133	5	are	be	VERB
ejpam-3745	133	6	(	(	PUNCT
ejpam-3745	133	7	n−	n−	NOUN
ejpam-3745	133	8	t)(n	t)(n	X
ejpam-3745	133	9	+	+	CCONJ
ejpam-3745	133	10	1	1	X
ejpam-3745	133	11	)	)	PUNCT
ejpam-3745	133	12	+	+	NUM
ejpam-3745	133	13	n	n	PRON
ejpam-3745	133	14	vertices	vertex	NOUN
ejpam-3745	133	15	.	.	PUNCT
ejpam-3745	134	1	indeed	indeed	ADV
ejpam-3745	134	2	,	,	PUNCT
ejpam-3745	134	3	if	if	SCONJ
ejpam-3745	134	4	k	k	PROPN
ejpam-3745	134	5	=	=	PUNCT
ejpam-3745	134	6	n	n	PROPN
ejpam-3745	134	7	and	and	CCONJ
ejpam-3745	134	8	the	the	DET
ejpam-3745	134	9	vertices	vertex	NOUN
ejpam-3745	134	10	x	x	X
ejpam-3745	134	11	=	=	SYM
ejpam-3745	134	12	(	(	PUNCT
ejpam-3745	134	13	0	0	NUM
ejpam-3745	134	14	,	,	PUNCT
ejpam-3745	134	15	xn−t	xn−t	ADJ
ejpam-3745	134	16	)	)	PUNCT
ejpam-3745	134	17	and	and	CCONJ
ejpam-3745	134	18	y	y	PROPN
ejpam-3745	134	19	=	=	SYM
ejpam-3745	134	20	(	(	PUNCT
ejpam-3745	134	21	xa	xa	PROPN
ejpam-3745	134	22	,	,	PUNCT
ejpam-3745	134	23	xb	xb	PROPN
ejpam-3745	134	24	)	)	PUNCT
ejpam-3745	134	25	are	be	AUX
ejpam-3745	134	26	adjacent	adjacent	ADJ
ejpam-3745	134	27	,	,	PUNCT
ejpam-3745	134	28	then	then	ADV
ejpam-3745	134	29	0	0	PUNCT
ejpam-3745	135	1	+	+	ADJ
ejpam-3745	135	2	xn−t+b	xn−t+b	SYM
ejpam-3745	135	3	=	=	SYM
ejpam-3745	135	4	0	0	PROPN
ejpam-3745	135	5	.	.	PUNCT
ejpam-3745	136	1	so	so	ADV
ejpam-3745	136	2	n−	n−	PROPN
ejpam-3745	136	3	t+	t+	PUNCT
ejpam-3745	136	4	b	b	X
ejpam-3745	136	5	>	>	X
ejpam-3745	136	6	n	n	PROPN
ejpam-3745	136	7	or	or	CCONJ
ejpam-3745	136	8	b	b	PROPN
ejpam-3745	136	9	=	=	PROPN
ejpam-3745	136	10	0sn	0sn	NOUN
ejpam-3745	136	11	.	.	PUNCT
ejpam-3745	137	1	hence	hence	ADV
ejpam-3745	137	2	similarly	similarly	ADV
ejpam-3745	137	3	to	to	ADP
ejpam-3745	137	4	the	the	DET
ejpam-3745	137	5	previous	previous	ADJ
ejpam-3745	137	6	case	case	NOUN
ejpam-3745	137	7	,	,	PUNCT
ejpam-3745	137	8	we	we	PRON
ejpam-3745	137	9	have	have	VERB
ejpam-3745	137	10	[	[	X
ejpam-3745	137	11	c](n+1)×(n+1	c](n+1)×(n+1	PRON
ejpam-3745	137	12	)	)	PUNCT
ejpam-3745	137	13	=	=	VERB
ejpam-3745	137	14			NOUN
ejpam-3745	137	15	.	.	PUNCT
ejpam-3745	137	16	.	.	PUNCT
ejpam-3745	137	17	.	.	PUNCT
ejpam-3745	138	1	c0(t+1	c0(t+1	X
ejpam-3745	138	2	)	)	PUNCT
ejpam-3745	138	3	c0(t+2	c0(t+2	PROPN
ejpam-3745	138	4	)	)	PUNCT
ejpam-3745	138	5	.	.	PUNCT
ejpam-3745	138	6	.	.	PUNCT
ejpam-3745	138	7	.	.	PUNCT
ejpam-3745	139	1	c0(n−1	c0(n−1	X
ejpam-3745	139	2	)	)	PUNCT
ejpam-3745	139	3	c0n	c0n	NOUN
ejpam-3745	139	4	...	...	PUNCT
ejpam-3745	139	5	.	.	PUNCT
ejpam-3745	139	6	.	.	PUNCT
ejpam-3745	139	7	.	.	PUNCT
ejpam-3745	140	1	...	...	PUNCT
ejpam-3745	140	2	...	...	PUNCT
ejpam-3745	140	3	.	.	PUNCT
ejpam-3745	140	4	.	.	PUNCT
ejpam-3745	141	1	.	.	PUNCT
ejpam-3745	142	1	...	...	PUNCT
ejpam-3745	143	1	...	...	PUNCT
ejpam-3745	144	1	c(k+1)0	c(k+1)0	NOUN
ejpam-3745	144	2	.	.	PUNCT
ejpam-3745	144	3	.	.	PUNCT
ejpam-3745	144	4	.	.	PUNCT
ejpam-3745	145	1	c(k+1)(t+1	c(k+1)(t+1	PROPN
ejpam-3745	145	2	)	)	PUNCT
ejpam-3745	145	3	c(k+1)(t+2	c(k+1)(t+2	PROPN
ejpam-3745	145	4	)	)	PUNCT
ejpam-3745	145	5	.	.	PUNCT
ejpam-3745	145	6	.	.	PUNCT
ejpam-3745	145	7	.	.	PUNCT
ejpam-3745	146	1	c(k+1)(n−1	c(k+1)(n−1	X
ejpam-3745	146	2	)	)	PUNCT
ejpam-3745	146	3	c(k+1)n	c(k+1)n	PROPN
ejpam-3745	146	4	c(k+2)0	c(k+2)0	PROPN
ejpam-3745	146	5	.	.	PUNCT
ejpam-3745	146	6	.	.	PUNCT
ejpam-3745	146	7	.	.	PUNCT
ejpam-3745	147	1	c(k+2)(t+1	c(k+2)(t+1	PROPN
ejpam-3745	147	2	)	)	PUNCT
ejpam-3745	147	3	c(k+2)(t+2	c(k+2)(t+2	PROPN
ejpam-3745	147	4	)	)	PUNCT
ejpam-3745	147	5	.	.	PUNCT
ejpam-3745	147	6	.	.	PUNCT
ejpam-3745	147	7	.	.	PUNCT
ejpam-3745	148	1	c(k+2)(n−1	c(k+2)(n−1	X
ejpam-3745	148	2	)	)	PUNCT
ejpam-3745	148	3	c(k+2)n	c(k+2)n	NOUN
ejpam-3745	148	4	...	...	PUNCT
ejpam-3745	148	5	.	.	PUNCT
ejpam-3745	148	6	.	.	PUNCT
ejpam-3745	148	7	.	.	PUNCT
ejpam-3745	149	1	...	...	PUNCT
ejpam-3745	149	2	...	...	PUNCT
ejpam-3745	149	3	.	.	PUNCT
ejpam-3745	149	4	.	.	PUNCT
ejpam-3745	150	1	.	.	PUNCT
ejpam-3745	151	1	...	...	PUNCT
ejpam-3745	151	2	...	...	PUNCT
ejpam-3745	152	1	c(n−1)0	c(n−1)0	NOUN
ejpam-3745	152	2	.	.	PUNCT
ejpam-3745	152	3	.	.	PUNCT
ejpam-3745	152	4	.	.	PUNCT
ejpam-3745	153	1	c(n−1)(t+1	c(n−1)(t+1	X
ejpam-3745	153	2	)	)	PUNCT
ejpam-3745	153	3	c(n−1)(t+2	c(n−1)(t+2	PROPN
ejpam-3745	153	4	)	)	PUNCT
ejpam-3745	153	5	.	.	PUNCT
ejpam-3745	153	6	.	.	PUNCT
ejpam-3745	153	7	.	.	PUNCT
ejpam-3745	154	1	c(n−1)(n−1	c(n−1)(n−1	PUNCT
ejpam-3745	154	2	)	)	PUNCT
ejpam-3745	155	1	c(n−1)n	c(n−1)n	PROPN
ejpam-3745	155	2	cn0	cn0	PROPN
ejpam-3745	155	3	.	.	PUNCT
ejpam-3745	155	4	.	.	PUNCT
ejpam-3745	155	5	.	.	PUNCT
ejpam-3745	156	1	cn(t+1	cn(t+1	X
ejpam-3745	156	2	)	)	PUNCT
ejpam-3745	157	1	cn(t+2	cn(t+2	NOUN
ejpam-3745	157	2	)	)	PUNCT
ejpam-3745	157	3	.	.	PUNCT
ejpam-3745	158	1	.	.	PUNCT
ejpam-3745	158	2	.	.	PUNCT
ejpam-3745	159	1	cn(n−1	cn(n−1	ADJ
ejpam-3745	159	2	)	)	PUNCT
ejpam-3745	159	3	cnn	cnn	NOUN
ejpam-3745	159	4			NUM
ejpam-3745	159	5	.	.	PUNCT
ejpam-3745	160	1	for	for	ADP
ejpam-3745	160	2	xb	xb	PROPN
ejpam-3745	160	3	,	,	PUNCT
ejpam-3745	160	4	the	the	DET
ejpam-3745	160	5	values	value	NOUN
ejpam-3745	160	6	of	of	ADP
ejpam-3745	160	7	b	b	NOUN
ejpam-3745	160	8	may	may	AUX
ejpam-3745	160	9	be	be	AUX
ejpam-3745	160	10	placed	place	VERB
ejpam-3745	160	11	in	in	ADP
ejpam-3745	160	12	the	the	DET
ejpam-3745	160	13	zero	zero	NUM
ejpam-3745	160	14	-	-	PUNCT
ejpam-3745	160	15	column	column	NOUN
ejpam-3745	160	16	and	and	CCONJ
ejpam-3745	160	17	also	also	ADV
ejpam-3745	160	18	in	in	ADP
ejpam-3745	160	19	the	the	DET
ejpam-3745	160	20	columns	column	NOUN
ejpam-3745	160	21	(	(	PUNCT
ejpam-3745	160	22	t+1	t+1	NOUN
ejpam-3745	160	23	)	)	PUNCT
ejpam-3745	160	24	to	to	PART
ejpam-3745	160	25	n.	n.	VERB
ejpam-3745	160	26	so	so	ADV
ejpam-3745	160	27	(	(	PUNCT
ejpam-3745	160	28	n−	n−	PROPN
ejpam-3745	160	29	(	(	PUNCT
ejpam-3745	160	30	t	t	NOUN
ejpam-3745	160	31	+	+	CCONJ
ejpam-3745	160	32	1	1	NUM
ejpam-3745	160	33	)	)	PUNCT
ejpam-3745	161	1	+	+	CCONJ
ejpam-3745	161	2	1	1	X
ejpam-3745	161	3	)	)	PUNCT
ejpam-3745	161	4	(	(	PUNCT
ejpam-3745	161	5	n	n	X
ejpam-3745	161	6	+	+	CCONJ
ejpam-3745	161	7	1	1	NUM
ejpam-3745	161	8	)	)	PUNCT
ejpam-3745	161	9	+	+	NUM
ejpam-3745	162	1	n	n	NOUN
ejpam-3745	162	2	=	=	SYM
ejpam-3745	162	3	(	(	PUNCT
ejpam-3745	162	4	n−	n−	NOUN
ejpam-3745	162	5	t	t	PROPN
ejpam-3745	162	6	)	)	PUNCT
ejpam-3745	162	7	(	(	PUNCT
ejpam-3745	162	8	n	n	X
ejpam-3745	162	9	+	+	CCONJ
ejpam-3745	162	10	1	1	NUM
ejpam-3745	162	11	)	)	PUNCT
ejpam-3745	162	12	+	+	NUM
ejpam-3745	162	13	n	n	NOUN
ejpam-3745	162	14	=	=	SYM
ejpam-3745	162	15	(	(	PUNCT
ejpam-3745	162	16	n−	n−	NOUN
ejpam-3745	162	17	t	t	PROPN
ejpam-3745	162	18	)	)	PUNCT
ejpam-3745	162	19	(	(	PUNCT
ejpam-3745	162	20	n	n	X
ejpam-3745	162	21	+	+	CCONJ
ejpam-3745	162	22	1	1	NUM
ejpam-3745	162	23	)	)	PUNCT
ejpam-3745	162	24	+	+	CCONJ
ejpam-3745	162	25	n	n	PRON
ejpam-3745	162	26	vertex	vertex	NOUN
ejpam-3745	162	27	pairs	pair	NOUN
ejpam-3745	162	28	have	have	VERB
ejpam-3745	162	29	distance	distance	NOUN
ejpam-3745	162	30	1	1	NUM
ejpam-3745	162	31	.	.	PUNCT
ejpam-3745	162	32	third	third	ADJ
ejpam-3745	162	33	case	case	NOUN
ejpam-3745	162	34	:	:	PUNCT
ejpam-3745	162	35	let	let	VERB
ejpam-3745	162	36	t	t	NOUN
ejpam-3745	162	37	=	=	PUNCT
ejpam-3745	162	38	n.	n.	NOUN
ejpam-3745	162	39	now	now	ADV
ejpam-3745	162	40	d((xn−k	d((xn−k	VERB
ejpam-3745	162	41	,	,	PUNCT
ejpam-3745	162	42	x0	x0	PROPN
ejpam-3745	162	43	)	)	PUNCT
ejpam-3745	162	44	,	,	PUNCT
ejpam-3745	162	45	(	(	PUNCT
ejpam-3745	162	46	xa	xa	PROPN
ejpam-3745	162	47	,	,	PUNCT
ejpam-3745	162	48	xb	xb	PROPN
ejpam-3745	162	49	)	)	PUNCT
ejpam-3745	162	50	)	)	PUNCT
ejpam-3745	163	1	=	=	SYM
ejpam-3745	163	2	d((xn−k	d((xn−k	NOUN
ejpam-3745	163	3	,	,	PUNCT
ejpam-3745	163	4	0	0	NUM
ejpam-3745	163	5	)	)	PUNCT
ejpam-3745	163	6	,	,	PUNCT
ejpam-3745	163	7	(	(	PUNCT
ejpam-3745	163	8	xa	xa	PROPN
ejpam-3745	163	9	,	,	PUNCT
ejpam-3745	163	10	xb	xb	PROPN
ejpam-3745	163	11	)	)	PUNCT
ejpam-3745	163	12	)	)	PUNCT
ejpam-3745	164	1	=	=	SYM
ejpam-3745	164	2	1	1	NUM
ejpam-3745	164	3	,	,	PUNCT
ejpam-3745	164	4	so	so	SCONJ
ejpam-3745	164	5	there	there	PRON
ejpam-3745	164	6	are	be	VERB
ejpam-3745	164	7	(	(	PUNCT
ejpam-3745	164	8	n−	n−	NOUN
ejpam-3745	164	9	k)(n	k)(n	VERB
ejpam-3745	165	1	+	+	CCONJ
ejpam-3745	166	1	1	1	X
ejpam-3745	166	2	)	)	PUNCT
ejpam-3745	166	3	+	+	NUM
ejpam-3745	166	4	n	n	PRON
ejpam-3745	166	5	vertices	vertex	NOUN
ejpam-3745	166	6	.	.	PUNCT
ejpam-3745	167	1	in	in	ADP
ejpam-3745	167	2	this	this	DET
ejpam-3745	167	3	case	case	NOUN
ejpam-3745	167	4	,	,	PUNCT
ejpam-3745	167	5	if	if	SCONJ
ejpam-3745	167	6	t	t	NOUN
ejpam-3745	167	7	=	=	SYM
ejpam-3745	167	8	n	n	PROPN
ejpam-3745	167	9	and	and	CCONJ
ejpam-3745	167	10	x	x	SYM
ejpam-3745	167	11	=	=	SYM
ejpam-3745	167	12	(	(	PUNCT
ejpam-3745	167	13	xn−k	xn−k	PROPN
ejpam-3745	167	14	,	,	PUNCT
ejpam-3745	167	15	0	0	NUM
ejpam-3745	167	16	)	)	PUNCT
ejpam-3745	167	17	and	and	CCONJ
ejpam-3745	167	18	y	y	PROPN
ejpam-3745	167	19	=	=	SYM
ejpam-3745	167	20	(	(	PUNCT
ejpam-3745	167	21	xa	xa	PROPN
ejpam-3745	167	22	,	,	PUNCT
ejpam-3745	167	23	xb	xb	PROPN
ejpam-3745	167	24	)	)	PUNCT
ejpam-3745	167	25	vertices	vertex	NOUN
ejpam-3745	167	26	are	be	AUX
ejpam-3745	167	27	adjacent	adjacent	ADJ
ejpam-3745	167	28	then	then	ADV
ejpam-3745	167	29	xn−k+b	xn−k+b	PUNCT
ejpam-3745	168	1	+	+	CCONJ
ejpam-3745	168	2	0	0	NUM
ejpam-3745	168	3	=	=	SYM
ejpam-3745	168	4	0	0	X
ejpam-3745	168	5	.	.	PUNCT
ejpam-3745	169	1	so	so	ADV
ejpam-3745	169	2	n−	n−	PROPN
ejpam-3745	169	3	k	k	PROPN
ejpam-3745	170	1	+	+	CCONJ
ejpam-3745	170	2	b	b	X
ejpam-3745	170	3	>	>	X
ejpam-3745	170	4	n	n	PROPN
ejpam-3745	170	5	or	or	CCONJ
ejpam-3745	170	6	a	a	DET
ejpam-3745	170	7	=	=	X
ejpam-3745	170	8	0sn	0sn	NOUN
ejpam-3745	170	9	.	.	PUNCT
ejpam-3745	171	1	similarly	similarly	ADV
ejpam-3745	171	2	to	to	ADP
ejpam-3745	171	3	the	the	DET
ejpam-3745	171	4	first	first	ADJ
ejpam-3745	171	5	case	case	NOUN
ejpam-3745	171	6	,	,	PUNCT
ejpam-3745	171	7	we	we	PRON
ejpam-3745	171	8	obtain	obtain	VERB
ejpam-3745	171	9	b.	b.	PROPN
ejpam-3745	171	10	aydın	aydın	PROPN
ejpam-3745	171	11	,	,	PUNCT
ejpam-3745	171	12	n.	n.	PROPN
ejpam-3745	171	13	akgüneş	akgüneş	PROPN
ejpam-3745	171	14	,	,	PUNCT
ejpam-3745	171	15	i.	i.	PROPN
ejpam-3745	171	16	n.	n.	PROPN
ejpam-3745	171	17	cangul	cangul	PROPN
ejpam-3745	171	18	/	/	SYM
ejpam-3745	171	19	eur	eur	NOUN
ejpam-3745	171	20	.	.	PUNCT
ejpam-3745	172	1	j.	j.	PROPN
ejpam-3745	172	2	pure	pure	PROPN
ejpam-3745	172	3	appl	appl	PROPN
ejpam-3745	172	4	.	.	PROPN
ejpam-3745	172	5	math	math	PROPN
ejpam-3745	172	6	,	,	PUNCT
ejpam-3745	172	7	13	13	NUM
ejpam-3745	172	8	(	(	PUNCT
ejpam-3745	172	9	5	5	NUM
ejpam-3745	172	10	)	)	PUNCT
ejpam-3745	172	11	(	(	PUNCT
ejpam-3745	172	12	2020	2020	NUM
ejpam-3745	172	13	)	)	PUNCT
ejpam-3745	172	14	,	,	PUNCT
ejpam-3745	172	15	1231	1231	NUM
ejpam-3745	172	16	-	-	SYM
ejpam-3745	172	17	1240	1240	NUM
ejpam-3745	172	18	1236	1236	NUM
ejpam-3745	172	19	[	[	X
ejpam-3745	172	20	c](n+1)×(n+1	c](n+1)×(n+1	NOUN
ejpam-3745	172	21	)	)	PUNCT
ejpam-3745	173	1	=	=	VERB
ejpam-3745	173	2			NOUN
ejpam-3745	173	3	.	.	PUNCT
ejpam-3745	173	4	.	.	PUNCT
ejpam-3745	173	5	.	.	PUNCT
ejpam-3745	174	1	c0(t+1	c0(t+1	X
ejpam-3745	174	2	)	)	PUNCT
ejpam-3745	174	3	c0(t+2	c0(t+2	PROPN
ejpam-3745	174	4	)	)	PUNCT
ejpam-3745	174	5	.	.	PUNCT
ejpam-3745	174	6	.	.	PUNCT
ejpam-3745	174	7	.	.	PUNCT
ejpam-3745	175	1	c0(n−1	c0(n−1	X
ejpam-3745	175	2	)	)	PUNCT
ejpam-3745	175	3	c0n	c0n	NOUN
ejpam-3745	175	4	...	...	PUNCT
ejpam-3745	175	5	.	.	PUNCT
ejpam-3745	175	6	.	.	PUNCT
ejpam-3745	175	7	.	.	PUNCT
ejpam-3745	176	1	...	...	PUNCT
ejpam-3745	176	2	...	...	PUNCT
ejpam-3745	176	3	.	.	PUNCT
ejpam-3745	176	4	.	.	PUNCT
ejpam-3745	177	1	.	.	PUNCT
ejpam-3745	178	1	...	...	PUNCT
ejpam-3745	179	1	...	...	PUNCT
ejpam-3745	180	1	c(k+1)0	c(k+1)0	NOUN
ejpam-3745	180	2	.	.	PUNCT
ejpam-3745	180	3	.	.	PUNCT
ejpam-3745	180	4	.	.	PUNCT
ejpam-3745	181	1	c(k+1)(t+1	c(k+1)(t+1	PROPN
ejpam-3745	181	2	)	)	PUNCT
ejpam-3745	181	3	c(k+1)(t+2	c(k+1)(t+2	PROPN
ejpam-3745	181	4	)	)	PUNCT
ejpam-3745	181	5	.	.	PUNCT
ejpam-3745	181	6	.	.	PUNCT
ejpam-3745	181	7	.	.	PUNCT
ejpam-3745	182	1	c(k+1)(n−1	c(k+1)(n−1	X
ejpam-3745	182	2	)	)	PUNCT
ejpam-3745	182	3	c(k+1)n	c(k+1)n	PROPN
ejpam-3745	182	4	c(k+2)0	c(k+2)0	PROPN
ejpam-3745	182	5	.	.	PUNCT
ejpam-3745	182	6	.	.	PUNCT
ejpam-3745	182	7	.	.	PUNCT
ejpam-3745	183	1	c(k+2)(t+1	c(k+2)(t+1	PROPN
ejpam-3745	183	2	)	)	PUNCT
ejpam-3745	183	3	c(k+2)(t+2	c(k+2)(t+2	PROPN
ejpam-3745	183	4	)	)	PUNCT
ejpam-3745	183	5	.	.	PUNCT
ejpam-3745	183	6	.	.	PUNCT
ejpam-3745	183	7	.	.	PUNCT
ejpam-3745	184	1	c(k+2)(n−1	c(k+2)(n−1	X
ejpam-3745	184	2	)	)	PUNCT
ejpam-3745	184	3	c(k+2)n	c(k+2)n	NOUN
ejpam-3745	184	4	...	...	PUNCT
ejpam-3745	184	5	.	.	PUNCT
ejpam-3745	184	6	.	.	PUNCT
ejpam-3745	184	7	.	.	PUNCT
ejpam-3745	185	1	...	...	PUNCT
ejpam-3745	185	2	...	...	PUNCT
ejpam-3745	185	3	.	.	PUNCT
ejpam-3745	185	4	.	.	PUNCT
ejpam-3745	186	1	.	.	PUNCT
ejpam-3745	187	1	...	...	PUNCT
ejpam-3745	187	2	...	...	PUNCT
ejpam-3745	188	1	c(n−1)0	c(n−1)0	NOUN
ejpam-3745	188	2	.	.	PUNCT
ejpam-3745	188	3	.	.	PUNCT
ejpam-3745	188	4	.	.	PUNCT
ejpam-3745	189	1	c(n−1)(t+1	c(n−1)(t+1	X
ejpam-3745	189	2	)	)	PUNCT
ejpam-3745	189	3	c(n−1)(t+2	c(n−1)(t+2	PROPN
ejpam-3745	189	4	)	)	PUNCT
ejpam-3745	189	5	.	.	PUNCT
ejpam-3745	189	6	.	.	PUNCT
ejpam-3745	189	7	.	.	PUNCT
ejpam-3745	190	1	c(n−1)(n−1	c(n−1)(n−1	PUNCT
ejpam-3745	190	2	)	)	PUNCT
ejpam-3745	191	1	c(n−1)n	c(n−1)n	PROPN
ejpam-3745	191	2	cn0	cn0	PROPN
ejpam-3745	191	3	.	.	PUNCT
ejpam-3745	191	4	.	.	PUNCT
ejpam-3745	191	5	.	.	PUNCT
ejpam-3745	192	1	cn(t+1	cn(t+1	X
ejpam-3745	192	2	)	)	PUNCT
ejpam-3745	193	1	cn(t+2	cn(t+2	NOUN
ejpam-3745	193	2	)	)	PUNCT
ejpam-3745	193	3	.	.	PUNCT
ejpam-3745	194	1	.	.	PUNCT
ejpam-3745	194	2	.	.	PUNCT
ejpam-3745	195	1	cn(n−1	cn(n−1	ADJ
ejpam-3745	195	2	)	)	PUNCT
ejpam-3745	195	3	cnn	cnn	NOUN
ejpam-3745	195	4			NUM
ejpam-3745	195	5	.	.	PUNCT
ejpam-3745	196	1	for	for	ADP
ejpam-3745	196	2	xa	xa	PROPN
ejpam-3745	196	3	,	,	PUNCT
ejpam-3745	196	4	the	the	DET
ejpam-3745	196	5	values	value	NOUN
ejpam-3745	196	6	of	of	ADP
ejpam-3745	196	7	a	a	PRON
ejpam-3745	196	8	are	be	AUX
ejpam-3745	196	9	placed	place	VERB
ejpam-3745	196	10	in	in	ADP
ejpam-3745	196	11	zero	zero	NUM
ejpam-3745	196	12	-	-	PUNCT
ejpam-3745	196	13	row	row	NOUN
ejpam-3745	196	14	and	and	CCONJ
ejpam-3745	196	15	also	also	ADV
ejpam-3745	196	16	in	in	ADP
ejpam-3745	196	17	the	the	DET
ejpam-3745	196	18	rows	row	NOUN
ejpam-3745	196	19	(	(	PUNCT
ejpam-3745	196	20	k	k	NOUN
ejpam-3745	196	21	+	+	PROPN
ejpam-3745	196	22	1	1	NUM
ejpam-3745	196	23	)	)	PUNCT
ejpam-3745	196	24	to	to	PART
ejpam-3745	196	25	n.	n.	VERB
ejpam-3745	196	26	so	so	ADV
ejpam-3745	196	27	(	(	PUNCT
ejpam-3745	196	28	n−	n−	PROPN
ejpam-3745	196	29	(	(	PUNCT
ejpam-3745	196	30	k	k	PROPN
ejpam-3745	197	1	+	+	PROPN
ejpam-3745	197	2	1	1	X
ejpam-3745	197	3	)	)	PUNCT
ejpam-3745	197	4	+	+	CCONJ
ejpam-3745	197	5	1	1	X
ejpam-3745	197	6	)	)	PUNCT
ejpam-3745	197	7	(	(	PUNCT
ejpam-3745	197	8	n	n	X
ejpam-3745	197	9	+	+	CCONJ
ejpam-3745	197	10	1	1	NUM
ejpam-3745	197	11	)	)	PUNCT
ejpam-3745	197	12	+	+	NUM
ejpam-3745	197	13	n	n	NOUN
ejpam-3745	197	14	=	=	SYM
ejpam-3745	197	15	(	(	PUNCT
ejpam-3745	197	16	n−	n−	NOUN
ejpam-3745	197	17	k	k	NOUN
ejpam-3745	197	18	−	−	PROPN
ejpam-3745	197	19	1	1	NUM
ejpam-3745	197	20	+	+	NUM
ejpam-3745	197	21	1	1	NUM
ejpam-3745	197	22	)	)	PUNCT
ejpam-3745	197	23	(	(	PUNCT
ejpam-3745	197	24	n	n	X
ejpam-3745	197	25	+	+	CCONJ
ejpam-3745	197	26	1	1	NUM
ejpam-3745	197	27	)	)	PUNCT
ejpam-3745	197	28	+	+	NUM
ejpam-3745	197	29	n	n	NOUN
ejpam-3745	197	30	=	=	SYM
ejpam-3745	197	31	(	(	PUNCT
ejpam-3745	197	32	n−	n−	NOUN
ejpam-3745	197	33	k	k	NOUN
ejpam-3745	197	34	)	)	PUNCT
ejpam-3745	197	35	(	(	PUNCT
ejpam-3745	197	36	n	n	X
ejpam-3745	197	37	+	+	CCONJ
ejpam-3745	197	38	1	1	NUM
ejpam-3745	197	39	)	)	PUNCT
ejpam-3745	197	40	+	+	CCONJ
ejpam-3745	197	41	n	n	PRON
ejpam-3745	197	42	vertex	vertex	NOUN
ejpam-3745	197	43	pairs	pair	NOUN
ejpam-3745	197	44	have	have	VERB
ejpam-3745	197	45	distance	distance	NOUN
ejpam-3745	197	46	1	1	NUM
ejpam-3745	197	47	.	.	PUNCT
ejpam-3745	198	1	let	let	VERB
ejpam-3745	198	2	us	we	PRON
ejpam-3745	198	3	be	be	AUX
ejpam-3745	198	4	careful	careful	ADJ
ejpam-3745	198	5	about	about	ADP
ejpam-3745	198	6	the	the	DET
ejpam-3745	198	7	fact	fact	NOUN
ejpam-3745	198	8	that	that	SCONJ
ejpam-3745	198	9	we	we	PRON
ejpam-3745	198	10	have	have	AUX
ejpam-3745	198	11	not	not	PART
ejpam-3745	198	12	yet	yet	ADV
ejpam-3745	198	13	excluded	exclude	VERB
ejpam-3745	198	14	the	the	DET
ejpam-3745	198	15	vertices	vertex	NOUN
ejpam-3745	198	16	which	which	PRON
ejpam-3745	198	17	are	be	AUX
ejpam-3745	198	18	adjacent	adjacent	ADJ
ejpam-3745	198	19	to	to	ADP
ejpam-3745	198	20	themselves	themselves	PRON
ejpam-3745	198	21	and	and	CCONJ
ejpam-3745	198	22	the	the	DET
ejpam-3745	198	23	distances	distance	NOUN
ejpam-3745	198	24	between	between	ADP
ejpam-3745	198	25	such	such	ADJ
ejpam-3745	198	26	pairs	pair	NOUN
ejpam-3745	198	27	of	of	ADP
ejpam-3745	198	28	vertices	vertex	NOUN
ejpam-3745	198	29	do	do	AUX
ejpam-3745	198	30	not	not	PART
ejpam-3745	198	31	contribute	contribute	VERB
ejpam-3745	198	32	to	to	ADP
ejpam-3745	198	33	wiener	wiener	NOUN
ejpam-3745	198	34	index	index	NOUN
ejpam-3745	198	35	.	.	PUNCT
ejpam-3745	199	1	so	so	ADV
ejpam-3745	199	2	these	these	DET
ejpam-3745	199	3	values	value	NOUN
ejpam-3745	199	4	should	should	AUX
ejpam-3745	199	5	be	be	AUX
ejpam-3745	199	6	taken	take	VERB
ejpam-3745	199	7	away	away	ADV
ejpam-3745	199	8	from	from	ADP
ejpam-3745	199	9	the	the	DET
ejpam-3745	199	10	sum	sum	NOUN
ejpam-3745	199	11	we	we	PRON
ejpam-3745	199	12	have	have	AUX
ejpam-3745	199	13	just	just	ADV
ejpam-3745	199	14	found	find	VERB
ejpam-3745	199	15	.	.	PUNCT
ejpam-3745	200	1	now	now	ADV
ejpam-3745	200	2	,	,	PUNCT
ejpam-3745	200	3	let	let	VERB
ejpam-3745	200	4	us	we	PRON
ejpam-3745	200	5	find	find	VERB
ejpam-3745	200	6	how	how	SCONJ
ejpam-3745	200	7	many	many	ADJ
ejpam-3745	200	8	vertices	vertex	NOUN
ejpam-3745	200	9	are	be	AUX
ejpam-3745	200	10	adjacent	adjacent	ADJ
ejpam-3745	200	11	to	to	ADP
ejpam-3745	200	12	itself	itself	PRON
ejpam-3745	200	13	:	:	PUNCT
ejpam-3745	200	14	there	there	PRON
ejpam-3745	200	15	are	be	VERB
ejpam-3745	200	16	(	(	PUNCT
ejpam-3745	200	17	n−	n−	NOUN
ejpam-3745	200	18	⌊	⌊	VERB
ejpam-3745	200	19	n	n	ADV
ejpam-3745	200	20	2	2	NUM
ejpam-3745	200	21	⌋)2	⌋)2	NUM
ejpam-3745	201	1	+	+	CCONJ
ejpam-3745	201	2	2	2	NUM
ejpam-3745	201	3	(	(	PUNCT
ejpam-3745	201	4	n−	n−	NOUN
ejpam-3745	201	5	⌊	⌊	VERB
ejpam-3745	201	6	n	n	DET
ejpam-3745	201	7	2	2	NUM
ejpam-3745	201	8	⌋	⌋	NOUN
ejpam-3745	201	9	)	)	PUNCT
ejpam-3745	201	10	vertices	vertice	VERB
ejpam-3745	201	11	with	with	ADP
ejpam-3745	201	12	distance	distance	NOUN
ejpam-3745	201	13	1	1	NUM
ejpam-3745	201	14	to	to	ADP
ejpam-3745	201	15	itself	itself	PRON
ejpam-3745	201	16	.	.	PUNCT
ejpam-3745	202	1	hence	hence	ADV
ejpam-3745	202	2	there	there	PRON
ejpam-3745	202	3	are	be	VERB
ejpam-3745	202	4	|v	|v	ADJ
ejpam-3745	202	5	|−	|−	ADJ
ejpam-3745	202	6	[	[	X
ejpam-3745	202	7	(	(	PUNCT
ejpam-3745	202	8	n−	n−	NOUN
ejpam-3745	202	9	⌊	⌊	VERB
ejpam-3745	202	10	n	n	ADV
ejpam-3745	202	11	2	2	NUM
ejpam-3745	202	12	⌋)2	⌋)2	NUM
ejpam-3745	203	1	+	+	CCONJ
ejpam-3745	203	2	2	2	NUM
ejpam-3745	203	3	(	(	PUNCT
ejpam-3745	203	4	n−	n−	NOUN
ejpam-3745	203	5	⌊	⌊	VERB
ejpam-3745	203	6	n	n	DET
ejpam-3745	203	7	2	2	NUM
ejpam-3745	203	8	⌋	⌋	NOUN
ejpam-3745	203	9	)	)	PUNCT
ejpam-3745	203	10	]	]	PUNCT
ejpam-3745	203	11	vertices	vertice	VERB
ejpam-3745	203	12	having	have	VERB
ejpam-3745	203	13	distance	distance	NOUN
ejpam-3745	203	14	2	2	NUM
ejpam-3745	203	15	to	to	ADP
ejpam-3745	203	16	itself	itself	PRON
ejpam-3745	203	17	.	.	PUNCT
ejpam-3745	204	1	when	when	SCONJ
ejpam-3745	204	2	k	k	X
ejpam-3745	204	3	,	,	PUNCT
ejpam-3745	204	4	t	t	PROPN
ejpam-3745	204	5	∈	∈	PROPN
ejpam-3745	204	6	{	{	PUNCT
ejpam-3745	204	7	0	0	NUM
ejpam-3745	204	8	,	,	PUNCT
ejpam-3745	204	9	1	1	NUM
ejpam-3745	204	10	,	,	PUNCT
ejpam-3745	204	11	2	2	NUM
ejpam-3745	204	12	,	,	PUNCT
ejpam-3745	204	13	·	·	PUNCT
ejpam-3745	204	14	·	·	PUNCT
ejpam-3745	204	15	·	·	PUNCT
ejpam-3745	204	16	,	,	PUNCT
ejpam-3745	204	17	⌈	⌈	PROPN
ejpam-3745	204	18	n	n	CCONJ
ejpam-3745	204	19	2	2	NUM
ejpam-3745	204	20	⌉	⌉	NOUN
ejpam-3745	204	21	−	−	PROPN
ejpam-3745	204	22	1	1	NUM
ejpam-3745	204	23	,	,	PUNCT
ejpam-3745	204	24	⌈	⌈	NOUN
ejpam-3745	204	25	n	n	PRON
ejpam-3745	204	26	2	2	NUM
ejpam-3745	204	27	⌉	⌉	NOUN
ejpam-3745	204	28	,	,	PUNCT
ejpam-3745	204	29	⌈	⌈	NOUN
ejpam-3745	204	30	n	n	PRON
ejpam-3745	204	31	2	2	NUM
ejpam-3745	204	32	⌉	⌉	NOUN
ejpam-3745	204	33	+	+	CCONJ
ejpam-3745	204	34	1	1	NUM
ejpam-3745	204	35	,	,	PUNCT
ejpam-3745	204	36	·	·	PUNCT
ejpam-3745	204	37	·	·	PUNCT
ejpam-3745	204	38	·	·	PUNCT
ejpam-3745	204	39	,	,	PUNCT
ejpam-3745	204	40	n−	n−	NOUN
ejpam-3745	204	41	1	1	NUM
ejpam-3745	204	42	}	}	PUNCT
ejpam-3745	204	43	,	,	PUNCT
ejpam-3745	204	44	if	if	SCONJ
ejpam-3745	204	45	any	any	DET
ejpam-3745	204	46	vertex	vertex	NOUN
ejpam-3745	204	47	x	x	X
ejpam-3745	204	48	=	=	SYM
ejpam-3745	204	49	(	(	PUNCT
ejpam-3745	204	50	xn−k	xn−k	PROPN
ejpam-3745	204	51	,	,	PUNCT
ejpam-3745	204	52	xn−t	xn−t	PROPN
ejpam-3745	204	53	)	)	PUNCT
ejpam-3745	204	54	is	be	AUX
ejpam-3745	204	55	adjacent	adjacent	ADJ
ejpam-3745	204	56	to	to	ADP
ejpam-3745	204	57	itself	itself	PRON
ejpam-3745	204	58	,	,	PUNCT
ejpam-3745	204	59	then	then	ADV
ejpam-3745	204	60	x	x	X
ejpam-3745	204	61	·	·	PUNCT
ejpam-3745	204	62	x	x	PUNCT
ejpam-3745	205	1	=	=	SYM
ejpam-3745	205	2	0	0	NUM
ejpam-3745	206	1	so	so	SCONJ
ejpam-3745	206	2	that	that	SCONJ
ejpam-3745	206	3	x2(n−k	x2(n−k	PROPN
ejpam-3745	206	4	)	)	PUNCT
ejpam-3745	207	1	+	+	CCONJ
ejpam-3745	207	2	x2(n−t	x2(n−t	PROPN
ejpam-3745	207	3	)	)	PUNCT
ejpam-3745	208	1	=	=	PUNCT
ejpam-3745	208	2	0	0	X
ejpam-3745	208	3	.	.	PUNCT
ejpam-3745	209	1	this	this	DET
ejpam-3745	209	2	equality	equality	NOUN
ejpam-3745	209	3	holds	hold	VERB
ejpam-3745	209	4	when	when	SCONJ
ejpam-3745	209	5	2(n	2(n	NUM
ejpam-3745	209	6	−	−	PROPN
ejpam-3745	209	7	k	k	NOUN
ejpam-3745	209	8	)	)	PUNCT
ejpam-3745	209	9	>	>	PUNCT
ejpam-3745	210	1	n	n	PROPN
ejpam-3745	210	2	or	or	CCONJ
ejpam-3745	210	3	k	k	NOUN
ejpam-3745	210	4	=	=	PUNCT
ejpam-3745	210	5	n	n	PROPN
ejpam-3745	210	6	and	and	CCONJ
ejpam-3745	210	7	2(n	2(n	NUM
ejpam-3745	210	8	−	−	NOUN
ejpam-3745	210	9	t)n	t)n	NOUN
ejpam-3745	210	10	or	or	CCONJ
ejpam-3745	210	11	t	t	X
ejpam-3745	210	12	=	=	PUNCT
ejpam-3745	210	13	n.	n.	NOUN
ejpam-3745	210	14	it	it	PRON
ejpam-3745	210	15	means	mean	VERB
ejpam-3745	210	16	that	that	SCONJ
ejpam-3745	210	17	2n	2n	NUM
ejpam-3745	210	18	−	−	DET
ejpam-3745	210	19	2k	2k	NOUN
ejpam-3745	210	20	>	>	PUNCT
ejpam-3745	210	21	n	n	PROPN
ejpam-3745	210	22	or	or	CCONJ
ejpam-3745	210	23	k	k	NOUN
ejpam-3745	210	24	=	=	PUNCT
ejpam-3745	210	25	n	n	PROPN
ejpam-3745	210	26	and	and	CCONJ
ejpam-3745	210	27	2n	2n	NUM
ejpam-3745	210	28	−	−	ADP
ejpam-3745	210	29	2	2	NUM
ejpam-3745	210	30	t	t	NOUN
ejpam-3745	210	31	>	>	PUNCT
ejpam-3745	210	32	n	n	PROPN
ejpam-3745	210	33	or	or	CCONJ
ejpam-3745	210	34	t	t	NOUN
ejpam-3745	210	35	=	=	SYM
ejpam-3745	210	36	n	n	PROPN
ejpam-3745	210	37	and	and	CCONJ
ejpam-3745	210	38	equivalently	equivalently	ADV
ejpam-3745	210	39	n	n	CCONJ
ejpam-3745	210	40	>	>	X
ejpam-3745	210	41	2k	2k	PROPN
ejpam-3745	210	42	or	or	CCONJ
ejpam-3745	210	43	k	k	NOUN
ejpam-3745	210	44	=	=	PUNCT
ejpam-3745	210	45	n	n	PROPN
ejpam-3745	210	46	and	and	CCONJ
ejpam-3745	210	47	n	n	CCONJ
ejpam-3745	210	48	>	>	ADP
ejpam-3745	210	49	2	2	NUM
ejpam-3745	210	50	t	t	NOUN
ejpam-3745	210	51	or	or	CCONJ
ejpam-3745	210	52	t	t	NOUN
ejpam-3745	210	53	=	=	PUNCT
ejpam-3745	210	54	n.	n.	NOUN
ejpam-3745	210	55	this	this	PRON
ejpam-3745	210	56	is	be	AUX
ejpam-3745	210	57	equivalent	equivalent	ADJ
ejpam-3745	210	58	to	to	ADP
ejpam-3745	210	59	k	k	PROPN
ejpam-3745	210	60	<	<	X
ejpam-3745	210	61	n	n	PROPN
ejpam-3745	210	62	2	2	NUM
ejpam-3745	210	63	or	or	CCONJ
ejpam-3745	210	64	k	k	NOUN
ejpam-3745	210	65	=	=	PUNCT
ejpam-3745	210	66	n	n	PROPN
ejpam-3745	210	67	and	and	CCONJ
ejpam-3745	210	68	t	t	X
ejpam-3745	210	69	<	<	X
ejpam-3745	210	70	n	n	PROPN
ejpam-3745	210	71	2	2	NUM
ejpam-3745	210	72	or	or	CCONJ
ejpam-3745	210	73	t	t	NOUN
ejpam-3745	210	74	=	=	SYM
ejpam-3745	210	75	n.	n.	PROPN
ejpam-3745	210	76	therefore	therefore	ADV
ejpam-3745	210	77	,	,	PUNCT
ejpam-3745	210	78	we	we	PRON
ejpam-3745	210	79	get	get	VERB
ejpam-3745	210	80	d((xn−k	d((xn−k	NOUN
ejpam-3745	210	81	,	,	PUNCT
ejpam-3745	210	82	xn−t	xn−t	ADJ
ejpam-3745	210	83	)	)	PUNCT
ejpam-3745	210	84	,	,	PUNCT
ejpam-3745	210	85	(	(	PUNCT
ejpam-3745	210	86	xn−k	xn−k	PROPN
ejpam-3745	210	87	,	,	PUNCT
ejpam-3745	210	88	xn−t	xn−t	ADJ
ejpam-3745	210	89	)	)	PUNCT
ejpam-3745	210	90	)	)	PUNCT
ejpam-3745	211	1	=	=	SYM
ejpam-3745	211	2	1⇔	1⇔	NUM
ejpam-3745	211	3	k	k	PROPN
ejpam-3745	211	4	∈	∈	PROPN
ejpam-3745	211	5	{	{	PUNCT
ejpam-3745	211	6	0	0	NUM
ejpam-3745	211	7	,	,	PUNCT
ejpam-3745	211	8	1	1	NUM
ejpam-3745	211	9	,	,	PUNCT
ejpam-3745	211	10	2	2	NUM
ejpam-3745	211	11	,	,	PUNCT
ejpam-3745	211	12	·	·	PUNCT
ejpam-3745	211	13	·	·	PUNCT
ejpam-3745	211	14	·	·	PUNCT
ejpam-3745	211	15	,	,	PUNCT
ejpam-3745	211	16	⌈n	⌈n	NOUN
ejpam-3745	211	17	2	2	NUM
ejpam-3745	211	18	⌉	⌉	ADP
ejpam-3745	211	19	−	−	PROPN
ejpam-3745	211	20	1	1	NUM
ejpam-3745	211	21	,	,	PUNCT
ejpam-3745	211	22	n	n	CCONJ
ejpam-3745	211	23	}	}	PUNCT
ejpam-3745	211	24	and	and	CCONJ
ejpam-3745	211	25	t	t	PROPN
ejpam-3745	211	26	∈	∈	PROPN
ejpam-3745	211	27	{	{	PUNCT
ejpam-3745	211	28	0	0	NUM
ejpam-3745	211	29	,	,	PUNCT
ejpam-3745	211	30	1	1	NUM
ejpam-3745	211	31	,	,	PUNCT
ejpam-3745	211	32	2	2	NUM
ejpam-3745	211	33	,	,	PUNCT
ejpam-3745	211	34	·	·	PUNCT
ejpam-3745	211	35	·	·	PUNCT
ejpam-3745	211	36	·	·	PUNCT
ejpam-3745	211	37	,	,	PUNCT
ejpam-3745	211	38	⌈n	⌈n	NOUN
ejpam-3745	211	39	2	2	NUM
ejpam-3745	211	40	⌉	⌉	ADP
ejpam-3745	211	41	−	−	PROPN
ejpam-3745	211	42	1	1	NUM
ejpam-3745	211	43	,	,	PUNCT
ejpam-3745	211	44	n	n	CCONJ
ejpam-3745	211	45	}	}	PUNCT
ejpam-3745	211	46	.	.	PUNCT
ejpam-3745	212	1	so	so	ADV
ejpam-3745	212	2	(	(	PUNCT
ejpam-3745	212	3	n−	n−	NOUN
ejpam-3745	212	4	k	k	X
ejpam-3745	212	5	)	)	PUNCT
ejpam-3745	212	6	∈	∈	PROPN
ejpam-3745	212	7	{	{	PUNCT
ejpam-3745	212	8	n	n	CCONJ
ejpam-3745	212	9	,	,	PUNCT
ejpam-3745	212	10	n−	n−	NOUN
ejpam-3745	212	11	1	1	NUM
ejpam-3745	212	12	,	,	PUNCT
ejpam-3745	212	13	·	·	PUNCT
ejpam-3745	212	14	·	·	PUNCT
ejpam-3745	212	15	·	·	PUNCT
ejpam-3745	212	16	,	,	PUNCT
ejpam-3745	212	17	⌊	⌊	VERB
ejpam-3745	212	18	n	n	ADV
ejpam-3745	212	19	2	2	NUM
ejpam-3745	212	20	⌋	⌋	NOUN
ejpam-3745	212	21	+	+	CCONJ
ejpam-3745	212	22	1	1	NUM
ejpam-3745	212	23	,	,	PUNCT
ejpam-3745	212	24	0	0	NUM
ejpam-3745	212	25	}	}	PUNCT
ejpam-3745	212	26	and	and	CCONJ
ejpam-3745	212	27	(	(	PUNCT
ejpam-3745	212	28	n−	n−	NOUN
ejpam-3745	212	29	t	t	PROPN
ejpam-3745	212	30	)	)	PUNCT
ejpam-3745	212	31	∈	∈	PROPN
ejpam-3745	212	32	{	{	PUNCT
ejpam-3745	212	33	n	n	CCONJ
ejpam-3745	212	34	,	,	PUNCT
ejpam-3745	212	35	n−	n−	NOUN
ejpam-3745	212	36	1	1	NUM
ejpam-3745	212	37	,	,	PUNCT
ejpam-3745	212	38	·	·	PUNCT
ejpam-3745	212	39	·	·	PUNCT
ejpam-3745	212	40	·	·	PUNCT
ejpam-3745	212	41	,	,	PUNCT
ejpam-3745	212	42	⌊	⌊	VERB
ejpam-3745	212	43	n	n	ADV
ejpam-3745	212	44	2	2	NUM
ejpam-3745	212	45	⌋	⌋	NOUN
ejpam-3745	212	46	+	+	CCONJ
ejpam-3745	212	47	1	1	NUM
ejpam-3745	212	48	,	,	PUNCT
ejpam-3745	212	49	0	0	NUM
ejpam-3745	212	50	}	}	PUNCT
ejpam-3745	212	51	since	since	SCONJ
ejpam-3745	212	52	n−	n−	PROPN
ejpam-3745	212	53	⌈	⌈	NOUN
ejpam-3745	212	54	n	n	PRON
ejpam-3745	212	55	2	2	NUM
ejpam-3745	212	56	⌉	⌉	NOUN
ejpam-3745	212	57	=	=	SYM
ejpam-3745	212	58	⌊	⌊	VERB
ejpam-3745	212	59	n	n	PRON
ejpam-3745	212	60	2	2	NUM
ejpam-3745	212	61	⌋	⌋	NOUN
ejpam-3745	212	62	.	.	PUNCT
ejpam-3745	213	1	in	in	ADP
ejpam-3745	213	2	this	this	DET
ejpam-3745	213	3	case	case	NOUN
ejpam-3745	213	4	,	,	PUNCT
ejpam-3745	213	5	we	we	PRON
ejpam-3745	213	6	obtain	obtain	VERB
ejpam-3745	213	7	the	the	DET
ejpam-3745	213	8	following	follow	VERB
ejpam-3745	213	9	vertices	vertex	NOUN
ejpam-3745	213	10	[	[	X
ejpam-3745	213	11	c](n+1)×(n+1	c](n+1)×(n+1	NOUN
ejpam-3745	213	12	)	)	PUNCT
ejpam-3745	213	13	=	=	SYM
ejpam-3745	213	14			PROPN
ejpam-3745	213	15	.	.	PUNCT
ejpam-3745	213	16	.	.	PUNCT
ejpam-3745	213	17	.	.	PUNCT
ejpam-3745	214	1	c0(bn2	c0(bn2	PRON
ejpam-3745	214	2	c+1	c+1	NOUN
ejpam-3745	214	3	)	)	PUNCT
ejpam-3745	214	4	c0(bn2	c0(bn2	NOUN
ejpam-3745	214	5	c+2	c+2	NOUN
ejpam-3745	214	6	)	)	PUNCT
ejpam-3745	214	7	.	.	PUNCT
ejpam-3745	214	8	.	.	PUNCT
ejpam-3745	214	9	.	.	PUNCT
ejpam-3745	215	1	c0(n−1	c0(n−1	X
ejpam-3745	215	2	)	)	PUNCT
ejpam-3745	215	3	c0n	c0n	NOUN
ejpam-3745	215	4	...	...	PUNCT
ejpam-3745	215	5	.	.	PUNCT
ejpam-3745	215	6	.	.	PUNCT
ejpam-3745	215	7	.	.	PUNCT
ejpam-3745	216	1	...	...	PUNCT
ejpam-3745	216	2	...	...	PUNCT
ejpam-3745	216	3	.	.	PUNCT
ejpam-3745	216	4	.	.	PUNCT
ejpam-3745	217	1	.	.	PUNCT
ejpam-3745	217	2	...	...	PUNCT
ejpam-3745	218	1	...	...	PUNCT
ejpam-3745	219	1	c(bn2	c(bn2	VERB
ejpam-3745	219	2	c+1)0	c+1)0	NOUN
ejpam-3745	219	3	.	.	PUNCT
ejpam-3745	219	4	.	.	PUNCT
ejpam-3745	219	5	.	.	PUNCT
ejpam-3745	220	1	c(bn2	c(bn2	NOUN
ejpam-3745	220	2	c+1)(bn2	c+1)(bn2	NOUN
ejpam-3745	220	3	c+1	c+1	NOUN
ejpam-3745	220	4	)	)	PUNCT
ejpam-3745	220	5	c(bn2	c(bn2	NOUN
ejpam-3745	220	6	c+1)(bn2	c+1)(bn2	NOUN
ejpam-3745	220	7	c+2	c+2	NOUN
ejpam-3745	220	8	)	)	PUNCT
ejpam-3745	220	9	·	·	PUNCT
ejpam-3745	220	10	·	·	PUNCT
ejpam-3745	220	11	·	·	PUNCT
ejpam-3745	220	12	c(bn2	c(bn2	NOUN
ejpam-3745	220	13	c+1)(n−1	c+1)(n−1	PROPN
ejpam-3745	220	14	)	)	PUNCT
ejpam-3745	220	15	c(bn2	c(bn2	PROPN
ejpam-3745	220	16	c+1)n	c+1)n	PROPN
ejpam-3745	220	17	c(bn2	c(bn2	PROPN
ejpam-3745	220	18	c+2)0	c+2)0	PROPN
ejpam-3745	220	19	.	.	PUNCT
ejpam-3745	220	20	.	.	PUNCT
ejpam-3745	220	21	.	.	PUNCT
ejpam-3745	221	1	c(bn2	c(bn2	NOUN
ejpam-3745	221	2	c+2)(bn2	c+2)(bn2	ADP
ejpam-3745	221	3	c+1	c+1	NUM
ejpam-3745	221	4	)	)	PUNCT
ejpam-3745	221	5	c(bn2	c(bn2	NOUN
ejpam-3745	221	6	c+2)(bn2	c+2)(bn2	ADP
ejpam-3745	221	7	c+2	c+2	NUM
ejpam-3745	221	8	)	)	PUNCT
ejpam-3745	221	9	·	·	PUNCT
ejpam-3745	221	10	·	·	PUNCT
ejpam-3745	221	11	·	·	PUNCT
ejpam-3745	222	1	c(bn2	c(bn2	VERB
ejpam-3745	222	2	c+2)(n−1	c+2)(n−1	PROPN
ejpam-3745	222	3	)	)	PUNCT
ejpam-3745	222	4	c(bn2	c(bn2	NOUN
ejpam-3745	222	5	c+2)n	c+2)n	PROPN
ejpam-3745	222	6	...	...	PUNCT
ejpam-3745	222	7	·	·	PUNCT
ejpam-3745	222	8	·	·	PUNCT
ejpam-3745	222	9	·	·	PUNCT
ejpam-3745	222	10	...	...	PUNCT
ejpam-3745	222	11	...	...	PUNCT
ejpam-3745	223	1	·	·	PUNCT
ejpam-3745	223	2	·	·	PUNCT
ejpam-3745	223	3	·	·	PUNCT
ejpam-3745	223	4	...	...	PUNCT
ejpam-3745	223	5	...	...	PUNCT
ejpam-3745	223	6	c(n−1)0	c(n−1)0	NOUN
ejpam-3745	223	7	·	·	PUNCT
ejpam-3745	223	8	·	·	PUNCT
ejpam-3745	223	9	·	·	PUNCT
ejpam-3745	224	1	c(n−1)(bn2	c(n−1)(bn2	PROPN
ejpam-3745	224	2	c+1	c+1	NOUN
ejpam-3745	224	3	)	)	PUNCT
ejpam-3745	224	4	c(n−1)(bn2	c(n−1)(bn2	PROPN
ejpam-3745	224	5	c+2	c+2	PROPN
ejpam-3745	224	6	)	)	PUNCT
ejpam-3745	224	7	·	·	PUNCT
ejpam-3745	224	8	·	·	PUNCT
ejpam-3745	224	9	·	·	PUNCT
ejpam-3745	224	10	c(n−1)(n−1	c(n−1)(n−1	X
ejpam-3745	224	11	)	)	PUNCT
ejpam-3745	224	12	c(n−1)n	c(n−1)n	PROPN
ejpam-3745	224	13	cn0	cn0	X
ejpam-3745	224	14	·	·	PUNCT
ejpam-3745	224	15	·	·	PUNCT
ejpam-3745	224	16	·	·	PUNCT
ejpam-3745	224	17	cn(bn2	cn(bn2	ADP
ejpam-3745	225	1	c+1	c+1	NOUN
ejpam-3745	225	2	)	)	PUNCT
ejpam-3745	225	3	cn(bn2	cn(bn2	NOUN
ejpam-3745	226	1	c+2	c+2	NOUN
ejpam-3745	226	2	)	)	PUNCT
ejpam-3745	226	3	·	·	PUNCT
ejpam-3745	226	4	·	·	PUNCT
ejpam-3745	226	5	·	·	PUNCT
ejpam-3745	226	6	cn(n−1	cn(n−1	X
ejpam-3745	226	7	)	)	PUNCT
ejpam-3745	226	8	cnn	cnn	PROPN
ejpam-3745	226	9			NUM
ejpam-3745	226	10	.	.	PUNCT
ejpam-3745	227	1	b.	b.	PROPN
ejpam-3745	227	2	aydın	aydın	PROPN
ejpam-3745	227	3	,	,	PUNCT
ejpam-3745	227	4	n.	n.	PROPN
ejpam-3745	227	5	akgüneş	akgüneş	PROPN
ejpam-3745	227	6	,	,	PUNCT
ejpam-3745	227	7	i.	i.	PROPN
ejpam-3745	227	8	n.	n.	PROPN
ejpam-3745	227	9	cangul	cangul	PROPN
ejpam-3745	227	10	/	/	SYM
ejpam-3745	227	11	eur	eur	NOUN
ejpam-3745	227	12	.	.	PUNCT
ejpam-3745	228	1	j.	j.	PROPN
ejpam-3745	228	2	pure	pure	PROPN
ejpam-3745	228	3	appl	appl	PROPN
ejpam-3745	228	4	.	.	PROPN
ejpam-3745	228	5	math	math	PROPN
ejpam-3745	228	6	,	,	PUNCT
ejpam-3745	228	7	13	13	NUM
ejpam-3745	228	8	(	(	PUNCT
ejpam-3745	228	9	5	5	NUM
ejpam-3745	228	10	)	)	PUNCT
ejpam-3745	228	11	(	(	PUNCT
ejpam-3745	228	12	2020	2020	NUM
ejpam-3745	228	13	)	)	PUNCT
ejpam-3745	228	14	,	,	PUNCT
ejpam-3745	228	15	1231	1231	NUM
ejpam-3745	228	16	-	-	SYM
ejpam-3745	228	17	1240	1240	NUM
ejpam-3745	228	18	1237	1237	NUM
ejpam-3745	228	19	thus	thus	ADV
ejpam-3745	228	20	there	there	PRON
ejpam-3745	228	21	are	be	VERB
ejpam-3745	228	22	(	(	PUNCT
ejpam-3745	228	23	n	n	CCONJ
ejpam-3745	228	24	−	−	ADP
ejpam-3745	228	25	⌊	⌊	VERB
ejpam-3745	228	26	n	n	ADV
ejpam-3745	228	27	2	2	NUM
ejpam-3745	228	28	⌋	⌋	NOUN
ejpam-3745	228	29	)	)	PUNCT
ejpam-3745	228	30	2	2	NUM
ejpam-3745	229	1	+	+	NUM
ejpam-3745	229	2	2(n	2(n	NUM
ejpam-3745	229	3	−	−	ADP
ejpam-3745	229	4	⌊	⌊	PROPN
ejpam-3745	229	5	n	n	ADV
ejpam-3745	229	6	2	2	NUM
ejpam-3745	229	7	⌋	⌋	NOUN
ejpam-3745	229	8	)	)	PUNCT
ejpam-3745	229	9	vertices	vertice	VERB
ejpam-3745	229	10	with	with	ADP
ejpam-3745	229	11	a	a	DET
ejpam-3745	229	12	distance	distance	NOUN
ejpam-3745	229	13	of	of	ADP
ejpam-3745	229	14	1	1	NUM
ejpam-3745	229	15	to	to	ADP
ejpam-3745	229	16	itself	itself	PRON
ejpam-3745	229	17	.	.	PUNCT
ejpam-3745	230	1	hence	hence	ADV
ejpam-3745	230	2	there	there	PRON
ejpam-3745	230	3	are	be	VERB
ejpam-3745	230	4	|v	|v	ADJ
ejpam-3745	231	1	|	|	ADV
ejpam-3745	231	2	−	−	PROPN
ejpam-3745	232	1	[	[	X
ejpam-3745	232	2	(	(	PUNCT
ejpam-3745	232	3	n−	n−	NOUN
ejpam-3745	232	4	⌊	⌊	VERB
ejpam-3745	232	5	n	n	ADV
ejpam-3745	232	6	2	2	NUM
ejpam-3745	232	7	⌋	⌋	NOUN
ejpam-3745	232	8	)	)	PUNCT
ejpam-3745	232	9	2	2	NUM
ejpam-3745	233	1	+	+	SYM
ejpam-3745	233	2	2(n−	2(n−	NUM
ejpam-3745	233	3	⌊	⌊	PROPN
ejpam-3745	233	4	n	n	PRON
ejpam-3745	233	5	2	2	NUM
ejpam-3745	233	6	⌋	⌋	NOUN
ejpam-3745	233	7	)	)	PUNCT
ejpam-3745	233	8	]	]	PUNCT
ejpam-3745	233	9	vertices	vertice	VERB
ejpam-3745	233	10	with	with	ADP
ejpam-3745	233	11	a	a	DET
ejpam-3745	233	12	distance	distance	NOUN
ejpam-3745	233	13	of	of	ADP
ejpam-3745	233	14	2	2	NUM
ejpam-3745	233	15	to	to	ADP
ejpam-3745	233	16	itself	itself	PRON
ejpam-3745	233	17	.	.	PUNCT
ejpam-3745	234	1	considering	consider	VERB
ejpam-3745	234	2	the	the	DET
ejpam-3745	234	3	above	above	ADJ
ejpam-3745	234	4	claims	claim	NOUN
ejpam-3745	234	5	,	,	PUNCT
ejpam-3745	234	6	we	we	PRON
ejpam-3745	234	7	obtain	obtain	VERB
ejpam-3745	234	8	the	the	DET
ejpam-3745	234	9	following	following	ADJ
ejpam-3745	234	10	result	result	NOUN
ejpam-3745	234	11	:	:	PUNCT
ejpam-3745	234	12	since	since	SCONJ
ejpam-3745	234	13	v1	v1	PROPN
ejpam-3745	234	14	=	=	SYM
ejpam-3745	234	15	{	{	PUNCT
ejpam-3745	234	16	vi	vi	NOUN
ejpam-3745	234	17	:	:	PUNCT
ejpam-3745	234	18	vi	vi	NOUN
ejpam-3745	234	19	=	=	SYM
ejpam-3745	234	20	(	(	PUNCT
ejpam-3745	234	21	xa	xa	PROPN
ejpam-3745	234	22	,	,	PUNCT
ejpam-3745	234	23	xb	xb	PROPN
ejpam-3745	234	24	)	)	PUNCT
ejpam-3745	234	25	,	,	PUNCT
ejpam-3745	234	26	(	(	PUNCT
ejpam-3745	234	27	xa	xa	PROPN
ejpam-3745	234	28	,	,	PUNCT
ejpam-3745	234	29	xb	xb	PROPN
ejpam-3745	234	30	)	)	PUNCT
ejpam-3745	234	31	∼	∼	NOUN
ejpam-3745	234	32	(	(	PUNCT
ejpam-3745	234	33	xn−k	xn−k	PROPN
ejpam-3745	234	34	,	,	PUNCT
ejpam-3745	234	35	xn−t	xn−t	PROPN
ejpam-3745	234	36	)	)	PUNCT
ejpam-3745	234	37	,	,	PUNCT
ejpam-3745	234	38	k	k	PROPN
ejpam-3745	234	39	,	,	PUNCT
ejpam-3745	234	40	t	t	PROPN
ejpam-3745	234	41	∈	∈	PROPN
ejpam-3745	234	42	{	{	PUNCT
ejpam-3745	234	43	0	0	NUM
ejpam-3745	234	44	,	,	PUNCT
ejpam-3745	234	45	1	1	NUM
ejpam-3745	234	46	,	,	PUNCT
ejpam-3745	234	47	2	2	NUM
ejpam-3745	234	48	,	,	PUNCT
ejpam-3745	234	49	.	.	PUNCT
ejpam-3745	234	50	.	.	PUNCT
ejpam-3745	235	1	.	.	PUNCT
ejpam-3745	235	2	,	,	PUNCT
ejpam-3745	236	1	n	n	CCONJ
ejpam-3745	236	2	}	}	PUNCT
ejpam-3745	236	3	}	}	PUNCT
ejpam-3745	236	4	,	,	PUNCT
ejpam-3745	236	5	we	we	PRON
ejpam-3745	236	6	find	find	VERB
ejpam-3745	236	7	|v1|	|v1|	NOUN
ejpam-3745	236	8	=	=	SYM
ejpam-3745	236	9	∑	∑	PUNCT
ejpam-3745	236	10	k	k	PROPN
ejpam-3745	236	11	,	,	PUNCT
ejpam-3745	236	12	t∈{0,1,	t∈{0,1,	PRON
ejpam-3745	236	13	...	...	PUNCT
ejpam-3745	236	14	,n−1	,n−1	PUNCT
ejpam-3745	236	15	}	}	PUNCT
ejpam-3745	237	1	[	[	X
ejpam-3745	237	2	2n−	2n−	NUM
ejpam-3745	237	3	k	k	NOUN
ejpam-3745	237	4	−	−	PROPN
ejpam-3745	237	5	t	t	PROPN
ejpam-3745	237	6	+	+	CCONJ
ejpam-3745	237	7	(	(	PUNCT
ejpam-3745	237	8	n−	n−	NOUN
ejpam-3745	237	9	k)(n−	k)(n−	PROPN
ejpam-3745	237	10	t	t	PROPN
ejpam-3745	237	11	)	)	PUNCT
ejpam-3745	237	12	]	]	PUNCT
ejpam-3745	238	1	+	+	CCONJ
ejpam-3745	238	2	∑	∑	PUNCT
ejpam-3745	238	3	k∈{0,1,	k∈{0,1,	PROPN
ejpam-3745	238	4	...	...	PUNCT
ejpam-3745	238	5	,n−1	,n−1	PUNCT
ejpam-3745	238	6	}	}	PUNCT
ejpam-3745	238	7	t	t	PROPN
ejpam-3745	238	8	=	=	SYM
ejpam-3745	238	9	n	n	X
ejpam-3745	238	10	[	[	X
ejpam-3745	238	11	(	(	PUNCT
ejpam-3745	238	12	n−	n−	NOUN
ejpam-3745	238	13	k)(n	k)(n	VERB
ejpam-3745	238	14	+	+	CCONJ
ejpam-3745	238	15	1	1	X
ejpam-3745	238	16	)	)	PUNCT
ejpam-3745	238	17	+	+	NUM
ejpam-3745	238	18	n	n	CCONJ
ejpam-3745	238	19	]	]	PUNCT
ejpam-3745	239	1	+	+	CCONJ
ejpam-3745	239	2	∑	∑	PROPN
ejpam-3745	239	3	t∈{0,1,	t∈{0,1,	NOUN
ejpam-3745	239	4	...	...	PUNCT
ejpam-3745	239	5	,n−1	,n−1	PUNCT
ejpam-3745	239	6	}	}	PUNCT
ejpam-3745	239	7	k	k	X
ejpam-3745	239	8	=	=	NOUN
ejpam-3745	239	9	n	n	X
ejpam-3745	239	10	[	[	X
ejpam-3745	239	11	(	(	PUNCT
ejpam-3745	239	12	n−	n−	NOUN
ejpam-3745	239	13	t)(n	t)(n	X
ejpam-3745	239	14	+	+	CCONJ
ejpam-3745	239	15	1	1	X
ejpam-3745	239	16	)	)	PUNCT
ejpam-3745	239	17	+	+	NUM
ejpam-3745	239	18	n	n	CCONJ
ejpam-3745	239	19	]	]	PUNCT
ejpam-3745	239	20	.	.	PUNCT
ejpam-3745	240	1	consequently	consequently	ADV
ejpam-3745	240	2	,	,	PUNCT
ejpam-3745	240	3	we	we	PRON
ejpam-3745	240	4	conclude	conclude	VERB
ejpam-3745	240	5	that	that	SCONJ
ejpam-3745	240	6	w	w	PROPN
ejpam-3745	240	7	(	(	PUNCT
ejpam-3745	240	8	γ(s	γ(s	PROPN
ejpam-3745	240	9	)	)	PUNCT
ejpam-3745	240	10	)	)	PUNCT
ejpam-3745	241	1	=	=	SYM
ejpam-3745	242	1	1	1	NUM
ejpam-3745	242	2	2	2	NUM
ejpam-3745	242	3	∑	∑	PROPN
ejpam-3745	242	4	i	i	PROPN
ejpam-3745	242	5	,	,	PUNCT
ejpam-3745	242	6	j∈n	j∈n	PROPN
ejpam-3745	242	7	dγ(s)(vi	dγ(s)(vi	NOUN
ejpam-3745	242	8	,	,	PUNCT
ejpam-3745	242	9	vj	vj	ADJ
ejpam-3745	242	10	)	)	PUNCT
ejpam-3745	242	11	=	=	SYM
ejpam-3745	242	12	1	1	NUM
ejpam-3745	242	13	2	2	NUM
ejpam-3745	242	14			NUM
ejpam-3745	242	15	∑	∑	PUNCT
ejpam-3745	242	16	vi∈v	vi∈v	X
ejpam-3745	242	17	(	(	PUNCT
ejpam-3745	242	18	d(s	d(s	PROPN
ejpam-3745	242	19	)	)	PUNCT
ejpam-3745	242	20	)	)	PUNCT
ejpam-3745	243	1	[	[	X
ejpam-3745	243	2	2	2	NUM
ejpam-3745	243	3	·	·	PUNCT
ejpam-3745	243	4	|v	|v	NOUN
ejpam-3745	243	5	|	|	ADV
ejpam-3745	243	6	−	−	NOUN
ejpam-3745	243	7	|v1|]−	|v1|]−	PROPN
ejpam-3745	243	8	1	1	NUM
ejpam-3745	243	9	·	·	PUNCT
ejpam-3745	244	1	[	[	X
ejpam-3745	244	2	(	(	PUNCT
ejpam-3745	244	3	n−	n−	NOUN
ejpam-3745	244	4	⌊	⌊	VERB
ejpam-3745	244	5	n	n	ADV
ejpam-3745	244	6	2	2	NUM
ejpam-3745	244	7	⌋)2	⌋)2	NUM
ejpam-3745	244	8	+	+	CCONJ
ejpam-3745	244	9	2	2	NUM
ejpam-3745	244	10	(	(	PUNCT
ejpam-3745	244	11	n−	n−	NOUN
ejpam-3745	244	12	⌊	⌊	VERB
ejpam-3745	244	13	n	n	DET
ejpam-3745	244	14	2	2	NUM
ejpam-3745	244	15	⌋	⌋	NUM
ejpam-3745	244	16	)	)	PUNCT
ejpam-3745	244	17	]	]	PUNCT
ejpam-3745	245	1	−2	−2	NOUN
ejpam-3745	245	2	·	·	PUNCT
ejpam-3745	245	3	[	[	PUNCT
ejpam-3745	245	4	|v	|v	PROPN
ejpam-3745	245	5	|	|	ADV
ejpam-3745	245	6	−	−	PROPN
ejpam-3745	245	7	(	(	PUNCT
ejpam-3745	245	8	(	(	PUNCT
ejpam-3745	245	9	n−	n−	NOUN
ejpam-3745	245	10	⌊	⌊	VERB
ejpam-3745	245	11	n	n	ADV
ejpam-3745	245	12	2	2	NUM
ejpam-3745	245	13	⌋)2	⌋)2	NUM
ejpam-3745	245	14	+	+	CCONJ
ejpam-3745	245	15	2	2	NUM
ejpam-3745	245	16	(	(	PUNCT
ejpam-3745	245	17	n−	n−	NOUN
ejpam-3745	245	18	⌊	⌊	VERB
ejpam-3745	245	19	n	n	DET
ejpam-3745	245	20	2	2	NUM
ejpam-3745	245	21	⌋	⌋	NUM
ejpam-3745	245	22	)	)	PUNCT
ejpam-3745	245	23	)	)	PUNCT
ejpam-3745	245	24	]	]	PUNCT
ejpam-3745	246	1			NUM
ejpam-3745	246	2	=	=	SYM
ejpam-3745	246	3	1	1	NUM
ejpam-3745	246	4	2	2	NUM
ejpam-3745	246	5			NOUN
ejpam-3745	246	6	∑	∑	PROPN
ejpam-3745	246	7	k	k	PROPN
ejpam-3745	246	8	,	,	PUNCT
ejpam-3745	246	9	t∈{0,1,	t∈{0,1,	PRON
ejpam-3745	246	10	...	...	PUNCT
ejpam-3745	246	11	,n−1	,n−1	PUNCT
ejpam-3745	246	12	}	}	PUNCT
ejpam-3745	246	13	[	[	X
ejpam-3745	246	14	2	2	NUM
ejpam-3745	246	15	|v	|v	VERB
ejpam-3745	246	16	|	|	ADV
ejpam-3745	246	17	−	−	PROPN
ejpam-3745	246	18	(	(	PUNCT
ejpam-3745	246	19	n−	n−	NOUN
ejpam-3745	246	20	k)−	k)−	PROPN
ejpam-3745	246	21	(	(	PUNCT
ejpam-3745	246	22	n−	n−	NOUN
ejpam-3745	246	23	t)−	t)−	PROPN
ejpam-3745	246	24	(	(	PUNCT
ejpam-3745	246	25	n−	n−	NOUN
ejpam-3745	246	26	k)(n−	k)(n−	PROPN
ejpam-3745	246	27	t	t	PROPN
ejpam-3745	246	28	)	)	PUNCT
ejpam-3745	246	29	]	]	PUNCT
ejpam-3745	247	1	+	+	CCONJ
ejpam-3745	247	2	∑	∑	PUNCT
ejpam-3745	247	3	k∈{0,1,	k∈{0,1,	PROPN
ejpam-3745	247	4	...	...	PUNCT
ejpam-3745	247	5	,n−1	,n−1	PUNCT
ejpam-3745	247	6	}	}	PUNCT
ejpam-3745	247	7	t	t	PROPN
ejpam-3745	247	8	=	=	SYM
ejpam-3745	247	9	n	n	PROPN
ejpam-3745	247	10	[	[	X
ejpam-3745	247	11	2	2	NUM
ejpam-3745	247	12	|v	|v	NOUN
ejpam-3745	247	13	|	|	ADV
ejpam-3745	247	14	−	−	PROPN
ejpam-3745	247	15	(	(	PUNCT
ejpam-3745	247	16	n−	n−	NOUN
ejpam-3745	247	17	k)(n	k)(n	PROPN
ejpam-3745	247	18	+	+	PROPN
ejpam-3745	247	19	1)−	1)−	PROPN
ejpam-3745	247	20	n	n	CCONJ
ejpam-3745	247	21	]	]	PUNCT
ejpam-3745	248	1	+	+	CCONJ
ejpam-3745	248	2	∑	∑	PROPN
ejpam-3745	248	3	t∈{0,1,	t∈{0,1,	NOUN
ejpam-3745	248	4	...	...	PUNCT
ejpam-3745	248	5	,n−1	,n−1	PUNCT
ejpam-3745	248	6	}	}	PUNCT
ejpam-3745	248	7	k	k	X
ejpam-3745	248	8	=	=	NOUN
ejpam-3745	248	9	n	n	X
ejpam-3745	248	10	[	[	X
ejpam-3745	248	11	2	2	NUM
ejpam-3745	248	12	|v	|v	NOUN
ejpam-3745	248	13	|	|	ADV
ejpam-3745	248	14	−	−	PROPN
ejpam-3745	248	15	(	(	PUNCT
ejpam-3745	248	16	n−	n−	NOUN
ejpam-3745	248	17	t)(n	t)(n	X
ejpam-3745	248	18	+	+	PROPN
ejpam-3745	249	1	1)−	1)−	PROPN
ejpam-3745	249	2	n]−	n]−	ADJ
ejpam-3745	249	3	2	2	NUM
ejpam-3745	249	4	|v	|v	NOUN
ejpam-3745	249	5	|+	|+	X
ejpam-3745	249	6	2	2	NUM
ejpam-3745	250	1	[	[	X
ejpam-3745	250	2	(	(	PUNCT
ejpam-3745	250	3	n−	n−	NOUN
ejpam-3745	250	4	⌊	⌊	VERB
ejpam-3745	250	5	n	n	ADV
ejpam-3745	250	6	2	2	NUM
ejpam-3745	250	7	⌋)2	⌋)2	NUM
ejpam-3745	250	8	+	+	CCONJ
ejpam-3745	250	9	2	2	NUM
ejpam-3745	250	10	(	(	PUNCT
ejpam-3745	250	11	n−	n−	NOUN
ejpam-3745	250	12	⌊	⌊	VERB
ejpam-3745	250	13	n	n	DET
ejpam-3745	250	14	2	2	NUM
ejpam-3745	250	15	⌋	⌋	NOUN
ejpam-3745	250	16	)	)	PUNCT
ejpam-3745	250	17	]	]	PUNCT
ejpam-3745	251	1			VERB
ejpam-3745	251	2	=	=	SYM
ejpam-3745	251	3	1	1	NUM
ejpam-3745	251	4	2	2	NUM
ejpam-3745	251	5			NOUN
ejpam-3745	251	6	(	(	PUNCT
ejpam-3745	251	7	6n−	6n−	PROPN
ejpam-3745	251	8	2	2	NUM
ejpam-3745	251	9	)	)	PUNCT
ejpam-3745	251	10	(	(	PUNCT
ejpam-3745	251	11	(	(	PUNCT
ejpam-3745	251	12	n	n	X
ejpam-3745	251	13	+	+	CCONJ
ejpam-3745	251	14	1)2	1)2	NUM
ejpam-3745	251	15	−	−	NOUN
ejpam-3745	251	16	1	1	NUM
ejpam-3745	251	17	)	)	PUNCT
ejpam-3745	252	1	+	+	CCONJ
ejpam-3745	252	2	(	(	PUNCT
ejpam-3745	252	3	⌈	⌈	NUM
ejpam-3745	252	4	n	n	PRON
ejpam-3745	252	5	2	2	NUM
ejpam-3745	252	6	⌉	⌉	NOUN
ejpam-3745	252	7	+	+	X
ejpam-3745	252	8	1	1	NUM
ejpam-3745	252	9	)	)	SYM
ejpam-3745	252	10	2	2	NUM
ejpam-3745	252	11	−	−	PROPN
ejpam-3745	252	12	1−∑	1−∑	PROPN
ejpam-3745	253	1	k	k	PROPN
ejpam-3745	253	2	,	,	PUNCT
ejpam-3745	253	3	t∈{0,1,	t∈{0,1,	PRON
ejpam-3745	253	4	...	...	PUNCT
ejpam-3745	253	5	,n−1	,n−1	PUNCT
ejpam-3745	253	6	}	}	PUNCT
ejpam-3745	254	1	[	[	X
ejpam-3745	254	2	2n−	2n−	NUM
ejpam-3745	254	3	k	k	NOUN
ejpam-3745	254	4	−	−	PROPN
ejpam-3745	254	5	t	t	PROPN
ejpam-3745	254	6	+	+	CCONJ
ejpam-3745	254	7	(	(	PUNCT
ejpam-3745	254	8	n−	n−	NOUN
ejpam-3745	254	9	k)(n−	k)(n−	PROPN
ejpam-3745	254	10	t	t	PROPN
ejpam-3745	254	11	)	)	PUNCT
ejpam-3745	254	12	]	]	PUNCT
ejpam-3745	255	1	−	−	PROPN
ejpam-3745	255	2	∑	∑	PROPN
ejpam-3745	255	3	k∈{0,1,	k∈{0,1,	PROPN
ejpam-3745	255	4	...	...	PUNCT
ejpam-3745	255	5	,n−1	,n−1	PUNCT
ejpam-3745	255	6	}	}	PUNCT
ejpam-3745	255	7	t	t	PROPN
ejpam-3745	255	8	=	=	SYM
ejpam-3745	255	9	n	n	X
ejpam-3745	255	10	[	[	X
ejpam-3745	255	11	(	(	PUNCT
ejpam-3745	255	12	n−	n−	NOUN
ejpam-3745	255	13	k)(n	k)(n	VERB
ejpam-3745	255	14	+	+	CCONJ
ejpam-3745	255	15	1	1	X
ejpam-3745	255	16	)	)	PUNCT
ejpam-3745	255	17	+	+	CCONJ
ejpam-3745	255	18	n]−	n]−	ADV
ejpam-3745	255	19	∑	∑	PUNCT
ejpam-3745	255	20	t∈{0,1,	t∈{0,1,	NOUN
ejpam-3745	255	21	...	...	PUNCT
ejpam-3745	255	22	,n−1	,n−1	PUNCT
ejpam-3745	255	23	}	}	PUNCT
ejpam-3745	255	24	k	k	X
ejpam-3745	255	25	=	=	NOUN
ejpam-3745	255	26	n	n	X
ejpam-3745	255	27	[	[	X
ejpam-3745	255	28	(	(	PUNCT
ejpam-3745	255	29	n−	n−	NOUN
ejpam-3745	255	30	t)(n	t)(n	X
ejpam-3745	255	31	+	+	CCONJ
ejpam-3745	255	32	1	1	X
ejpam-3745	255	33	)	)	PUNCT
ejpam-3745	255	34	+	+	NUM
ejpam-3745	255	35	n	n	CCONJ
ejpam-3745	255	36	]	]	PUNCT
ejpam-3745	255	37			PUNCT
ejpam-3745	255	38	since	since	SCONJ
ejpam-3745	255	39	|v	|v	PROPN
ejpam-3745	255	40	|	|	ADV
ejpam-3745	255	41	=	=	PUNCT
ejpam-3745	255	42	(	(	PUNCT
ejpam-3745	255	43	n	n	PROPN
ejpam-3745	255	44	+	+	CCONJ
ejpam-3745	255	45	1)2	1)2	NUM
ejpam-3745	255	46	−	−	NOUN
ejpam-3745	255	47	1	1	NUM
ejpam-3745	255	48	and	and	CCONJ
ejpam-3745	255	49	n−	n−	NOUN
ejpam-3745	255	50	⌊	⌊	VERB
ejpam-3745	255	51	n	n	ADV
ejpam-3745	255	52	2	2	NUM
ejpam-3745	255	53	⌋	⌋	NOUN
ejpam-3745	255	54	=	=	PUNCT
ejpam-3745	255	55	⌈	⌈	NOUN
ejpam-3745	255	56	n	n	CCONJ
ejpam-3745	255	57	2	2	NUM
ejpam-3745	255	58	⌉	⌉	X
ejpam-3745	255	59	.	.	PUNCT
ejpam-3745	256	1	3	3	X
ejpam-3745	256	2	.	.	X
ejpam-3745	256	3	examples	example	NOUN
ejpam-3745	256	4	let	let	VERB
ejpam-3745	256	5	us	we	PRON
ejpam-3745	256	6	give	give	VERB
ejpam-3745	256	7	the	the	DET
ejpam-3745	256	8	following	follow	VERB
ejpam-3745	256	9	examples	example	NOUN
ejpam-3745	256	10	to	to	PART
ejpam-3745	256	11	strengthen	strengthen	VERB
ejpam-3745	256	12	the	the	DET
ejpam-3745	256	13	theory	theory	NOUN
ejpam-3745	256	14	.	.	PUNCT
ejpam-3745	257	1	b.	b.	PROPN
ejpam-3745	257	2	aydın	aydın	PROPN
ejpam-3745	257	3	,	,	PUNCT
ejpam-3745	257	4	n.	n.	PROPN
ejpam-3745	257	5	akgüneş	akgüneş	PROPN
ejpam-3745	257	6	,	,	PUNCT
ejpam-3745	257	7	i.	i.	PROPN
ejpam-3745	257	8	n.	n.	PROPN
ejpam-3745	257	9	cangul	cangul	PROPN
ejpam-3745	257	10	/	/	SYM
ejpam-3745	257	11	eur	eur	NOUN
ejpam-3745	257	12	.	.	PUNCT
ejpam-3745	258	1	j.	j.	PROPN
ejpam-3745	258	2	pure	pure	PROPN
ejpam-3745	258	3	appl	appl	PROPN
ejpam-3745	258	4	.	.	PROPN
ejpam-3745	258	5	math	math	PROPN
ejpam-3745	258	6	,	,	PUNCT
ejpam-3745	258	7	13	13	NUM
ejpam-3745	258	8	(	(	PUNCT
ejpam-3745	258	9	5	5	NUM
ejpam-3745	258	10	)	)	PUNCT
ejpam-3745	258	11	(	(	PUNCT
ejpam-3745	258	12	2020	2020	NUM
ejpam-3745	258	13	)	)	PUNCT
ejpam-3745	258	14	,	,	PUNCT
ejpam-3745	258	15	1231	1231	NUM
ejpam-3745	258	16	-	-	SYM
ejpam-3745	258	17	1240	1240	NUM
ejpam-3745	258	18	1238	1238	NUM
ejpam-3745	258	19	example	example	NOUN
ejpam-3745	258	20	1	1	NUM
ejpam-3745	258	21	.	.	PUNCT
ejpam-3745	259	1	let	let	VERB
ejpam-3745	259	2	n	n	NOUN
ejpam-3745	259	3	=	=	SYM
ejpam-3745	259	4	5	5	X
ejpam-3745	259	5	.	.	PUNCT
ejpam-3745	259	6	then	then	ADV
ejpam-3745	259	7	s	s	PART
ejpam-3745	259	8	=	=	SYM
ejpam-3745	259	9	s5	s5	PROPN
ejpam-3745	259	10	×	×	PROPN
ejpam-3745	259	11	s5	s5	PROPN
ejpam-3745	259	12	where	where	SCONJ
ejpam-3745	259	13	s5	s5	X
ejpam-3745	259	14	=	=	PUNCT
ejpam-3745	259	15	{	{	PUNCT
ejpam-3745	259	16	0	0	NUM
ejpam-3745	259	17	,	,	PUNCT
ejpam-3745	259	18	x	x	NOUN
ejpam-3745	259	19	,	,	PUNCT
ejpam-3745	259	20	x2	x2	PROPN
ejpam-3745	259	21	,	,	PUNCT
ejpam-3745	259	22	.	.	PUNCT
ejpam-3745	259	23	.	.	PUNCT
ejpam-3745	260	1	.	.	PUNCT
ejpam-3745	261	1	,	,	PUNCT
ejpam-3745	261	2	x5	x5	NOUN
ejpam-3745	261	3	}	}	PUNCT
ejpam-3745	261	4	.	.	PUNCT
ejpam-3745	262	1	then	then	ADV
ejpam-3745	262	2	we	we	PRON
ejpam-3745	262	3	can	can	AUX
ejpam-3745	262	4	list	list	VERB
ejpam-3745	262	5	the	the	DET
ejpam-3745	262	6	vertices	vertex	NOUN
ejpam-3745	262	7	of	of	ADP
ejpam-3745	262	8	s	s	PRON
ejpam-3745	262	9	as	as	SCONJ
ejpam-3745	262	10	follows	follow	VERB
ejpam-3745	262	11	:	:	PUNCT
ejpam-3745	262	12	v	v	X
ejpam-3745	262	13	(	(	PUNCT
ejpam-3745	262	14	s	s	NOUN
ejpam-3745	262	15	)	)	PUNCT
ejpam-3745	262	16	=	=	SYM
ejpam-3745	262	17			X
ejpam-3745	262	18	(	(	PUNCT
ejpam-3745	262	19	0	0	NUM
ejpam-3745	262	20	,	,	PUNCT
ejpam-3745	262	21	x	x	NOUN
ejpam-3745	262	22	)	)	PUNCT
ejpam-3745	262	23	(	(	PUNCT
ejpam-3745	262	24	0	0	NUM
ejpam-3745	262	25	,	,	PUNCT
ejpam-3745	262	26	x2	x2	PROPN
ejpam-3745	262	27	)	)	PUNCT
ejpam-3745	262	28	(	(	PUNCT
ejpam-3745	262	29	0	0	NUM
ejpam-3745	262	30	,	,	PUNCT
ejpam-3745	262	31	x3	x3	ADJ
ejpam-3745	262	32	)	)	PUNCT
ejpam-3745	262	33	(	(	PUNCT
ejpam-3745	262	34	0	0	NUM
ejpam-3745	262	35	,	,	PUNCT
ejpam-3745	262	36	x4	x4	PROPN
ejpam-3745	262	37	)	)	PUNCT
ejpam-3745	262	38	(	(	PUNCT
ejpam-3745	262	39	0	0	NUM
ejpam-3745	262	40	,	,	PUNCT
ejpam-3745	262	41	x5	x5	PROPN
ejpam-3745	262	42	)	)	PUNCT
ejpam-3745	262	43	(	(	PUNCT
ejpam-3745	262	44	x	x	X
ejpam-3745	262	45	,	,	PUNCT
ejpam-3745	262	46	0	0	NUM
ejpam-3745	262	47	)	)	PUNCT
ejpam-3745	262	48	(	(	PUNCT
ejpam-3745	262	49	x	x	X
ejpam-3745	262	50	,	,	PUNCT
ejpam-3745	262	51	x	x	X
ejpam-3745	262	52	)	)	PUNCT
ejpam-3745	262	53	(	(	PUNCT
ejpam-3745	262	54	x	x	X
ejpam-3745	262	55	,	,	PUNCT
ejpam-3745	262	56	x2	x2	PROPN
ejpam-3745	262	57	)	)	PUNCT
ejpam-3745	262	58	(	(	PUNCT
ejpam-3745	262	59	x	x	NOUN
ejpam-3745	262	60	,	,	PUNCT
ejpam-3745	262	61	x3	x3	ADJ
ejpam-3745	262	62	)	)	PUNCT
ejpam-3745	262	63	(	(	PUNCT
ejpam-3745	262	64	x	x	X
ejpam-3745	262	65	,	,	PUNCT
ejpam-3745	262	66	x4	x4	PROPN
ejpam-3745	262	67	)	)	PUNCT
ejpam-3745	262	68	(	(	PUNCT
ejpam-3745	262	69	x	x	X
ejpam-3745	262	70	,	,	PUNCT
ejpam-3745	262	71	x5	x5	PROPN
ejpam-3745	262	72	)	)	PUNCT
ejpam-3745	262	73	(	(	PUNCT
ejpam-3745	262	74	x2	x2	PROPN
ejpam-3745	262	75	,	,	PUNCT
ejpam-3745	262	76	0	0	NUM
ejpam-3745	262	77	)	)	PUNCT
ejpam-3745	262	78	(	(	PUNCT
ejpam-3745	262	79	x2	x2	PROPN
ejpam-3745	262	80	,	,	PUNCT
ejpam-3745	262	81	x	x	X
ejpam-3745	262	82	)	)	PUNCT
ejpam-3745	262	83	(	(	PUNCT
ejpam-3745	262	84	x2	x2	PROPN
ejpam-3745	262	85	,	,	PUNCT
ejpam-3745	262	86	x2	x2	PROPN
ejpam-3745	262	87	)	)	PUNCT
ejpam-3745	262	88	(	(	PUNCT
ejpam-3745	262	89	x2	x2	PROPN
ejpam-3745	262	90	,	,	PUNCT
ejpam-3745	262	91	x3	x3	ADJ
ejpam-3745	262	92	)	)	PUNCT
ejpam-3745	262	93	(	(	PUNCT
ejpam-3745	262	94	x2	x2	PROPN
ejpam-3745	262	95	,	,	PUNCT
ejpam-3745	262	96	x4	x4	PROPN
ejpam-3745	262	97	)	)	PUNCT
ejpam-3745	262	98	(	(	PUNCT
ejpam-3745	262	99	x2	x2	PROPN
ejpam-3745	262	100	,	,	PUNCT
ejpam-3745	262	101	x5	x5	PROPN
ejpam-3745	262	102	)	)	PUNCT
ejpam-3745	262	103	(	(	PUNCT
ejpam-3745	262	104	x3	x3	ADJ
ejpam-3745	262	105	,	,	PUNCT
ejpam-3745	262	106	0	0	NUM
ejpam-3745	262	107	)	)	PUNCT
ejpam-3745	262	108	(	(	PUNCT
ejpam-3745	262	109	x3	x3	ADJ
ejpam-3745	262	110	,	,	PUNCT
ejpam-3745	262	111	x	x	X
ejpam-3745	262	112	)	)	PUNCT
ejpam-3745	262	113	(	(	PUNCT
ejpam-3745	262	114	x3	x3	ADJ
ejpam-3745	262	115	,	,	PUNCT
ejpam-3745	262	116	x2	x2	PROPN
ejpam-3745	262	117	)	)	PUNCT
ejpam-3745	262	118	(	(	PUNCT
ejpam-3745	262	119	x3	x3	ADJ
ejpam-3745	262	120	,	,	PUNCT
ejpam-3745	262	121	x3	x3	ADJ
ejpam-3745	262	122	)	)	PUNCT
ejpam-3745	262	123	(	(	PUNCT
ejpam-3745	262	124	x3	x3	PROPN
ejpam-3745	262	125	,	,	PUNCT
ejpam-3745	262	126	x4	x4	PROPN
ejpam-3745	262	127	)	)	PUNCT
ejpam-3745	262	128	(	(	PUNCT
ejpam-3745	262	129	x3	x3	ADJ
ejpam-3745	262	130	,	,	PUNCT
ejpam-3745	262	131	x5	x5	PROPN
ejpam-3745	262	132	)	)	PUNCT
ejpam-3745	262	133	(	(	PUNCT
ejpam-3745	262	134	x4	x4	PROPN
ejpam-3745	262	135	,	,	PUNCT
ejpam-3745	262	136	0	0	NUM
ejpam-3745	262	137	)	)	PUNCT
ejpam-3745	262	138	(	(	PUNCT
ejpam-3745	262	139	x4	x4	PROPN
ejpam-3745	262	140	,	,	PUNCT
ejpam-3745	262	141	x	x	X
ejpam-3745	262	142	)	)	PUNCT
ejpam-3745	262	143	(	(	PUNCT
ejpam-3745	262	144	x4	x4	PROPN
ejpam-3745	262	145	,	,	PUNCT
ejpam-3745	262	146	x2	x2	PROPN
ejpam-3745	262	147	)	)	PUNCT
ejpam-3745	262	148	(	(	PUNCT
ejpam-3745	262	149	x4	x4	PROPN
ejpam-3745	262	150	,	,	PUNCT
ejpam-3745	262	151	x3	x3	ADJ
ejpam-3745	262	152	)	)	PUNCT
ejpam-3745	262	153	(	(	PUNCT
ejpam-3745	262	154	x4	x4	PROPN
ejpam-3745	262	155	,	,	PUNCT
ejpam-3745	262	156	x4	x4	PROPN
ejpam-3745	262	157	)	)	PUNCT
ejpam-3745	262	158	(	(	PUNCT
ejpam-3745	262	159	x4	x4	PROPN
ejpam-3745	262	160	,	,	PUNCT
ejpam-3745	262	161	x5	x5	PROPN
ejpam-3745	262	162	)	)	PUNCT
ejpam-3745	262	163	(	(	PUNCT
ejpam-3745	262	164	x5	x5	PROPN
ejpam-3745	262	165	,	,	PUNCT
ejpam-3745	262	166	0	0	NUM
ejpam-3745	262	167	)	)	PUNCT
ejpam-3745	262	168	(	(	PUNCT
ejpam-3745	262	169	x5	x5	PROPN
ejpam-3745	262	170	,	,	PUNCT
ejpam-3745	262	171	x	x	X
ejpam-3745	262	172	)	)	PUNCT
ejpam-3745	262	173	(	(	PUNCT
ejpam-3745	262	174	x5	x5	PROPN
ejpam-3745	262	175	,	,	PUNCT
ejpam-3745	262	176	x2	x2	PROPN
ejpam-3745	262	177	)	)	PUNCT
ejpam-3745	262	178	(	(	PUNCT
ejpam-3745	262	179	x5	x5	PROPN
ejpam-3745	262	180	,	,	PUNCT
ejpam-3745	262	181	x3	x3	ADJ
ejpam-3745	262	182	)	)	PUNCT
ejpam-3745	262	183	(	(	PUNCT
ejpam-3745	262	184	x5	x5	PROPN
ejpam-3745	262	185	,	,	PUNCT
ejpam-3745	262	186	x4	x4	PROPN
ejpam-3745	262	187	)	)	PUNCT
ejpam-3745	262	188	(	(	PUNCT
ejpam-3745	262	189	x5	x5	PROPN
ejpam-3745	262	190	,	,	PUNCT
ejpam-3745	262	191	x5	x5	NOUN
ejpam-3745	262	192	)	)	PUNCT
ejpam-3745	262	193			NOUN
ejpam-3745	262	194	.	.	PUNCT
ejpam-3745	263	1	let	let	VERB
ejpam-3745	263	2	now	now	ADV
ejpam-3745	263	3	k	k	NOUN
ejpam-3745	263	4	=	=	SYM
ejpam-3745	263	5	4	4	NUM
ejpam-3745	263	6	and	and	CCONJ
ejpam-3745	263	7	t	t	NOUN
ejpam-3745	264	1	=	=	SYM
ejpam-3745	264	2	4	4	X
ejpam-3745	264	3	.	.	PUNCT
ejpam-3745	265	1	the	the	DET
ejpam-3745	265	2	values	value	NOUN
ejpam-3745	265	3	(	(	PUNCT
ejpam-3745	265	4	xa	xa	PROPN
ejpam-3745	265	5	,	,	PUNCT
ejpam-3745	265	6	xb	xb	PROPN
ejpam-3745	265	7	)	)	PUNCT
ejpam-3745	265	8	satisfying	satisfy	VERB
ejpam-3745	265	9	the	the	DET
ejpam-3745	265	10	condition	condition	NOUN
ejpam-3745	265	11	dγ(s)((x	dγ(s)((x	NOUN
ejpam-3745	265	12	5−4	5−4	NUM
ejpam-3745	265	13	,	,	PUNCT
ejpam-3745	265	14	x5−4	x5−4	PROPN
ejpam-3745	265	15	)	)	PUNCT
ejpam-3745	265	16	,	,	PUNCT
ejpam-3745	265	17	(	(	PUNCT
ejpam-3745	265	18	xa	xa	PROPN
ejpam-3745	265	19	,	,	PUNCT
ejpam-3745	265	20	xb	xb	PROPN
ejpam-3745	265	21	)	)	PUNCT
ejpam-3745	265	22	)	)	PUNCT
ejpam-3745	266	1	=	=	PUNCT
ejpam-3745	266	2	dγ(s)((x	dγ(s)((x	NOUN
ejpam-3745	266	3	,	,	PUNCT
ejpam-3745	266	4	x	x	NOUN
ejpam-3745	266	5	)	)	PUNCT
ejpam-3745	266	6	,	,	PUNCT
ejpam-3745	266	7	(	(	PUNCT
ejpam-3745	266	8	xa	xa	PROPN
ejpam-3745	266	9	,	,	PUNCT
ejpam-3745	266	10	xb	xb	PROPN
ejpam-3745	266	11	)	)	PUNCT
ejpam-3745	266	12	)	)	PUNCT
ejpam-3745	267	1	=	=	SYM
ejpam-3745	267	2	1	1	NUM
ejpam-3745	267	3	are	be	AUX
ejpam-3745	267	4			NUM
ejpam-3745	267	5	(	(	PUNCT
ejpam-3745	267	6	0	0	NUM
ejpam-3745	267	7	,	,	PUNCT
ejpam-3745	267	8	x5	x5	PROPN
ejpam-3745	267	9	)	)	PUNCT
ejpam-3745	267	10	(	(	PUNCT
ejpam-3745	267	11	x5	x5	PROPN
ejpam-3745	267	12	,	,	PUNCT
ejpam-3745	267	13	0	0	NUM
ejpam-3745	267	14	)	)	PUNCT
ejpam-3745	267	15	(	(	PUNCT
ejpam-3745	267	16	x5	x5	PROPN
ejpam-3745	267	17	,	,	PUNCT
ejpam-3745	267	18	x5	x5	NOUN
ejpam-3745	267	19	)	)	PUNCT
ejpam-3745	267	20			NOUN
ejpam-3745	267	21	.	.	PUNCT
ejpam-3745	268	1	hence	hence	ADV
ejpam-3745	268	2	there	there	PRON
ejpam-3745	268	3	are	be	VERB
ejpam-3745	268	4	(	(	PUNCT
ejpam-3745	268	5	n−	n−	NOUN
ejpam-3745	268	6	k)(n−	k)(n−	PROPN
ejpam-3745	268	7	t	t	PROPN
ejpam-3745	268	8	)	)	PUNCT
ejpam-3745	269	1	+	+	CCONJ
ejpam-3745	270	1	2n−	2n−	NUM
ejpam-3745	270	2	k	k	X
ejpam-3745	270	3	−	−	PROPN
ejpam-3745	270	4	t	t	NOUN
ejpam-3745	270	5	=	=	SYM
ejpam-3745	270	6	(	(	PUNCT
ejpam-3745	270	7	5−	5−	NUM
ejpam-3745	270	8	4)(5−	4)(5−	X
ejpam-3745	270	9	4	4	NUM
ejpam-3745	270	10	)	)	PUNCT
ejpam-3745	270	11	+	+	CCONJ
ejpam-3745	270	12	2	2	NUM
ejpam-3745	270	13	·	·	SYM
ejpam-3745	270	14	5−	5−	NUM
ejpam-3745	270	15	4−	4−	NUM
ejpam-3745	270	16	4	4	NUM
ejpam-3745	270	17	=	=	SYM
ejpam-3745	270	18	1	1	NUM
ejpam-3745	270	19	·	·	SYM
ejpam-3745	270	20	1	1	NUM
ejpam-3745	270	21	+	+	SYM
ejpam-3745	270	22	1	1	NUM
ejpam-3745	270	23	+	+	SYM
ejpam-3745	270	24	1	1	NUM
ejpam-3745	270	25	=	=	SYM
ejpam-3745	270	26	3	3	NUM
ejpam-3745	270	27	vertices	vertex	NOUN
ejpam-3745	270	28	.	.	PUNCT
ejpam-3745	271	1	let	let	VERB
ejpam-3745	271	2	us	we	PRON
ejpam-3745	271	3	see	see	VERB
ejpam-3745	271	4	the	the	DET
ejpam-3745	271	5	same	same	ADJ
ejpam-3745	271	6	example	example	NOUN
ejpam-3745	271	7	for	for	ADP
ejpam-3745	271	8	another	another	DET
ejpam-3745	271	9	values	value	NOUN
ejpam-3745	271	10	of	of	ADP
ejpam-3745	271	11	k	k	PROPN
ejpam-3745	271	12	and	and	CCONJ
ejpam-3745	271	13	t	t	PROPN
ejpam-3745	271	14	:	:	PUNCT
ejpam-3745	271	15	let	let	VERB
ejpam-3745	271	16	k	k	NOUN
ejpam-3745	271	17	=	=	SYM
ejpam-3745	271	18	1	1	NUM
ejpam-3745	271	19	and	and	CCONJ
ejpam-3745	271	20	t	t	NOUN
ejpam-3745	272	1	=	=	SYM
ejpam-3745	272	2	2	2	X
ejpam-3745	272	3	.	.	PUNCT
ejpam-3745	273	1	then	then	ADV
ejpam-3745	273	2	the	the	DET
ejpam-3745	273	3	pairs	pair	NOUN
ejpam-3745	273	4	of	of	ADP
ejpam-3745	273	5	vertices	vertex	NOUN
ejpam-3745	273	6	(	(	PUNCT
ejpam-3745	273	7	xa	xa	PROPN
ejpam-3745	273	8	,	,	PUNCT
ejpam-3745	273	9	xb	xb	PROPN
ejpam-3745	273	10	)	)	PUNCT
ejpam-3745	273	11	which	which	PRON
ejpam-3745	273	12	satisfy	satisfy	VERB
ejpam-3745	273	13	the	the	DET
ejpam-3745	273	14	condition	condition	NOUN
ejpam-3745	273	15	dγ(s)((x	dγ(s)((x	NOUN
ejpam-3745	273	16	5−1	5−1	NUM
ejpam-3745	273	17	,	,	PUNCT
ejpam-3745	273	18	x5−2	x5−2	X
ejpam-3745	273	19	)	)	PUNCT
ejpam-3745	273	20	,	,	PUNCT
ejpam-3745	273	21	(	(	PUNCT
ejpam-3745	273	22	xa	xa	PROPN
ejpam-3745	273	23	,	,	PUNCT
ejpam-3745	273	24	xb	xb	PROPN
ejpam-3745	273	25	)	)	PUNCT
ejpam-3745	273	26	)	)	PUNCT
ejpam-3745	274	1	=	=	PUNCT
ejpam-3745	274	2	dγ(s)((x	dγ(s)((x	VERB
ejpam-3745	274	3	4	4	NUM
ejpam-3745	274	4	,	,	PUNCT
ejpam-3745	274	5	x3	x3	ADJ
ejpam-3745	274	6	)	)	PUNCT
ejpam-3745	274	7	,	,	PUNCT
ejpam-3745	274	8	(	(	PUNCT
ejpam-3745	274	9	xa	xa	PROPN
ejpam-3745	274	10	,	,	PUNCT
ejpam-3745	274	11	xb	xb	PROPN
ejpam-3745	274	12	)	)	PUNCT
ejpam-3745	274	13	)	)	PUNCT
ejpam-3745	275	1	=	=	SYM
ejpam-3745	275	2	1	1	NUM
ejpam-3745	275	3	are	be	AUX
ejpam-3745	275	4	listed	list	VERB
ejpam-3745	275	5	as	as	ADP
ejpam-3745	275	6			NUM
ejpam-3745	275	7	(	(	PUNCT
ejpam-3745	275	8	0	0	NUM
ejpam-3745	275	9	,	,	PUNCT
ejpam-3745	275	10	x3	x3	ADJ
ejpam-3745	275	11	)	)	PUNCT
ejpam-3745	275	12	(	(	PUNCT
ejpam-3745	275	13	0	0	NUM
ejpam-3745	275	14	,	,	PUNCT
ejpam-3745	275	15	x4	x4	PROPN
ejpam-3745	275	16	)	)	PUNCT
ejpam-3745	275	17	(	(	PUNCT
ejpam-3745	275	18	0	0	NUM
ejpam-3745	275	19	,	,	PUNCT
ejpam-3745	275	20	x5	x5	PROPN
ejpam-3745	275	21	)	)	PUNCT
ejpam-3745	275	22	(	(	PUNCT
ejpam-3745	275	23	x2	x2	PROPN
ejpam-3745	275	24	,	,	PUNCT
ejpam-3745	275	25	0	0	NUM
ejpam-3745	275	26	)	)	PUNCT
ejpam-3745	275	27	(	(	PUNCT
ejpam-3745	275	28	x2	x2	PROPN
ejpam-3745	275	29	,	,	PUNCT
ejpam-3745	275	30	x3	x3	ADJ
ejpam-3745	275	31	)	)	PUNCT
ejpam-3745	275	32	(	(	PUNCT
ejpam-3745	275	33	x2	x2	PROPN
ejpam-3745	275	34	,	,	PUNCT
ejpam-3745	275	35	x4	x4	PROPN
ejpam-3745	275	36	)	)	PUNCT
ejpam-3745	275	37	(	(	PUNCT
ejpam-3745	275	38	x2	x2	PROPN
ejpam-3745	275	39	,	,	PUNCT
ejpam-3745	275	40	x5	x5	PROPN
ejpam-3745	275	41	)	)	PUNCT
ejpam-3745	275	42	(	(	PUNCT
ejpam-3745	275	43	x3	x3	ADJ
ejpam-3745	275	44	,	,	PUNCT
ejpam-3745	275	45	0	0	NUM
ejpam-3745	275	46	)	)	PUNCT
ejpam-3745	275	47	(	(	PUNCT
ejpam-3745	275	48	x3	x3	ADJ
ejpam-3745	275	49	,	,	PUNCT
ejpam-3745	275	50	x3	x3	ADJ
ejpam-3745	275	51	)	)	PUNCT
ejpam-3745	275	52	(	(	PUNCT
ejpam-3745	275	53	x3	x3	PROPN
ejpam-3745	275	54	,	,	PUNCT
ejpam-3745	275	55	x4	x4	PROPN
ejpam-3745	275	56	)	)	PUNCT
ejpam-3745	275	57	(	(	PUNCT
ejpam-3745	275	58	x3	x3	ADJ
ejpam-3745	275	59	,	,	PUNCT
ejpam-3745	275	60	x5	x5	PROPN
ejpam-3745	275	61	)	)	PUNCT
ejpam-3745	275	62	(	(	PUNCT
ejpam-3745	275	63	x4	x4	PROPN
ejpam-3745	275	64	,	,	PUNCT
ejpam-3745	275	65	0	0	NUM
ejpam-3745	275	66	)	)	PUNCT
ejpam-3745	275	67	(	(	PUNCT
ejpam-3745	275	68	x4	x4	PROPN
ejpam-3745	275	69	,	,	PUNCT
ejpam-3745	275	70	x3	x3	ADJ
ejpam-3745	275	71	)	)	PUNCT
ejpam-3745	275	72	(	(	PUNCT
ejpam-3745	275	73	x4	x4	PROPN
ejpam-3745	275	74	,	,	PUNCT
ejpam-3745	275	75	x4	x4	PROPN
ejpam-3745	275	76	)	)	PUNCT
ejpam-3745	275	77	(	(	PUNCT
ejpam-3745	275	78	x4	x4	PROPN
ejpam-3745	275	79	,	,	PUNCT
ejpam-3745	275	80	x5	x5	PROPN
ejpam-3745	275	81	)	)	PUNCT
ejpam-3745	275	82	(	(	PUNCT
ejpam-3745	275	83	x5	x5	PROPN
ejpam-3745	275	84	,	,	PUNCT
ejpam-3745	275	85	0	0	NUM
ejpam-3745	275	86	)	)	PUNCT
ejpam-3745	275	87	(	(	PUNCT
ejpam-3745	275	88	x5	x5	PROPN
ejpam-3745	275	89	,	,	PUNCT
ejpam-3745	275	90	x3	x3	ADJ
ejpam-3745	275	91	)	)	PUNCT
ejpam-3745	275	92	(	(	PUNCT
ejpam-3745	275	93	x5	x5	PROPN
ejpam-3745	275	94	,	,	PUNCT
ejpam-3745	275	95	x4	x4	PROPN
ejpam-3745	275	96	)	)	PUNCT
ejpam-3745	275	97	(	(	PUNCT
ejpam-3745	275	98	x5	x5	PROPN
ejpam-3745	275	99	,	,	PUNCT
ejpam-3745	275	100	x5	x5	NOUN
ejpam-3745	275	101	)	)	PUNCT
ejpam-3745	275	102			NOUN
ejpam-3745	275	103	.	.	PUNCT
ejpam-3745	276	1	since	since	SCONJ
ejpam-3745	276	2	,	,	PUNCT
ejpam-3745	276	3	in	in	ADP
ejpam-3745	276	4	the	the	DET
ejpam-3745	276	5	above	above	ADJ
ejpam-3745	276	6	example	example	NOUN
ejpam-3745	276	7	,	,	PUNCT
ejpam-3745	276	8	n	n	NOUN
ejpam-3745	276	9	=	=	SYM
ejpam-3745	276	10	5	5	NUM
ejpam-3745	276	11	,	,	PUNCT
ejpam-3745	276	12	k	k	NOUN
ejpam-3745	276	13	=	=	SYM
ejpam-3745	276	14	1	1	NUM
ejpam-3745	276	15	and	and	CCONJ
ejpam-3745	276	16	t	t	NOUN
ejpam-3745	276	17	=	=	SYM
ejpam-3745	276	18	2	2	NUM
ejpam-3745	276	19	,	,	PUNCT
ejpam-3745	276	20	we	we	PRON
ejpam-3745	276	21	obtain	obtain	VERB
ejpam-3745	276	22	the	the	DET
ejpam-3745	276	23	number	number	NOUN
ejpam-3745	276	24	of	of	ADP
ejpam-3745	276	25	vertices	vertex	NOUN
ejpam-3745	276	26	satisfying	satisfy	VERB
ejpam-3745	276	27	this	this	DET
ejpam-3745	276	28	condition	condition	NOUN
ejpam-3745	276	29	as	as	ADP
ejpam-3745	276	30	(	(	PUNCT
ejpam-3745	276	31	n−	n−	NOUN
ejpam-3745	276	32	k)(n−	k)(n−	PROPN
ejpam-3745	276	33	t	t	PROPN
ejpam-3745	276	34	)	)	PUNCT
ejpam-3745	276	35	+	+	CCONJ
ejpam-3745	277	1	2n−	2n−	NUM
ejpam-3745	277	2	k	k	X
ejpam-3745	277	3	−	−	PROPN
ejpam-3745	277	4	t	t	NOUN
ejpam-3745	277	5	=	=	SYM
ejpam-3745	277	6	(	(	PUNCT
ejpam-3745	277	7	5−	5−	NUM
ejpam-3745	277	8	1)(5−	1)(5−	NUM
ejpam-3745	277	9	2	2	NUM
ejpam-3745	277	10	)	)	PUNCT
ejpam-3745	277	11	+	+	CCONJ
ejpam-3745	277	12	2	2	NUM
ejpam-3745	277	13	·	·	SYM
ejpam-3745	277	14	5−	5−	NUM
ejpam-3745	277	15	1−	1−	NUM
ejpam-3745	277	16	2	2	NUM
ejpam-3745	277	17	=	=	SYM
ejpam-3745	277	18	4	4	NUM
ejpam-3745	277	19	·	·	SYM
ejpam-3745	277	20	3	3	NUM
ejpam-3745	277	21	+	+	CCONJ
ejpam-3745	277	22	4	4	NUM
ejpam-3745	277	23	+	+	SYM
ejpam-3745	277	24	3	3	NUM
ejpam-3745	277	25	=	=	SYM
ejpam-3745	277	26	19	19	NUM
ejpam-3745	277	27	.	.	PUNCT
ejpam-3745	277	28	references	reference	NOUN
ejpam-3745	277	29	1239	1239	NUM
ejpam-3745	277	30	so	so	ADV
ejpam-3745	277	31	for	for	ADP
ejpam-3745	277	32	n	n	NOUN
ejpam-3745	277	33	=	=	SYM
ejpam-3745	277	34	5	5	NUM
ejpam-3745	277	35	,	,	PUNCT
ejpam-3745	277	36	the	the	DET
ejpam-3745	277	37	vertices	vertex	NOUN
ejpam-3745	277	38	adjacent	adjacent	ADJ
ejpam-3745	277	39	to	to	ADP
ejpam-3745	277	40	itself	itself	PRON
ejpam-3745	277	41	,	,	PUNCT
ejpam-3745	277	42	in	in	ADP
ejpam-3745	277	43	other	other	ADJ
ejpam-3745	277	44	words	word	NOUN
ejpam-3745	277	45	,	,	PUNCT
ejpam-3745	277	46	the	the	DET
ejpam-3745	277	47	vertices	vertex	NOUN
ejpam-3745	277	48	whose	whose	DET
ejpam-3745	277	49	distance	distance	NOUN
ejpam-3745	277	50	to	to	ADP
ejpam-3745	277	51	itself	itself	PRON
ejpam-3745	277	52	is	be	AUX
ejpam-3745	277	53	1	1	NUM
ejpam-3745	277	54	can	can	AUX
ejpam-3745	277	55	be	be	AUX
ejpam-3745	277	56	listed	list	VERB
ejpam-3745	277	57	as	as	ADP
ejpam-3745	277	58	follows:	follows:	PROPN
ejpam-3745	277	59	(	(	PUNCT
ejpam-3745	277	60	0	0	NUM
ejpam-3745	277	61	,	,	PUNCT
ejpam-3745	277	62	x3	x3	ADJ
ejpam-3745	277	63	)	)	PUNCT
ejpam-3745	277	64	(	(	PUNCT
ejpam-3745	277	65	0	0	NUM
ejpam-3745	277	66	,	,	PUNCT
ejpam-3745	277	67	x4	x4	PROPN
ejpam-3745	277	68	)	)	PUNCT
ejpam-3745	277	69	(	(	PUNCT
ejpam-3745	277	70	0	0	NUM
ejpam-3745	277	71	,	,	PUNCT
ejpam-3745	277	72	x5	x5	PROPN
ejpam-3745	277	73	)	)	PUNCT
ejpam-3745	277	74	(	(	PUNCT
ejpam-3745	277	75	x3	x3	ADJ
ejpam-3745	277	76	,	,	PUNCT
ejpam-3745	277	77	0	0	NUM
ejpam-3745	277	78	)	)	PUNCT
ejpam-3745	277	79	(	(	PUNCT
ejpam-3745	277	80	x3	x3	ADJ
ejpam-3745	277	81	,	,	PUNCT
ejpam-3745	277	82	x3	x3	ADJ
ejpam-3745	277	83	)	)	PUNCT
ejpam-3745	277	84	(	(	PUNCT
ejpam-3745	277	85	x3	x3	PROPN
ejpam-3745	277	86	,	,	PUNCT
ejpam-3745	277	87	x4	x4	PROPN
ejpam-3745	277	88	)	)	PUNCT
ejpam-3745	277	89	(	(	PUNCT
ejpam-3745	277	90	x3	x3	ADJ
ejpam-3745	277	91	,	,	PUNCT
ejpam-3745	277	92	x5	x5	PROPN
ejpam-3745	277	93	)	)	PUNCT
ejpam-3745	277	94	(	(	PUNCT
ejpam-3745	277	95	x4	x4	PROPN
ejpam-3745	277	96	,	,	PUNCT
ejpam-3745	277	97	0	0	NUM
ejpam-3745	277	98	)	)	PUNCT
ejpam-3745	277	99	(	(	PUNCT
ejpam-3745	277	100	x4	x4	PROPN
ejpam-3745	277	101	,	,	PUNCT
ejpam-3745	277	102	x3	x3	ADJ
ejpam-3745	277	103	)	)	PUNCT
ejpam-3745	277	104	(	(	PUNCT
ejpam-3745	277	105	x4	x4	PROPN
ejpam-3745	277	106	,	,	PUNCT
ejpam-3745	277	107	x4	x4	PROPN
ejpam-3745	277	108	)	)	PUNCT
ejpam-3745	277	109	(	(	PUNCT
ejpam-3745	277	110	x4	x4	PROPN
ejpam-3745	277	111	,	,	PUNCT
ejpam-3745	277	112	x5	x5	PROPN
ejpam-3745	277	113	)	)	PUNCT
ejpam-3745	277	114	(	(	PUNCT
ejpam-3745	277	115	x5	x5	PROPN
ejpam-3745	277	116	,	,	PUNCT
ejpam-3745	277	117	0	0	NUM
ejpam-3745	277	118	)	)	PUNCT
ejpam-3745	277	119	(	(	PUNCT
ejpam-3745	277	120	x5	x5	PROPN
ejpam-3745	277	121	,	,	PUNCT
ejpam-3745	277	122	x3	x3	ADJ
ejpam-3745	277	123	)	)	PUNCT
ejpam-3745	277	124	(	(	PUNCT
ejpam-3745	277	125	x5	x5	PROPN
ejpam-3745	277	126	,	,	PUNCT
ejpam-3745	277	127	x4	x4	PROPN
ejpam-3745	277	128	)	)	PUNCT
ejpam-3745	277	129	(	(	PUNCT
ejpam-3745	277	130	x5	x5	PROPN
ejpam-3745	277	131	,	,	PUNCT
ejpam-3745	277	132	x5	x5	NOUN
ejpam-3745	277	133	)	)	PUNCT
ejpam-3745	277	134			NOUN
ejpam-3745	277	135	.	.	PUNCT
ejpam-3745	278	1	the	the	DET
ejpam-3745	278	2	total	total	ADJ
ejpam-3745	278	3	number	number	NOUN
ejpam-3745	278	4	of	of	ADP
ejpam-3745	278	5	these	these	DET
ejpam-3745	278	6	vertex	vertex	NOUN
ejpam-3745	278	7	pairs	pair	NOUN
ejpam-3745	278	8	is	be	AUX
ejpam-3745	278	9	15	15	NUM
ejpam-3745	278	10	which	which	PRON
ejpam-3745	278	11	can	can	AUX
ejpam-3745	278	12	also	also	ADV
ejpam-3745	278	13	be	be	AUX
ejpam-3745	278	14	found	find	VERB
ejpam-3745	278	15	by	by	ADP
ejpam-3745	278	16	the	the	DET
ejpam-3745	278	17	formula	formula	NOUN
ejpam-3745	278	18	(	(	PUNCT
ejpam-3745	278	19	n−	n−	NOUN
ejpam-3745	278	20	⌊n	⌊n	NOUN
ejpam-3745	278	21	2	2	NUM
ejpam-3745	278	22	⌋	⌋	NOUN
ejpam-3745	278	23	)	)	PUNCT
ejpam-3745	278	24	2	2	NUM
ejpam-3745	279	1	+	+	SYM
ejpam-3745	279	2	2(n−	2(n−	NUM
ejpam-3745	279	3	⌊n	⌊n	ADJ
ejpam-3745	279	4	2	2	NUM
ejpam-3745	279	5	⌋	⌋	NOUN
ejpam-3745	279	6	)	)	PUNCT
ejpam-3745	280	1	=	=	PUNCT
ejpam-3745	280	2	(	(	PUNCT
ejpam-3745	280	3	5−	5−	NUM
ejpam-3745	280	4	⌊	⌊	PROPN
ejpam-3745	280	5	5	5	NUM
ejpam-3745	280	6	2	2	NUM
ejpam-3745	280	7	⌋	⌋	NOUN
ejpam-3745	280	8	)	)	PUNCT
ejpam-3745	280	9	2	2	NUM
ejpam-3745	281	1	+	+	SYM
ejpam-3745	281	2	2(5−	2(5−	NUM
ejpam-3745	281	3	⌊	⌊	PART
ejpam-3745	281	4	5	5	NUM
ejpam-3745	281	5	2	2	NUM
ejpam-3745	281	6	⌋	⌋	NOUN
ejpam-3745	281	7	)	)	PUNCT
ejpam-3745	282	1	=	=	PUNCT
ejpam-3745	282	2	(	(	PUNCT
ejpam-3745	282	3	5−2)2	5−2)2	NUM
ejpam-3745	282	4	+	+	NOUN
ejpam-3745	282	5	2(5−2	2(5−2	NUM
ejpam-3745	282	6	)	)	PUNCT
ejpam-3745	282	7	=	=	PUNCT
ejpam-3745	283	1	32	32	NUM
ejpam-3745	283	2	+	+	NOUN
ejpam-3745	283	3	2·3	2·3	NUM
ejpam-3745	283	4	=	=	SYM
ejpam-3745	283	5	9	9	NUM
ejpam-3745	283	6	+	+	SYM
ejpam-3745	283	7	6	6	NUM
ejpam-3745	283	8	=	=	SYM
ejpam-3745	283	9	15	15	NUM
ejpam-3745	283	10	vertices	vertex	NOUN
ejpam-3745	283	11	.	.	PUNCT
ejpam-3745	284	1	consequently	consequently	ADV
ejpam-3745	284	2	,	,	PUNCT
ejpam-3745	284	3	the	the	DET
ejpam-3745	284	4	wiener	wiener	NOUN
ejpam-3745	284	5	index	index	NOUN
ejpam-3745	284	6	of	of	ADP
ejpam-3745	284	7	the	the	DET
ejpam-3745	284	8	γ(s5	γ(s5	NOUN
ejpam-3745	284	9	×	×	PROPN
ejpam-3745	284	10	s5	s5	PROPN
ejpam-3745	284	11	)	)	PUNCT
ejpam-3745	284	12	which	which	PRON
ejpam-3745	284	13	is	be	AUX
ejpam-3745	284	14	equal	equal	ADJ
ejpam-3745	284	15	to	to	ADP
ejpam-3745	284	16	895	895	NUM
ejpam-3745	284	17	,	,	PUNCT
ejpam-3745	284	18	can	can	AUX
ejpam-3745	284	19	also	also	ADV
ejpam-3745	284	20	be	be	AUX
ejpam-3745	284	21	found	find	VERB
ejpam-3745	284	22	by	by	ADP
ejpam-3745	284	23	the	the	DET
ejpam-3745	284	24	above	above	ADJ
ejpam-3745	284	25	formula	formula	NOUN
ejpam-3745	284	26	.	.	PUNCT
ejpam-3745	285	1	references	reference	NOUN
ejpam-3745	285	2	[	[	X
ejpam-3745	285	3	1	1	X
ejpam-3745	285	4	]	]	PUNCT
ejpam-3745	285	5	i	i	PROPN
ejpam-3745	285	6	beck	beck	PROPN
ejpam-3745	285	7	.	.	PUNCT
ejpam-3745	286	1	coloring	coloring	NOUN
ejpam-3745	286	2	of	of	ADP
ejpam-3745	286	3	commutating	commutate	VERB
ejpam-3745	286	4	ring	ring	NOUN
ejpam-3745	286	5	.	.	PUNCT
ejpam-3745	287	1	j.	j.	PROPN
ejpam-3745	287	2	algebra	algebra	PROPN
ejpam-3745	287	3	,	,	PUNCT
ejpam-3745	287	4	116:208	116:208	NUM
ejpam-3745	287	5	-	-	SYM
ejpam-3745	287	6	226	226	NUM
ejpam-3745	287	7	,	,	PUNCT
ejpam-3745	287	8	1988	1988	NUM
ejpam-3745	287	9	.	.	PUNCT
ejpam-3745	288	1	[	[	X
ejpam-3745	288	2	2	2	NUM
ejpam-3745	288	3	]	]	X
ejpam-3745	288	4	d	d	X
ejpam-3745	288	5	f	f	PROPN
ejpam-3745	288	6	anderson	anderson	PROPN
ejpam-3745	288	7	,	,	PUNCT
ejpam-3745	288	8	p	p	PROPN
ejpam-3745	288	9	s	s	PROPN
ejpam-3745	288	10	livingston	livingston	PROPN
ejpam-3745	288	11	.	.	PUNCT
ejpam-3745	289	1	the	the	DET
ejpam-3745	289	2	zero	zero	NUM
ejpam-3745	289	3	-	-	PUNCT
ejpam-3745	289	4	divisor	divisor	NOUN
ejpam-3745	289	5	graph	graph	NOUN
ejpam-3745	289	6	of	of	ADP
ejpam-3745	289	7	a	a	DET
ejpam-3745	289	8	commutative	commutative	ADJ
ejpam-3745	289	9	ring	ring	NOUN
ejpam-3745	289	10	.	.	PUNCT
ejpam-3745	290	1	journal	journal	PROPN
ejpam-3745	290	2	of	of	ADP
ejpam-3745	290	3	algebra	algebra	PROPN
ejpam-3745	290	4	,	,	PUNCT
ejpam-3745	290	5	217:434	217:434	PROPN
ejpam-3745	290	6	-	-	NOUN
ejpam-3745	290	7	447	447	NUM
ejpam-3745	290	8	,	,	PUNCT
ejpam-3745	290	9	1999	1999	NUM
ejpam-3745	290	10	.	.	PUNCT
ejpam-3745	291	1	[	[	X
ejpam-3745	291	2	3	3	X
ejpam-3745	291	3	]	]	X
ejpam-3745	291	4	f	f	PROPN
ejpam-3745	291	5	r	r	PROPN
ejpam-3745	291	6	de	de	X
ejpam-3745	291	7	meyer	meyer	PROPN
ejpam-3745	291	8	,	,	PUNCT
ejpam-3745	291	9	l	l	PROPN
ejpam-3745	291	10	de	de	X
ejpam-3745	291	11	meyer	meyer	PROPN
ejpam-3745	291	12	.	.	PROPN
ejpam-3745	291	13	zero	zero	NUM
ejpam-3745	291	14	-	-	PUNCT
ejpam-3745	291	15	divisor	divisor	NOUN
ejpam-3745	291	16	graphs	graph	NOUN
ejpam-3745	291	17	of	of	ADP
ejpam-3745	291	18	semigroups	semigroup	NOUN
ejpam-3745	291	19	.	.	PUNCT
ejpam-3745	292	1	j.	j.	PROPN
ejpam-3745	292	2	algebra	algebra	PROPN
ejpam-3745	292	3	,	,	PUNCT
ejpam-3745	292	4	283:190198	283:190198	NUM
ejpam-3745	292	5	,	,	PUNCT
ejpam-3745	292	6	2005	2005	NUM
ejpam-3745	292	7	.	.	PUNCT
ejpam-3745	293	1	[	[	X
ejpam-3745	293	2	4	4	NUM
ejpam-3745	293	3	]	]	X
ejpam-3745	293	4	l	l	PROPN
ejpam-3745	293	5	de	de	X
ejpam-3745	293	6	meyer	meyer	PROPN
ejpam-3745	293	7	,	,	PUNCT
ejpam-3745	293	8	l	l	PROPN
ejpam-3745	293	9	greve	greve	PROPN
ejpam-3745	293	10	,	,	PUNCT
ejpam-3745	293	11	a	a	DET
ejpam-3745	293	12	sabbaghi	sabbaghi	PROPN
ejpam-3745	293	13	,	,	PUNCT
ejpam-3745	293	14	j	j	PROPN
ejpam-3745	293	15	wang	wang	PROPN
ejpam-3745	293	16	.	.	PUNCT
ejpam-3745	294	1	the	the	DET
ejpam-3745	294	2	zero	zero	NUM
ejpam-3745	294	3	-	-	PUNCT
ejpam-3745	294	4	divisor	divisor	NOUN
ejpam-3745	294	5	graph	graph	NOUN
ejpam-3745	294	6	associated	associate	VERB
ejpam-3745	294	7	to	to	ADP
ejpam-3745	294	8	a	a	DET
ejpam-3745	294	9	semigroup	semigroup	NOUN
ejpam-3745	294	10	.	.	PUNCT
ejpam-3745	295	1	communications	communication	NOUN
ejpam-3745	295	2	in	in	ADP
ejpam-3745	295	3	algebra	algebra	NOUN
ejpam-3745	295	4	,	,	PUNCT
ejpam-3745	295	5	38(9):3370	38(9):3370	NUM
ejpam-3745	295	6	-	-	SYM
ejpam-3745	295	7	3391	3391	NUM
ejpam-3745	295	8	,	,	PUNCT
ejpam-3745	295	9	2010	2010	NUM
ejpam-3745	295	10	.	.	PUNCT
ejpam-3745	296	1	[	[	X
ejpam-3745	296	2	5	5	NUM
ejpam-3745	296	3	]	]	SYM
ejpam-3745	296	4	f	f	PROPN
ejpam-3745	296	5	r	r	PROPN
ejpam-3745	296	6	de	de	X
ejpam-3745	296	7	meyer	meyer	PROPN
ejpam-3745	296	8	,	,	PUNCT
ejpam-3745	296	9	t	t	PROPN
ejpam-3745	296	10	mc	mc	PROPN
ejpam-3745	296	11	kenzie	kenzie	PROPN
ejpam-3745	296	12	,	,	PUNCT
ejpam-3745	296	13	k	k	PROPN
ejpam-3745	296	14	schneider	schneider	PROPN
ejpam-3745	296	15	.	.	PUNCT
ejpam-3745	297	1	the	the	DET
ejpam-3745	297	2	zero	zero	NUM
ejpam-3745	297	3	-	-	PUNCT
ejpam-3745	297	4	divisor	divisor	NOUN
ejpam-3745	297	5	graph	graph	NOUN
ejpam-3745	297	6	of	of	ADP
ejpam-3745	297	7	a	a	DET
ejpam-3745	297	8	commutative	commutative	ADJ
ejpam-3745	297	9	semigroup	semigroup	NOUN
ejpam-3745	297	10	.	.	PUNCT
ejpam-3745	298	1	semigroup	semigroup	PROPN
ejpam-3745	298	2	forum	forum	PROPN
ejpam-3745	298	3	,	,	PUNCT
ejpam-3745	298	4	65:206	65:206	PROPN
ejpam-3745	298	5	-	-	SYM
ejpam-3745	298	6	214	214	NUM
ejpam-3745	298	7	,	,	PUNCT
ejpam-3745	298	8	2002	2002	NUM
ejpam-3745	298	9	.	.	PUNCT
ejpam-3745	299	1	[	[	X
ejpam-3745	299	2	6	6	NUM
ejpam-3745	299	3	]	]	PUNCT
ejpam-3745	299	4	s	s	PART
ejpam-3745	299	5	akbari	akbari	PROPN
ejpam-3745	299	6	,	,	PUNCT
ejpam-3745	299	7	h	h	NOUN
ejpam-3745	299	8	r	r	NOUN
ejpam-3745	299	9	maimani	maimani	NOUN
ejpam-3745	299	10	,	,	PUNCT
ejpam-3745	299	11	s	s	NOUN
ejpam-3745	299	12	yassemi	yassemi	NOUN
ejpam-3745	299	13	.	.	PUNCT
ejpam-3745	300	1	when	when	SCONJ
ejpam-3745	300	2	a	a	DET
ejpam-3745	300	3	zero	zero	NUM
ejpam-3745	300	4	-	-	PUNCT
ejpam-3745	300	5	divisor	divisor	NOUN
ejpam-3745	300	6	graph	graph	NOUN
ejpam-3745	300	7	is	be	AUX
ejpam-3745	300	8	planar	planar	ADJ
ejpam-3745	300	9	or	or	CCONJ
ejpam-3745	300	10	a	a	DET
ejpam-3745	300	11	complete	complete	ADJ
ejpam-3745	300	12	r	r	NOUN
ejpam-3745	300	13	-	-	ADJ
ejpam-3745	300	14	partite	partite	ADJ
ejpam-3745	300	15	graph	graph	NOUN
ejpam-3745	300	16	.	.	PUNCT
ejpam-3745	301	1	j.	j.	PROPN
ejpam-3745	301	2	algebra	algebra	PROPN
ejpam-3745	301	3	,	,	PUNCT
ejpam-3745	301	4	270:169	270:169	NOUN
ejpam-3745	301	5	-	-	PUNCT
ejpam-3745	301	6	180	180	NUM
ejpam-3745	301	7	,	,	PUNCT
ejpam-3745	301	8	2003	2003	NUM
ejpam-3745	301	9	.	.	PUNCT
ejpam-3745	302	1	[	[	X
ejpam-3745	302	2	7	7	NUM
ejpam-3745	302	3	]	]	X
ejpam-3745	302	4	s	s	PART
ejpam-3745	302	5	akbari	akbari	PROPN
ejpam-3745	302	6	,	,	PUNCT
ejpam-3745	302	7	a	a	DET
ejpam-3745	302	8	mohammadian	mohammadian	NOUN
ejpam-3745	302	9	.	.	PUNCT
ejpam-3745	303	1	on	on	ADP
ejpam-3745	303	2	the	the	DET
ejpam-3745	303	3	zero	zero	NUM
ejpam-3745	303	4	-	-	PUNCT
ejpam-3745	303	5	divisor	divisor	NOUN
ejpam-3745	303	6	graph	graph	NOUN
ejpam-3745	303	7	of	of	ADP
ejpam-3745	303	8	a	a	DET
ejpam-3745	303	9	commutative	commutative	ADJ
ejpam-3745	303	10	ring	ring	NOUN
ejpam-3745	303	11	.	.	PUNCT
ejpam-3745	304	1	journal	journal	PROPN
ejpam-3745	304	2	of	of	ADP
ejpam-3745	304	3	algebra	algebra	PROPN
ejpam-3745	304	4	,	,	PUNCT
ejpam-3745	304	5	274:847	274:847	PROPN
ejpam-3745	304	6	-	-	PUNCT
ejpam-3745	304	7	855	855	NUM
ejpam-3745	304	8	,	,	PUNCT
ejpam-3745	304	9	2004	2004	NUM
ejpam-3745	304	10	.	.	PUNCT
ejpam-3745	305	1	[	[	X
ejpam-3745	305	2	8	8	NUM
ejpam-3745	305	3	]	]	SYM
ejpam-3745	305	4	s	s	PROPN
ejpam-3745	305	5	e	e	X
ejpam-3745	305	6	wright	wright	PROPN
ejpam-3745	305	7	.	.	PUNCT
ejpam-3745	306	1	lengths	length	NOUN
ejpam-3745	306	2	of	of	ADP
ejpam-3745	306	3	paths	path	NOUN
ejpam-3745	306	4	and	and	CCONJ
ejpam-3745	306	5	cycles	cycle	NOUN
ejpam-3745	306	6	in	in	ADP
ejpam-3745	306	7	zero	zero	NUM
ejpam-3745	306	8	-	-	PUNCT
ejpam-3745	306	9	divisor	divisor	NOUN
ejpam-3745	306	10	graphs	graph	NOUN
ejpam-3745	306	11	and	and	CCONJ
ejpam-3745	306	12	digraphs	digraph	NOUN
ejpam-3745	306	13	of	of	ADP
ejpam-3745	306	14	semigroups	semigroup	NOUN
ejpam-3745	306	15	.	.	PUNCT
ejpam-3745	307	1	comm	comm	NOUN
ejpam-3745	307	2	.	.	PUNCT
ejpam-3745	308	1	algebra	algebra	PROPN
ejpam-3745	308	2	,	,	PUNCT
ejpam-3745	308	3	35:1987	35:1987	NUM
ejpam-3745	308	4	-	-	SYM
ejpam-3745	308	5	1991	1991	NUM
ejpam-3745	308	6	,	,	PUNCT
ejpam-3745	308	7	2007	2007	NUM
ejpam-3745	308	8	.	.	PUNCT
ejpam-3745	309	1	[	[	X
ejpam-3745	309	2	9	9	NUM
ejpam-3745	309	3	]	]	X
ejpam-3745	309	4	r	r	NOUN
ejpam-3745	309	5	belsho	belsho	NOUN
ejpam-3745	309	6	,	,	PUNCT
ejpam-3745	309	7	j	j	PROPN
ejpam-3745	309	8	chapman	chapman	PROPN
ejpam-3745	309	9	.	.	PUNCT
ejpam-3745	309	10	planar	planar	PROPN
ejpam-3745	309	11	zero	zero	NUM
ejpam-3745	309	12	-	-	PUNCT
ejpam-3745	309	13	divisor	divisor	NOUN
ejpam-3745	309	14	graphs	graph	NOUN
ejpam-3745	309	15	.	.	PUNCT
ejpam-3745	310	1	j.	j.	PROPN
ejpam-3745	310	2	algebra	algebra	PROPN
ejpam-3745	310	3	,	,	PUNCT
ejpam-3745	310	4	316:471	316:471	PROPN
ejpam-3745	310	5	-	-	PUNCT
ejpam-3745	310	6	480	480	NUM
ejpam-3745	310	7	,	,	PUNCT
ejpam-3745	310	8	2007	2007	NUM
ejpam-3745	310	9	.	.	PUNCT
ejpam-3745	311	1	references	reference	NOUN
ejpam-3745	311	2	1240	1240	NUM
ejpam-3745	311	3	[	[	X
ejpam-3745	311	4	10	10	NUM
ejpam-3745	311	5	]	]	X
ejpam-3745	311	6	a	a	DET
ejpam-3745	311	7	badawi	badawi	NOUN
ejpam-3745	311	8	.	.	PUNCT
ejpam-3745	312	1	on	on	ADP
ejpam-3745	312	2	the	the	DET
ejpam-3745	312	3	dot	dot	NOUN
ejpam-3745	312	4	product	product	NOUN
ejpam-3745	312	5	graph	graph	NOUN
ejpam-3745	312	6	of	of	ADP
ejpam-3745	312	7	a	a	DET
ejpam-3745	312	8	commutative	commutative	ADJ
ejpam-3745	312	9	ring	ring	NOUN
ejpam-3745	312	10	.	.	PUNCT
ejpam-3745	313	1	communications	communication	NOUN
ejpam-3745	313	2	in	in	ADP
ejpam-3745	313	3	algebra	algebra	NOUN
ejpam-3745	313	4	,	,	PUNCT
ejpam-3745	313	5	43:43	43:43	NUM
ejpam-3745	313	6	-	-	SYM
ejpam-3745	313	7	50	50	NUM
ejpam-3745	313	8	,	,	PUNCT
ejpam-3745	313	9	2015	2015	NUM
ejpam-3745	313	10	.	.	PUNCT
ejpam-3745	314	1	[	[	X
ejpam-3745	314	2	11	11	NUM
ejpam-3745	314	3	]	]	X
ejpam-3745	314	4	k	k	PROPN
ejpam-3745	314	5	c	c	PROPN
ejpam-3745	314	6	das	das	PROPN
ejpam-3745	314	7	,	,	PUNCT
ejpam-3745	314	8	n	n	PRON
ejpam-3745	314	9	akgunes	akgune	NOUN
ejpam-3745	314	10	,	,	PUNCT
ejpam-3745	314	11	a	a	DET
ejpam-3745	314	12	s	s	NOUN
ejpam-3745	314	13	cevik	cevik	NOUN
ejpam-3745	314	14	.	.	PUNCT
ejpam-3745	315	1	on	on	ADP
ejpam-3745	315	2	a	a	DET
ejpam-3745	315	3	graph	graph	NOUN
ejpam-3745	315	4	of	of	ADP
ejpam-3745	315	5	monogenic	monogenic	ADJ
ejpam-3745	315	6	semigroups	semigroup	NOUN
ejpam-3745	315	7	.	.	PUNCT
ejpam-3745	315	8	journal	journal	PROPN
ejpam-3745	315	9	of	of	ADP
ejpam-3745	315	10	inequalities	inequality	NOUN
ejpam-3745	315	11	and	and	CCONJ
ejpam-3745	315	12	applications	application	NOUN
ejpam-3745	315	13	,	,	PUNCT
ejpam-3745	315	14	2013:44	2013:44	NUM
ejpam-3745	315	15	,	,	PUNCT
ejpam-3745	315	16	2013	2013	NUM
ejpam-3745	315	17	.	.	PUNCT
ejpam-3745	316	1	[	[	X
ejpam-3745	316	2	12	12	NUM
ejpam-3745	316	3	]	]	PUNCT
ejpam-3745	316	4	n	n	PRON
ejpam-3745	316	5	akgunes	akgune	NOUN
ejpam-3745	316	6	,	,	PUNCT
ejpam-3745	316	7	b	b	PROPN
ejpam-3745	316	8	cagan	cagan	NOUN
ejpam-3745	316	9	.	.	PUNCT
ejpam-3745	317	1	on	on	ADP
ejpam-3745	317	2	the	the	DET
ejpam-3745	317	3	dot	dot	NOUN
ejpam-3745	317	4	product	product	NOUN
ejpam-3745	317	5	of	of	ADP
ejpam-3745	317	6	graphs	graph	NOUN
ejpam-3745	317	7	over	over	ADP
ejpam-3745	317	8	monogenic	monogenic	ADJ
ejpam-3745	317	9	semigroups	semigroup	NOUN
ejpam-3745	317	10	.	.	PUNCT
ejpam-3745	317	11	applied	apply	VERB
ejpam-3745	317	12	mathematics	mathematic	NOUN
ejpam-3745	317	13	and	and	CCONJ
ejpam-3745	317	14	computation	computation	NOUN
ejpam-3745	317	15	,	,	PUNCT
ejpam-3745	317	16	322:1	322:1	NOUN
ejpam-3745	317	17	-	-	SYM
ejpam-3745	317	18	5	5	NUM
ejpam-3745	317	19	,	,	PUNCT
ejpam-3745	317	20	2018	2018	NUM
ejpam-3745	317	21	.	.	PUNCT
ejpam-3745	318	1	[	[	X
ejpam-3745	318	2	13	13	NUM
ejpam-3745	318	3	]	]	PUNCT
ejpam-3745	318	4	h	h	NOUN
ejpam-3745	318	5	wiener	wiener	NOUN
ejpam-3745	318	6	.	.	PUNCT
ejpam-3745	319	1	structural	structural	ADJ
ejpam-3745	319	2	determination	determination	NOUN
ejpam-3745	319	3	of	of	ADP
ejpam-3745	319	4	paraffin	paraffin	NOUN
ejpam-3745	319	5	boiling	boiling	NOUN
ejpam-3745	319	6	points	point	NOUN
ejpam-3745	319	7	.	.	PUNCT
ejpam-3745	320	1	j.	j.	PROPN
ejpam-3745	320	2	amer	amer	PROPN
ejpam-3745	320	3	.	.	PROPN
ejpam-3745	320	4	chem	chem	PROPN
ejpam-3745	320	5	.	.	PUNCT
ejpam-3745	321	1	soc	soc	PROPN
ejpam-3745	321	2	.	.	PROPN
ejpam-3745	321	3	,	,	PUNCT
ejpam-3745	321	4	69:17	69:17	NUM
ejpam-3745	321	5	-	-	SYM
ejpam-3745	321	6	20	20	NUM
ejpam-3745	321	7	,	,	PUNCT
ejpam-3745	321	8	1947	1947	NUM
ejpam-3745	321	9	.	.	PUNCT
ejpam-3745	322	1	[	[	X
ejpam-3745	322	2	14	14	NUM
ejpam-3745	322	3	]	]	X
ejpam-3745	322	4	r	r	NOUN
ejpam-3745	322	5	c	c	NOUN
ejpam-3745	322	6	entringer	entringer	NOUN
ejpam-3745	322	7	,	,	PUNCT
ejpam-3745	322	8	d	d	PROPN
ejpam-3745	322	9	e	e	PROPN
ejpam-3745	322	10	jackson	jackson	PROPN
ejpam-3745	322	11	,	,	PUNCT
ejpam-3745	322	12	d	d	X
ejpam-3745	322	13	a	a	DET
ejpam-3745	322	14	snyder	snyder	NOUN
ejpam-3745	322	15	.	.	PUNCT
ejpam-3745	323	1	distance	distance	NOUN
ejpam-3745	323	2	in	in	ADP
ejpam-3745	323	3	graphs	graph	NOUN
ejpam-3745	323	4	.	.	PUNCT
ejpam-3745	324	1	czech	czech	PROPN
ejpam-3745	324	2	.	.	PUNCT
ejpam-3745	325	1	math	math	PROPN
ejpam-3745	325	2	.	.	PUNCT
ejpam-3745	326	1	j.	j.	PROPN
ejpam-3745	326	2	,	,	PUNCT
ejpam-3745	326	3	26:283	26:283	NUM
ejpam-3745	326	4	-	-	SYM
ejpam-3745	326	5	296	296	NUM
ejpam-3745	326	6	,	,	PUNCT
ejpam-3745	326	7	1976	1976	NUM
ejpam-3745	326	8	.	.	PUNCT
ejpam-3745	327	1	[	[	X
ejpam-3745	327	2	15	15	NUM
ejpam-3745	327	3	]	]	X
ejpam-3745	327	4	a	a	DET
ejpam-3745	327	5	a	a	DET
ejpam-3745	327	6	dobrynin	dobrynin	NOUN
ejpam-3745	327	7	,	,	PUNCT
ejpam-3745	327	8	i	i	PROPN
ejpam-3745	327	9	gutman	gutman	NOUN
ejpam-3745	327	10	.	.	PUNCT
ejpam-3745	328	1	the	the	DET
ejpam-3745	328	2	wiener	wiener	NOUN
ejpam-3745	328	3	index	index	NOUN
ejpam-3745	328	4	for	for	ADP
ejpam-3745	328	5	trees	tree	NOUN
ejpam-3745	328	6	and	and	CCONJ
ejpam-3745	328	7	graphs	graph	NOUN
ejpam-3745	328	8	of	of	ADP
ejpam-3745	328	9	hexagonal	hexagonal	ADJ
ejpam-3745	328	10	systems	system	NOUN
ejpam-3745	328	11	.	.	PUNCT
ejpam-3745	329	1	diskretn	diskretn	PROPN
ejpam-3745	329	2	.	.	PUNCT
ejpam-3745	330	1	anal	anal	PROPN
ejpam-3745	330	2	.	.	PUNCT
ejpam-3745	331	1	issled	issle	VERB
ejpam-3745	331	2	.	.	PUNCT
ejpam-3745	332	1	oper	oper	PROPN
ejpam-3745	332	2	.	.	PROPN
ejpam-3745	332	3	,	,	PUNCT
ejpam-3745	332	4	5(2):34	5(2):34	NUM
ejpam-3745	332	5	-	-	SYM
ejpam-3745	332	6	60	60	NUM
ejpam-3745	332	7	,	,	PUNCT
ejpam-3745	332	8	1998	1998	NUM
ejpam-3745	332	9	.	.	PUNCT
ejpam-3745	333	1	[	[	X
ejpam-3745	333	2	16	16	NUM
ejpam-3745	333	3	]	]	X
ejpam-3745	333	4	a	a	DET
ejpam-3745	333	5	a	a	DET
ejpam-3745	333	6	dobrynin	dobrynin	NOUN
ejpam-3745	333	7	,	,	PUNCT
ejpam-3745	333	8	r	r	NOUN
ejpam-3745	333	9	entringer	entringer	NOUN
ejpam-3745	333	10	,	,	PUNCT
ejpam-3745	333	11	i	i	PROPN
ejpam-3745	333	12	gutman	gutman	PROPN
ejpam-3745	333	13	.	.	PUNCT
ejpam-3745	334	1	wiener	wiener	NOUN
ejpam-3745	334	2	index	index	NOUN
ejpam-3745	334	3	of	of	ADP
ejpam-3745	334	4	trees	tree	NOUN
ejpam-3745	334	5	:	:	PUNCT
ejpam-3745	334	6	theory	theory	NOUN
ejpam-3745	334	7	and	and	CCONJ
ejpam-3745	334	8	applications	application	NOUN
ejpam-3745	334	9	.	.	PUNCT
ejpam-3745	335	1	acta	acta	PROPN
ejpam-3745	335	2	applicandae	applicandae	PROPN
ejpam-3745	335	3	mathematicae	mathematicae	PROPN
ejpam-3745	335	4	,	,	PUNCT
ejpam-3745	335	5	66:211	66:211	NUM
ejpam-3745	335	6	-	-	SYM
ejpam-3745	335	7	249	249	NUM
ejpam-3745	335	8	,	,	PUNCT
ejpam-3745	335	9	2011	2011	NUM
ejpam-3745	335	10	.	.	PUNCT
ejpam-3745	336	1	[	[	X
ejpam-3745	336	2	17	17	NUM
ejpam-3745	336	3	]	]	PUNCT
ejpam-3745	336	4	a	a	DET
ejpam-3745	336	5	a	a	DET
ejpam-3745	336	6	dobrynin	dobrynin	NOUN
ejpam-3745	336	7	,	,	PUNCT
ejpam-3745	336	8	i	i	PROPN
ejpam-3745	336	9	gutman	gutman	PROPN
ejpam-3745	336	10	,	,	PUNCT
ejpam-3745	336	11	s	s	PART
ejpam-3745	336	12	klavžar	klavžar	PROPN
ejpam-3745	336	13	,	,	PUNCT
ejpam-3745	336	14	p	p	PROPN
ejpam-3745	336	15	ziegert	ziegert	PROPN
ejpam-3745	336	16	.	.	PROPN
ejpam-3745	337	1	wiener	wiener	NOUN
ejpam-3745	337	2	index	index	NOUN
ejpam-3745	337	3	of	of	ADP
ejpam-3745	337	4	hexagonal	hexagonal	ADJ
ejpam-3745	337	5	systems	system	NOUN
ejpam-3745	337	6	.	.	PUNCT
ejpam-3745	338	1	acta	acta	PROPN
ejpam-3745	338	2	applicandae	applicandae	PROPN
ejpam-3745	338	3	mathematicae	mathematicae	PROPN
ejpam-3745	338	4	,	,	PUNCT
ejpam-3745	338	5	72:247	72:247	NUM
ejpam-3745	338	6	-	-	SYM
ejpam-3745	338	7	294	294	NUM
ejpam-3745	338	8	,	,	PUNCT
ejpam-3745	338	9	2002	2002	NUM
ejpam-3745	338	10	.	.	PUNCT
ejpam-3745	339	1	[	[	X
ejpam-3745	339	2	18	18	NUM
ejpam-3745	339	3	]	]	PUNCT
ejpam-3745	339	4	n	n	DET
ejpam-3745	339	5	akgunes	akgune	NOUN
ejpam-3745	339	6	,	,	PUNCT
ejpam-3745	339	7	k	k	PROPN
ejpam-3745	339	8	c	c	PROPN
ejpam-3745	339	9	das	das	PROPN
ejpam-3745	339	10	,	,	PUNCT
ejpam-3745	339	11	a	a	DET
ejpam-3745	339	12	s	s	NOUN
ejpam-3745	339	13	cevik	cevik	NOUN
ejpam-3745	339	14	.	.	PUNCT
ejpam-3745	340	1	some	some	DET
ejpam-3745	340	2	properties	property	NOUN
ejpam-3745	340	3	on	on	ADP
ejpam-3745	340	4	the	the	DET
ejpam-3745	340	5	tensor	tensor	NOUN
ejpam-3745	340	6	product	product	NOUN
ejpam-3745	340	7	of	of	ADP
ejpam-3745	340	8	graphs	graph	NOUN
ejpam-3745	340	9	obtained	obtain	VERB
ejpam-3745	340	10	by	by	ADP
ejpam-3745	340	11	monogenic	monogenic	ADJ
ejpam-3745	340	12	semigroups	semigroup	NOUN
ejpam-3745	340	13	.	.	PUNCT
ejpam-3745	341	1	applied	apply	VERB
ejpam-3745	341	2	mathematics	mathematic	NOUN
ejpam-3745	341	3	and	and	CCONJ
ejpam-3745	341	4	computation	computation	NOUN
ejpam-3745	341	5	,	,	PUNCT
ejpam-3745	341	6	235:352	235:352	NOUN
ejpam-3745	341	7	-	-	SYM
ejpam-3745	341	8	357	357	NUM
ejpam-3745	341	9	,	,	PUNCT
ejpam-3745	341	10	2014	2014	NUM
ejpam-3745	341	11	.	.	PUNCT
ejpam-3745	342	1	[	[	X
ejpam-3745	342	2	19	19	NUM
ejpam-3745	342	3	]	]	SYM
ejpam-3745	342	4	n	n	DET
ejpam-3745	342	5	akgunes	akgune	NOUN
ejpam-3745	342	6	,	,	PUNCT
ejpam-3745	342	7	k	k	PROPN
ejpam-3745	342	8	c	c	PROPN
ejpam-3745	342	9	das	das	PROPN
ejpam-3745	342	10	,	,	PUNCT
ejpam-3745	342	11	a	a	DET
ejpam-3745	342	12	s	s	X
ejpam-3745	342	13	cevik	cevik	NOUN
ejpam-3745	342	14	et	et	PROPN
ejpam-3745	342	15	al	al	PROPN
ejpam-3745	342	16	.	.	PUNCT
ejpam-3745	343	1	some	some	DET
ejpam-3745	343	2	properties	property	NOUN
ejpam-3745	343	3	on	on	ADP
ejpam-3745	343	4	the	the	DET
ejpam-3745	343	5	lexicographic	lexicographic	ADJ
ejpam-3745	343	6	product	product	NOUN
ejpam-3745	343	7	of	of	ADP
ejpam-3745	343	8	graphs	graph	NOUN
ejpam-3745	343	9	obtained	obtain	VERB
ejpam-3745	343	10	by	by	ADP
ejpam-3745	343	11	monogenic	monogenic	ADJ
ejpam-3745	343	12	semigroups	semigroup	NOUN
ejpam-3745	343	13	.	.	PUNCT
ejpam-3745	344	1	j	j	PROPN
ejpam-3745	344	2	inequal	inequal	PROPN
ejpam-3745	344	3	appl	appl	PROPN
ejpam-3745	344	4	,	,	PUNCT
ejpam-3745	344	5	2013:238	2013:238	NUM
ejpam-3745	344	6	,	,	PUNCT
ejpam-3745	344	7	2013	2013	NUM
ejpam-3745	344	8	.	.	PUNCT
ejpam-3745	345	1	[	[	X
ejpam-3745	345	2	20	20	NUM
ejpam-3745	345	3	]	]	PUNCT
ejpam-3745	345	4	n	n	PRON
ejpam-3745	345	5	akgunes	akgune	NOUN
ejpam-3745	345	6	.	.	PUNCT
ejpam-3745	346	1	some	some	DET
ejpam-3745	346	2	graph	graph	NOUN
ejpam-3745	346	3	parameters	parameter	NOUN
ejpam-3745	346	4	on	on	ADP
ejpam-3745	346	5	the	the	DET
ejpam-3745	346	6	strong	strong	ADJ
ejpam-3745	346	7	product	product	NOUN
ejpam-3745	346	8	of	of	ADP
ejpam-3745	346	9	monogenic	monogenic	ADJ
ejpam-3745	346	10	semigroup	semigroup	NOUN
ejpam-3745	346	11	graphs	graph	NOUN
ejpam-3745	346	12	.	.	PUNCT
ejpam-3745	347	1	balıkesir	balıkesir	NOUN
ejpam-3745	347	2	üniversitesi	üniversitesi	PROPN
ejpam-3745	347	3	fen	fen	PROPN
ejpam-3745	347	4	bilimleri	bilimleri	PROPN
ejpam-3745	347	5	enstitüsü	enstitüsü	PROPN
ejpam-3745	347	6	dergisi	dergisi	ADJ
ejpam-3745	347	7	,	,	PUNCT
ejpam-3745	347	8	20(1):412	20(1):412	NUM
ejpam-3745	347	9	-	-	PUNCT
ejpam-3745	347	10	420	420	NUM
ejpam-3745	347	11	.	.	PUNCT
ejpam-3745	348	1	2017	2017	NUM
ejpam-3745	348	2	.	.	PUNCT
ejpam-3745	349	1	[	[	X
ejpam-3745	349	2	21	21	NUM
ejpam-3745	349	3	]	]	PUNCT
ejpam-3745	349	4	n	n	PRON
ejpam-3745	349	5	akgunes	akgune	NOUN
ejpam-3745	349	6	.	.	PUNCT
ejpam-3745	350	1	some	some	DET
ejpam-3745	350	2	properties	property	NOUN
ejpam-3745	350	3	on	on	ADP
ejpam-3745	350	4	the	the	DET
ejpam-3745	350	5	disjunctive	disjunctive	ADJ
ejpam-3745	350	6	product	product	NOUN
ejpam-3745	350	7	over	over	ADP
ejpam-3745	350	8	graphs	graph	NOUN
ejpam-3745	350	9	of	of	ADP
ejpam-3745	350	10	monogenic	monogenic	ADJ
ejpam-3745	350	11	semigroups	semigroup	NOUN
ejpam-3745	350	12	.	.	PUNCT
ejpam-3745	351	1	advances	advance	NOUN
ejpam-3745	351	2	and	and	CCONJ
ejpam-3745	351	3	applications	application	NOUN
ejpam-3745	351	4	in	in	ADP
ejpam-3745	351	5	discrete	discrete	ADJ
ejpam-3745	351	6	mathematics	mathematic	NOUN
ejpam-3745	351	7	,	,	PUNCT
ejpam-3745	351	8	19(2):147	19(2):147	NUM
ejpam-3745	351	9	-	-	SYM
ejpam-3745	351	10	159	159	NUM
ejpam-3745	351	11	,	,	PUNCT
ejpam-3745	351	12	2018	2018	NUM
ejpam-3745	351	13	.	.	PUNCT
ejpam-3745	352	1	[	[	X
ejpam-3745	352	2	22	22	NUM
ejpam-3745	352	3	]	]	PUNCT
ejpam-3745	352	4	n	n	PRON
ejpam-3745	352	5	akgunes	akgune	NOUN
ejpam-3745	352	6	,	,	PUNCT
ejpam-3745	352	7	k	k	PROPN
ejpam-3745	352	8	c	c	PROPN
ejpam-3745	352	9	das	das	PROPN
ejpam-3745	352	10	,	,	PUNCT
ejpam-3745	352	11	a	a	DET
ejpam-3745	352	12	s	s	NOUN
ejpam-3745	352	13	cevik	cevik	NOUN
ejpam-3745	352	14	.	.	PUNCT
ejpam-3745	353	1	topological	topological	ADJ
ejpam-3745	353	2	indices	index	NOUN
ejpam-3745	353	3	on	on	ADP
ejpam-3745	353	4	a	a	DET
ejpam-3745	353	5	graph	graph	NOUN
ejpam-3745	353	6	of	of	ADP
ejpam-3745	353	7	monogenic	monogenic	ADJ
ejpam-3745	353	8	semigroups	semigroup	NOUN
ejpam-3745	353	9	.	.	PUNCT
ejpam-3745	354	1	topics	topic	NOUN
ejpam-3745	354	2	in	in	ADP
ejpam-3745	354	3	chemical	chemical	NOUN
ejpam-3745	354	4	graph	graph	NOUN
ejpam-3745	354	5	theory	theory	NOUN
ejpam-3745	354	6	,	,	PUNCT
ejpam-3745	354	7	16:3	16:3	NUM
ejpam-3745	354	8	-	-	SYM
ejpam-3745	354	9	20	20	NUM
ejpam-3745	354	10	,	,	PUNCT
ejpam-3745	354	11	2014	2014	NUM
ejpam-3745	354	12	.	.	PUNCT
ejpam-3745	355	1	[	[	X
ejpam-3745	355	2	23	23	NUM
ejpam-3745	355	3	]	]	PUNCT
ejpam-3745	355	4	n	n	DET
ejpam-3745	355	5	akgunes	akgune	NOUN
ejpam-3745	355	6	,	,	PUNCT
ejpam-3745	355	7	y	y	PROPN
ejpam-3745	355	8	nacaroglu	nacaroglu	PROPN
ejpam-3745	355	9	.	.	PUNCT
ejpam-3745	356	1	on	on	ADP
ejpam-3745	356	2	the	the	DET
ejpam-3745	356	3	sigma	sigma	PROPN
ejpam-3745	356	4	index	index	NOUN
ejpam-3745	356	5	of	of	ADP
ejpam-3745	356	6	the	the	DET
ejpam-3745	356	7	corona	corona	NOUN
ejpam-3745	356	8	products	product	NOUN
ejpam-3745	356	9	of	of	ADP
ejpam-3745	356	10	monogenic	monogenic	ADJ
ejpam-3745	356	11	semigroup	semigroup	NOUN
ejpam-3745	356	12	graphs	graph	NOUN
ejpam-3745	356	13	.	.	PUNCT
ejpam-3745	357	1	journal	journal	NOUN
ejpam-3745	357	2	of	of	ADP
ejpam-3745	357	3	universal	universal	ADJ
ejpam-3745	357	4	mathematics	mathematic	NOUN
ejpam-3745	357	5	,	,	PUNCT
ejpam-3745	357	6	2(1):68	2(1):68	NOUN
ejpam-3745	357	7	-	-	PUNCT
ejpam-3745	357	8	74	74	NUM
ejpam-3745	357	9	,	,	PUNCT
ejpam-3745	357	10	2019	2019	NUM
ejpam-3745	357	11	.	.	PUNCT
ejpam-3745	358	1	[	[	X
ejpam-3745	358	2	24	24	NUM
ejpam-3745	358	3	]	]	PUNCT
ejpam-3745	358	4	n	n	PRON
ejpam-3745	358	5	akgunes	akgune	NOUN
ejpam-3745	358	6	.	.	PUNCT
ejpam-3745	359	1	a	a	DET
ejpam-3745	359	2	further	further	ADJ
ejpam-3745	359	3	note	note	NOUN
ejpam-3745	359	4	on	on	ADP
ejpam-3745	359	5	the	the	DET
ejpam-3745	359	6	graph	graph	NOUN
ejpam-3745	359	7	of	of	ADP
ejpam-3745	359	8	monogenic	monogenic	ADJ
ejpam-3745	359	9	semigroups	semigroup	NOUN
ejpam-3745	359	10	.	.	PUNCT
ejpam-3745	360	1	konuralp	konuralp	PROPN
ejpam-3745	360	2	journal	journal	PROPN
ejpam-3745	360	3	of	of	ADP
ejpam-3745	360	4	mathematics	mathematic	NOUN
ejpam-3745	360	5	,	,	PUNCT
ejpam-3745	360	6	6(1):49	6(1):49	NUM
ejpam-3745	360	7	-	-	SYM
ejpam-3745	360	8	53	53	NUM
ejpam-3745	360	9	,	,	PUNCT
ejpam-3745	360	10	2018	2018	NUM
ejpam-3745	360	11	.	.	PUNCT
ejpam-3745	361	1	[	[	X
ejpam-3745	361	2	25	25	NUM
ejpam-3745	361	3	]	]	PUNCT
ejpam-3745	361	4	n	n	DET
ejpam-3745	361	5	akgunes	akgune	NOUN
ejpam-3745	361	6	,	,	PUNCT
ejpam-3745	361	7	a	a	DET
ejpam-3745	361	8	s	s	NOUN
ejpam-3745	361	9	cevik	cevik	NOUN
ejpam-3745	361	10	,	,	PUNCT
ejpam-3745	361	11	i	i	PRON
ejpam-3745	361	12	n	n	PRON
ejpam-3745	361	13	cangul	cangul	VERB
ejpam-3745	361	14	.	.	PUNCT
ejpam-3745	362	1	new	new	ADJ
ejpam-3745	362	2	indices	index	NOUN
ejpam-3745	362	3	on	on	ADP
ejpam-3745	362	4	special	special	ADJ
ejpam-3745	362	5	graphs	graph	NOUN
ejpam-3745	362	6	.	.	PUNCT
ejpam-3745	363	1	icrapam	icrapam	PROPN
ejpam-3745	363	2	,	,	PUNCT
ejpam-3745	363	3	2014	2014	NUM
ejpam-3745	363	4	.	.	PUNCT