id	sid	tid	token	lemma	pos
ejpam-5166	1	1	european	european	PROPN
ejpam-5166	1	2	journal	journal	PROPN
ejpam-5166	1	3	of	of	ADP
ejpam-5166	1	4	pure	pure	ADJ
ejpam-5166	1	5	and	and	CCONJ
ejpam-5166	1	6	applied	apply	VERB
ejpam-5166	1	7	mathematics	mathematic	NOUN
ejpam-5166	1	8	vol	vol	NOUN
ejpam-5166	1	9	.	.	PROPN
ejpam-5166	2	1	17	17	NUM
ejpam-5166	2	2	,	,	PUNCT
ejpam-5166	2	3	no	no	INTJ
ejpam-5166	2	4	.	.	NOUN
ejpam-5166	2	5	3	3	NUM
ejpam-5166	2	6	,	,	PUNCT
ejpam-5166	2	7	2024	2024	NUM
ejpam-5166	2	8	,	,	PUNCT
ejpam-5166	2	9	1659	1659	NUM
ejpam-5166	2	10	-	-	SYM
ejpam-5166	2	11	1673	1673	NUM
ejpam-5166	2	12	issn	issn	PROPN
ejpam-5166	2	13	1307	1307	NUM
ejpam-5166	2	14	-	-	SYM
ejpam-5166	2	15	5543	5543	NUM
ejpam-5166	2	16	–	–	PUNCT
ejpam-5166	3	1	ejpam.com	ejpam.com	X
ejpam-5166	3	2	published	publish	VERB
ejpam-5166	3	3	by	by	ADP
ejpam-5166	3	4	new	new	PROPN
ejpam-5166	3	5	york	york	PROPN
ejpam-5166	3	6	business	business	PROPN
ejpam-5166	3	7	global	global	PROPN
ejpam-5166	3	8	the	the	DET
ejpam-5166	3	9	wiener	wiener	NOUN
ejpam-5166	3	10	index	index	NOUN
ejpam-5166	3	11	of	of	ADP
ejpam-5166	3	12	prime	prime	ADJ
ejpam-5166	3	13	graph	graph	NOUN
ejpam-5166	3	14	pg(zn	pg(zn	PROPN
ejpam-5166	3	15	)	)	PUNCT
ejpam-5166	3	16	noor	noor	PROPN
ejpam-5166	3	17	hidayat1,∗	hidayat1,∗	PROPN
ejpam-5166	3	18	,	,	PUNCT
ejpam-5166	3	19	vira	vira	PROPN
ejpam-5166	3	20	hari	hari	PROPN
ejpam-5166	3	21	krisnawati1	krisnawati1	PROPN
ejpam-5166	3	22	,	,	PUNCT
ejpam-5166	3	23	muhammad	muhammad	PROPN
ejpam-5166	3	24	husnul	husnul	PROPN
ejpam-5166	3	25	khuluq1	khuluq1	PROPN
ejpam-5166	3	26	,	,	PUNCT
ejpam-5166	3	27	farah	farah	PROPN
ejpam-5166	3	28	maulidya	maulidya	PROPN
ejpam-5166	3	29	fatimah1	fatimah1	PROPN
ejpam-5166	3	30	,	,	PUNCT
ejpam-5166	3	31	ayunda	ayunda	SCONJ
ejpam-5166	3	32	faizatul	faizatul	PROPN
ejpam-5166	3	33	musyarrofah1	musyarrofah1	PROPN
ejpam-5166	3	34	1	1	NUM
ejpam-5166	3	35	department	department	NOUN
ejpam-5166	3	36	of	of	ADP
ejpam-5166	3	37	mathematics	mathematic	NOUN
ejpam-5166	3	38	,	,	PUNCT
ejpam-5166	3	39	faculty	faculty	NOUN
ejpam-5166	3	40	of	of	ADP
ejpam-5166	3	41	mathematics	mathematic	NOUN
ejpam-5166	3	42	and	and	CCONJ
ejpam-5166	3	43	natural	natural	ADJ
ejpam-5166	3	44	sciences	science	NOUN
ejpam-5166	3	45	,	,	PUNCT
ejpam-5166	3	46	university	university	NOUN
ejpam-5166	3	47	of	of	ADP
ejpam-5166	3	48	brawijaya	brawijaya	PROPN
ejpam-5166	3	49	,	,	PUNCT
ejpam-5166	3	50	malang	malang	PROPN
ejpam-5166	3	51	,	,	PUNCT
ejpam-5166	3	52	east	east	PROPN
ejpam-5166	3	53	java	java	PROPN
ejpam-5166	3	54	,	,	PUNCT
ejpam-5166	3	55	indonesia	indonesia	PROPN
ejpam-5166	3	56	abstract	abstract	NOUN
ejpam-5166	3	57	.	.	PUNCT
ejpam-5166	4	1	let	let	VERB
ejpam-5166	4	2	g	g	PROPN
ejpam-5166	4	3	=	=	SYM
ejpam-5166	4	4	(	(	PUNCT
ejpam-5166	4	5	v	v	NOUN
ejpam-5166	4	6	,	,	PUNCT
ejpam-5166	4	7	e	e	NOUN
ejpam-5166	4	8	)	)	PUNCT
ejpam-5166	4	9	be	be	AUX
ejpam-5166	4	10	a	a	DET
ejpam-5166	4	11	simple	simple	ADJ
ejpam-5166	4	12	graph	graph	NOUN
ejpam-5166	4	13	and	and	CCONJ
ejpam-5166	4	14	(	(	PUNCT
ejpam-5166	4	15	r,+	r,+	NUM
ejpam-5166	4	16	,	,	PUNCT
ejpam-5166	4	17	·	·	PUNCT
ejpam-5166	4	18	)	)	PUNCT
ejpam-5166	4	19	be	be	AUX
ejpam-5166	4	20	a	a	DET
ejpam-5166	4	21	ring	ring	NOUN
ejpam-5166	4	22	with	with	ADP
ejpam-5166	4	23	zero	zero	NUM
ejpam-5166	4	24	element	element	NOUN
ejpam-5166	4	25	0r	0r	NUM
ejpam-5166	4	26	.	.	PUNCT
ejpam-5166	5	1	the	the	DET
ejpam-5166	5	2	wiener	wiener	NOUN
ejpam-5166	5	3	index	index	NOUN
ejpam-5166	5	4	of	of	ADP
ejpam-5166	5	5	g	g	NOUN
ejpam-5166	5	6	,	,	PUNCT
ejpam-5166	5	7	denoted	denote	VERB
ejpam-5166	5	8	by	by	ADP
ejpam-5166	5	9	w	w	PROPN
ejpam-5166	5	10	(	(	PUNCT
ejpam-5166	5	11	g	g	NOUN
ejpam-5166	5	12	)	)	PUNCT
ejpam-5166	5	13	,	,	PUNCT
ejpam-5166	5	14	is	be	AUX
ejpam-5166	5	15	defined	define	VERB
ejpam-5166	5	16	as	as	ADP
ejpam-5166	5	17	the	the	DET
ejpam-5166	5	18	sum	sum	NOUN
ejpam-5166	5	19	of	of	ADP
ejpam-5166	5	20	distances	distance	NOUN
ejpam-5166	5	21	of	of	ADP
ejpam-5166	5	22	every	every	DET
ejpam-5166	5	23	vertex	vertex	NOUN
ejpam-5166	5	24	u	u	NOUN
ejpam-5166	5	25	and	and	CCONJ
ejpam-5166	5	26	v	v	NOUN
ejpam-5166	5	27	,	,	PUNCT
ejpam-5166	5	28	or	or	CCONJ
ejpam-5166	5	29	half	half	NOUN
ejpam-5166	5	30	of	of	ADP
ejpam-5166	5	31	the	the	DET
ejpam-5166	5	32	sum	sum	NOUN
ejpam-5166	5	33	of	of	ADP
ejpam-5166	5	34	all	all	DET
ejpam-5166	5	35	entries	entry	NOUN
ejpam-5166	5	36	of	of	ADP
ejpam-5166	5	37	its	its	PRON
ejpam-5166	5	38	distance	distance	NOUN
ejpam-5166	5	39	matrix	matrix	NOUN
ejpam-5166	5	40	.	.	PUNCT
ejpam-5166	6	1	the	the	DET
ejpam-5166	6	2	prime	prime	ADJ
ejpam-5166	6	3	graph	graph	NOUN
ejpam-5166	6	4	of	of	ADP
ejpam-5166	6	5	r	r	NOUN
ejpam-5166	6	6	,	,	PUNCT
ejpam-5166	6	7	denoted	denote	VERB
ejpam-5166	6	8	by	by	ADP
ejpam-5166	6	9	pg(r	pg(r	PROPN
ejpam-5166	6	10	)	)	PUNCT
ejpam-5166	6	11	,	,	PUNCT
ejpam-5166	6	12	is	be	AUX
ejpam-5166	6	13	defined	define	VERB
ejpam-5166	6	14	as	as	ADP
ejpam-5166	6	15	a	a	DET
ejpam-5166	6	16	graph	graph	NOUN
ejpam-5166	6	17	with	with	ADP
ejpam-5166	6	18	v	v	NOUN
ejpam-5166	6	19	(	(	PUNCT
ejpam-5166	6	20	pg(r	pg(r	NOUN
ejpam-5166	6	21	)	)	PUNCT
ejpam-5166	6	22	)	)	PUNCT
ejpam-5166	7	1	=	=	PUNCT
ejpam-5166	7	2	r	r	NOUN
ejpam-5166	7	3	such	such	ADJ
ejpam-5166	7	4	that	that	DET
ejpam-5166	7	5	uv	uv	PROPN
ejpam-5166	7	6	∈	∈	PROPN
ejpam-5166	7	7	e(pg(r	e(pg(r	PROPN
ejpam-5166	7	8	)	)	PUNCT
ejpam-5166	7	9	)	)	PUNCT
ejpam-5166	8	1	if	if	SCONJ
ejpam-5166	8	2	and	and	CCONJ
ejpam-5166	8	3	only	only	ADV
ejpam-5166	8	4	if	if	SCONJ
ejpam-5166	8	5	urv	urv	ADP
ejpam-5166	8	6	=	=	SYM
ejpam-5166	8	7	{	{	PUNCT
ejpam-5166	8	8	0r	0r	NOUN
ejpam-5166	8	9	}	}	PUNCT
ejpam-5166	8	10	or	or	CCONJ
ejpam-5166	8	11	vru	vru	NOUN
ejpam-5166	8	12	=	=	PUNCT
ejpam-5166	8	13	{	{	PUNCT
ejpam-5166	8	14	0r	0r	NUM
ejpam-5166	8	15	}	}	PUNCT
ejpam-5166	8	16	.	.	PUNCT
ejpam-5166	9	1	in	in	ADP
ejpam-5166	9	2	this	this	DET
ejpam-5166	9	3	article	article	NOUN
ejpam-5166	9	4	,	,	PUNCT
ejpam-5166	9	5	we	we	PRON
ejpam-5166	9	6	determine	determine	VERB
ejpam-5166	9	7	the	the	DET
ejpam-5166	9	8	wiener	wiener	NOUN
ejpam-5166	9	9	index	index	NOUN
ejpam-5166	9	10	of	of	ADP
ejpam-5166	9	11	pg(zn	pg(zn	PROPN
ejpam-5166	9	12	)	)	PUNCT
ejpam-5166	9	13	in	in	ADP
ejpam-5166	9	14	some	some	DET
ejpam-5166	9	15	cases	case	NOUN
ejpam-5166	9	16	n	n	VERB
ejpam-5166	9	17	by	by	ADP
ejpam-5166	9	18	constructing	construct	VERB
ejpam-5166	9	19	its	its	PRON
ejpam-5166	9	20	distance	distance	NOUN
ejpam-5166	9	21	matrix	matrix	NOUN
ejpam-5166	9	22	.	.	PUNCT
ejpam-5166	10	1	we	we	PRON
ejpam-5166	10	2	partition	partition	VERB
ejpam-5166	10	3	the	the	DET
ejpam-5166	10	4	set	set	NOUN
ejpam-5166	10	5	zn	zn	PROPN
ejpam-5166	10	6	into	into	ADP
ejpam-5166	10	7	three	three	NUM
ejpam-5166	10	8	types	type	NOUN
ejpam-5166	10	9	of	of	ADP
ejpam-5166	10	10	sets	set	NOUN
ejpam-5166	10	11	,	,	PUNCT
ejpam-5166	10	12	namely	namely	ADV
ejpam-5166	10	13	zero	zero	NUM
ejpam-5166	10	14	sets	set	NOUN
ejpam-5166	10	15	,	,	PUNCT
ejpam-5166	10	16	nontrivial	nontrivial	NOUN
ejpam-5166	10	17	zero	zero	NUM
ejpam-5166	10	18	divisor	divisor	NOUN
ejpam-5166	10	19	sets	set	NOUN
ejpam-5166	10	20	,	,	PUNCT
ejpam-5166	10	21	and	and	CCONJ
ejpam-5166	10	22	unit	unit	NOUN
ejpam-5166	10	23	sets	set	NOUN
ejpam-5166	10	24	.	.	PUNCT
ejpam-5166	11	1	there	there	PRON
ejpam-5166	11	2	are	be	VERB
ejpam-5166	11	3	two	two	NUM
ejpam-5166	11	4	objectives	objective	NOUN
ejpam-5166	11	5	to	to	PART
ejpam-5166	11	6	be	be	AUX
ejpam-5166	11	7	achieved	achieve	VERB
ejpam-5166	11	8	.	.	PUNCT
ejpam-5166	12	1	firstly	firstly	ADV
ejpam-5166	12	2	,	,	PUNCT
ejpam-5166	12	3	we	we	PRON
ejpam-5166	12	4	revise	revise	VERB
ejpam-5166	12	5	the	the	DET
ejpam-5166	12	6	wiener	wiener	NOUN
ejpam-5166	12	7	index	index	NOUN
ejpam-5166	12	8	formula	formula	NOUN
ejpam-5166	12	9	of	of	ADP
ejpam-5166	12	10	pg(zn	pg(zn	NOUN
ejpam-5166	12	11	)	)	PUNCT
ejpam-5166	12	12	for	for	ADP
ejpam-5166	12	13	n	n	NOUN
ejpam-5166	12	14	=	=	SYM
ejpam-5166	12	15	p2	p2	PROPN
ejpam-5166	12	16	and	and	CCONJ
ejpam-5166	12	17	n	n	CCONJ
ejpam-5166	12	18	=	=	PROPN
ejpam-5166	12	19	p3	p3	PROPN
ejpam-5166	12	20	for	for	ADP
ejpam-5166	12	21	prime	prime	ADJ
ejpam-5166	12	22	number	number	NOUN
ejpam-5166	12	23	p	p	NOUN
ejpam-5166	12	24	and	and	CCONJ
ejpam-5166	12	25	we	we	PRON
ejpam-5166	12	26	compare	compare	VERB
ejpam-5166	12	27	this	this	DET
ejpam-5166	12	28	results	result	NOUN
ejpam-5166	12	29	with	with	ADP
ejpam-5166	12	30	the	the	DET
ejpam-5166	12	31	results	result	NOUN
ejpam-5166	12	32	carried	carry	VERB
ejpam-5166	12	33	out	out	ADP
ejpam-5166	12	34	by	by	ADP
ejpam-5166	12	35	previous	previous	ADJ
ejpam-5166	12	36	researchers	researcher	NOUN
ejpam-5166	12	37	.	.	PUNCT
ejpam-5166	13	1	secondly	secondly	ADV
ejpam-5166	13	2	,	,	PUNCT
ejpam-5166	13	3	we	we	PRON
ejpam-5166	13	4	determine	determine	VERB
ejpam-5166	13	5	the	the	DET
ejpam-5166	13	6	wiener	wiener	NOUN
ejpam-5166	13	7	index	index	NOUN
ejpam-5166	13	8	formula	formula	NOUN
ejpam-5166	13	9	of	of	ADP
ejpam-5166	13	10	pg(zn	pg(zn	NOUN
ejpam-5166	13	11	)	)	PUNCT
ejpam-5166	13	12	for	for	ADP
ejpam-5166	13	13	n	n	PROPN
ejpam-5166	13	14	=	=	SYM
ejpam-5166	13	15	pq	pq	PROPN
ejpam-5166	13	16	,	,	PUNCT
ejpam-5166	13	17	n	n	NOUN
ejpam-5166	13	18	=	=	PUNCT
ejpam-5166	13	19	p2q	p2q	NOUN
ejpam-5166	13	20	,	,	PUNCT
ejpam-5166	13	21	n	n	NOUN
ejpam-5166	13	22	=	=	SYM
ejpam-5166	13	23	p2q2	p2q2	NOUN
ejpam-5166	13	24	,	,	PUNCT
ejpam-5166	13	25	and	and	CCONJ
ejpam-5166	13	26	n	n	CCONJ
ejpam-5166	13	27	=	=	SYM
ejpam-5166	13	28	pqr	pqr	PROPN
ejpam-5166	13	29	for	for	ADP
ejpam-5166	13	30	distinct	distinct	ADJ
ejpam-5166	13	31	prime	prime	ADJ
ejpam-5166	13	32	numbers	number	NOUN
ejpam-5166	13	33	p	p	X
ejpam-5166	13	34	,	,	PUNCT
ejpam-5166	13	35	q	q	X
ejpam-5166	13	36	,	,	PUNCT
ejpam-5166	13	37	and	and	CCONJ
ejpam-5166	13	38	r.	r.	PROPN
ejpam-5166	13	39	2020	2020	NUM
ejpam-5166	13	40	mathematics	mathematics	PROPN
ejpam-5166	13	41	subject	subject	NOUN
ejpam-5166	13	42	classifications	classification	NOUN
ejpam-5166	13	43	:	:	PUNCT
ejpam-5166	13	44	05c09	05c09	NUM
ejpam-5166	13	45	,	,	PUNCT
ejpam-5166	13	46	05c25	05c25	NUM
ejpam-5166	13	47	.	.	PUNCT
ejpam-5166	14	1	key	key	ADJ
ejpam-5166	14	2	words	word	NOUN
ejpam-5166	14	3	and	and	CCONJ
ejpam-5166	14	4	phrases	phrase	NOUN
ejpam-5166	14	5	:	:	PUNCT
ejpam-5166	14	6	distance	distance	NOUN
ejpam-5166	14	7	matrix	matrix	NOUN
ejpam-5166	14	8	,	,	PUNCT
ejpam-5166	14	9	prime	prime	ADJ
ejpam-5166	14	10	graph	graph	NOUN
ejpam-5166	14	11	,	,	PUNCT
ejpam-5166	14	12	ring	ring	NOUN
ejpam-5166	14	13	,	,	PUNCT
ejpam-5166	14	14	wiener	wiener	NOUN
ejpam-5166	14	15	index	index	NOUN
ejpam-5166	14	16	1	1	NUM
ejpam-5166	14	17	.	.	PUNCT
ejpam-5166	14	18	introduction	introduction	NOUN
ejpam-5166	14	19	a	a	DET
ejpam-5166	14	20	graph	graph	NOUN
ejpam-5166	14	21	g	g	PROPN
ejpam-5166	14	22	is	be	AUX
ejpam-5166	14	23	a	a	DET
ejpam-5166	14	24	system	system	NOUN
ejpam-5166	14	25	consisting	consist	VERB
ejpam-5166	14	26	of	of	ADP
ejpam-5166	14	27	a	a	DET
ejpam-5166	14	28	finite	finite	ADJ
ejpam-5166	14	29	non	non	ADJ
ejpam-5166	14	30	-	-	ADJ
ejpam-5166	14	31	empty	empty	ADJ
ejpam-5166	14	32	vertex	vertex	NOUN
ejpam-5166	14	33	set	set	NOUN
ejpam-5166	14	34	and	and	CCONJ
ejpam-5166	14	35	a	a	DET
ejpam-5166	14	36	finite	finite	ADJ
ejpam-5166	14	37	edge	edge	NOUN
ejpam-5166	14	38	set	set	VERB
ejpam-5166	14	39	such	such	ADJ
ejpam-5166	14	40	that	that	SCONJ
ejpam-5166	14	41	every	every	DET
ejpam-5166	14	42	element	element	NOUN
ejpam-5166	14	43	is	be	AUX
ejpam-5166	14	44	identified	identify	VERB
ejpam-5166	14	45	with	with	ADP
ejpam-5166	14	46	a	a	DET
ejpam-5166	14	47	pair	pair	NOUN
ejpam-5166	14	48	of	of	ADP
ejpam-5166	14	49	vertices	vertex	NOUN
ejpam-5166	14	50	[	[	X
ejpam-5166	14	51	14	14	NUM
ejpam-5166	14	52	]	]	PUNCT
ejpam-5166	14	53	.	.	PUNCT
ejpam-5166	15	1	the	the	DET
ejpam-5166	15	2	development	development	NOUN
ejpam-5166	15	3	of	of	ADP
ejpam-5166	15	4	graph	graph	NOUN
ejpam-5166	15	5	theory	theory	NOUN
ejpam-5166	15	6	and	and	CCONJ
ejpam-5166	15	7	its	its	PRON
ejpam-5166	15	8	applications	application	NOUN
ejpam-5166	15	9	has	have	AUX
ejpam-5166	15	10	been	be	AUX
ejpam-5166	15	11	carried	carry	VERB
ejpam-5166	15	12	out	out	ADP
ejpam-5166	15	13	by	by	ADP
ejpam-5166	15	14	many	many	ADJ
ejpam-5166	15	15	researchers	researcher	NOUN
ejpam-5166	15	16	.	.	PUNCT
ejpam-5166	16	1	one	one	NUM
ejpam-5166	16	2	of	of	ADP
ejpam-5166	16	3	the	the	DET
ejpam-5166	16	4	developments	development	NOUN
ejpam-5166	16	5	is	be	AUX
ejpam-5166	16	6	the	the	DET
ejpam-5166	16	7	construction	construction	NOUN
ejpam-5166	16	8	of	of	ADP
ejpam-5166	16	9	graphs	graph	NOUN
ejpam-5166	16	10	be	be	AUX
ejpam-5166	16	11	related	relate	VERB
ejpam-5166	16	12	with	with	ADP
ejpam-5166	16	13	algebraic	algebraic	ADJ
ejpam-5166	16	14	structures	structure	NOUN
ejpam-5166	16	15	.	.	PUNCT
ejpam-5166	17	1	the	the	DET
ejpam-5166	17	2	study	study	NOUN
ejpam-5166	17	3	of	of	ADP
ejpam-5166	17	4	graph	graph	NOUN
ejpam-5166	17	5	theory	theory	NOUN
ejpam-5166	17	6	for	for	ADP
ejpam-5166	17	7	a	a	DET
ejpam-5166	17	8	commutative	commutative	ADJ
ejpam-5166	17	9	ring	ring	NOUN
ejpam-5166	17	10	was	be	AUX
ejpam-5166	17	11	began	begin	VERB
ejpam-5166	17	12	in	in	ADP
ejpam-5166	17	13	1988	1988	NUM
ejpam-5166	17	14	,	,	PUNCT
ejpam-5166	17	15	when	when	SCONJ
ejpam-5166	17	16	beck	beck	NOUN
ejpam-5166	17	17	in	in	ADP
ejpam-5166	17	18	[	[	X
ejpam-5166	17	19	11	11	NUM
ejpam-5166	17	20	]	]	PUNCT
ejpam-5166	17	21	introduced	introduce	VERB
ejpam-5166	17	22	the	the	DET
ejpam-5166	17	23	notion	notion	NOUN
ejpam-5166	17	24	of	of	ADP
ejpam-5166	17	25	zero	zero	NUM
ejpam-5166	17	26	divisor	divisor	NOUN
ejpam-5166	17	27	of	of	ADP
ejpam-5166	17	28	the	the	DET
ejpam-5166	17	29	graph	graph	NOUN
ejpam-5166	17	30	.	.	PUNCT
ejpam-5166	18	1	other	other	ADJ
ejpam-5166	18	2	construction	construction	NOUN
ejpam-5166	18	3	of	of	ADP
ejpam-5166	18	4	graphs	graph	NOUN
ejpam-5166	18	5	related	relate	VERB
ejpam-5166	18	6	to	to	ADP
ejpam-5166	18	7	algebraic	algebraic	ADJ
ejpam-5166	18	8	structures	structure	NOUN
ejpam-5166	18	9	is	be	AUX
ejpam-5166	18	10	zero	zero	NUM
ejpam-5166	18	11	divisor	divisor	NOUN
ejpam-5166	18	12	graphs	graph	NOUN
ejpam-5166	18	13	(	(	PUNCT
ejpam-5166	18	14	[	[	X
ejpam-5166	18	15	4	4	NUM
ejpam-5166	18	16	]	]	PUNCT
ejpam-5166	18	17	,	,	PUNCT
ejpam-5166	18	18	[	[	X
ejpam-5166	18	19	5	5	NUM
ejpam-5166	18	20	]	]	PUNCT
ejpam-5166	18	21	,	,	PUNCT
ejpam-5166	18	22	and	and	CCONJ
ejpam-5166	19	1	[	[	X
ejpam-5166	19	2	20	20	NUM
ejpam-5166	19	3	]	]	NUM
ejpam-5166	19	4	)	)	PUNCT
ejpam-5166	19	5	.	.	PUNCT
ejpam-5166	20	1	further	further	ADJ
ejpam-5166	20	2	development	development	NOUN
ejpam-5166	20	3	was	be	AUX
ejpam-5166	20	4	carried	carry	VERB
ejpam-5166	20	5	out	out	ADP
ejpam-5166	20	6	by	by	ADP
ejpam-5166	20	7	anderson	anderson	PROPN
ejpam-5166	20	8	and	and	CCONJ
ejpam-5166	20	9	badawi	badawi	VERB
ejpam-5166	20	10	in	in	ADP
ejpam-5166	20	11	2008	2008	NUM
ejpam-5166	20	12	by	by	ADP
ejpam-5166	20	13	defining	define	VERB
ejpam-5166	20	14	and	and	CCONJ
ejpam-5166	20	15	discussing	discuss	VERB
ejpam-5166	20	16	the	the	DET
ejpam-5166	20	17	properties	property	NOUN
ejpam-5166	20	18	of	of	ADP
ejpam-5166	20	19	the	the	DET
ejpam-5166	20	20	total	total	ADJ
ejpam-5166	20	21	∗corresponding	∗corresponde	VERB
ejpam-5166	20	22	author	author	NOUN
ejpam-5166	20	23	.	.	PUNCT
ejpam-5166	21	1	doi	doi	NOUN
ejpam-5166	21	2	:	:	PUNCT
ejpam-5166	21	3	https://doi.org/10.29020/nybg.ejpam.v17i3.5166	https://doi.org/10.29020/nybg.ejpam.v17i3.5166	ADJ
ejpam-5166	21	4	email	email	NOUN
ejpam-5166	21	5	addresses	address	NOUN
ejpam-5166	21	6	:	:	PUNCT
ejpam-5166	21	7	noorh@ub.ac.id	noorh@ub.ac.id	PROPN
ejpam-5166	21	8	(	(	PUNCT
ejpam-5166	21	9	n.	n.	PROPN
ejpam-5166	21	10	hidayat	hidayat	PROPN
ejpam-5166	21	11	)	)	PUNCT
ejpam-5166	21	12	,	,	PUNCT
ejpam-5166	21	13	virahari@ub.ac.id	virahari@ub.ac.id	PROPN
ejpam-5166	21	14	(	(	PUNCT
ejpam-5166	21	15	v.	v.	ADP
ejpam-5166	21	16	h.	h.	PROPN
ejpam-5166	21	17	krisnawati	krisnawati	PROPN
ejpam-5166	21	18	)	)	PUNCT
ejpam-5166	21	19	,	,	PUNCT
ejpam-5166	21	20	husnulkhu@gmail.com	husnulkhu@gmail.com	X
ejpam-5166	21	21	(	(	PUNCT
ejpam-5166	21	22	m.	m.	PROPN
ejpam-5166	21	23	h.	h.	PROPN
ejpam-5166	21	24	khuluq	khuluq	PROPN
ejpam-5166	21	25	)	)	PUNCT
ejpam-5166	21	26	,	,	PUNCT
ejpam-5166	21	27	farahmaulidya19@gmail.com	farahmaulidya19@gmail.com	PROPN
ejpam-5166	21	28	(	(	PUNCT
ejpam-5166	21	29	f.	f.	PROPN
ejpam-5166	21	30	m.	m.	PROPN
ejpam-5166	21	31	fatimah	fatimah	PROPN
ejpam-5166	21	32	)	)	PUNCT
ejpam-5166	21	33	,	,	PUNCT
ejpam-5166	21	34	ayundafaiza02@gmail.com	ayundafaiza02@gmail.com	X
ejpam-5166	21	35	(	(	PUNCT
ejpam-5166	21	36	a.	a.	PROPN
ejpam-5166	21	37	f.	f.	PROPN
ejpam-5166	21	38	musyarrofah	musyarrofah	PROPN
ejpam-5166	21	39	)	)	PUNCT
ejpam-5166	21	40	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-5166	21	41	1659	1659	NUM
ejpam-5166	21	42	©	©	ADP
ejpam-5166	21	43	2024	2024	NUM
ejpam-5166	21	44	ejpam	ejpam	NOUN
ejpam-5166	21	45	all	all	DET
ejpam-5166	21	46	rights	right	NOUN
ejpam-5166	21	47	reserved	reserve	VERB
ejpam-5166	21	48	.	.	PUNCT
ejpam-5166	22	1	n.	n.	PROPN
ejpam-5166	22	2	hidayat	hidayat	PROPN
ejpam-5166	22	3	et	et	PROPN
ejpam-5166	22	4	al	al	PROPN
ejpam-5166	22	5	/	/	PUNCT
ejpam-5166	22	6	eur	eur	PROPN
ejpam-5166	22	7	.	.	PUNCT
ejpam-5166	23	1	j.	j.	PROPN
ejpam-5166	23	2	pure	pure	PROPN
ejpam-5166	23	3	appl	appl	PROPN
ejpam-5166	23	4	.	.	PROPN
ejpam-5166	23	5	math	math	PROPN
ejpam-5166	23	6	,	,	PUNCT
ejpam-5166	23	7	17	17	NUM
ejpam-5166	23	8	(	(	PUNCT
ejpam-5166	23	9	3	3	NUM
ejpam-5166	23	10	)	)	PUNCT
ejpam-5166	23	11	(	(	PUNCT
ejpam-5166	23	12	2024	2024	NUM
ejpam-5166	23	13	)	)	PUNCT
ejpam-5166	23	14	,	,	PUNCT
ejpam-5166	23	15	1659	1659	NUM
ejpam-5166	23	16	-	-	SYM
ejpam-5166	23	17	1673	1673	NUM
ejpam-5166	23	18	1660	1660	NUM
ejpam-5166	23	19	graph	graph	NOUN
ejpam-5166	23	20	of	of	ADP
ejpam-5166	23	21	the	the	DET
ejpam-5166	23	22	ring	ring	NOUN
ejpam-5166	23	23	[	[	X
ejpam-5166	23	24	6	6	NUM
ejpam-5166	23	25	]	]	PUNCT
ejpam-5166	23	26	.	.	PUNCT
ejpam-5166	24	1	in	in	ADP
ejpam-5166	24	2	2010	2010	NUM
ejpam-5166	24	3	subhakar	subhakar	NOUN
ejpam-5166	24	4	discussed	discuss	VERB
ejpam-5166	24	5	about	about	ADP
ejpam-5166	24	6	associate	associate	ADJ
ejpam-5166	24	7	ring	ring	NOUN
ejpam-5166	24	8	graph	graph	NOUN
ejpam-5166	24	9	[	[	X
ejpam-5166	24	10	37	37	NUM
ejpam-5166	24	11	]	]	PUNCT
ejpam-5166	24	12	.	.	PUNCT
ejpam-5166	25	1	ashrafi	ashrafi	PROPN
ejpam-5166	25	2	et	et	PROPN
ejpam-5166	25	3	al	al	PROPN
ejpam-5166	26	1	[	[	X
ejpam-5166	26	2	7	7	NUM
ejpam-5166	26	3	]	]	PUNCT
ejpam-5166	26	4	investigated	investigate	VERB
ejpam-5166	26	5	the	the	DET
ejpam-5166	26	6	basic	basic	ADJ
ejpam-5166	26	7	properties	property	NOUN
ejpam-5166	26	8	of	of	ADP
ejpam-5166	26	9	unit	unit	NOUN
ejpam-5166	26	10	graph	graph	NOUN
ejpam-5166	26	11	and	and	CCONJ
ejpam-5166	26	12	given	give	VERB
ejpam-5166	26	13	some	some	DET
ejpam-5166	26	14	characterization	characterization	NOUN
ejpam-5166	26	15	results	result	NOUN
ejpam-5166	26	16	regarding	regard	VERB
ejpam-5166	26	17	connectedness	connectedness	NOUN
ejpam-5166	26	18	,	,	PUNCT
ejpam-5166	26	19	chromatic	chromatic	ADJ
ejpam-5166	26	20	,	,	PUNCT
ejpam-5166	26	21	index	index	NOUN
ejpam-5166	26	22	,	,	PUNCT
ejpam-5166	26	23	diameter	diameter	NOUN
ejpam-5166	26	24	,	,	PUNCT
ejpam-5166	26	25	girth	girth	ADV
ejpam-5166	26	26	,	,	PUNCT
ejpam-5166	26	27	and	and	CCONJ
ejpam-5166	26	28	planarity	planarity	NOUN
ejpam-5166	26	29	of	of	ADP
ejpam-5166	26	30	total	total	ADJ
ejpam-5166	26	31	graph	graph	NOUN
ejpam-5166	26	32	.	.	PUNCT
ejpam-5166	27	1	the	the	DET
ejpam-5166	27	2	development	development	NOUN
ejpam-5166	27	3	of	of	ADP
ejpam-5166	27	4	prime	prime	ADJ
ejpam-5166	27	5	graph	graph	NOUN
ejpam-5166	27	6	was	be	AUX
ejpam-5166	27	7	studied	study	VERB
ejpam-5166	27	8	by	by	ADP
ejpam-5166	27	9	bhavanari	bhavanari	PROPN
ejpam-5166	27	10	et	et	PROPN
ejpam-5166	27	11	al	al	PROPN
ejpam-5166	27	12	in	in	ADP
ejpam-5166	27	13	2010	2010	NUM
ejpam-5166	28	1	[	[	X
ejpam-5166	28	2	12	12	NUM
ejpam-5166	28	3	]	]	PUNCT
ejpam-5166	28	4	.	.	PUNCT
ejpam-5166	29	1	they	they	PRON
ejpam-5166	29	2	presented	present	VERB
ejpam-5166	29	3	several	several	ADJ
ejpam-5166	29	4	examples	example	NOUN
ejpam-5166	29	5	of	of	ADP
ejpam-5166	29	6	prime	prime	ADJ
ejpam-5166	29	7	graphs	graph	NOUN
ejpam-5166	29	8	on	on	ADP
ejpam-5166	29	9	rings	ring	NOUN
ejpam-5166	29	10	zn	zn	PROPN
ejpam-5166	29	11	for	for	ADP
ejpam-5166	29	12	n	n	CCONJ
ejpam-5166	29	13	prime	prime	ADJ
ejpam-5166	29	14	numbers	number	NOUN
ejpam-5166	29	15	.	.	PUNCT
ejpam-5166	30	1	they	they	PRON
ejpam-5166	30	2	also	also	ADV
ejpam-5166	30	3	proved	prove	VERB
ejpam-5166	30	4	the	the	DET
ejpam-5166	30	5	relationship	relationship	NOUN
ejpam-5166	30	6	between	between	ADP
ejpam-5166	30	7	a	a	DET
ejpam-5166	30	8	prime	prime	ADJ
ejpam-5166	30	9	ring	ring	NOUN
ejpam-5166	30	10	and	and	CCONJ
ejpam-5166	30	11	a	a	DET
ejpam-5166	30	12	prime	prime	ADJ
ejpam-5166	30	13	graph	graph	NOUN
ejpam-5166	30	14	of	of	ADP
ejpam-5166	30	15	the	the	DET
ejpam-5166	30	16	ring	ring	NOUN
ejpam-5166	30	17	.	.	PUNCT
ejpam-5166	31	1	furthermore	furthermore	ADV
ejpam-5166	31	2	,	,	PUNCT
ejpam-5166	31	3	kalita	kalita	PROPN
ejpam-5166	31	4	and	and	CCONJ
ejpam-5166	31	5	patra	patra	PROPN
ejpam-5166	31	6	in	in	ADP
ejpam-5166	31	7	2014	2014	NUM
ejpam-5166	31	8	determined	determine	VERB
ejpam-5166	31	9	the	the	DET
ejpam-5166	31	10	chromatic	chromatic	ADJ
ejpam-5166	31	11	number	number	NOUN
ejpam-5166	31	12	of	of	ADP
ejpam-5166	31	13	prime	prime	ADJ
ejpam-5166	31	14	graphs	graph	NOUN
ejpam-5166	31	15	of	of	ADP
ejpam-5166	31	16	a	a	DET
ejpam-5166	31	17	ring	ring	NOUN
ejpam-5166	31	18	zn	zn	PROPN
ejpam-5166	32	1	[	[	X
ejpam-5166	32	2	26	26	NUM
ejpam-5166	32	3	]	]	PUNCT
ejpam-5166	32	4	.	.	PUNCT
ejpam-5166	33	1	pawar	pawar	PROPN
ejpam-5166	33	2	and	and	CCONJ
ejpam-5166	33	3	joshi	joshi	PROPN
ejpam-5166	33	4	introduced	introduce	VERB
ejpam-5166	33	5	prime	prime	ADJ
ejpam-5166	33	6	graphs	graph	NOUN
ejpam-5166	33	7	pg1(r	pg1(r	NOUN
ejpam-5166	33	8	)	)	PUNCT
ejpam-5166	33	9	in	in	ADP
ejpam-5166	33	10	2017	2017	NUM
ejpam-5166	33	11	[	[	SYM
ejpam-5166	33	12	27	27	NUM
ejpam-5166	33	13	]	]	PUNCT
ejpam-5166	33	14	and	and	CCONJ
ejpam-5166	33	15	pg2(r	pg2(r	PROPN
ejpam-5166	33	16	)	)	PUNCT
ejpam-5166	33	17	in	in	ADP
ejpam-5166	33	18	2019	2019	NUM
ejpam-5166	33	19	[	[	SYM
ejpam-5166	33	20	19	19	NUM
ejpam-5166	33	21	]	]	PUNCT
ejpam-5166	33	22	.	.	PUNCT
ejpam-5166	34	1	the	the	DET
ejpam-5166	34	2	application	application	NOUN
ejpam-5166	34	3	of	of	ADP
ejpam-5166	34	4	graph	graph	NOUN
ejpam-5166	34	5	theory	theory	NOUN
ejpam-5166	34	6	has	have	AUX
ejpam-5166	34	7	been	be	AUX
ejpam-5166	34	8	carried	carry	VERB
ejpam-5166	34	9	out	out	ADP
ejpam-5166	34	10	in	in	ADP
ejpam-5166	34	11	many	many	ADJ
ejpam-5166	34	12	fields	field	NOUN
ejpam-5166	34	13	such	such	ADJ
ejpam-5166	34	14	as	as	ADP
ejpam-5166	34	15	networks	network	NOUN
ejpam-5166	34	16	,	,	PUNCT
ejpam-5166	34	17	cryptography	cryptography	NOUN
ejpam-5166	34	18	,	,	PUNCT
ejpam-5166	34	19	transportation	transportation	NOUN
ejpam-5166	34	20	,	,	PUNCT
ejpam-5166	34	21	coding	code	VERB
ejpam-5166	34	22	theory	theory	NOUN
ejpam-5166	34	23	,	,	PUNCT
ejpam-5166	34	24	chemistry	chemistry	NOUN
ejpam-5166	34	25	,	,	PUNCT
ejpam-5166	34	26	crystallography	crystallography	NOUN
ejpam-5166	34	27	,	,	PUNCT
ejpam-5166	34	28	and	and	CCONJ
ejpam-5166	34	29	information	information	NOUN
ejpam-5166	34	30	systems	system	NOUN
ejpam-5166	34	31	(	(	PUNCT
ejpam-5166	34	32	see	see	VERB
ejpam-5166	34	33	[	[	X
ejpam-5166	34	34	1	1	NUM
ejpam-5166	34	35	]	]	PUNCT
ejpam-5166	34	36	,	,	PUNCT
ejpam-5166	34	37	[	[	X
ejpam-5166	34	38	2	2	NUM
ejpam-5166	34	39	]	]	PUNCT
ejpam-5166	34	40	,	,	PUNCT
ejpam-5166	34	41	[	[	X
ejpam-5166	34	42	15	15	NUM
ejpam-5166	34	43	]	]	PUNCT
ejpam-5166	34	44	,	,	PUNCT
ejpam-5166	34	45	[	[	X
ejpam-5166	34	46	21	21	NUM
ejpam-5166	34	47	]	]	PUNCT
ejpam-5166	34	48	,	,	PUNCT
ejpam-5166	34	49	[	[	X
ejpam-5166	34	50	22	22	NUM
ejpam-5166	34	51	]	]	PUNCT
ejpam-5166	34	52	,	,	PUNCT
ejpam-5166	34	53	[	[	X
ejpam-5166	34	54	23	23	NUM
ejpam-5166	34	55	]	]	PUNCT
ejpam-5166	34	56	,	,	PUNCT
ejpam-5166	34	57	[	[	X
ejpam-5166	34	58	24	24	NUM
ejpam-5166	34	59	]	]	PUNCT
ejpam-5166	34	60	,	,	PUNCT
ejpam-5166	34	61	[	[	X
ejpam-5166	34	62	29	29	NUM
ejpam-5166	34	63	]	]	PUNCT
ejpam-5166	34	64	,	,	PUNCT
ejpam-5166	34	65	[	[	X
ejpam-5166	34	66	30	30	NUM
ejpam-5166	34	67	]	]	PUNCT
ejpam-5166	34	68	,	,	PUNCT
ejpam-5166	34	69	[	[	X
ejpam-5166	34	70	31	31	NUM
ejpam-5166	34	71	]	]	PUNCT
ejpam-5166	34	72	,	,	PUNCT
ejpam-5166	34	73	[	[	X
ejpam-5166	34	74	35	35	NUM
ejpam-5166	34	75	]	]	PUNCT
ejpam-5166	34	76	,	,	PUNCT
ejpam-5166	34	77	and	and	CCONJ
ejpam-5166	34	78	[	[	X
ejpam-5166	34	79	39	39	NUM
ejpam-5166	34	80	]	]	PUNCT
ejpam-5166	34	81	)	)	PUNCT
ejpam-5166	34	82	.	.	PUNCT
ejpam-5166	35	1	the	the	DET
ejpam-5166	35	2	application	application	NOUN
ejpam-5166	35	3	of	of	ADP
ejpam-5166	35	4	graph	graph	NOUN
ejpam-5166	35	5	theory	theory	NOUN
ejpam-5166	35	6	to	to	ADP
ejpam-5166	35	7	the	the	DET
ejpam-5166	35	8	field	field	NOUN
ejpam-5166	35	9	of	of	ADP
ejpam-5166	35	10	chemistry	chemistry	NOUN
ejpam-5166	35	11	was	be	AUX
ejpam-5166	35	12	first	first	ADV
ejpam-5166	35	13	introduced	introduce	VERB
ejpam-5166	35	14	by	by	ADP
ejpam-5166	35	15	wiener	wiener	NOUN
ejpam-5166	35	16	in	in	ADP
ejpam-5166	35	17	1947	1947	NUM
ejpam-5166	35	18	to	to	PART
ejpam-5166	35	19	predict	predict	VERB
ejpam-5166	35	20	the	the	DET
ejpam-5166	35	21	boiling	boiling	NOUN
ejpam-5166	35	22	point	point	NOUN
ejpam-5166	35	23	of	of	ADP
ejpam-5166	35	24	the	the	DET
ejpam-5166	35	25	paraffin	paraffin	NOUN
ejpam-5166	35	26	molecular	molecular	ADJ
ejpam-5166	35	27	structure	structure	NOUN
ejpam-5166	35	28	[	[	X
ejpam-5166	35	29	40	40	NUM
ejpam-5166	35	30	]	]	PUNCT
ejpam-5166	35	31	.	.	PUNCT
ejpam-5166	36	1	the	the	DET
ejpam-5166	36	2	value	value	NOUN
ejpam-5166	36	3	of	of	ADP
ejpam-5166	36	4	that	that	DET
ejpam-5166	36	5	prediction	prediction	NOUN
ejpam-5166	36	6	is	be	AUX
ejpam-5166	36	7	then	then	ADV
ejpam-5166	36	8	known	know	VERB
ejpam-5166	36	9	as	as	ADP
ejpam-5166	36	10	wiener	wiener	NOUN
ejpam-5166	36	11	index	index	NOUN
ejpam-5166	36	12	which	which	PRON
ejpam-5166	36	13	is	be	AUX
ejpam-5166	36	14	defined	define	VERB
ejpam-5166	36	15	as	as	ADP
ejpam-5166	36	16	the	the	DET
ejpam-5166	36	17	sum	sum	NOUN
ejpam-5166	36	18	of	of	ADP
ejpam-5166	36	19	the	the	DET
ejpam-5166	36	20	distances	distance	NOUN
ejpam-5166	36	21	between	between	ADP
ejpam-5166	36	22	vertices	vertex	NOUN
ejpam-5166	36	23	in	in	ADP
ejpam-5166	36	24	a	a	DET
ejpam-5166	36	25	chemical	chemical	NOUN
ejpam-5166	36	26	graph	graph	NOUN
ejpam-5166	36	27	representing	represent	VERB
ejpam-5166	36	28	non	non	ADJ
ejpam-5166	36	29	-	-	ADJ
ejpam-5166	36	30	hydrogen	hydrogen	ADJ
ejpam-5166	36	31	atoms	atom	NOUN
ejpam-5166	36	32	in	in	ADP
ejpam-5166	36	33	the	the	DET
ejpam-5166	36	34	molecule	molecule	NOUN
ejpam-5166	36	35	[	[	X
ejpam-5166	36	36	13	13	NUM
ejpam-5166	36	37	]	]	PUNCT
ejpam-5166	36	38	.	.	PUNCT
ejpam-5166	37	1	the	the	DET
ejpam-5166	37	2	highly	highly	ADV
ejpam-5166	37	3	anticipated	anticipated	ADJ
ejpam-5166	37	4	physicochemical	physicochemical	ADJ
ejpam-5166	37	5	features	feature	NOUN
ejpam-5166	37	6	of	of	ADP
ejpam-5166	37	7	all	all	DET
ejpam-5166	37	8	sorts	sort	NOUN
ejpam-5166	37	9	of	of	ADP
ejpam-5166	37	10	alkanes	alkane	NOUN
ejpam-5166	37	11	are	be	AUX
ejpam-5166	37	12	found	find	VERB
ejpam-5166	37	13	using	use	VERB
ejpam-5166	37	14	the	the	DET
ejpam-5166	37	15	distance	distance	NOUN
ejpam-5166	37	16	-	-	PUNCT
ejpam-5166	37	17	based	base	VERB
ejpam-5166	37	18	topological	topological	ADJ
ejpam-5166	37	19	indices	index	NOUN
ejpam-5166	37	20	known	know	VERB
ejpam-5166	37	21	as	as	ADP
ejpam-5166	37	22	the	the	DET
ejpam-5166	37	23	wiener	wiener	NOUN
ejpam-5166	37	24	index	index	NOUN
ejpam-5166	38	1	[	[	X
ejpam-5166	38	2	25	25	NUM
ejpam-5166	38	3	]	]	PUNCT
ejpam-5166	38	4	.	.	PUNCT
ejpam-5166	39	1	the	the	DET
ejpam-5166	39	2	mathematical	mathematical	ADJ
ejpam-5166	39	3	representation	representation	NOUN
ejpam-5166	39	4	of	of	ADP
ejpam-5166	39	5	the	the	DET
ejpam-5166	39	6	wiener	wiener	NOUN
ejpam-5166	39	7	index	index	NOUN
ejpam-5166	39	8	is	be	AUX
ejpam-5166	39	9	given	give	VERB
ejpam-5166	39	10	by	by	ADP
ejpam-5166	39	11	hosoya	hosoya	NOUN
ejpam-5166	39	12	as	as	ADP
ejpam-5166	39	13	the	the	DET
ejpam-5166	39	14	sum	sum	NOUN
ejpam-5166	39	15	of	of	ADP
ejpam-5166	39	16	the	the	DET
ejpam-5166	39	17	distances	distance	NOUN
ejpam-5166	39	18	of	of	ADP
ejpam-5166	39	19	each	each	DET
ejpam-5166	39	20	pair	pair	NOUN
ejpam-5166	39	21	of	of	ADP
ejpam-5166	39	22	vertices	vertex	NOUN
ejpam-5166	39	23	in	in	ADP
ejpam-5166	39	24	the	the	DET
ejpam-5166	39	25	graph	graph	NOUN
ejpam-5166	39	26	[	[	X
ejpam-5166	39	27	17	17	NUM
ejpam-5166	39	28	]	]	PUNCT
ejpam-5166	39	29	.	.	PUNCT
ejpam-5166	40	1	many	many	ADJ
ejpam-5166	40	2	researchers	researcher	NOUN
ejpam-5166	40	3	have	have	AUX
ejpam-5166	40	4	developed	develop	VERB
ejpam-5166	40	5	the	the	DET
ejpam-5166	40	6	concept	concept	NOUN
ejpam-5166	40	7	of	of	ADP
ejpam-5166	40	8	the	the	DET
ejpam-5166	40	9	wiener	wiener	NOUN
ejpam-5166	40	10	index	index	NOUN
ejpam-5166	40	11	for	for	ADP
ejpam-5166	40	12	graphs	graph	NOUN
ejpam-5166	40	13	of	of	ADP
ejpam-5166	40	14	rings	ring	NOUN
ejpam-5166	40	15	.	.	PUNCT
ejpam-5166	41	1	ramane	ramane	PROPN
ejpam-5166	41	2	et	et	PROPN
ejpam-5166	41	3	al	al	PROPN
ejpam-5166	42	1	[	[	X
ejpam-5166	42	2	32	32	NUM
ejpam-5166	42	3	]	]	PUNCT
ejpam-5166	42	4	obtain	obtain	VERB
ejpam-5166	42	5	the	the	DET
ejpam-5166	42	6	wiener	wiener	NOUN
ejpam-5166	42	7	index	index	NOUN
ejpam-5166	42	8	of	of	ADP
ejpam-5166	42	9	line	line	NOUN
ejpam-5166	42	10	graphs	graph	NOUN
ejpam-5166	42	11	and	and	CCONJ
ejpam-5166	42	12	some	some	DET
ejpam-5166	42	13	class	class	NOUN
ejpam-5166	42	14	of	of	ADP
ejpam-5166	42	15	graphs	graph	NOUN
ejpam-5166	42	16	.	.	PUNCT
ejpam-5166	43	1	suthar	suthar	VERB
ejpam-5166	43	2	and	and	CCONJ
ejpam-5166	43	3	prakash	prakash	PROPN
ejpam-5166	43	4	provided	provide	VERB
ejpam-5166	43	5	the	the	DET
ejpam-5166	43	6	wiener	wiener	NOUN
ejpam-5166	43	7	index	index	NOUN
ejpam-5166	43	8	formula	formula	NOUN
ejpam-5166	43	9	for	for	ADP
ejpam-5166	43	10	total	total	ADJ
ejpam-5166	43	11	graphs	graph	NOUN
ejpam-5166	43	12	over	over	ADP
ejpam-5166	43	13	the	the	DET
ejpam-5166	43	14	ring	ring	NOUN
ejpam-5166	43	15	zn	zn	PROPN
ejpam-5166	44	1	[	[	X
ejpam-5166	44	2	38	38	NUM
ejpam-5166	44	3	]	]	PUNCT
ejpam-5166	44	4	.	.	PUNCT
ejpam-5166	45	1	the	the	DET
ejpam-5166	45	2	wiener	wiener	NOUN
ejpam-5166	45	3	index	index	NOUN
ejpam-5166	45	4	formula	formula	NOUN
ejpam-5166	45	5	for	for	ADP
ejpam-5166	45	6	zero	zero	NUM
ejpam-5166	45	7	divisor	divisor	NOUN
ejpam-5166	45	8	graph	graph	NOUN
ejpam-5166	45	9	of	of	ADP
ejpam-5166	45	10	ring	ring	NOUN
ejpam-5166	45	11	was	be	AUX
ejpam-5166	45	12	given	give	VERB
ejpam-5166	45	13	in	in	ADP
ejpam-5166	45	14	(	(	PUNCT
ejpam-5166	45	15	[	[	X
ejpam-5166	45	16	3	3	NUM
ejpam-5166	45	17	]	]	PUNCT
ejpam-5166	45	18	,	,	PUNCT
ejpam-5166	45	19	[	[	X
ejpam-5166	45	20	8	8	NUM
ejpam-5166	45	21	]	]	PUNCT
ejpam-5166	45	22	,	,	PUNCT
ejpam-5166	45	23	[	[	X
ejpam-5166	45	24	28	28	NUM
ejpam-5166	45	25	]	]	PUNCT
ejpam-5166	45	26	,	,	PUNCT
ejpam-5166	45	27	[	[	X
ejpam-5166	45	28	33	33	NUM
ejpam-5166	45	29	]	]	PUNCT
ejpam-5166	45	30	,	,	PUNCT
ejpam-5166	45	31	[	[	X
ejpam-5166	45	32	34	34	NUM
ejpam-5166	45	33	]	]	PUNCT
ejpam-5166	45	34	,	,	PUNCT
ejpam-5166	45	35	and	and	CCONJ
ejpam-5166	45	36	[	[	X
ejpam-5166	45	37	36	36	NUM
ejpam-5166	45	38	]	]	NUM
ejpam-5166	45	39	)	)	PUNCT
ejpam-5166	45	40	.	.	PUNCT
ejpam-5166	46	1	asir	asir	PROPN
ejpam-5166	46	2	et	et	PROPN
ejpam-5166	46	3	al	al	PROPN
ejpam-5166	47	1	[	[	X
ejpam-5166	47	2	10	10	NUM
ejpam-5166	47	3	]	]	PUNCT
ejpam-5166	47	4	gave	give	VERB
ejpam-5166	47	5	the	the	DET
ejpam-5166	47	6	wiener	wiener	NOUN
ejpam-5166	47	7	index	index	NOUN
ejpam-5166	47	8	formula	formula	NOUN
ejpam-5166	47	9	for	for	ADP
ejpam-5166	47	10	unit	unit	NOUN
ejpam-5166	47	11	graph	graph	NOUN
ejpam-5166	47	12	of	of	ADP
ejpam-5166	47	13	ring	ring	PROPN
ejpam-5166	47	14	r.	r.	PROPN
ejpam-5166	47	15	furthermore	furthermore	ADV
ejpam-5166	47	16	,	,	PUNCT
ejpam-5166	47	17	joshi	joshi	PROPN
ejpam-5166	47	18	and	and	CCONJ
ejpam-5166	47	19	pawar	pawar	PROPN
ejpam-5166	48	1	[	[	X
ejpam-5166	48	2	18	18	NUM
ejpam-5166	48	3	]	]	PUNCT
ejpam-5166	48	4	introduced	introduce	VERB
ejpam-5166	48	5	the	the	DET
ejpam-5166	48	6	formula	formula	NOUN
ejpam-5166	48	7	of	of	ADP
ejpam-5166	48	8	wiener	wiener	NOUN
ejpam-5166	48	9	index	index	NOUN
ejpam-5166	48	10	of	of	ADP
ejpam-5166	48	11	the	the	DET
ejpam-5166	48	12	prime	prime	ADJ
ejpam-5166	48	13	graph	graph	NOUN
ejpam-5166	48	14	of	of	ADP
ejpam-5166	48	15	the	the	DET
ejpam-5166	48	16	ring	ring	NOUN
ejpam-5166	48	17	zn	zn	PROPN
ejpam-5166	48	18	,	,	PUNCT
ejpam-5166	48	19	for	for	ADP
ejpam-5166	48	20	n	n	NOUN
ejpam-5166	48	21	=	=	SYM
ejpam-5166	48	22	p	p	NOUN
ejpam-5166	48	23	,	,	PUNCT
ejpam-5166	48	24	n	n	NOUN
ejpam-5166	48	25	=	=	NOUN
ejpam-5166	48	26	p2	p2	PROPN
ejpam-5166	48	27	and	and	CCONJ
ejpam-5166	48	28	n	n	CCONJ
ejpam-5166	48	29	=	=	PROPN
ejpam-5166	48	30	p3	p3	PROPN
ejpam-5166	48	31	where	where	SCONJ
ejpam-5166	48	32	p	p	NOUN
ejpam-5166	48	33	is	be	AUX
ejpam-5166	48	34	a	a	DET
ejpam-5166	48	35	prime	prime	ADJ
ejpam-5166	48	36	number	number	NOUN
ejpam-5166	48	37	.	.	PUNCT
ejpam-5166	49	1	all	all	DET
ejpam-5166	49	2	wiener	wiener	NOUN
ejpam-5166	49	3	index	index	NOUN
ejpam-5166	49	4	formulas	formula	NOUN
ejpam-5166	49	5	that	that	PRON
ejpam-5166	49	6	have	have	AUX
ejpam-5166	49	7	been	be	AUX
ejpam-5166	49	8	constructed	construct	VERB
ejpam-5166	49	9	for	for	ADP
ejpam-5166	49	10	ring	ring	NOUN
ejpam-5166	49	11	graphs	graph	NOUN
ejpam-5166	49	12	(	(	PUNCT
ejpam-5166	49	13	zero	zero	NUM
ejpam-5166	49	14	divisor	divisor	NOUN
ejpam-5166	49	15	graph	graph	NOUN
ejpam-5166	49	16	,	,	PUNCT
ejpam-5166	49	17	unit	unit	NOUN
ejpam-5166	49	18	graph	graph	NOUN
ejpam-5166	49	19	,	,	PUNCT
ejpam-5166	49	20	total	total	ADJ
ejpam-5166	49	21	graph	graph	NOUN
ejpam-5166	49	22	,	,	PUNCT
ejpam-5166	49	23	and	and	CCONJ
ejpam-5166	49	24	prime	prime	ADJ
ejpam-5166	49	25	graph	graph	NOUN
ejpam-5166	49	26	)	)	PUNCT
ejpam-5166	49	27	can	can	AUX
ejpam-5166	49	28	be	be	AUX
ejpam-5166	49	29	seen	see	VERB
ejpam-5166	49	30	in	in	ADP
ejpam-5166	49	31	the	the	DET
ejpam-5166	49	32	survey	survey	NOUN
ejpam-5166	49	33	results	result	NOUN
ejpam-5166	49	34	arranged	arrange	VERB
ejpam-5166	49	35	by	by	ADP
ejpam-5166	49	36	asir	asir	PROPN
ejpam-5166	49	37	et	et	PROPN
ejpam-5166	49	38	al	al	PROPN
ejpam-5166	50	1	[	[	X
ejpam-5166	50	2	9	9	NUM
ejpam-5166	50	3	]	]	PUNCT
ejpam-5166	50	4	.	.	PUNCT
ejpam-5166	51	1	in	in	ADP
ejpam-5166	51	2	this	this	DET
ejpam-5166	51	3	article	article	NOUN
ejpam-5166	51	4	,	,	PUNCT
ejpam-5166	51	5	we	we	PRON
ejpam-5166	51	6	determine	determine	VERB
ejpam-5166	51	7	thewiener	thewiener	NOUN
ejpam-5166	51	8	index	index	NOUN
ejpam-5166	51	9	of	of	ADP
ejpam-5166	51	10	pg(zn	pg(zn	PROPN
ejpam-5166	51	11	)	)	PUNCT
ejpam-5166	51	12	for	for	ADP
ejpam-5166	51	13	some	some	DET
ejpam-5166	51	14	cases	case	NOUN
ejpam-5166	51	15	n	n	PRON
ejpam-5166	51	16	=	=	SYM
ejpam-5166	51	17	p	p	NOUN
ejpam-5166	51	18	,	,	PUNCT
ejpam-5166	51	19	p2	p2	NOUN
ejpam-5166	51	20	,	,	PUNCT
ejpam-5166	51	21	p3	p3	PROPN
ejpam-5166	51	22	,	,	PUNCT
ejpam-5166	51	23	pq	pq	NOUN
ejpam-5166	51	24	,	,	PUNCT
ejpam-5166	51	25	p2q	p2q	NOUN
ejpam-5166	51	26	,	,	PUNCT
ejpam-5166	51	27	pqr	pqr	NOUN
ejpam-5166	51	28	,	,	PUNCT
ejpam-5166	51	29	with	with	ADP
ejpam-5166	51	30	distinct	distinct	ADJ
ejpam-5166	51	31	prime	prime	NOUN
ejpam-5166	51	32	p	p	X
ejpam-5166	51	33	,	,	PUNCT
ejpam-5166	51	34	q	q	ADJ
ejpam-5166	51	35	,	,	PUNCT
ejpam-5166	51	36	and	and	CCONJ
ejpam-5166	51	37	r	r	NOUN
ejpam-5166	51	38	,	,	PUNCT
ejpam-5166	51	39	using	use	VERB
ejpam-5166	51	40	distance	distance	NOUN
ejpam-5166	51	41	matrix	matrix	NOUN
ejpam-5166	51	42	method	method	NOUN
ejpam-5166	51	43	.	.	PUNCT
ejpam-5166	52	1	we	we	PRON
ejpam-5166	52	2	partition	partition	VERB
ejpam-5166	52	3	the	the	DET
ejpam-5166	52	4	set	set	NOUN
ejpam-5166	52	5	zn	zn	PROPN
ejpam-5166	52	6	into	into	ADP
ejpam-5166	52	7	three	three	NUM
ejpam-5166	52	8	types	type	NOUN
ejpam-5166	52	9	of	of	ADP
ejpam-5166	52	10	sets	set	NOUN
ejpam-5166	52	11	,	,	PUNCT
ejpam-5166	52	12	namely	namely	ADV
ejpam-5166	52	13	zero	zero	NUM
ejpam-5166	52	14	sets	set	NOUN
ejpam-5166	52	15	,	,	PUNCT
ejpam-5166	52	16	nontrivial	nontrivial	NOUN
ejpam-5166	52	17	zero	zero	NUM
ejpam-5166	52	18	divisor	divisor	NOUN
ejpam-5166	52	19	sets	set	NOUN
ejpam-5166	52	20	,	,	PUNCT
ejpam-5166	52	21	and	and	CCONJ
ejpam-5166	52	22	unit	unit	NOUN
ejpam-5166	52	23	sets	set	NOUN
ejpam-5166	52	24	.	.	PUNCT
ejpam-5166	53	1	wiener	wiener	NOUN
ejpam-5166	53	2	index	index	NOUN
ejpam-5166	53	3	is	be	AUX
ejpam-5166	53	4	obtained	obtain	VERB
ejpam-5166	53	5	from	from	ADP
ejpam-5166	53	6	a	a	DET
ejpam-5166	53	7	half	half	NOUN
ejpam-5166	53	8	of	of	ADP
ejpam-5166	53	9	the	the	DET
ejpam-5166	53	10	sum	sum	NOUN
ejpam-5166	53	11	of	of	ADP
ejpam-5166	53	12	all	all	DET
ejpam-5166	53	13	entries	entry	NOUN
ejpam-5166	53	14	of	of	ADP
ejpam-5166	53	15	the	the	DET
ejpam-5166	53	16	distance	distance	NOUN
ejpam-5166	53	17	matrix	matrix	NOUN
ejpam-5166	53	18	.	.	PUNCT
ejpam-5166	54	1	the	the	DET
ejpam-5166	54	2	discussion	discussion	NOUN
ejpam-5166	54	3	is	be	AUX
ejpam-5166	54	4	divided	divide	VERB
ejpam-5166	54	5	into	into	ADP
ejpam-5166	54	6	four	four	NUM
ejpam-5166	54	7	sections	section	NOUN
ejpam-5166	54	8	.	.	PUNCT
ejpam-5166	55	1	in	in	ADP
ejpam-5166	55	2	the	the	DET
ejpam-5166	55	3	second	second	ADJ
ejpam-5166	55	4	section	section	NOUN
ejpam-5166	55	5	,	,	PUNCT
ejpam-5166	55	6	we	we	PRON
ejpam-5166	55	7	give	give	VERB
ejpam-5166	55	8	a	a	DET
ejpam-5166	55	9	literature	literature	NOUN
ejpam-5166	55	10	review	review	NOUN
ejpam-5166	55	11	to	to	PART
ejpam-5166	55	12	understand	understand	VERB
ejpam-5166	55	13	the	the	DET
ejpam-5166	55	14	theory	theory	NOUN
ejpam-5166	55	15	which	which	PRON
ejpam-5166	55	16	is	be	AUX
ejpam-5166	55	17	used	use	VERB
ejpam-5166	55	18	in	in	ADP
ejpam-5166	55	19	this	this	DET
ejpam-5166	55	20	article	article	NOUN
ejpam-5166	55	21	.	.	PUNCT
ejpam-5166	56	1	in	in	ADP
ejpam-5166	56	2	the	the	DET
ejpam-5166	56	3	third	third	ADJ
ejpam-5166	56	4	section	section	NOUN
ejpam-5166	56	5	,	,	PUNCT
ejpam-5166	56	6	we	we	PRON
ejpam-5166	56	7	compare	compare	VERB
ejpam-5166	56	8	the	the	DET
ejpam-5166	56	9	wiener	wiener	NOUN
ejpam-5166	56	10	index	index	NOUN
ejpam-5166	56	11	formula	formula	NOUN
ejpam-5166	56	12	of	of	ADP
ejpam-5166	56	13	pg(zn	pg(zn	NOUN
ejpam-5166	56	14	)	)	PUNCT
ejpam-5166	56	15	where	where	SCONJ
ejpam-5166	56	16	n	n	NOUN
ejpam-5166	56	17	=	=	SYM
ejpam-5166	56	18	p	p	NOUN
ejpam-5166	56	19	,	,	PUNCT
ejpam-5166	56	20	p2	p2	NOUN
ejpam-5166	56	21	,	,	PUNCT
ejpam-5166	56	22	p3	p3	NOUN
ejpam-5166	56	23	for	for	ADP
ejpam-5166	56	24	any	any	DET
ejpam-5166	56	25	prime	prime	ADJ
ejpam-5166	56	26	number	number	NOUN
ejpam-5166	56	27	p	p	NOUN
ejpam-5166	56	28	with	with	ADP
ejpam-5166	56	29	the	the	DET
ejpam-5166	56	30	results	result	NOUN
ejpam-5166	56	31	carried	carry	VERB
ejpam-5166	56	32	out	out	ADP
ejpam-5166	56	33	by	by	ADP
ejpam-5166	56	34	joshi	joshi	PROPN
ejpam-5166	56	35	and	and	CCONJ
ejpam-5166	56	36	pawar	pawar	PROPN
ejpam-5166	57	1	[	[	X
ejpam-5166	57	2	18	18	NUM
ejpam-5166	57	3	]	]	PUNCT
ejpam-5166	57	4	and	and	CCONJ
ejpam-5166	57	5	we	we	PRON
ejpam-5166	57	6	determine	determine	VERB
ejpam-5166	57	7	the	the	DET
ejpam-5166	57	8	wiener	wiener	NOUN
ejpam-5166	57	9	index	index	NOUN
ejpam-5166	57	10	formula	formula	NOUN
ejpam-5166	57	11	of	of	ADP
ejpam-5166	57	12	pg(zn	pg(zn	NOUN
ejpam-5166	57	13	)	)	PUNCT
ejpam-5166	57	14	where	where	SCONJ
ejpam-5166	57	15	n	n	PROPN
ejpam-5166	57	16	=	=	SYM
ejpam-5166	57	17	pq	pq	PROPN
ejpam-5166	57	18	,	,	PUNCT
ejpam-5166	57	19	p2q	p2q	NOUN
ejpam-5166	57	20	,	,	PUNCT
ejpam-5166	57	21	p2q2	p2q2	NOUN
ejpam-5166	57	22	,	,	PUNCT
ejpam-5166	57	23	pqr	pqr	NOUN
ejpam-5166	57	24	for	for	ADP
ejpam-5166	57	25	distinct	distinct	ADJ
ejpam-5166	57	26	prime	prime	ADJ
ejpam-5166	57	27	numbers	number	NOUN
ejpam-5166	57	28	p	p	X
ejpam-5166	57	29	,	,	PUNCT
ejpam-5166	57	30	q	q	AUX
ejpam-5166	57	31	,	,	PUNCT
ejpam-5166	57	32	and	and	CCONJ
ejpam-5166	57	33	r.	r.	NOUN
ejpam-5166	57	34	the	the	DET
ejpam-5166	57	35	last	last	ADJ
ejpam-5166	57	36	section	section	NOUN
ejpam-5166	57	37	concludes	conclude	VERB
ejpam-5166	57	38	the	the	DET
ejpam-5166	57	39	contents	content	NOUN
ejpam-5166	57	40	of	of	ADP
ejpam-5166	57	41	this	this	DET
ejpam-5166	57	42	article	article	NOUN
ejpam-5166	57	43	.	.	PUNCT
ejpam-5166	58	1	n.	n.	PROPN
ejpam-5166	58	2	hidayat	hidayat	PROPN
ejpam-5166	58	3	et	et	PROPN
ejpam-5166	58	4	al	al	PROPN
ejpam-5166	58	5	/	/	PUNCT
ejpam-5166	58	6	eur	eur	PROPN
ejpam-5166	58	7	.	.	PUNCT
ejpam-5166	59	1	j.	j.	PROPN
ejpam-5166	59	2	pure	pure	PROPN
ejpam-5166	59	3	appl	appl	PROPN
ejpam-5166	59	4	.	.	PROPN
ejpam-5166	59	5	math	math	PROPN
ejpam-5166	59	6	,	,	PUNCT
ejpam-5166	59	7	17	17	NUM
ejpam-5166	59	8	(	(	PUNCT
ejpam-5166	59	9	3	3	NUM
ejpam-5166	59	10	)	)	PUNCT
ejpam-5166	59	11	(	(	PUNCT
ejpam-5166	59	12	2024	2024	NUM
ejpam-5166	59	13	)	)	PUNCT
ejpam-5166	59	14	,	,	PUNCT
ejpam-5166	59	15	1659	1659	NUM
ejpam-5166	59	16	-	-	SYM
ejpam-5166	59	17	1673	1673	NUM
ejpam-5166	59	18	1661	1661	NUM
ejpam-5166	59	19	2	2	NUM
ejpam-5166	59	20	.	.	PUNCT
ejpam-5166	59	21	preliminaries	preliminary	NOUN
ejpam-5166	59	22	the	the	DET
ejpam-5166	59	23	graph	graph	NOUN
ejpam-5166	59	24	referred	refer	VERB
ejpam-5166	59	25	to	to	ADP
ejpam-5166	59	26	in	in	ADP
ejpam-5166	59	27	this	this	DET
ejpam-5166	59	28	article	article	NOUN
ejpam-5166	59	29	is	be	AUX
ejpam-5166	59	30	a	a	DET
ejpam-5166	59	31	simple	simple	ADJ
ejpam-5166	59	32	graph	graph	NOUN
ejpam-5166	59	33	,	,	PUNCT
ejpam-5166	59	34	that	that	ADV
ejpam-5166	59	35	is	is	ADV
ejpam-5166	59	36	,	,	PUNCT
ejpam-5166	59	37	undirected	undirected	ADJ
ejpam-5166	59	38	graphs	graph	NOUN
ejpam-5166	59	39	that	that	PRON
ejpam-5166	59	40	have	have	VERB
ejpam-5166	59	41	no	no	DET
ejpam-5166	59	42	loops	loop	NOUN
ejpam-5166	59	43	and	and	CCONJ
ejpam-5166	59	44	multiple	multiple	ADJ
ejpam-5166	59	45	edges	edge	NOUN
ejpam-5166	59	46	.	.	PUNCT
ejpam-5166	60	1	more	more	ADJ
ejpam-5166	60	2	contents	content	NOUN
ejpam-5166	60	3	on	on	ADP
ejpam-5166	60	4	graph	graph	NOUN
ejpam-5166	60	5	theory	theory	NOUN
ejpam-5166	60	6	can	can	AUX
ejpam-5166	60	7	be	be	AUX
ejpam-5166	60	8	studied	study	VERB
ejpam-5166	60	9	in	in	ADP
ejpam-5166	60	10	[	[	X
ejpam-5166	60	11	14	14	NUM
ejpam-5166	60	12	]	]	PUNCT
ejpam-5166	60	13	,	,	PUNCT
ejpam-5166	60	14	while	while	SCONJ
ejpam-5166	60	15	topics	topic	NOUN
ejpam-5166	60	16	on	on	ADP
ejpam-5166	60	17	algebraic	algebraic	ADJ
ejpam-5166	60	18	structure	structure	NOUN
ejpam-5166	60	19	can	can	AUX
ejpam-5166	60	20	be	be	AUX
ejpam-5166	60	21	studied	study	VERB
ejpam-5166	60	22	in	in	ADP
ejpam-5166	60	23	[	[	X
ejpam-5166	60	24	16	16	NUM
ejpam-5166	60	25	]	]	PUNCT
ejpam-5166	60	26	.	.	PUNCT
ejpam-5166	61	1	a	a	DET
ejpam-5166	61	2	graph	graph	NOUN
ejpam-5166	61	3	g	g	NOUN
ejpam-5166	61	4	=	=	SYM
ejpam-5166	61	5	(	(	PUNCT
ejpam-5166	61	6	v	v	NOUN
ejpam-5166	61	7	,	,	PUNCT
ejpam-5166	61	8	e	e	NOUN
ejpam-5166	61	9	)	)	PUNCT
ejpam-5166	61	10	is	be	AUX
ejpam-5166	61	11	a	a	DET
ejpam-5166	61	12	system	system	NOUN
ejpam-5166	61	13	consisting	consist	VERB
ejpam-5166	61	14	of	of	ADP
ejpam-5166	61	15	a	a	DET
ejpam-5166	61	16	finite	finite	ADJ
ejpam-5166	61	17	non	non	ADJ
ejpam-5166	61	18	-	-	ADJ
ejpam-5166	61	19	empty	empty	ADJ
ejpam-5166	61	20	vertex	vertex	NOUN
ejpam-5166	61	21	set	set	VERB
ejpam-5166	61	22	v	v	NOUN
ejpam-5166	61	23	(	(	PUNCT
ejpam-5166	61	24	g	g	NOUN
ejpam-5166	61	25	)	)	PUNCT
ejpam-5166	61	26	and	and	CCONJ
ejpam-5166	61	27	a	a	DET
ejpam-5166	61	28	finite	finite	ADJ
ejpam-5166	61	29	edge	edge	NOUN
ejpam-5166	61	30	set	set	VERB
ejpam-5166	61	31	e(g	e(g	PROPN
ejpam-5166	61	32	)	)	PUNCT
ejpam-5166	61	33	,	,	PUNCT
ejpam-5166	61	34	which	which	PRON
ejpam-5166	61	35	is	be	AUX
ejpam-5166	61	36	a	a	DET
ejpam-5166	61	37	subset	subset	NOUN
ejpam-5166	61	38	of	of	ADP
ejpam-5166	61	39	v	v	NOUN
ejpam-5166	61	40	(	(	PUNCT
ejpam-5166	61	41	g)×	g)×	NOUN
ejpam-5166	61	42	v	v	NOUN
ejpam-5166	61	43	(	(	PUNCT
ejpam-5166	61	44	g	g	NOUN
ejpam-5166	61	45	)	)	PUNCT
ejpam-5166	61	46	.	.	PUNCT
ejpam-5166	62	1	the	the	DET
ejpam-5166	62	2	order	order	NOUN
ejpam-5166	62	3	and	and	CCONJ
ejpam-5166	62	4	size	size	NOUN
ejpam-5166	62	5	of	of	ADP
ejpam-5166	62	6	g	g	NOUN
ejpam-5166	62	7	,	,	PUNCT
ejpam-5166	62	8	are	be	AUX
ejpam-5166	62	9	the	the	DET
ejpam-5166	62	10	cardinality	cardinality	NOUN
ejpam-5166	62	11	of	of	ADP
ejpam-5166	62	12	v	v	NOUN
ejpam-5166	62	13	(	(	PUNCT
ejpam-5166	62	14	g	g	NOUN
ejpam-5166	62	15	)	)	PUNCT
ejpam-5166	62	16	and	and	CCONJ
ejpam-5166	62	17	e(g	e(g	PROPN
ejpam-5166	62	18	)	)	PUNCT
ejpam-5166	62	19	,	,	PUNCT
ejpam-5166	62	20	respectively	respectively	ADV
ejpam-5166	62	21	.	.	PUNCT
ejpam-5166	63	1	generally	generally	ADV
ejpam-5166	63	2	,	,	PUNCT
ejpam-5166	63	3	the	the	DET
ejpam-5166	63	4	edge	edge	NOUN
ejpam-5166	63	5	(	(	PUNCT
ejpam-5166	63	6	u	u	NOUN
ejpam-5166	63	7	,	,	PUNCT
ejpam-5166	63	8	v	v	NOUN
ejpam-5166	63	9	)	)	PUNCT
ejpam-5166	63	10	∈	∈	PROPN
ejpam-5166	63	11	e(g	e(g	PROPN
ejpam-5166	63	12	)	)	PUNCT
ejpam-5166	63	13	is	be	AUX
ejpam-5166	63	14	written	write	VERB
ejpam-5166	63	15	as	as	ADP
ejpam-5166	63	16	uv	uv	NOUN
ejpam-5166	63	17	or	or	CCONJ
ejpam-5166	63	18	vu	vu	NOUN
ejpam-5166	63	19	.	.	PROPN
ejpam-5166	64	1	two	two	NUM
ejpam-5166	64	2	vertex	vertex	NOUN
ejpam-5166	64	3	u	u	NOUN
ejpam-5166	64	4	and	and	CCONJ
ejpam-5166	64	5	v	v	NOUN
ejpam-5166	64	6	are	be	AUX
ejpam-5166	64	7	called	call	VERB
ejpam-5166	64	8	adjacent	adjacent	ADJ
ejpam-5166	64	9	if	if	SCONJ
ejpam-5166	64	10	uv	uv	NOUN
ejpam-5166	64	11	is	be	AUX
ejpam-5166	64	12	an	an	DET
ejpam-5166	64	13	edge	edge	NOUN
ejpam-5166	64	14	.	.	PUNCT
ejpam-5166	65	1	the	the	DET
ejpam-5166	65	2	open	open	ADJ
ejpam-5166	65	3	neighborhood	neighborhood	NOUN
ejpam-5166	65	4	set	set	NOUN
ejpam-5166	65	5	of	of	ADP
ejpam-5166	65	6	u	u	PROPN
ejpam-5166	65	7	∈	∈	PROPN
ejpam-5166	65	8	v	v	ADP
ejpam-5166	65	9	(	(	PUNCT
ejpam-5166	65	10	g	g	NOUN
ejpam-5166	65	11	)	)	PUNCT
ejpam-5166	65	12	,	,	PUNCT
ejpam-5166	65	13	denoted	denote	VERB
ejpam-5166	65	14	by	by	ADP
ejpam-5166	65	15	n(u	n(u	PROPN
ejpam-5166	65	16	)	)	PUNCT
ejpam-5166	65	17	,	,	PUNCT
ejpam-5166	65	18	is	be	AUX
ejpam-5166	65	19	the	the	DET
ejpam-5166	65	20	set	set	NOUN
ejpam-5166	65	21	of	of	ADP
ejpam-5166	65	22	vertices	vertex	NOUN
ejpam-5166	65	23	that	that	PRON
ejpam-5166	65	24	are	be	AUX
ejpam-5166	65	25	adjacent	adjacent	ADJ
ejpam-5166	65	26	to	to	ADP
ejpam-5166	65	27	u	u	NOUN
ejpam-5166	65	28	,	,	PUNCT
ejpam-5166	65	29	and	and	CCONJ
ejpam-5166	65	30	the	the	DET
ejpam-5166	65	31	cardinality	cardinality	NOUN
ejpam-5166	65	32	of	of	ADP
ejpam-5166	65	33	n(u	n(u	PROPN
ejpam-5166	65	34	)	)	PUNCT
ejpam-5166	65	35	is	be	AUX
ejpam-5166	65	36	called	call	VERB
ejpam-5166	65	37	the	the	DET
ejpam-5166	65	38	degree	degree	NOUN
ejpam-5166	65	39	of	of	ADP
ejpam-5166	65	40	u	u	NOUN
ejpam-5166	65	41	,	,	PUNCT
ejpam-5166	65	42	denoted	denote	VERB
ejpam-5166	65	43	by	by	ADP
ejpam-5166	65	44	deg(u	deg(u	PROPN
ejpam-5166	65	45	)	)	PUNCT
ejpam-5166	65	46	.	.	PUNCT
ejpam-5166	66	1	a	a	DET
ejpam-5166	66	2	graph	graph	NOUN
ejpam-5166	66	3	g	g	NOUN
ejpam-5166	66	4	is	be	AUX
ejpam-5166	66	5	said	say	VERB
ejpam-5166	66	6	to	to	PART
ejpam-5166	66	7	be	be	AUX
ejpam-5166	66	8	connected	connect	VERB
ejpam-5166	66	9	if	if	SCONJ
ejpam-5166	66	10	any	any	DET
ejpam-5166	66	11	two	two	NUM
ejpam-5166	66	12	of	of	ADP
ejpam-5166	66	13	its	its	PRON
ejpam-5166	66	14	vertices	vertex	NOUN
ejpam-5166	66	15	are	be	AUX
ejpam-5166	66	16	connected	connect	VERB
ejpam-5166	66	17	.	.	PUNCT
ejpam-5166	67	1	the	the	DET
ejpam-5166	67	2	distance	distance	NOUN
ejpam-5166	67	3	between	between	ADP
ejpam-5166	67	4	vertices	vertex	NOUN
ejpam-5166	67	5	u	u	NOUN
ejpam-5166	67	6	and	and	CCONJ
ejpam-5166	67	7	v	v	NOUN
ejpam-5166	67	8	in	in	ADP
ejpam-5166	67	9	a	a	DET
ejpam-5166	67	10	connected	connected	ADJ
ejpam-5166	67	11	graph	graph	NOUN
ejpam-5166	67	12	,	,	PUNCT
ejpam-5166	67	13	denoted	denote	VERB
ejpam-5166	67	14	as	as	ADP
ejpam-5166	67	15	d(u	d(u	PROPN
ejpam-5166	67	16	,	,	PUNCT
ejpam-5166	67	17	v	v	NOUN
ejpam-5166	67	18	)	)	PUNCT
ejpam-5166	67	19	,	,	PUNCT
ejpam-5166	67	20	is	be	AUX
ejpam-5166	67	21	defined	define	VERB
ejpam-5166	67	22	as	as	ADP
ejpam-5166	67	23	the	the	DET
ejpam-5166	67	24	size	size	NOUN
ejpam-5166	67	25	of	of	ADP
ejpam-5166	67	26	the	the	DET
ejpam-5166	67	27	shortest	short	ADJ
ejpam-5166	67	28	path	path	NOUN
ejpam-5166	67	29	subgraph	subgraph	NOUN
ejpam-5166	67	30	between	between	ADP
ejpam-5166	67	31	vertices	vertex	NOUN
ejpam-5166	67	32	u	u	NOUN
ejpam-5166	67	33	and	and	CCONJ
ejpam-5166	67	34	v.	v.	ADP
ejpam-5166	67	35	the	the	DET
ejpam-5166	67	36	distance	distance	NOUN
ejpam-5166	67	37	matrix	matrix	NOUN
ejpam-5166	67	38	of	of	ADP
ejpam-5166	67	39	a	a	DET
ejpam-5166	67	40	graph	graph	NOUN
ejpam-5166	67	41	g	g	NOUN
ejpam-5166	67	42	,	,	PUNCT
ejpam-5166	67	43	denoted	denote	VERB
ejpam-5166	67	44	d(g	d(g	PROPN
ejpam-5166	67	45	)	)	PUNCT
ejpam-5166	67	46	,	,	PUNCT
ejpam-5166	67	47	is	be	AUX
ejpam-5166	67	48	the	the	DET
ejpam-5166	67	49	matrix	matrix	NOUN
ejpam-5166	67	50	[	[	X
ejpam-5166	67	51	dij	dij	X
ejpam-5166	67	52	]	]	PUNCT
ejpam-5166	67	53	defined	define	VERB
ejpam-5166	67	54	as	as	ADP
ejpam-5166	67	55	dij	dij	NOUN
ejpam-5166	67	56	=	=	SYM
ejpam-5166	67	57	d(vi	d(vi	PROPN
ejpam-5166	67	58	,	,	PUNCT
ejpam-5166	67	59	vj	vj	NOUN
ejpam-5166	67	60	)	)	PUNCT
ejpam-5166	67	61	for	for	ADP
ejpam-5166	67	62	i	i	PROPN
ejpam-5166	67	63	̸=	̸=	PROPN
ejpam-5166	67	64	j	j	PROPN
ejpam-5166	67	65	and	and	CCONJ
ejpam-5166	67	66	dii	dii	PROPN
ejpam-5166	67	67	=	=	SYM
ejpam-5166	67	68	0	0	X
ejpam-5166	67	69	.	.	PUNCT
ejpam-5166	68	1	the	the	DET
ejpam-5166	68	2	wiener	wiener	NOUN
ejpam-5166	68	3	index	index	NOUN
ejpam-5166	68	4	of	of	ADP
ejpam-5166	68	5	g	g	PROPN
ejpam-5166	68	6	is	be	AUX
ejpam-5166	68	7	the	the	DET
ejpam-5166	68	8	sum	sum	NOUN
ejpam-5166	68	9	of	of	ADP
ejpam-5166	68	10	the	the	DET
ejpam-5166	68	11	distances	distance	NOUN
ejpam-5166	68	12	of	of	ADP
ejpam-5166	68	13	all	all	DET
ejpam-5166	68	14	pairs	pair	NOUN
ejpam-5166	68	15	of	of	ADP
ejpam-5166	68	16	vertices	vertex	NOUN
ejpam-5166	68	17	in	in	ADP
ejpam-5166	68	18	g.	g.	PROPN
ejpam-5166	68	19	the	the	DET
ejpam-5166	68	20	definition	definition	NOUN
ejpam-5166	68	21	of	of	ADP
ejpam-5166	68	22	the	the	DET
ejpam-5166	68	23	wiener	wiener	NOUN
ejpam-5166	68	24	index	index	NOUN
ejpam-5166	68	25	can	can	AUX
ejpam-5166	68	26	be	be	AUX
ejpam-5166	68	27	related	relate	VERB
ejpam-5166	68	28	to	to	ADP
ejpam-5166	68	29	the	the	DET
ejpam-5166	68	30	concept	concept	NOUN
ejpam-5166	68	31	of	of	ADP
ejpam-5166	68	32	the	the	DET
ejpam-5166	68	33	distance	distance	NOUN
ejpam-5166	68	34	matrix	matrix	NOUN
ejpam-5166	68	35	as	as	SCONJ
ejpam-5166	68	36	follows	follow	VERB
ejpam-5166	68	37	:	:	PUNCT
ejpam-5166	68	38	definition	definition	NOUN
ejpam-5166	68	39	1	1	NUM
ejpam-5166	68	40	.	.	PUNCT
ejpam-5166	69	1	[	[	X
ejpam-5166	69	2	17	17	NUM
ejpam-5166	69	3	]	]	PUNCT
ejpam-5166	69	4	let	let	VERB
ejpam-5166	69	5	g	g	PRON
ejpam-5166	69	6	be	be	AUX
ejpam-5166	69	7	a	a	DET
ejpam-5166	69	8	graph	graph	NOUN
ejpam-5166	69	9	,	,	PUNCT
ejpam-5166	69	10	and	and	CCONJ
ejpam-5166	69	11	d(g	d(g	NUM
ejpam-5166	69	12	)	)	PUNCT
ejpam-5166	69	13	be	be	VERB
ejpam-5166	69	14	the	the	DET
ejpam-5166	69	15	distance	distance	NOUN
ejpam-5166	69	16	matrix	matrix	NOUN
ejpam-5166	69	17	of	of	ADP
ejpam-5166	69	18	g.	g.	PROPN
ejpam-5166	69	19	the	the	DET
ejpam-5166	69	20	wiener	wiener	NOUN
ejpam-5166	69	21	index	index	NOUN
ejpam-5166	69	22	of	of	ADP
ejpam-5166	69	23	g	g	NOUN
ejpam-5166	69	24	,	,	PUNCT
ejpam-5166	69	25	denoted	denote	VERB
ejpam-5166	69	26	w	w	ADP
ejpam-5166	69	27	(	(	PUNCT
ejpam-5166	69	28	g	g	NOUN
ejpam-5166	69	29	)	)	PUNCT
ejpam-5166	69	30	,	,	PUNCT
ejpam-5166	69	31	is	be	AUX
ejpam-5166	69	32	defined	define	VERB
ejpam-5166	69	33	as	as	ADP
ejpam-5166	69	34	w	w	PROPN
ejpam-5166	69	35	(	(	PUNCT
ejpam-5166	69	36	g	g	NOUN
ejpam-5166	69	37	)	)	PUNCT
ejpam-5166	69	38	=	=	SYM
ejpam-5166	70	1	1	1	NUM
ejpam-5166	70	2	2	2	NUM
ejpam-5166	70	3	n∑	n∑	NOUN
ejpam-5166	70	4	i=1	i=1	PROPN
ejpam-5166	70	5	n∑	n∑	PROPN
ejpam-5166	71	1	j=1	j=1	PROPN
ejpam-5166	71	2	dij	dij	INTJ
ejpam-5166	71	3	.	.	PUNCT
ejpam-5166	72	1	the	the	DET
ejpam-5166	72	2	definition	definition	NOUN
ejpam-5166	72	3	and	and	CCONJ
ejpam-5166	72	4	some	some	DET
ejpam-5166	72	5	properties	property	NOUN
ejpam-5166	72	6	of	of	ADP
ejpam-5166	72	7	prime	prime	ADJ
ejpam-5166	72	8	graphs	graph	NOUN
ejpam-5166	72	9	of	of	ADP
ejpam-5166	72	10	ring	ring	NOUN
ejpam-5166	72	11	r	r	NOUN
ejpam-5166	72	12	as	as	SCONJ
ejpam-5166	72	13	follows	follow	VERB
ejpam-5166	72	14	:	:	PUNCT
ejpam-5166	72	15	definition	definition	NOUN
ejpam-5166	72	16	2	2	NUM
ejpam-5166	72	17	.	.	PUNCT
ejpam-5166	73	1	[	[	X
ejpam-5166	73	2	12	12	NUM
ejpam-5166	73	3	]	]	X
ejpam-5166	73	4	let	let	VERB
ejpam-5166	73	5	(	(	PUNCT
ejpam-5166	73	6	r,+	r,+	NUM
ejpam-5166	73	7	,	,	PUNCT
ejpam-5166	73	8	·	·	PUNCT
ejpam-5166	73	9	)	)	PUNCT
ejpam-5166	73	10	be	be	AUX
ejpam-5166	73	11	a	a	DET
ejpam-5166	73	12	ring	ring	NOUN
ejpam-5166	73	13	.	.	PUNCT
ejpam-5166	74	1	the	the	DET
ejpam-5166	74	2	prime	prime	ADJ
ejpam-5166	74	3	graph	graph	NOUN
ejpam-5166	74	4	of	of	ADP
ejpam-5166	74	5	ring	ring	NOUN
ejpam-5166	74	6	r	r	NOUN
ejpam-5166	74	7	,	,	PUNCT
ejpam-5166	74	8	denoted	denote	VERB
ejpam-5166	74	9	by	by	ADP
ejpam-5166	74	10	pg(r	pg(r	PROPN
ejpam-5166	74	11	)	)	PUNCT
ejpam-5166	74	12	,	,	PUNCT
ejpam-5166	74	13	is	be	AUX
ejpam-5166	74	14	a	a	DET
ejpam-5166	74	15	graph	graph	NOUN
ejpam-5166	74	16	with	with	ADP
ejpam-5166	74	17	v	v	NOUN
ejpam-5166	74	18	(	(	PUNCT
ejpam-5166	74	19	pg(r	pg(r	NOUN
ejpam-5166	74	20	)	)	PUNCT
ejpam-5166	74	21	)	)	PUNCT
ejpam-5166	75	1	=	=	SYM
ejpam-5166	75	2	r	r	NOUN
ejpam-5166	75	3	and	and	CCONJ
ejpam-5166	75	4	e(pg(r	e(pg(r	PROPN
ejpam-5166	75	5	)	)	PUNCT
ejpam-5166	75	6	)	)	PUNCT
ejpam-5166	76	1	=	=	PRON
ejpam-5166	76	2	{	{	PUNCT
ejpam-5166	76	3	uv|urv	uv|urv	INTJ
ejpam-5166	76	4	=	=	X
ejpam-5166	76	5	{	{	PUNCT
ejpam-5166	76	6	0r	0r	NOUN
ejpam-5166	76	7	}	}	PUNCT
ejpam-5166	76	8	or	or	CCONJ
ejpam-5166	76	9	vru	vru	NOUN
ejpam-5166	76	10	=	=	PUNCT
ejpam-5166	76	11	{	{	PUNCT
ejpam-5166	76	12	0r	0r	X
ejpam-5166	76	13	}	}	PUNCT
ejpam-5166	76	14	and	and	CCONJ
ejpam-5166	76	15	u	u	PROPN
ejpam-5166	76	16	̸=	̸=	PROPN
ejpam-5166	76	17	v	v	NOUN
ejpam-5166	76	18	}	}	PUNCT
ejpam-5166	76	19	.	.	PUNCT
ejpam-5166	77	1	the	the	DET
ejpam-5166	77	2	following	follow	VERB
ejpam-5166	77	3	theorem	theorem	ADJ
ejpam-5166	77	4	1	1	NUM
ejpam-5166	77	5	shows	show	VERB
ejpam-5166	77	6	a	a	DET
ejpam-5166	77	7	property	property	NOUN
ejpam-5166	77	8	of	of	ADP
ejpam-5166	77	9	a	a	DET
ejpam-5166	77	10	prime	prime	ADJ
ejpam-5166	77	11	grphs	grphs	NOUN
ejpam-5166	77	12	of	of	ADP
ejpam-5166	77	13	a	a	DET
ejpam-5166	77	14	ring	ring	NOUN
ejpam-5166	77	15	.	.	PUNCT
ejpam-5166	78	1	while	while	SCONJ
ejpam-5166	78	2	other	other	ADJ
ejpam-5166	78	3	properties	property	NOUN
ejpam-5166	78	4	can	can	AUX
ejpam-5166	78	5	be	be	AUX
ejpam-5166	78	6	seen	see	VERB
ejpam-5166	78	7	in	in	ADP
ejpam-5166	78	8	[	[	X
ejpam-5166	78	9	12	12	NUM
ejpam-5166	78	10	]	]	PUNCT
ejpam-5166	78	11	.	.	PUNCT
ejpam-5166	79	1	theorem	theorem	NOUN
ejpam-5166	79	2	1	1	NUM
ejpam-5166	79	3	.	.	PUNCT
ejpam-5166	80	1	[	[	X
ejpam-5166	80	2	12	12	NUM
ejpam-5166	80	3	]	]	X
ejpam-5166	80	4	let	let	VERB
ejpam-5166	80	5	(	(	PUNCT
ejpam-5166	80	6	r,+	r,+	NUM
ejpam-5166	80	7	,	,	PUNCT
ejpam-5166	80	8	·	·	PUNCT
ejpam-5166	80	9	)	)	PUNCT
ejpam-5166	80	10	be	be	AUX
ejpam-5166	80	11	a	a	DET
ejpam-5166	80	12	ring	ring	NOUN
ejpam-5166	80	13	and	and	CCONJ
ejpam-5166	80	14	pg(r	pg(r	PRON
ejpam-5166	80	15	)	)	PUNCT
ejpam-5166	80	16	be	be	AUX
ejpam-5166	80	17	its	its	PRON
ejpam-5166	80	18	prime	prime	ADJ
ejpam-5166	80	19	graph	graph	NOUN
ejpam-5166	80	20	.	.	PUNCT
ejpam-5166	81	1	(	(	PUNCT
ejpam-5166	81	2	i	i	NOUN
ejpam-5166	81	3	)	)	PUNCT
ejpam-5166	81	4	every	every	DET
ejpam-5166	81	5	non	non	ADJ
ejpam-5166	81	6	-	-	ADJ
ejpam-5166	81	7	zero	zero	NUM
ejpam-5166	81	8	vertex	vertex	NOUN
ejpam-5166	81	9	v	v	ADP
ejpam-5166	81	10	∈	∈	NOUN
ejpam-5166	81	11	r	r	NOUN
ejpam-5166	81	12	is	be	AUX
ejpam-5166	81	13	adjacent	adjacent	ADJ
ejpam-5166	81	14	to	to	ADP
ejpam-5166	81	15	0r	0r	PROPN
ejpam-5166	81	16	.	.	PUNCT
ejpam-5166	82	1	(	(	PUNCT
ejpam-5166	82	2	ii	ii	X
ejpam-5166	82	3	)	)	PUNCT
ejpam-5166	82	4	d(u	d(u	PROPN
ejpam-5166	82	5	,	,	PUNCT
ejpam-5166	82	6	v	v	NOUN
ejpam-5166	82	7	)	)	PUNCT
ejpam-5166	82	8	=	=	SYM
ejpam-5166	82	9	2	2	NUM
ejpam-5166	82	10	if	if	SCONJ
ejpam-5166	82	11	and	and	CCONJ
ejpam-5166	82	12	only	only	ADV
ejpam-5166	82	13	if	if	SCONJ
ejpam-5166	82	14	the	the	DET
ejpam-5166	82	15	vertices	vertex	NOUN
ejpam-5166	82	16	u	u	NOUN
ejpam-5166	82	17	and	and	CCONJ
ejpam-5166	82	18	v	v	NOUN
ejpam-5166	82	19	are	be	AUX
ejpam-5166	82	20	not	not	PART
ejpam-5166	82	21	adjacent	adjacent	ADJ
ejpam-5166	82	22	.	.	PUNCT
ejpam-5166	83	1	(	(	PUNCT
ejpam-5166	83	2	iii	iii	X
ejpam-5166	83	3	)	)	PUNCT
ejpam-5166	83	4	if	if	SCONJ
ejpam-5166	83	5	r	r	NOUN
ejpam-5166	83	6	is	be	AUX
ejpam-5166	83	7	commutative	commutative	ADJ
ejpam-5166	83	8	ring	ring	NOUN
ejpam-5166	83	9	unity	unity	NOUN
ejpam-5166	83	10	1r	1r	NUM
ejpam-5166	83	11	,	,	PUNCT
ejpam-5166	83	12	then	then	ADV
ejpam-5166	83	13	the	the	DET
ejpam-5166	83	14	vertices	vertex	NOUN
ejpam-5166	83	15	u	u	NOUN
ejpam-5166	83	16	and	and	CCONJ
ejpam-5166	83	17	v	v	NOUN
ejpam-5166	83	18	are	be	AUX
ejpam-5166	83	19	adjacent	adjacent	ADJ
ejpam-5166	83	20	if	if	SCONJ
ejpam-5166	83	21	and	and	CCONJ
ejpam-5166	83	22	only	only	ADV
ejpam-5166	83	23	if	if	SCONJ
ejpam-5166	83	24	uv	uv	NOUN
ejpam-5166	83	25	=	=	PUNCT
ejpam-5166	83	26	0r	0r	X
ejpam-5166	83	27	.	.	PUNCT
ejpam-5166	84	1	(	(	PUNCT
ejpam-5166	84	2	iv	iv	X
ejpam-5166	84	3	)	)	PUNCT
ejpam-5166	84	4	if	if	SCONJ
ejpam-5166	84	5	r	r	NOUN
ejpam-5166	84	6	is	be	AUX
ejpam-5166	84	7	a	a	DET
ejpam-5166	84	8	commutative	commutative	ADJ
ejpam-5166	84	9	ring	ring	NOUN
ejpam-5166	84	10	with	with	ADP
ejpam-5166	84	11	unity	unity	NOUN
ejpam-5166	84	12	1r	1r	NUM
ejpam-5166	84	13	,	,	PUNCT
ejpam-5166	84	14	then	then	ADV
ejpam-5166	84	15	u	u	NOUN
ejpam-5166	84	16	is	be	AUX
ejpam-5166	84	17	only	only	ADV
ejpam-5166	84	18	adjacent	adjacent	ADJ
ejpam-5166	84	19	to	to	ADP
ejpam-5166	84	20	0r	0r	NUM
ejpam-5166	84	21	.	.	PUNCT
ejpam-5166	85	1	(	(	PUNCT
ejpam-5166	85	2	v	v	NOUN
ejpam-5166	85	3	)	)	PUNCT
ejpam-5166	85	4	if	if	SCONJ
ejpam-5166	85	5	r	r	NOUN
ejpam-5166	85	6	=	=	SYM
ejpam-5166	85	7	zp	zp	PROPN
ejpam-5166	85	8	for	for	ADP
ejpam-5166	85	9	p	p	NOUN
ejpam-5166	85	10	primes	prime	NOUN
ejpam-5166	85	11	or	or	CCONJ
ejpam-5166	85	12	p	p	NOUN
ejpam-5166	85	13	=	=	NOUN
ejpam-5166	85	14	4	4	NUM
ejpam-5166	85	15	,	,	PUNCT
ejpam-5166	85	16	then	then	ADV
ejpam-5166	85	17	pg(zp	pg(zp	NOUN
ejpam-5166	85	18	)	)	PUNCT
ejpam-5166	85	19	∼=	∼=	PROPN
ejpam-5166	85	20	k1,p−1	k1,p−1	NOUN
ejpam-5166	85	21	.	.	PUNCT
ejpam-5166	86	1	n.	n.	PROPN
ejpam-5166	86	2	hidayat	hidayat	PROPN
ejpam-5166	86	3	et	et	PROPN
ejpam-5166	86	4	al	al	PROPN
ejpam-5166	86	5	/	/	PUNCT
ejpam-5166	86	6	eur	eur	PROPN
ejpam-5166	86	7	.	.	PUNCT
ejpam-5166	87	1	j.	j.	PROPN
ejpam-5166	87	2	pure	pure	PROPN
ejpam-5166	87	3	appl	appl	PROPN
ejpam-5166	87	4	.	.	PROPN
ejpam-5166	87	5	math	math	PROPN
ejpam-5166	87	6	,	,	PUNCT
ejpam-5166	87	7	17	17	NUM
ejpam-5166	87	8	(	(	PUNCT
ejpam-5166	87	9	3	3	NUM
ejpam-5166	87	10	)	)	PUNCT
ejpam-5166	87	11	(	(	PUNCT
ejpam-5166	87	12	2024	2024	NUM
ejpam-5166	87	13	)	)	PUNCT
ejpam-5166	87	14	,	,	PUNCT
ejpam-5166	87	15	1659	1659	NUM
ejpam-5166	87	16	-	-	SYM
ejpam-5166	87	17	1673	1673	NUM
ejpam-5166	87	18	1662	1662	NUM
ejpam-5166	87	19	the	the	DET
ejpam-5166	87	20	wiener	wiener	NOUN
ejpam-5166	87	21	index	index	NOUN
ejpam-5166	87	22	of	of	ADP
ejpam-5166	87	23	the	the	DET
ejpam-5166	87	24	prime	prime	ADJ
ejpam-5166	87	25	graph	graph	NOUN
ejpam-5166	87	26	of	of	ADP
ejpam-5166	87	27	the	the	DET
ejpam-5166	87	28	ring	ring	NOUN
ejpam-5166	87	29	zn	zn	PROPN
ejpam-5166	87	30	for	for	ADP
ejpam-5166	87	31	n	n	PROPN
ejpam-5166	87	32	=	=	SYM
ejpam-5166	87	33	p	p	NOUN
ejpam-5166	87	34	,	,	PUNCT
ejpam-5166	87	35	n	n	NOUN
ejpam-5166	87	36	=	=	PUNCT
ejpam-5166	87	37	p2	p2	NOUN
ejpam-5166	87	38	,	,	PUNCT
ejpam-5166	87	39	n	n	NOUN
ejpam-5166	87	40	=	=	PROPN
ejpam-5166	87	41	p3	p3	PROPN
ejpam-5166	87	42	with	with	ADP
ejpam-5166	87	43	p	p	PRON
ejpam-5166	87	44	a	a	DET
ejpam-5166	87	45	prime	prime	ADJ
ejpam-5166	87	46	number	number	NOUN
ejpam-5166	87	47	,	,	PUNCT
ejpam-5166	87	48	as	as	SCONJ
ejpam-5166	87	49	obtained	obtain	VERB
ejpam-5166	87	50	by	by	ADP
ejpam-5166	87	51	joshi	joshi	PROPN
ejpam-5166	87	52	and	and	CCONJ
ejpam-5166	87	53	pawar	pawar	PROPN
ejpam-5166	87	54	[	[	X
ejpam-5166	87	55	18	18	NUM
ejpam-5166	87	56	]	]	PUNCT
ejpam-5166	87	57	as	as	SCONJ
ejpam-5166	87	58	follows	follow	VERB
ejpam-5166	87	59	:	:	PUNCT
ejpam-5166	87	60	theorem	theorem	NOUN
ejpam-5166	87	61	2	2	NUM
ejpam-5166	87	62	.	.	PUNCT
ejpam-5166	88	1	[	[	X
ejpam-5166	88	2	18	18	NUM
ejpam-5166	88	3	]	]	X
ejpam-5166	88	4	if	if	SCONJ
ejpam-5166	88	5	p	p	NOUN
ejpam-5166	88	6	is	be	AUX
ejpam-5166	88	7	a	a	DET
ejpam-5166	88	8	prime	prime	ADJ
ejpam-5166	88	9	number	number	NOUN
ejpam-5166	88	10	,	,	PUNCT
ejpam-5166	88	11	then	then	ADV
ejpam-5166	88	12	w	w	PROPN
ejpam-5166	88	13	(	(	PUNCT
ejpam-5166	88	14	pg(zp	pg(zp	NOUN
ejpam-5166	88	15	)	)	PUNCT
ejpam-5166	88	16	)	)	PUNCT
ejpam-5166	89	1	=	=	PUNCT
ejpam-5166	89	2	(	(	PUNCT
ejpam-5166	89	3	p−	p−	NOUN
ejpam-5166	89	4	1)2	1)2	NUM
ejpam-5166	89	5	.	.	PUNCT
ejpam-5166	90	1	theorem	theorem	NOUN
ejpam-5166	90	2	3	3	NUM
ejpam-5166	90	3	.	.	PUNCT
ejpam-5166	91	1	[	[	X
ejpam-5166	91	2	18	18	NUM
ejpam-5166	91	3	]	]	X
ejpam-5166	91	4	if	if	SCONJ
ejpam-5166	91	5	p	p	NOUN
ejpam-5166	91	6	is	be	AUX
ejpam-5166	91	7	a	a	DET
ejpam-5166	91	8	prime	prime	ADJ
ejpam-5166	91	9	number	number	NOUN
ejpam-5166	91	10	,	,	PUNCT
ejpam-5166	91	11	then	then	ADV
ejpam-5166	91	12	w	w	PROPN
ejpam-5166	91	13	(	(	PUNCT
ejpam-5166	91	14	pg(zp2	pg(zp2	PROPN
ejpam-5166	91	15	)	)	PUNCT
ejpam-5166	91	16	)	)	PUNCT
ejpam-5166	92	1	=	=	PUNCT
ejpam-5166	92	2	p(p−	p(p−	VERB
ejpam-5166	92	3	1)(2p2	1)(2p2	NUM
ejpam-5166	92	4	−	−	NUM
ejpam-5166	92	5	2p+	2p+	NUM
ejpam-5166	92	6	1	1	NUM
ejpam-5166	92	7	)	)	SYM
ejpam-5166	92	8	2	2	NUM
ejpam-5166	92	9	.	.	PUNCT
ejpam-5166	92	10	theorem	theorem	VERB
ejpam-5166	92	11	4	4	NUM
ejpam-5166	92	12	.	.	PUNCT
ejpam-5166	93	1	[	[	X
ejpam-5166	93	2	18	18	NUM
ejpam-5166	93	3	]	]	X
ejpam-5166	93	4	if	if	SCONJ
ejpam-5166	93	5	p	p	NOUN
ejpam-5166	93	6	is	be	AUX
ejpam-5166	93	7	a	a	DET
ejpam-5166	93	8	prime	prime	ADJ
ejpam-5166	93	9	number	number	NOUN
ejpam-5166	93	10	,	,	PUNCT
ejpam-5166	93	11	then	then	ADV
ejpam-5166	93	12	w	w	PROPN
ejpam-5166	93	13	(	(	PUNCT
ejpam-5166	93	14	pg(zp3	pg(zp3	X
ejpam-5166	93	15	)	)	PUNCT
ejpam-5166	93	16	)	)	PUNCT
ejpam-5166	93	17	=	=	PUNCT
ejpam-5166	93	18	p(p−	p(p−	VERB
ejpam-5166	93	19	1)(2p4	1)(2p4	NUM
ejpam-5166	93	20	+	+	CCONJ
ejpam-5166	93	21	2p3	2p3	NUM
ejpam-5166	94	1	−	−	NOUN
ejpam-5166	94	2	2p−	2p−	NOUN
ejpam-5166	94	3	3	3	NUM
ejpam-5166	94	4	)	)	PUNCT
ejpam-5166	94	5	2	2	NUM
ejpam-5166	94	6	.	.	PUNCT
ejpam-5166	95	1	3	3	X
ejpam-5166	95	2	.	.	X
ejpam-5166	95	3	main	main	ADJ
ejpam-5166	95	4	result	result	NOUN
ejpam-5166	95	5	in	in	ADP
ejpam-5166	95	6	this	this	DET
ejpam-5166	95	7	section	section	NOUN
ejpam-5166	95	8	we	we	PRON
ejpam-5166	95	9	will	will	AUX
ejpam-5166	95	10	determine	determine	VERB
ejpam-5166	95	11	the	the	DET
ejpam-5166	95	12	wiener	wiener	NOUN
ejpam-5166	95	13	index	index	NOUN
ejpam-5166	95	14	formula	formula	NOUN
ejpam-5166	95	15	of	of	ADP
ejpam-5166	95	16	pg(zn	pg(zn	NOUN
ejpam-5166	95	17	)	)	PUNCT
ejpam-5166	95	18	in	in	ADP
ejpam-5166	95	19	several	several	ADJ
ejpam-5166	95	20	cases	case	NOUN
ejpam-5166	95	21	of	of	ADP
ejpam-5166	95	22	n	n	CCONJ
ejpam-5166	95	23	,	,	PUNCT
ejpam-5166	95	24	especially	especially	ADV
ejpam-5166	95	25	for	for	ADP
ejpam-5166	95	26	n	n	PROPN
ejpam-5166	95	27	=	=	SYM
ejpam-5166	95	28	pq	pq	PROPN
ejpam-5166	95	29	,	,	PUNCT
ejpam-5166	95	30	n	n	NOUN
ejpam-5166	95	31	=	=	PUNCT
ejpam-5166	95	32	p2q	p2q	NOUN
ejpam-5166	95	33	,	,	PUNCT
ejpam-5166	95	34	n	n	NOUN
ejpam-5166	95	35	=	=	SYM
ejpam-5166	95	36	p2q2	p2q2	NOUN
ejpam-5166	95	37	,	,	PUNCT
ejpam-5166	95	38	n	n	PROPN
ejpam-5166	95	39	=	=	SYM
ejpam-5166	95	40	pqr	pqr	PROPN
ejpam-5166	95	41	,	,	PUNCT
ejpam-5166	95	42	where	where	SCONJ
ejpam-5166	95	43	p	p	X
ejpam-5166	95	44	,	,	PUNCT
ejpam-5166	95	45	q	q	INTJ
ejpam-5166	95	46	,	,	PUNCT
ejpam-5166	95	47	r	r	NOUN
ejpam-5166	95	48	are	be	AUX
ejpam-5166	95	49	prime	prime	ADJ
ejpam-5166	95	50	numbers	number	NOUN
ejpam-5166	95	51	.	.	PUNCT
ejpam-5166	96	1	however	however	ADV
ejpam-5166	96	2	,	,	PUNCT
ejpam-5166	96	3	firstly	firstly	ADV
ejpam-5166	96	4	we	we	PRON
ejpam-5166	96	5	determined	determine	VERB
ejpam-5166	96	6	thewiener	thewiener	NOUN
ejpam-5166	96	7	index	index	NOUN
ejpam-5166	96	8	formula	formula	NOUN
ejpam-5166	96	9	for	for	ADP
ejpam-5166	96	10	the	the	DET
ejpam-5166	96	11	case	case	NOUN
ejpam-5166	96	12	n	n	NOUN
ejpam-5166	96	13	=	=	SYM
ejpam-5166	96	14	p	p	NOUN
ejpam-5166	96	15	,	,	PUNCT
ejpam-5166	96	16	n	n	NOUN
ejpam-5166	96	17	=	=	PUNCT
ejpam-5166	96	18	p2	p2	NOUN
ejpam-5166	96	19	,	,	PUNCT
ejpam-5166	96	20	n	n	NOUN
ejpam-5166	96	21	=	=	SYM
ejpam-5166	96	22	p3	p3	PROPN
ejpam-5166	96	23	,	,	PUNCT
ejpam-5166	96	24	although	although	SCONJ
ejpam-5166	96	25	the	the	DET
ejpam-5166	96	26	formula	formula	NOUN
ejpam-5166	96	27	for	for	ADP
ejpam-5166	96	28	this	this	DET
ejpam-5166	96	29	case	case	NOUN
ejpam-5166	96	30	has	have	AUX
ejpam-5166	96	31	been	be	AUX
ejpam-5166	96	32	determined	determine	VERB
ejpam-5166	96	33	by	by	ADP
ejpam-5166	96	34	joshi	joshi	PROPN
ejpam-5166	96	35	and	and	CCONJ
ejpam-5166	96	36	pawar	pawar	PROPN
ejpam-5166	97	1	[	[	X
ejpam-5166	97	2	18	18	NUM
ejpam-5166	97	3	]	]	PUNCT
ejpam-5166	97	4	.	.	PUNCT
ejpam-5166	98	1	theorem	theorem	NOUN
ejpam-5166	98	2	5	5	NUM
ejpam-5166	98	3	.	.	PUNCT
ejpam-5166	99	1	if	if	SCONJ
ejpam-5166	99	2	p	p	NOUN
ejpam-5166	99	3	is	be	AUX
ejpam-5166	99	4	a	a	DET
ejpam-5166	99	5	prime	prime	NOUN
ejpam-5166	99	6	,	,	PUNCT
ejpam-5166	99	7	then	then	ADV
ejpam-5166	99	8	w	w	PROPN
ejpam-5166	99	9	(	(	PUNCT
ejpam-5166	99	10	pg(zp	pg(zp	NOUN
ejpam-5166	99	11	)	)	PUNCT
ejpam-5166	99	12	)	)	PUNCT
ejpam-5166	100	1	=	=	PUNCT
ejpam-5166	100	2	(	(	PUNCT
ejpam-5166	100	3	p−	p−	NOUN
ejpam-5166	100	4	1)2	1)2	NUM
ejpam-5166	100	5	.	.	PUNCT
ejpam-5166	101	1	proof	proof	NOUN
ejpam-5166	101	2	.	.	PUNCT
ejpam-5166	102	1	for	for	ADP
ejpam-5166	102	2	prime	prime	ADJ
ejpam-5166	102	3	p	p	X
ejpam-5166	102	4	,	,	PUNCT
ejpam-5166	102	5	it	it	PRON
ejpam-5166	102	6	holds	hold	VERB
ejpam-5166	102	7	d(u	d(u	PROPN
ejpam-5166	102	8	,	,	PUNCT
ejpam-5166	102	9	v	v	NOUN
ejpam-5166	102	10	)	)	PUNCT
ejpam-5166	102	11	=	=	SYM
ejpam-5166	102	12	2	2	NUM
ejpam-5166	102	13	if	if	SCONJ
ejpam-5166	102	14	u	u	NOUN
ejpam-5166	102	15	and	and	CCONJ
ejpam-5166	102	16	v	v	NOUN
ejpam-5166	102	17	are	be	AUX
ejpam-5166	102	18	not	not	PART
ejpam-5166	102	19	adjacent	adjacent	ADJ
ejpam-5166	102	20	and	and	CCONJ
ejpam-5166	102	21	d(u	d(u	PROPN
ejpam-5166	102	22	,	,	PUNCT
ejpam-5166	102	23	v	v	NOUN
ejpam-5166	102	24	)	)	PUNCT
ejpam-5166	102	25	=	=	SYM
ejpam-5166	102	26	1	1	NUM
ejpam-5166	102	27	if	if	SCONJ
ejpam-5166	102	28	u	u	NOUN
ejpam-5166	102	29	and	and	CCONJ
ejpam-5166	102	30	v	v	NOUN
ejpam-5166	102	31	are	be	AUX
ejpam-5166	102	32	adjacent	adjacent	ADJ
ejpam-5166	102	33	.	.	PUNCT
ejpam-5166	103	1	next	next	ADV
ejpam-5166	103	2	we	we	PRON
ejpam-5166	103	3	partition	partition	VERB
ejpam-5166	103	4	zp	zp	PROPN
ejpam-5166	103	5	into	into	ADP
ejpam-5166	103	6	two	two	NUM
ejpam-5166	103	7	sets	set	NOUN
ejpam-5166	103	8	,	,	PUNCT
ejpam-5166	103	9	namely	namely	ADV
ejpam-5166	103	10	the	the	DET
ejpam-5166	103	11	zero	zero	NUM
ejpam-5166	103	12	set	set	VERB
ejpam-5166	103	13	o	o	X
ejpam-5166	103	14	=	=	PUNCT
ejpam-5166	103	15	{	{	PUNCT
ejpam-5166	103	16	0	0	NUM
ejpam-5166	103	17	}	}	PUNCT
ejpam-5166	103	18	,	,	PUNCT
ejpam-5166	103	19	the	the	DET
ejpam-5166	103	20	unit	unit	NOUN
ejpam-5166	103	21	set	set	VERB
ejpam-5166	103	22	u	u	NOUN
ejpam-5166	103	23	=	=	PUNCT
ejpam-5166	103	24	{	{	PUNCT
ejpam-5166	103	25	x	x	SYM
ejpam-5166	103	26	∈	∈	PROPN
ejpam-5166	103	27	zp|x	zp|x	PROPN
ejpam-5166	103	28	is	be	AUX
ejpam-5166	103	29	unit	unit	NOUN
ejpam-5166	103	30	in	in	ADP
ejpam-5166	103	31	ring	ring	PROPN
ejpam-5166	103	32	zp	zp	PROPN
ejpam-5166	103	33	}	}	PUNCT
ejpam-5166	103	34	.	.	PUNCT
ejpam-5166	104	1	based	base	VERB
ejpam-5166	104	2	on	on	ADP
ejpam-5166	104	3	theorem	theorem	ADJ
ejpam-5166	104	4	1	1	NUM
ejpam-5166	104	5	,	,	PUNCT
ejpam-5166	104	6	pg(zp	pg(zp	NOUN
ejpam-5166	104	7	)	)	PUNCT
ejpam-5166	104	8	∼=	∼=	PROPN
ejpam-5166	104	9	k1,p−1	k1,p−1	NOUN
ejpam-5166	104	10	and	and	CCONJ
ejpam-5166	104	11	the	the	DET
ejpam-5166	104	12	distance	distance	NOUN
ejpam-5166	104	13	matrix	matrix	NOUN
ejpam-5166	104	14	of	of	ADP
ejpam-5166	104	15	pg(zp	pg(zp	NOUN
ejpam-5166	104	16	)	)	PUNCT
ejpam-5166	104	17	is	be	AUX
ejpam-5166	104	18	given	give	VERB
ejpam-5166	104	19	as	as	ADP
ejpam-5166	104	20	d(pg(zp	d(pg(zp	NOUN
ejpam-5166	104	21	)	)	PUNCT
ejpam-5166	104	22	)	)	PUNCT
ejpam-5166	105	1	=	=	PRON
ejpam-5166	105	2	(	(	PUNCT
ejpam-5166	105	3	o	o	X
ejpam-5166	105	4	u	u	NOUN
ejpam-5166	105	5	o	o	PROPN
ejpam-5166	105	6	0	0	NUM
ejpam-5166	105	7	11×(p−1	11×(p−1	NUM
ejpam-5166	105	8	)	)	PUNCT
ejpam-5166	105	9	u	u	NOUN
ejpam-5166	105	10	1(p−1)×1	1(p−1)×1	NUM
ejpam-5166	105	11	2(jp−1	2(jp−1	NUM
ejpam-5166	105	12	−	−	NOUN
ejpam-5166	105	13	ip−1	ip−1	NOUN
ejpam-5166	105	14	)	)	PUNCT
ejpam-5166	105	15	)	)	PUNCT
ejpam-5166	105	16	,	,	PUNCT
ejpam-5166	105	17	where	where	SCONJ
ejpam-5166	105	18	1m×n	1m×n	NOUN
ejpam-5166	105	19	is	be	AUX
ejpam-5166	105	20	a	a	DET
ejpam-5166	105	21	matrix	matrix	NOUN
ejpam-5166	105	22	of	of	ADP
ejpam-5166	105	23	order	order	NOUN
ejpam-5166	105	24	m×	m×	X
ejpam-5166	105	25	n	n	CCONJ
ejpam-5166	105	26	with	with	ADP
ejpam-5166	105	27	all	all	DET
ejpam-5166	105	28	entries	entry	NOUN
ejpam-5166	105	29	1	1	NUM
ejpam-5166	105	30	and	and	CCONJ
ejpam-5166	105	31	jn	jn	PROPN
ejpam-5166	105	32	=	=	PROPN
ejpam-5166	106	1	1n×n	1n×n	PROPN
ejpam-5166	106	2	.	.	PUNCT
ejpam-5166	107	1	we	we	PRON
ejpam-5166	107	2	obtain	obtain	VERB
ejpam-5166	107	3	w	w	ADP
ejpam-5166	107	4	(	(	PUNCT
ejpam-5166	107	5	pg(zp	pg(zp	NOUN
ejpam-5166	107	6	)	)	PUNCT
ejpam-5166	107	7	)	)	PUNCT
ejpam-5166	108	1	=	=	SYM
ejpam-5166	108	2	1	1	NUM
ejpam-5166	108	3	2	2	NUM
ejpam-5166	108	4	(	(	PUNCT
ejpam-5166	108	5	2(p−	2(p−	NUM
ejpam-5166	108	6	1	1	NUM
ejpam-5166	108	7	)	)	PUNCT
ejpam-5166	108	8	+	+	CCONJ
ejpam-5166	109	1	2(p−	2(p−	NUM
ejpam-5166	109	2	1)2	1)2	NUM
ejpam-5166	109	3	−	−	NOUN
ejpam-5166	109	4	2(p−	2(p−	NUM
ejpam-5166	109	5	1	1	NUM
ejpam-5166	109	6	)	)	PUNCT
ejpam-5166	109	7	)	)	PUNCT
ejpam-5166	110	1	=	=	PUNCT
ejpam-5166	110	2	(	(	PUNCT
ejpam-5166	110	3	p−	p−	NOUN
ejpam-5166	110	4	1)2	1)2	NUM
ejpam-5166	110	5	.	.	PUNCT
ejpam-5166	111	1	thus	thus	ADV
ejpam-5166	111	2	,	,	PUNCT
ejpam-5166	111	3	w	w	PROPN
ejpam-5166	111	4	(	(	PUNCT
ejpam-5166	111	5	pg(zp	pg(zp	NOUN
ejpam-5166	111	6	)	)	PUNCT
ejpam-5166	111	7	)	)	PUNCT
ejpam-5166	112	1	=	=	PUNCT
ejpam-5166	112	2	(	(	PUNCT
ejpam-5166	112	3	p−	p−	NOUN
ejpam-5166	112	4	1)2	1)2	NUM
ejpam-5166	112	5	.	.	PUNCT
ejpam-5166	113	1	we	we	PRON
ejpam-5166	113	2	see	see	VERB
ejpam-5166	113	3	that	that	SCONJ
ejpam-5166	113	4	the	the	DET
ejpam-5166	113	5	wiener	wiener	NOUN
ejpam-5166	113	6	index	index	NOUN
ejpam-5166	113	7	formula	formula	NOUN
ejpam-5166	113	8	of	of	ADP
ejpam-5166	113	9	pg(zp	pg(zp	NOUN
ejpam-5166	113	10	)	)	PUNCT
ejpam-5166	113	11	in	in	ADP
ejpam-5166	113	12	theorem	theorem	NOUN
ejpam-5166	113	13	5	5	NUM
ejpam-5166	113	14	is	be	AUX
ejpam-5166	113	15	equal	equal	ADJ
ejpam-5166	113	16	to	to	ADP
ejpam-5166	113	17	the	the	DET
ejpam-5166	113	18	formula	formula	NOUN
ejpam-5166	113	19	in	in	ADP
ejpam-5166	113	20	theorem	theorem	NOUN
ejpam-5166	113	21	2	2	NUM
ejpam-5166	113	22	.	.	PUNCT
ejpam-5166	113	23	therefore	therefore	ADV
ejpam-5166	113	24	,	,	PUNCT
ejpam-5166	113	25	the	the	DET
ejpam-5166	113	26	result	result	NOUN
ejpam-5166	113	27	in	in	ADP
ejpam-5166	113	28	theorem	theorem	ADJ
ejpam-5166	113	29	5	5	NUM
ejpam-5166	113	30	strengthen	strengthen	NOUN
ejpam-5166	113	31	theorem	theorem	NOUN
ejpam-5166	113	32	2	2	NUM
ejpam-5166	113	33	,	,	PUNCT
ejpam-5166	113	34	considering	consider	VERB
ejpam-5166	113	35	that	that	SCONJ
ejpam-5166	113	36	theorem	theorem	NOUN
ejpam-5166	113	37	2	2	NUM
ejpam-5166	113	38	does	do	AUX
ejpam-5166	113	39	not	not	PART
ejpam-5166	113	40	provide	provide	VERB
ejpam-5166	113	41	analytical	analytical	ADJ
ejpam-5166	113	42	proof	proof	NOUN
ejpam-5166	113	43	.	.	PUNCT
ejpam-5166	114	1	the	the	DET
ejpam-5166	114	2	wiener	wiener	NOUN
ejpam-5166	114	3	index	index	NOUN
ejpam-5166	114	4	formula	formula	NOUN
ejpam-5166	114	5	of	of	ADP
ejpam-5166	114	6	pg(zp2	pg(zp2	PROPN
ejpam-5166	114	7	)	)	PUNCT
ejpam-5166	114	8	and	and	CCONJ
ejpam-5166	114	9	pg(zp3	pg(zp3	NUM
ejpam-5166	114	10	)	)	PUNCT
ejpam-5166	114	11	with	with	ADP
ejpam-5166	114	12	p	p	NOUN
ejpam-5166	114	13	prime	prime	ADJ
ejpam-5166	114	14	numbers	number	NOUN
ejpam-5166	114	15	as	as	SCONJ
ejpam-5166	114	16	follows	follow	VERB
ejpam-5166	114	17	:	:	PUNCT
ejpam-5166	114	18	n.	n.	PROPN
ejpam-5166	114	19	hidayat	hidayat	PROPN
ejpam-5166	114	20	et	et	PROPN
ejpam-5166	114	21	al	al	PROPN
ejpam-5166	114	22	/	/	PUNCT
ejpam-5166	114	23	eur	eur	PROPN
ejpam-5166	114	24	.	.	PUNCT
ejpam-5166	115	1	j.	j.	PROPN
ejpam-5166	115	2	pure	pure	PROPN
ejpam-5166	115	3	appl	appl	PROPN
ejpam-5166	115	4	.	.	PROPN
ejpam-5166	115	5	math	math	PROPN
ejpam-5166	115	6	,	,	PUNCT
ejpam-5166	115	7	17	17	NUM
ejpam-5166	115	8	(	(	PUNCT
ejpam-5166	115	9	3	3	NUM
ejpam-5166	115	10	)	)	PUNCT
ejpam-5166	115	11	(	(	PUNCT
ejpam-5166	115	12	2024	2024	NUM
ejpam-5166	115	13	)	)	PUNCT
ejpam-5166	115	14	,	,	PUNCT
ejpam-5166	115	15	1659	1659	NUM
ejpam-5166	115	16	-	-	SYM
ejpam-5166	115	17	1673	1673	NUM
ejpam-5166	115	18	1663	1663	NUM
ejpam-5166	115	19	theorem	theorem	VERB
ejpam-5166	115	20	6	6	NUM
ejpam-5166	115	21	.	.	PUNCT
ejpam-5166	116	1	if	if	SCONJ
ejpam-5166	116	2	p	p	NOUN
ejpam-5166	116	3	is	be	AUX
ejpam-5166	116	4	a	a	DET
ejpam-5166	116	5	prime	prime	ADJ
ejpam-5166	116	6	number	number	NOUN
ejpam-5166	116	7	,	,	PUNCT
ejpam-5166	116	8	then	then	ADV
ejpam-5166	116	9	w	w	PROPN
ejpam-5166	116	10	(	(	PUNCT
ejpam-5166	116	11	pg(zp2	pg(zp2	PROPN
ejpam-5166	116	12	)	)	PUNCT
ejpam-5166	116	13	)	)	PUNCT
ejpam-5166	117	1	=	=	PUNCT
ejpam-5166	117	2	p(p−	p(p−	VERB
ejpam-5166	117	3	1)(2p2	1)(2p2	NUM
ejpam-5166	118	1	+	+	PUNCT
ejpam-5166	118	2	2p−	2p−	NUM
ejpam-5166	118	3	3	3	NUM
ejpam-5166	118	4	)	)	PUNCT
ejpam-5166	118	5	2	2	NUM
ejpam-5166	118	6	.	.	PUNCT
ejpam-5166	119	1	proof	proof	NOUN
ejpam-5166	119	2	.	.	PUNCT
ejpam-5166	120	1	for	for	ADP
ejpam-5166	120	2	every	every	DET
ejpam-5166	120	3	prime	prime	ADJ
ejpam-5166	120	4	p	p	NOUN
ejpam-5166	120	5	,	,	PUNCT
ejpam-5166	120	6	the	the	DET
ejpam-5166	120	7	ring	ring	NOUN
ejpam-5166	120	8	zp2	zp2	PROPN
ejpam-5166	120	9	has	have	AUX
ejpam-5166	120	10	p2	p2	VERB
ejpam-5166	120	11	−	−	PROPN
ejpam-5166	120	12	p	p	PROPN
ejpam-5166	120	13	units	unit	NOUN
ejpam-5166	120	14	and	and	CCONJ
ejpam-5166	120	15	p	p	NOUN
ejpam-5166	120	16	−	−	PROPN
ejpam-5166	120	17	1	1	NUM
ejpam-5166	120	18	nontrivial	nontrivial	ADJ
ejpam-5166	120	19	zero	zero	NUM
ejpam-5166	120	20	divisors	divisor	NOUN
ejpam-5166	120	21	.	.	PUNCT
ejpam-5166	121	1	next	next	ADV
ejpam-5166	121	2	we	we	PRON
ejpam-5166	121	3	partition	partition	VERB
ejpam-5166	121	4	zp2	zp2	VERB
ejpam-5166	121	5	into	into	ADP
ejpam-5166	121	6	three	three	NUM
ejpam-5166	121	7	sets	set	NOUN
ejpam-5166	121	8	,	,	PUNCT
ejpam-5166	121	9	namely	namely	ADV
ejpam-5166	121	10	the	the	DET
ejpam-5166	121	11	zero	zero	NUM
ejpam-5166	121	12	set	set	VERB
ejpam-5166	121	13	o	o	X
ejpam-5166	121	14	=	=	PUNCT
ejpam-5166	121	15	{	{	PUNCT
ejpam-5166	121	16	0	0	NUM
ejpam-5166	121	17	}	}	PUNCT
ejpam-5166	121	18	,	,	PUNCT
ejpam-5166	121	19	the	the	DET
ejpam-5166	121	20	unit	unit	NOUN
ejpam-5166	121	21	set	set	VERB
ejpam-5166	121	22	u	u	NOUN
ejpam-5166	121	23	=	=	PUNCT
ejpam-5166	121	24	{	{	PUNCT
ejpam-5166	121	25	x	x	SYM
ejpam-5166	121	26	∈	∈	NOUN
ejpam-5166	121	27	zp2	zp2	NOUN
ejpam-5166	121	28	|x	|x	NOUN
ejpam-5166	121	29	is	be	AUX
ejpam-5166	121	30	unit	unit	NOUN
ejpam-5166	121	31	in	in	ADP
ejpam-5166	121	32	ring	ring	NOUN
ejpam-5166	121	33	zp2	zp2	PROPN
ejpam-5166	121	34	}	}	PUNCT
ejpam-5166	121	35	,	,	PUNCT
ejpam-5166	121	36	and	and	CCONJ
ejpam-5166	121	37	the	the	DET
ejpam-5166	121	38	set	set	NOUN
ejpam-5166	121	39	of	of	ADP
ejpam-5166	121	40	nontrivial	nontrivial	ADJ
ejpam-5166	121	41	zero	zero	NUM
ejpam-5166	121	42	divisors	divisor	NOUN
ejpam-5166	121	43	zp2	zp2	X
ejpam-5166	121	44	are	be	AUX
ejpam-5166	121	45	z	z	NOUN
ejpam-5166	121	46	=	=	PUNCT
ejpam-5166	121	47	{	{	PUNCT
ejpam-5166	121	48	p	p	X
ejpam-5166	121	49	,	,	PUNCT
ejpam-5166	121	50	2p	2p	NUM
ejpam-5166	121	51	,	,	PUNCT
ejpam-5166	121	52	.	.	PUNCT
ejpam-5166	121	53	.	.	PUNCT
ejpam-5166	121	54	.	.	PUNCT
ejpam-5166	122	1	,	,	PUNCT
ejpam-5166	122	2	(	(	PUNCT
ejpam-5166	122	3	p−	p−	NOUN
ejpam-5166	122	4	1)p	1)p	NUM
ejpam-5166	122	5	}	}	PUNCT
ejpam-5166	122	6	=	=	SYM
ejpam-5166	122	7	⟨p⟩	⟨p⟩	PROPN
ejpam-5166	122	8	\	\	PROPN
ejpam-5166	122	9	{	{	PUNCT
ejpam-5166	122	10	0	0	NUM
ejpam-5166	122	11	}	}	PUNCT
ejpam-5166	122	12	.	.	PUNCT
ejpam-5166	123	1	based	base	VERB
ejpam-5166	123	2	on	on	ADP
ejpam-5166	123	3	theorem	theorem	NOUN
ejpam-5166	123	4	1	1	NUM
ejpam-5166	123	5	,	,	PUNCT
ejpam-5166	123	6	we	we	PRON
ejpam-5166	123	7	obtain	obtain	VERB
ejpam-5166	123	8	(	(	PUNCT
ejpam-5166	123	9	i	i	NOUN
ejpam-5166	123	10	)	)	PUNCT
ejpam-5166	123	11	every	every	DET
ejpam-5166	123	12	vertex	vertex	NOUN
ejpam-5166	123	13	in	in	ADP
ejpam-5166	123	14	o	o	PROPN
ejpam-5166	123	15	is	be	AUX
ejpam-5166	123	16	adjacent	adjacent	ADJ
ejpam-5166	123	17	to	to	ADP
ejpam-5166	123	18	every	every	DET
ejpam-5166	123	19	vertex	vertex	NOUN
ejpam-5166	123	20	in	in	ADP
ejpam-5166	123	21	z	z	PROPN
ejpam-5166	123	22	and	and	CCONJ
ejpam-5166	123	23	u	u	PROPN
ejpam-5166	123	24	.	.	PUNCT
ejpam-5166	124	1	(	(	PUNCT
ejpam-5166	124	2	ii	ii	NOUN
ejpam-5166	124	3	)	)	PUNCT
ejpam-5166	124	4	every	every	DET
ejpam-5166	124	5	vertex	vertex	NOUN
ejpam-5166	124	6	in	in	ADP
ejpam-5166	124	7	z	z	PROPN
ejpam-5166	124	8	is	be	AUX
ejpam-5166	124	9	adjacent	adjacent	ADJ
ejpam-5166	124	10	to	to	ADP
ejpam-5166	124	11	every	every	DET
ejpam-5166	124	12	vertex	vertex	NOUN
ejpam-5166	124	13	in	in	ADP
ejpam-5166	124	14	o	o	PROPN
ejpam-5166	124	15	and	and	CCONJ
ejpam-5166	124	16	z.	z.	PROPN
ejpam-5166	124	17	(	(	PUNCT
ejpam-5166	124	18	iii	iii	X
ejpam-5166	124	19	)	)	PUNCT
ejpam-5166	124	20	every	every	DET
ejpam-5166	124	21	vertex	vertex	NOUN
ejpam-5166	124	22	in	in	ADP
ejpam-5166	124	23	u	u	NOUN
ejpam-5166	124	24	is	be	AUX
ejpam-5166	124	25	only	only	ADV
ejpam-5166	124	26	adjcacent	adjcacent	ADJ
ejpam-5166	124	27	to	to	ADP
ejpam-5166	124	28	every	every	DET
ejpam-5166	124	29	vertex	vertex	NOUN
ejpam-5166	124	30	in	in	ADP
ejpam-5166	124	31	o.	o.	PROPN
ejpam-5166	124	32	thus	thus	ADV
ejpam-5166	124	33	,	,	PUNCT
ejpam-5166	124	34	the	the	DET
ejpam-5166	124	35	distance	distance	NOUN
ejpam-5166	124	36	matrix	matrix	NOUN
ejpam-5166	124	37	of	of	ADP
ejpam-5166	124	38	pg(zp2	pg(zp2	PROPN
ejpam-5166	124	39	)	)	PUNCT
ejpam-5166	124	40	is	be	AUX
ejpam-5166	124	41	d(pg(zp2	d(pg(zp2	NOUN
ejpam-5166	124	42	)	)	PUNCT
ejpam-5166	124	43	)	)	PUNCT
ejpam-5166	125	1	=	=	PUNCT
ejpam-5166	126	1			PROPN
ejpam-5166	126	2	o	o	NOUN
ejpam-5166	126	3	z	z	NOUN
ejpam-5166	126	4	u	u	NOUN
ejpam-5166	126	5	o	o	NOUN
ejpam-5166	126	6	0	0	NUM
ejpam-5166	126	7	11×(p−1	11×(p−1	NUM
ejpam-5166	126	8	)	)	PUNCT
ejpam-5166	126	9	11×p(p−1	11×p(p−1	NUM
ejpam-5166	126	10	)	)	PUNCT
ejpam-5166	126	11	z	z	NOUN
ejpam-5166	126	12	1(p−1)×1	1(p−1)×1	NUM
ejpam-5166	126	13	jp−1	jp−1	PROPN
ejpam-5166	126	14	−	−	PROPN
ejpam-5166	126	15	ip−1	ip−1	PROPN
ejpam-5166	126	16	2(p−1)×p(p−1	2(p−1)×p(p−1	NUM
ejpam-5166	126	17	)	)	PUNCT
ejpam-5166	126	18	u	u	NOUN
ejpam-5166	126	19	1p(p−1)×1	1p(p−1)×1	NUM
ejpam-5166	126	20	2p(p−1)×(p−1	2p(p−1)×(p−1	NUM
ejpam-5166	126	21	)	)	PUNCT
ejpam-5166	126	22	2(jp(p−1	2(jp(p−1	PROPN
ejpam-5166	126	23	)	)	PUNCT
ejpam-5166	126	24	−	−	PROPN
ejpam-5166	126	25	ip(p−1	ip(p−1	NOUN
ejpam-5166	126	26	)	)	PUNCT
ejpam-5166	126	27	)	)	PUNCT
ejpam-5166	127	1	.	.	ADV
ejpam-5166	127	2	where	where	SCONJ
ejpam-5166	127	3	1m×n	1m×n	NOUN
ejpam-5166	127	4	is	be	AUX
ejpam-5166	127	5	a	a	DET
ejpam-5166	127	6	matrix	matrix	NOUN
ejpam-5166	127	7	of	of	ADP
ejpam-5166	127	8	order	order	NOUN
ejpam-5166	127	9	m	m	VERB
ejpam-5166	127	10	×	×	NOUN
ejpam-5166	127	11	n	n	INTJ
ejpam-5166	127	12	with	with	ADP
ejpam-5166	127	13	all	all	DET
ejpam-5166	127	14	entries	entry	NOUN
ejpam-5166	127	15	1	1	NUM
ejpam-5166	127	16	,	,	PUNCT
ejpam-5166	127	17	2m×n	2m×n	NUM
ejpam-5166	127	18	is	be	AUX
ejpam-5166	127	19	a	a	DET
ejpam-5166	127	20	matrix	matrix	NOUN
ejpam-5166	127	21	of	of	ADP
ejpam-5166	127	22	order	order	NOUN
ejpam-5166	127	23	m	m	VERB
ejpam-5166	127	24	×	×	NOUN
ejpam-5166	127	25	n	n	INTJ
ejpam-5166	127	26	with	with	ADP
ejpam-5166	127	27	all	all	DET
ejpam-5166	127	28	entries	entry	NOUN
ejpam-5166	127	29	2	2	NUM
ejpam-5166	127	30	,	,	PUNCT
ejpam-5166	127	31	and	and	CCONJ
ejpam-5166	127	32	jn	jn	PROPN
ejpam-5166	127	33	=	=	PROPN
ejpam-5166	128	1	1n×n	1n×n	PROPN
ejpam-5166	128	2	.	.	PUNCT
ejpam-5166	129	1	a	a	DET
ejpam-5166	129	2	half	half	NOUN
ejpam-5166	129	3	of	of	ADP
ejpam-5166	129	4	the	the	DET
ejpam-5166	129	5	sum	sum	NOUN
ejpam-5166	129	6	of	of	ADP
ejpam-5166	129	7	all	all	DET
ejpam-5166	129	8	entries	entry	NOUN
ejpam-5166	129	9	in	in	ADP
ejpam-5166	129	10	the	the	DET
ejpam-5166	129	11	matrix	matrix	NOUN
ejpam-5166	129	12	d(pg(zp2	d(pg(zp2	NOUN
ejpam-5166	129	13	)	)	PUNCT
ejpam-5166	129	14	)	)	PUNCT
ejpam-5166	129	15	is	be	AUX
ejpam-5166	129	16	w	w	PROPN
ejpam-5166	129	17	(	(	PUNCT
ejpam-5166	129	18	pg(zp2	pg(zp2	PROPN
ejpam-5166	129	19	)	)	PUNCT
ejpam-5166	129	20	)	)	PUNCT
ejpam-5166	130	1	=	=	SYM
ejpam-5166	130	2	1	1	NUM
ejpam-5166	130	3	2	2	NUM
ejpam-5166	130	4	(	(	PUNCT
ejpam-5166	130	5	2p4	2p4	NUM
ejpam-5166	130	6	−	−	PROPN
ejpam-5166	130	7	2p2	2p2	NUM
ejpam-5166	130	8	−	−	PROPN
ejpam-5166	130	9	2(p2	2(p2	NUM
ejpam-5166	130	10	−	−	PROPN
ejpam-5166	131	1	1)−	1)−	NUM
ejpam-5166	131	2	(	(	PUNCT
ejpam-5166	131	3	p−	p−	NOUN
ejpam-5166	131	4	1)2	1)2	NUM
ejpam-5166	131	5	+	+	CCONJ
ejpam-5166	131	6	(	(	PUNCT
ejpam-5166	131	7	p−	p−	NOUN
ejpam-5166	131	8	1	1	NUM
ejpam-5166	131	9	)	)	PUNCT
ejpam-5166	131	10	)	)	PUNCT
ejpam-5166	132	1	=	=	SYM
ejpam-5166	133	1	2p4	2p4	NUM
ejpam-5166	133	2	−	−	NUM
ejpam-5166	133	3	5p2	5p2	NUM
ejpam-5166	133	4	+	+	CCONJ
ejpam-5166	133	5	3p	3p	NUM
ejpam-5166	133	6	2	2	NUM
ejpam-5166	133	7	=	=	NUM
ejpam-5166	133	8	p(p−	p(p−	VERB
ejpam-5166	133	9	1)(2p2	1)(2p2	NUM
ejpam-5166	134	1	+	+	PUNCT
ejpam-5166	134	2	2p−	2p−	NUM
ejpam-5166	134	3	3	3	NUM
ejpam-5166	134	4	)	)	PUNCT
ejpam-5166	134	5	2	2	NUM
ejpam-5166	134	6	.	.	PUNCT
ejpam-5166	135	1	hence	hence	ADV
ejpam-5166	135	2	,	,	PUNCT
ejpam-5166	135	3	w	w	X
ejpam-5166	135	4	(	(	PUNCT
ejpam-5166	135	5	pg(zp2	pg(zp2	PROPN
ejpam-5166	135	6	)	)	PUNCT
ejpam-5166	135	7	)	)	PUNCT
ejpam-5166	135	8	=	=	PUNCT
ejpam-5166	135	9	p(p−	p(p−	VERB
ejpam-5166	135	10	1)(2p2	1)(2p2	NUM
ejpam-5166	135	11	+	+	PUNCT
ejpam-5166	136	1	2p−	2p−	NUM
ejpam-5166	136	2	3	3	NUM
ejpam-5166	136	3	)	)	SYM
ejpam-5166	136	4	2	2	NUM
ejpam-5166	136	5	.	.	PUNCT
ejpam-5166	136	6	theorem	theorem	VERB
ejpam-5166	136	7	7	7	NUM
ejpam-5166	136	8	.	.	PUNCT
ejpam-5166	137	1	if	if	SCONJ
ejpam-5166	137	2	p	p	NOUN
ejpam-5166	137	3	is	be	AUX
ejpam-5166	137	4	prime	prime	ADJ
ejpam-5166	137	5	,	,	PUNCT
ejpam-5166	137	6	then	then	ADV
ejpam-5166	137	7	w	w	PROPN
ejpam-5166	137	8	(	(	PUNCT
ejpam-5166	137	9	pg(zp3	pg(zp3	X
ejpam-5166	137	10	)	)	PUNCT
ejpam-5166	137	11	)	)	PUNCT
ejpam-5166	138	1	=	=	PUNCT
ejpam-5166	138	2	p(p−	p(p−	VERB
ejpam-5166	138	3	1)(2p4	1)(2p4	NUM
ejpam-5166	138	4	+	+	CCONJ
ejpam-5166	138	5	2p3	2p3	NUM
ejpam-5166	139	1	+	+	CCONJ
ejpam-5166	139	2	2p2	2p2	NUM
ejpam-5166	139	3	−	−	PROPN
ejpam-5166	140	1	4p−	4p−	NUM
ejpam-5166	140	2	1	1	NUM
ejpam-5166	140	3	)	)	PUNCT
ejpam-5166	140	4	2	2	NUM
ejpam-5166	140	5	.	.	PUNCT
ejpam-5166	141	1	proof	proof	NOUN
ejpam-5166	141	2	.	.	PUNCT
ejpam-5166	142	1	for	for	ADP
ejpam-5166	142	2	every	every	DET
ejpam-5166	142	3	prime	prime	ADJ
ejpam-5166	142	4	p	p	NOUN
ejpam-5166	142	5	,	,	PUNCT
ejpam-5166	142	6	the	the	DET
ejpam-5166	142	7	ring	ring	NOUN
ejpam-5166	142	8	zp3	zp3	PROPN
ejpam-5166	142	9	has	have	VERB
ejpam-5166	142	10	p3	p3	PROPN
ejpam-5166	142	11	−	−	NOUN
ejpam-5166	142	12	p2	p2	PROPN
ejpam-5166	142	13	units	unit	NOUN
ejpam-5166	142	14	and	and	CCONJ
ejpam-5166	142	15	p2	p2	PROPN
ejpam-5166	142	16	−	−	PROPN
ejpam-5166	142	17	1	1	NUM
ejpam-5166	142	18	nontrivial	nontrivial	ADJ
ejpam-5166	142	19	zero	zero	NUM
ejpam-5166	142	20	divisors	divisor	NOUN
ejpam-5166	142	21	.	.	PUNCT
ejpam-5166	143	1	the	the	DET
ejpam-5166	143	2	nontrivial	nontrivial	ADJ
ejpam-5166	143	3	zero	zero	NUM
ejpam-5166	143	4	divisors	divisor	NOUN
ejpam-5166	143	5	in	in	ADP
ejpam-5166	143	6	zp3	zp3	PROPN
ejpam-5166	143	7	are	be	AUX
ejpam-5166	143	8	z	z	NOUN
ejpam-5166	143	9	=	=	PUNCT
ejpam-5166	143	10	{	{	PUNCT
ejpam-5166	143	11	p	p	X
ejpam-5166	143	12	,	,	PUNCT
ejpam-5166	143	13	2p	2p	NUM
ejpam-5166	143	14	,	,	PUNCT
ejpam-5166	143	15	.	.	PUNCT
ejpam-5166	143	16	.	.	PUNCT
ejpam-5166	143	17	.	.	PUNCT
ejpam-5166	144	1	,	,	PUNCT
ejpam-5166	144	2	(	(	PUNCT
ejpam-5166	144	3	p−	p−	NOUN
ejpam-5166	144	4	1)p	1)p	NUM
ejpam-5166	144	5	,	,	PUNCT
ejpam-5166	144	6	p2	p2	X
ejpam-5166	144	7	,	,	PUNCT
ejpam-5166	144	8	(	(	PUNCT
ejpam-5166	144	9	p+	p+	PROPN
ejpam-5166	144	10	1)p	1)p	NUM
ejpam-5166	144	11	,	,	PUNCT
ejpam-5166	144	12	.	.	PUNCT
ejpam-5166	144	13	.	.	PUNCT
ejpam-5166	145	1	.	.	PUNCT
ejpam-5166	146	1	,	,	PUNCT
ejpam-5166	146	2	2(p−	2(p−	NUM
ejpam-5166	146	3	1)p	1)p	NUM
ejpam-5166	146	4	,	,	PUNCT
ejpam-5166	146	5	2p2	2p2	NUM
ejpam-5166	146	6	,	,	PUNCT
ejpam-5166	146	7	.	.	PUNCT
ejpam-5166	146	8	.	.	PUNCT
ejpam-5166	146	9	.	.	PUNCT
ejpam-5166	147	1	,	,	PUNCT
ejpam-5166	147	2	(	(	PUNCT
ejpam-5166	147	3	p2	p2	PROPN
ejpam-5166	147	4	−	−	PROPN
ejpam-5166	147	5	1)p	1)p	NUM
ejpam-5166	147	6	}	}	PUNCT
ejpam-5166	147	7	.	.	PUNCT
ejpam-5166	148	1	n.	n.	PROPN
ejpam-5166	148	2	hidayat	hidayat	PROPN
ejpam-5166	148	3	et	et	PROPN
ejpam-5166	148	4	al	al	PROPN
ejpam-5166	148	5	/	/	PUNCT
ejpam-5166	148	6	eur	eur	PROPN
ejpam-5166	148	7	.	.	PUNCT
ejpam-5166	149	1	j.	j.	PROPN
ejpam-5166	149	2	pure	pure	PROPN
ejpam-5166	149	3	appl	appl	PROPN
ejpam-5166	149	4	.	.	PROPN
ejpam-5166	149	5	math	math	PROPN
ejpam-5166	149	6	,	,	PUNCT
ejpam-5166	149	7	17	17	NUM
ejpam-5166	149	8	(	(	PUNCT
ejpam-5166	149	9	3	3	NUM
ejpam-5166	149	10	)	)	PUNCT
ejpam-5166	149	11	(	(	PUNCT
ejpam-5166	149	12	2024	2024	NUM
ejpam-5166	149	13	)	)	PUNCT
ejpam-5166	149	14	,	,	PUNCT
ejpam-5166	149	15	1659	1659	NUM
ejpam-5166	149	16	-	-	SYM
ejpam-5166	149	17	1673	1673	NUM
ejpam-5166	149	18	1664	1664	NUM
ejpam-5166	149	19	next	next	ADV
ejpam-5166	149	20	,	,	PUNCT
ejpam-5166	149	21	we	we	PRON
ejpam-5166	149	22	partition	partition	VERB
ejpam-5166	149	23	zp3	zp3	NOUN
ejpam-5166	149	24	into	into	ADP
ejpam-5166	149	25	three	three	NUM
ejpam-5166	149	26	sets	set	NOUN
ejpam-5166	149	27	,	,	PUNCT
ejpam-5166	149	28	namely	namely	ADV
ejpam-5166	149	29	the	the	DET
ejpam-5166	149	30	zero	zero	NUM
ejpam-5166	149	31	set	set	VERB
ejpam-5166	149	32	o	o	X
ejpam-5166	149	33	=	=	PUNCT
ejpam-5166	149	34	{	{	PUNCT
ejpam-5166	149	35	0	0	NUM
ejpam-5166	149	36	}	}	PUNCT
ejpam-5166	149	37	,	,	PUNCT
ejpam-5166	149	38	the	the	DET
ejpam-5166	149	39	unit	unit	NOUN
ejpam-5166	149	40	set	set	VERB
ejpam-5166	149	41	u	u	NOUN
ejpam-5166	149	42	=	=	PUNCT
ejpam-5166	149	43	{	{	PUNCT
ejpam-5166	149	44	x	x	SYM
ejpam-5166	149	45	∈	∈	PROPN
ejpam-5166	149	46	zp3	zp3	NOUN
ejpam-5166	149	47	|x	|x	PROPN
ejpam-5166	149	48	is	be	AUX
ejpam-5166	149	49	unit	unit	NOUN
ejpam-5166	149	50	in	in	ADP
ejpam-5166	149	51	ring	ring	NOUN
ejpam-5166	149	52	zp3	zp3	PROPN
ejpam-5166	149	53	}	}	PUNCT
ejpam-5166	149	54	,	,	PUNCT
ejpam-5166	149	55	and	and	CCONJ
ejpam-5166	149	56	the	the	DET
ejpam-5166	149	57	set	set	NOUN
ejpam-5166	149	58	of	of	ADP
ejpam-5166	149	59	nontrivial	nontrivial	ADJ
ejpam-5166	149	60	zero	zero	NUM
ejpam-5166	149	61	divisors	divisor	NOUN
ejpam-5166	149	62	zp3	zp3	X
ejpam-5166	149	63	are	be	AUX
ejpam-5166	149	64	a	a	DET
ejpam-5166	149	65	=	=	X
ejpam-5166	149	66	{	{	PUNCT
ejpam-5166	149	67	p2	p2	NOUN
ejpam-5166	149	68	,	,	PUNCT
ejpam-5166	149	69	2p2	2p2	NUM
ejpam-5166	149	70	,	,	PUNCT
ejpam-5166	149	71	.	.	PUNCT
ejpam-5166	149	72	.	.	PUNCT
ejpam-5166	150	1	.	.	PUNCT
ejpam-5166	151	1	,	,	PUNCT
ejpam-5166	151	2	(	(	PUNCT
ejpam-5166	151	3	p−	p−	NOUN
ejpam-5166	151	4	1)p2	1)p2	NUM
ejpam-5166	151	5	}	}	PUNCT
ejpam-5166	151	6	=	=	SYM
ejpam-5166	151	7	⟨p2⟩	⟨p2⟩	X
ejpam-5166	151	8	\	\	PUNCT
ejpam-5166	151	9	{	{	PUNCT
ejpam-5166	151	10	0	0	NUM
ejpam-5166	151	11	}	}	PUNCT
ejpam-5166	151	12	,	,	PUNCT
ejpam-5166	151	13	|a|	|a|	PROPN
ejpam-5166	151	14	=	=	NOUN
ejpam-5166	151	15	p−	p−	NOUN
ejpam-5166	151	16	1	1	NUM
ejpam-5166	151	17	,	,	PUNCT
ejpam-5166	151	18	b	b	NOUN
ejpam-5166	151	19	=	=	SYM
ejpam-5166	151	20	⟨p⟩	⟨p⟩	PROPN
ejpam-5166	151	21	\	\	X
ejpam-5166	151	22	⟨p2⟩	⟨p2⟩	PROPN
ejpam-5166	151	23	,	,	PUNCT
ejpam-5166	151	24	|b|	|b|	PROPN
ejpam-5166	151	25	=	=	PUNCT
ejpam-5166	151	26	p2	p2	PROPN
ejpam-5166	151	27	−	−	PROPN
ejpam-5166	151	28	p.	p.	NOUN
ejpam-5166	151	29	based	base	VERB
ejpam-5166	151	30	on	on	ADP
ejpam-5166	151	31	theorem	theorem	NOUN
ejpam-5166	151	32	1	1	NUM
ejpam-5166	151	33	,	,	PUNCT
ejpam-5166	151	34	the	the	DET
ejpam-5166	151	35	adjacency	adjacency	NOUN
ejpam-5166	151	36	of	of	ADP
ejpam-5166	151	37	every	every	DET
ejpam-5166	151	38	vertex	vertex	NOUN
ejpam-5166	151	39	in	in	ADP
ejpam-5166	151	40	pg(zp3	pg(zp3	PROPN
ejpam-5166	151	41	)	)	PUNCT
ejpam-5166	151	42	is	be	AUX
ejpam-5166	151	43	as	as	SCONJ
ejpam-5166	151	44	follows	follow	VERB
ejpam-5166	151	45	:	:	PUNCT
ejpam-5166	151	46	(	(	PUNCT
ejpam-5166	151	47	i	i	NOUN
ejpam-5166	151	48	)	)	PUNCT
ejpam-5166	151	49	every	every	DET
ejpam-5166	151	50	vertex	vertex	NOUN
ejpam-5166	151	51	in	in	ADP
ejpam-5166	151	52	o	o	PROPN
ejpam-5166	151	53	is	be	AUX
ejpam-5166	151	54	adjacent	adjacent	ADJ
ejpam-5166	151	55	to	to	ADP
ejpam-5166	151	56	every	every	DET
ejpam-5166	151	57	vertex	vertex	NOUN
ejpam-5166	151	58	in	in	ADP
ejpam-5166	151	59	a	a	DET
ejpam-5166	151	60	,	,	PUNCT
ejpam-5166	151	61	b	b	NOUN
ejpam-5166	151	62	,	,	PUNCT
ejpam-5166	151	63	and	and	CCONJ
ejpam-5166	151	64	u	u	NOUN
ejpam-5166	151	65	.	.	PUNCT
ejpam-5166	152	1	(	(	PUNCT
ejpam-5166	152	2	ii	ii	NOUN
ejpam-5166	152	3	)	)	PUNCT
ejpam-5166	152	4	every	every	DET
ejpam-5166	152	5	vertex	vertex	NOUN
ejpam-5166	152	6	in	in	ADP
ejpam-5166	152	7	a	a	PRON
ejpam-5166	152	8	is	be	AUX
ejpam-5166	152	9	adjacent	adjacent	ADJ
ejpam-5166	152	10	to	to	ADP
ejpam-5166	152	11	every	every	DET
ejpam-5166	152	12	vertex	vertex	NOUN
ejpam-5166	152	13	in	in	ADP
ejpam-5166	152	14	o	o	PROPN
ejpam-5166	152	15	,	,	PUNCT
ejpam-5166	152	16	a	a	PRON
ejpam-5166	152	17	and	and	CCONJ
ejpam-5166	152	18	b.	b.	PROPN
ejpam-5166	152	19	(	(	PUNCT
ejpam-5166	152	20	iii	iii	NOUN
ejpam-5166	152	21	)	)	PUNCT
ejpam-5166	152	22	every	every	DET
ejpam-5166	152	23	vertex	vertex	NOUN
ejpam-5166	152	24	in	in	ADP
ejpam-5166	152	25	b	b	PROPN
ejpam-5166	152	26	is	be	AUX
ejpam-5166	152	27	adjacent	adjacent	ADJ
ejpam-5166	152	28	to	to	ADP
ejpam-5166	152	29	every	every	DET
ejpam-5166	152	30	vertex	vertex	NOUN
ejpam-5166	152	31	in	in	ADP
ejpam-5166	152	32	o	o	PROPN
ejpam-5166	152	33	and	and	CCONJ
ejpam-5166	152	34	a.	a.	NOUN
ejpam-5166	152	35	(	(	PUNCT
ejpam-5166	152	36	iv	iv	X
ejpam-5166	152	37	)	)	PUNCT
ejpam-5166	152	38	every	every	DET
ejpam-5166	152	39	vertex	vertex	NOUN
ejpam-5166	152	40	in	in	ADP
ejpam-5166	152	41	u	u	NOUN
ejpam-5166	152	42	is	be	AUX
ejpam-5166	152	43	only	only	ADV
ejpam-5166	152	44	adjcacent	adjcacent	ADJ
ejpam-5166	152	45	to	to	ADP
ejpam-5166	152	46	every	every	DET
ejpam-5166	152	47	vertex	vertex	NOUN
ejpam-5166	152	48	in	in	ADP
ejpam-5166	152	49	o.	o.	PROPN
ejpam-5166	153	1	so	so	ADV
ejpam-5166	153	2	,	,	PUNCT
ejpam-5166	153	3	we	we	PRON
ejpam-5166	153	4	obtain	obtain	VERB
ejpam-5166	153	5	the	the	DET
ejpam-5166	153	6	distance	distance	NOUN
ejpam-5166	153	7	matrix	matrix	NOUN
ejpam-5166	153	8	of	of	ADP
ejpam-5166	153	9	pg(zp3	pg(zp3	PROPN
ejpam-5166	153	10	)	)	PUNCT
ejpam-5166	153	11	is	be	AUX
ejpam-5166	153	12	d(pg(zp3	d(pg(zp3	NOUN
ejpam-5166	153	13	)	)	PUNCT
ejpam-5166	153	14	)	)	PUNCT
ejpam-5166	154	1	=	=	PUNCT
ejpam-5166	154	2			NOUN
ejpam-5166	154	3	o	o	NOUN
ejpam-5166	154	4	a	a	DET
ejpam-5166	154	5	b	b	X
ejpam-5166	154	6	u	u	NOUN
ejpam-5166	154	7	o	o	NOUN
ejpam-5166	154	8	0	0	NUM
ejpam-5166	154	9	11×(p2−p	11×(p2−p	NUM
ejpam-5166	154	10	)	)	PUNCT
ejpam-5166	154	11	11×(p−1	11×(p−1	NUM
ejpam-5166	154	12	)	)	PUNCT
ejpam-5166	154	13	11×(p3−p2	11×(p3−p2	NUM
ejpam-5166	154	14	)	)	PUNCT
ejpam-5166	154	15	a	a	DET
ejpam-5166	154	16	1(p2−p)×1	1(p2−p)×1	NUM
ejpam-5166	154	17	2(jp2−p	2(jp2−p	NUM
ejpam-5166	154	18	−	−	PROPN
ejpam-5166	154	19	ip2−p	ip2−p	PROPN
ejpam-5166	154	20	)	)	PUNCT
ejpam-5166	154	21	1(p2−p)×(p−1	1(p2−p)×(p−1	NUM
ejpam-5166	154	22	)	)	PUNCT
ejpam-5166	154	23	2(p2−p)×(p3−p2	2(p2−p)×(p3−p2	NUM
ejpam-5166	154	24	)	)	PUNCT
ejpam-5166	154	25	b	b	NOUN
ejpam-5166	154	26	1(p−1)×1	1(p−1)×1	NUM
ejpam-5166	154	27	1(p−1)×(p2−p	1(p−1)×(p2−p	NUM
ejpam-5166	154	28	)	)	PUNCT
ejpam-5166	154	29	jp−1	jp−1	PROPN
ejpam-5166	154	30	−	−	PROPN
ejpam-5166	154	31	ip−1	ip−1	PROPN
ejpam-5166	154	32	2(p−1)×(p3−p2	2(p−1)×(p3−p2	NUM
ejpam-5166	154	33	)	)	PUNCT
ejpam-5166	154	34	u	u	NOUN
ejpam-5166	154	35	1(p3−p2)×1	1(p3−p2)×1	NUM
ejpam-5166	154	36	2(p3−p2)×(p2−p	2(p3−p2)×(p2−p	X
ejpam-5166	154	37	)	)	PUNCT
ejpam-5166	154	38	2(p3−p2)×(p−1	2(p3−p2)×(p−1	NUM
ejpam-5166	154	39	)	)	PUNCT
ejpam-5166	154	40	2(jp3−p2	2(jp3−p2	NUM
ejpam-5166	154	41	−	−	NOUN
ejpam-5166	154	42	ip3−p2	ip3−p2	NOUN
ejpam-5166	154	43	)	)	PUNCT
ejpam-5166	154	44			NOUN
ejpam-5166	154	45	,	,	PUNCT
ejpam-5166	154	46	where	where	SCONJ
ejpam-5166	154	47	1m×n	1m×n	NOUN
ejpam-5166	154	48	is	be	AUX
ejpam-5166	154	49	a	a	DET
ejpam-5166	154	50	matrix	matrix	NOUN
ejpam-5166	154	51	of	of	ADP
ejpam-5166	154	52	order	order	NOUN
ejpam-5166	154	53	m	m	VERB
ejpam-5166	154	54	×	×	NOUN
ejpam-5166	154	55	n	n	INTJ
ejpam-5166	154	56	with	with	ADP
ejpam-5166	154	57	all	all	DET
ejpam-5166	154	58	entries	entry	NOUN
ejpam-5166	154	59	1	1	NUM
ejpam-5166	154	60	,	,	PUNCT
ejpam-5166	154	61	2m×n	2m×n	NUM
ejpam-5166	154	62	is	be	AUX
ejpam-5166	154	63	a	a	DET
ejpam-5166	154	64	matrix	matrix	NOUN
ejpam-5166	154	65	of	of	ADP
ejpam-5166	154	66	order	order	NOUN
ejpam-5166	154	67	m	m	VERB
ejpam-5166	154	68	×	×	NOUN
ejpam-5166	154	69	n	n	INTJ
ejpam-5166	154	70	with	with	ADP
ejpam-5166	154	71	all	all	DET
ejpam-5166	154	72	entries	entry	NOUN
ejpam-5166	154	73	2	2	NUM
ejpam-5166	154	74	,	,	PUNCT
ejpam-5166	154	75	and	and	CCONJ
ejpam-5166	154	76	jn	jn	PROPN
ejpam-5166	154	77	=	=	PROPN
ejpam-5166	155	1	1n×n	1n×n	PROPN
ejpam-5166	155	2	.	.	PUNCT
ejpam-5166	156	1	a	a	DET
ejpam-5166	156	2	half	half	NOUN
ejpam-5166	156	3	of	of	ADP
ejpam-5166	156	4	the	the	DET
ejpam-5166	156	5	sum	sum	NOUN
ejpam-5166	156	6	of	of	ADP
ejpam-5166	156	7	all	all	DET
ejpam-5166	156	8	entries	entry	NOUN
ejpam-5166	156	9	in	in	ADP
ejpam-5166	156	10	the	the	DET
ejpam-5166	156	11	matrix	matrix	NOUN
ejpam-5166	156	12	d(pg(zp3	d(pg(zp3	NOUN
ejpam-5166	156	13	)	)	PUNCT
ejpam-5166	156	14	)	)	PUNCT
ejpam-5166	156	15	is	be	AUX
ejpam-5166	156	16	w	w	PROPN
ejpam-5166	156	17	(	(	PUNCT
ejpam-5166	156	18	pg(zp3	pg(zp3	X
ejpam-5166	156	19	)	)	PUNCT
ejpam-5166	156	20	)	)	PUNCT
ejpam-5166	157	1	=	=	SYM
ejpam-5166	157	2	1	1	NUM
ejpam-5166	157	3	2	2	NUM
ejpam-5166	157	4	(	(	PUNCT
ejpam-5166	157	5	2p6	2p6	NUM
ejpam-5166	157	6	−	−	NUM
ejpam-5166	157	7	2p3	2p3	NUM
ejpam-5166	157	8	−	−	NOUN
ejpam-5166	157	9	2(p3	2(p3	NOUN
ejpam-5166	157	10	−	−	PROPN
ejpam-5166	157	11	1)−	1)−	NUM
ejpam-5166	157	12	2(p2	2(p2	NUM
ejpam-5166	157	13	−	−	ADP
ejpam-5166	157	14	p)(p−	p)(p−	VERB
ejpam-5166	157	15	1)−	1)−	PROPN
ejpam-5166	157	16	(	(	PUNCT
ejpam-5166	157	17	p−	p−	NOUN
ejpam-5166	157	18	1)2	1)2	NUM
ejpam-5166	157	19	+	+	CCONJ
ejpam-5166	157	20	(	(	PUNCT
ejpam-5166	157	21	p−	p−	NOUN
ejpam-5166	157	22	1	1	NUM
ejpam-5166	157	23	)	)	PUNCT
ejpam-5166	157	24	)	)	PUNCT
ejpam-5166	158	1	=	=	SYM
ejpam-5166	158	2	2p6	2p6	NUM
ejpam-5166	158	3	−	−	NOUN
ejpam-5166	158	4	6p3	6p3	NUM
ejpam-5166	159	1	+	+	CCONJ
ejpam-5166	159	2	3p2	3p2	NUM
ejpam-5166	159	3	+	+	CCONJ
ejpam-5166	159	4	p	p	SYM
ejpam-5166	159	5	2	2	NUM
ejpam-5166	159	6	=	=	NUM
ejpam-5166	159	7	p(p−	p(p−	VERB
ejpam-5166	159	8	1)(2p4	1)(2p4	NUM
ejpam-5166	159	9	+	+	CCONJ
ejpam-5166	159	10	2p3	2p3	NUM
ejpam-5166	160	1	+	+	CCONJ
ejpam-5166	160	2	2p2	2p2	NUM
ejpam-5166	160	3	−	−	PROPN
ejpam-5166	161	1	4p−	4p−	NUM
ejpam-5166	161	2	1	1	NUM
ejpam-5166	161	3	)	)	PUNCT
ejpam-5166	161	4	2	2	NUM
ejpam-5166	161	5	.	.	PUNCT
ejpam-5166	162	1	thus	thus	ADV
ejpam-5166	162	2	,	,	PUNCT
ejpam-5166	162	3	we	we	PRON
ejpam-5166	162	4	obtain	obtain	VERB
ejpam-5166	162	5	w	w	ADP
ejpam-5166	162	6	(	(	PUNCT
ejpam-5166	162	7	pg(zp3	pg(zp3	X
ejpam-5166	162	8	)	)	PUNCT
ejpam-5166	162	9	)	)	PUNCT
ejpam-5166	163	1	=	=	PUNCT
ejpam-5166	163	2	p(p−	p(p−	VERB
ejpam-5166	163	3	1)(2p4	1)(2p4	NUM
ejpam-5166	163	4	+	+	CCONJ
ejpam-5166	163	5	2p3	2p3	NUM
ejpam-5166	164	1	+	+	CCONJ
ejpam-5166	164	2	2p2	2p2	NUM
ejpam-5166	164	3	−	−	PROPN
ejpam-5166	165	1	4p−	4p−	NUM
ejpam-5166	165	2	1	1	NUM
ejpam-5166	165	3	)	)	PUNCT
ejpam-5166	165	4	2	2	NUM
ejpam-5166	165	5	.	.	PUNCT
ejpam-5166	166	1	the	the	DET
ejpam-5166	166	2	wiener	wiener	NOUN
ejpam-5166	166	3	index	index	NOUN
ejpam-5166	166	4	formulas	formula	NOUN
ejpam-5166	166	5	of	of	ADP
ejpam-5166	166	6	pg(zn	pg(zn	NOUN
ejpam-5166	166	7	)	)	PUNCT
ejpam-5166	166	8	in	in	ADP
ejpam-5166	166	9	theorem	theorem	NOUN
ejpam-5166	166	10	6	6	NUM
ejpam-5166	166	11	and	and	CCONJ
ejpam-5166	166	12	theorem	theorem	VERB
ejpam-5166	166	13	7	7	NUM
ejpam-5166	166	14	are	be	AUX
ejpam-5166	166	15	different	different	ADJ
ejpam-5166	166	16	from	from	ADP
ejpam-5166	166	17	the	the	DET
ejpam-5166	166	18	formula	formula	NOUN
ejpam-5166	166	19	in	in	ADP
ejpam-5166	166	20	theorem	theorem	ADJ
ejpam-5166	166	21	3	3	NUM
ejpam-5166	166	22	and	and	CCONJ
ejpam-5166	166	23	theorem	theorem	VERB
ejpam-5166	166	24	4	4	NUM
ejpam-5166	166	25	,	,	PUNCT
ejpam-5166	166	26	respectively	respectively	ADV
ejpam-5166	166	27	.	.	PUNCT
ejpam-5166	167	1	we	we	PRON
ejpam-5166	167	2	claim	claim	VERB
ejpam-5166	167	3	that	that	SCONJ
ejpam-5166	167	4	theorem	theorem	VERB
ejpam-5166	167	5	6	6	NUM
ejpam-5166	167	6	and	and	CCONJ
ejpam-5166	167	7	theorem	theorem	VERB
ejpam-5166	167	8	7	7	NUM
ejpam-5166	167	9	are	be	AUX
ejpam-5166	167	10	correct	correct	ADJ
ejpam-5166	167	11	.	.	PUNCT
ejpam-5166	168	1	we	we	PRON
ejpam-5166	168	2	give	give	VERB
ejpam-5166	168	3	a	a	DET
ejpam-5166	168	4	simple	simple	ADJ
ejpam-5166	168	5	example	example	NOUN
ejpam-5166	168	6	for	for	ADP
ejpam-5166	168	7	p	p	NOUN
ejpam-5166	168	8	=	=	NOUN
ejpam-5166	168	9	2	2	NUM
ejpam-5166	168	10	.	.	PUNCT
ejpam-5166	169	1	the	the	DET
ejpam-5166	169	2	prime	prime	ADJ
ejpam-5166	169	3	graphs	graph	NOUN
ejpam-5166	169	4	of	of	ADP
ejpam-5166	169	5	pg(z4	pg(z4	NOUN
ejpam-5166	169	6	)	)	PUNCT
ejpam-5166	169	7	and	and	CCONJ
ejpam-5166	169	8	pg(z8	pg(z8	NUM
ejpam-5166	169	9	)	)	PUNCT
ejpam-5166	169	10	are	be	AUX
ejpam-5166	169	11	given	give	VERB
ejpam-5166	169	12	in	in	ADP
ejpam-5166	169	13	figure	figure	NOUN
ejpam-5166	169	14	1	1	NUM
ejpam-5166	169	15	.	.	PUNCT
ejpam-5166	169	16	n.	n.	PROPN
ejpam-5166	169	17	hidayat	hidayat	PROPN
ejpam-5166	169	18	et	et	PROPN
ejpam-5166	169	19	al	al	PROPN
ejpam-5166	169	20	/	/	PUNCT
ejpam-5166	169	21	eur	eur	PROPN
ejpam-5166	169	22	.	.	PUNCT
ejpam-5166	170	1	j.	j.	PROPN
ejpam-5166	170	2	pure	pure	PROPN
ejpam-5166	170	3	appl	appl	PROPN
ejpam-5166	170	4	.	.	PROPN
ejpam-5166	170	5	math	math	PROPN
ejpam-5166	170	6	,	,	PUNCT
ejpam-5166	170	7	17	17	NUM
ejpam-5166	170	8	(	(	PUNCT
ejpam-5166	170	9	3	3	NUM
ejpam-5166	170	10	)	)	PUNCT
ejpam-5166	170	11	(	(	PUNCT
ejpam-5166	170	12	2024	2024	NUM
ejpam-5166	170	13	)	)	PUNCT
ejpam-5166	170	14	,	,	PUNCT
ejpam-5166	170	15	1659	1659	NUM
ejpam-5166	170	16	-	-	SYM
ejpam-5166	170	17	1673	1673	NUM
ejpam-5166	170	18	1665	1665	NUM
ejpam-5166	170	19	figure	figure	NOUN
ejpam-5166	170	20	1	1	NUM
ejpam-5166	170	21	:	:	PUNCT
ejpam-5166	170	22	(	(	PUNCT
ejpam-5166	170	23	a	a	NOUN
ejpam-5166	170	24	)	)	PUNCT
ejpam-5166	170	25	.	.	PUNCT
ejpam-5166	171	1	prime	prime	ADJ
ejpam-5166	171	2	graph	graph	NOUN
ejpam-5166	171	3	of	of	ADP
ejpam-5166	171	4	ring	ring	NOUN
ejpam-5166	171	5	z4	z4	PROPN
ejpam-5166	171	6	,	,	PUNCT
ejpam-5166	171	7	and	and	CCONJ
ejpam-5166	171	8	(	(	PUNCT
ejpam-5166	171	9	b	b	NOUN
ejpam-5166	171	10	)	)	PUNCT
ejpam-5166	171	11	.	.	PUNCT
ejpam-5166	172	1	prime	prime	ADJ
ejpam-5166	172	2	graph	graph	NOUN
ejpam-5166	172	3	of	of	ADP
ejpam-5166	172	4	ring	ring	NOUN
ejpam-5166	172	5	z8	z8	NOUN
ejpam-5166	172	6	we	we	PRON
ejpam-5166	172	7	compare	compare	VERB
ejpam-5166	172	8	the	the	DET
ejpam-5166	172	9	wiener	wiener	NOUN
ejpam-5166	172	10	index	index	NOUN
ejpam-5166	172	11	formula	formula	NOUN
ejpam-5166	172	12	of	of	ADP
ejpam-5166	172	13	pg(z4	pg(z4	NOUN
ejpam-5166	172	14	)	)	PUNCT
ejpam-5166	172	15	resulting	result	VERB
ejpam-5166	172	16	from	from	ADP
ejpam-5166	172	17	theorem	theorem	ADJ
ejpam-5166	172	18	6	6	NUM
ejpam-5166	172	19	and	and	CCONJ
ejpam-5166	172	20	theorem	theorem	VERB
ejpam-5166	172	21	3	3	NUM
ejpam-5166	172	22	with	with	ADP
ejpam-5166	172	23	definition	definition	NOUN
ejpam-5166	172	24	1	1	NUM
ejpam-5166	172	25	.	.	PUNCT
ejpam-5166	172	26	based	base	VERB
ejpam-5166	172	27	on	on	ADP
ejpam-5166	172	28	theorem	theorem	NOUN
ejpam-5166	172	29	3	3	NUM
ejpam-5166	172	30	,	,	PUNCT
ejpam-5166	172	31	we	we	PRON
ejpam-5166	172	32	get	get	VERB
ejpam-5166	172	33	w	w	NOUN
ejpam-5166	172	34	(	(	PUNCT
ejpam-5166	172	35	pg(z4	pg(z4	NOUN
ejpam-5166	172	36	)	)	PUNCT
ejpam-5166	172	37	)	)	PUNCT
ejpam-5166	173	1	=	=	SYM
ejpam-5166	173	2	5	5	NUM
ejpam-5166	173	3	and	and	CCONJ
ejpam-5166	173	4	based	base	VERB
ejpam-5166	173	5	on	on	ADP
ejpam-5166	173	6	theorem	theorem	NOUN
ejpam-5166	173	7	6	6	NUM
ejpam-5166	173	8	,	,	PUNCT
ejpam-5166	173	9	we	we	PRON
ejpam-5166	173	10	get	get	VERB
ejpam-5166	173	11	w	w	NOUN
ejpam-5166	173	12	(	(	PUNCT
ejpam-5166	173	13	pg(z4	pg(z4	NOUN
ejpam-5166	173	14	)	)	PUNCT
ejpam-5166	173	15	)	)	PUNCT
ejpam-5166	174	1	=	=	SYM
ejpam-5166	174	2	9	9	X
ejpam-5166	174	3	.	.	PUNCT
ejpam-5166	175	1	however	however	ADV
ejpam-5166	175	2	,	,	PUNCT
ejpam-5166	175	3	by	by	ADP
ejpam-5166	175	4	definition	definition	NOUN
ejpam-5166	175	5	1	1	NUM
ejpam-5166	175	6	,	,	PUNCT
ejpam-5166	175	7	since	since	SCONJ
ejpam-5166	175	8	d(0	d(0	NOUN
ejpam-5166	175	9	,	,	PUNCT
ejpam-5166	175	10	1	1	NUM
ejpam-5166	175	11	)	)	PUNCT
ejpam-5166	175	12	=	=	SYM
ejpam-5166	175	13	d(0	d(0	NOUN
ejpam-5166	175	14	,	,	PUNCT
ejpam-5166	175	15	2	2	NUM
ejpam-5166	175	16	)	)	PUNCT
ejpam-5166	175	17	=	=	SYM
ejpam-5166	175	18	d(0	d(0	NOUN
ejpam-5166	175	19	,	,	PUNCT
ejpam-5166	175	20	3	3	NUM
ejpam-5166	175	21	)	)	PUNCT
ejpam-5166	175	22	=	=	SYM
ejpam-5166	175	23	1	1	X
ejpam-5166	175	24	,	,	PUNCT
ejpam-5166	175	25	d(1	d(1	NOUN
ejpam-5166	175	26	,	,	PUNCT
ejpam-5166	175	27	2	2	NUM
ejpam-5166	175	28	)	)	PUNCT
ejpam-5166	175	29	=	=	PUNCT
ejpam-5166	175	30	d(1	d(1	PROPN
ejpam-5166	175	31	,	,	PUNCT
ejpam-5166	175	32	3	3	X
ejpam-5166	175	33	)	)	PUNCT
ejpam-5166	175	34	=	=	SYM
ejpam-5166	175	35	d(2	d(2	PROPN
ejpam-5166	175	36	,	,	PUNCT
ejpam-5166	175	37	3	3	NUM
ejpam-5166	175	38	)	)	PUNCT
ejpam-5166	175	39	=	=	SYM
ejpam-5166	175	40	2	2	NUM
ejpam-5166	175	41	,	,	PUNCT
ejpam-5166	175	42	the	the	DET
ejpam-5166	175	43	wiener	wiener	NOUN
ejpam-5166	175	44	index	index	NOUN
ejpam-5166	175	45	of	of	ADP
ejpam-5166	175	46	pg(z4	pg(z4	NOUN
ejpam-5166	175	47	)	)	PUNCT
ejpam-5166	175	48	isw	isw	NOUN
ejpam-5166	175	49	(	(	PUNCT
ejpam-5166	175	50	pg(z4	pg(z4	NOUN
ejpam-5166	175	51	)	)	PUNCT
ejpam-5166	175	52	)	)	PUNCT
ejpam-5166	176	1	=	=	SYM
ejpam-5166	176	2	9	9	X
ejpam-5166	176	3	.	.	PUNCT
ejpam-5166	177	1	now	now	ADV
ejpam-5166	177	2	,	,	PUNCT
ejpam-5166	177	3	we	we	PRON
ejpam-5166	177	4	compare	compare	VERB
ejpam-5166	177	5	the	the	DET
ejpam-5166	177	6	wiener	wiener	NOUN
ejpam-5166	177	7	index	index	NOUN
ejpam-5166	177	8	formula	formula	NOUN
ejpam-5166	177	9	of	of	ADP
ejpam-5166	177	10	pg(z8	pg(z8	NUM
ejpam-5166	177	11	)	)	PUNCT
ejpam-5166	177	12	resulting	result	VERB
ejpam-5166	177	13	from	from	ADP
ejpam-5166	177	14	theorem	theorem	ADJ
ejpam-5166	177	15	7	7	NUM
ejpam-5166	177	16	and	and	CCONJ
ejpam-5166	177	17	theorem	theorem	VERB
ejpam-5166	177	18	4	4	NUM
ejpam-5166	177	19	with	with	ADP
ejpam-5166	177	20	definition	definition	NOUN
ejpam-5166	177	21	1	1	NUM
ejpam-5166	177	22	.	.	PUNCT
ejpam-5166	177	23	based	base	VERB
ejpam-5166	177	24	on	on	ADP
ejpam-5166	177	25	theorem	theorem	NOUN
ejpam-5166	177	26	4	4	NUM
ejpam-5166	177	27	,	,	PUNCT
ejpam-5166	177	28	we	we	PRON
ejpam-5166	177	29	get	get	VERB
ejpam-5166	177	30	w	w	NOUN
ejpam-5166	177	31	(	(	PUNCT
ejpam-5166	177	32	pg(z8	pg(z8	NUM
ejpam-5166	177	33	)	)	PUNCT
ejpam-5166	177	34	)	)	PUNCT
ejpam-5166	178	1	=	=	SYM
ejpam-5166	178	2	41	41	NUM
ejpam-5166	178	3	and	and	CCONJ
ejpam-5166	178	4	based	base	VERB
ejpam-5166	178	5	on	on	ADP
ejpam-5166	178	6	theorem	theorem	NOUN
ejpam-5166	178	7	7	7	NUM
ejpam-5166	178	8	,	,	PUNCT
ejpam-5166	178	9	we	we	PRON
ejpam-5166	178	10	get	get	VERB
ejpam-5166	178	11	w	w	NOUN
ejpam-5166	178	12	(	(	PUNCT
ejpam-5166	178	13	pg(z8	pg(z8	NUM
ejpam-5166	178	14	)	)	PUNCT
ejpam-5166	178	15	)	)	PUNCT
ejpam-5166	179	1	=	=	PUNCT
ejpam-5166	179	2	47	47	NUM
ejpam-5166	179	3	.	.	PUNCT
ejpam-5166	180	1	however	however	ADV
ejpam-5166	180	2	,	,	PUNCT
ejpam-5166	180	3	by	by	ADP
ejpam-5166	180	4	definition	definition	NOUN
ejpam-5166	180	5	1	1	NUM
ejpam-5166	180	6	,	,	PUNCT
ejpam-5166	180	7	the	the	DET
ejpam-5166	180	8	wiener	wiener	NOUN
ejpam-5166	180	9	index	index	NOUN
ejpam-5166	180	10	of	of	ADP
ejpam-5166	180	11	pg(z8	pg(z8	NOUN
ejpam-5166	180	12	)	)	PUNCT
ejpam-5166	180	13	is	be	AUX
ejpam-5166	180	14	w	w	NOUN
ejpam-5166	180	15	(	(	PUNCT
ejpam-5166	180	16	pg(z8	pg(z8	NUM
ejpam-5166	180	17	)	)	PUNCT
ejpam-5166	180	18	)	)	PUNCT
ejpam-5166	181	1	=	=	PUNCT
ejpam-5166	182	1	47	47	NUM
ejpam-5166	182	2	.	.	PUNCT
ejpam-5166	183	1	next	next	ADV
ejpam-5166	183	2	,	,	PUNCT
ejpam-5166	183	3	we	we	PRON
ejpam-5166	183	4	investigate	investigate	VERB
ejpam-5166	183	5	the	the	DET
ejpam-5166	183	6	wiener	wiener	NOUN
ejpam-5166	183	7	index	index	NOUN
ejpam-5166	183	8	formula	formula	NOUN
ejpam-5166	183	9	for	for	ADP
ejpam-5166	183	10	other	other	ADJ
ejpam-5166	183	11	cases	case	NOUN
ejpam-5166	183	12	of	of	ADP
ejpam-5166	183	13	n	n	CCONJ
ejpam-5166	183	14	,	,	PUNCT
ejpam-5166	183	15	that	that	ADV
ejpam-5166	183	16	is	is	ADV
ejpam-5166	183	17	,	,	PUNCT
ejpam-5166	183	18	for	for	ADP
ejpam-5166	183	19	n	n	PROPN
ejpam-5166	183	20	=	=	SYM
ejpam-5166	183	21	pq	pq	PROPN
ejpam-5166	183	22	,	,	PUNCT
ejpam-5166	183	23	n	n	PROPN
ejpam-5166	183	24	=	=	SYM
ejpam-5166	183	25	pqr	pqr	PROPN
ejpam-5166	183	26	,	,	PUNCT
ejpam-5166	183	27	n	n	NOUN
ejpam-5166	183	28	=	=	PUNCT
ejpam-5166	183	29	p2q	p2q	NOUN
ejpam-5166	183	30	,	,	PUNCT
ejpam-5166	183	31	and	and	CCONJ
ejpam-5166	183	32	n	n	NOUN
ejpam-5166	183	33	=	=	SYM
ejpam-5166	183	34	p2q2	p2q2	X
ejpam-5166	183	35	where	where	SCONJ
ejpam-5166	183	36	p	p	X
ejpam-5166	183	37	,	,	PUNCT
ejpam-5166	183	38	q	q	X
ejpam-5166	183	39	,	,	PUNCT
ejpam-5166	183	40	and	and	CCONJ
ejpam-5166	183	41	r	r	NOUN
ejpam-5166	183	42	are	be	AUX
ejpam-5166	183	43	different	different	ADJ
ejpam-5166	183	44	primes	prime	NOUN
ejpam-5166	183	45	.	.	PUNCT
ejpam-5166	184	1	the	the	DET
ejpam-5166	184	2	wiener	wiener	NOUN
ejpam-5166	184	3	index	index	NOUN
ejpam-5166	184	4	formula	formula	NOUN
ejpam-5166	184	5	for	for	ADP
ejpam-5166	184	6	pg(zpq	pg(zpq	PROPN
ejpam-5166	184	7	)	)	PUNCT
ejpam-5166	184	8	is	be	AUX
ejpam-5166	184	9	as	as	SCONJ
ejpam-5166	184	10	follows	follow	VERB
ejpam-5166	184	11	:	:	PUNCT
ejpam-5166	184	12	theorem	theorem	NOUN
ejpam-5166	184	13	8	8	NUM
ejpam-5166	184	14	.	.	PUNCT
ejpam-5166	185	1	if	if	SCONJ
ejpam-5166	185	2	p	p	X
ejpam-5166	185	3	,	,	PUNCT
ejpam-5166	185	4	q	q	X
ejpam-5166	185	5	are	be	AUX
ejpam-5166	185	6	two	two	NUM
ejpam-5166	185	7	distinct	distinct	ADJ
ejpam-5166	185	8	prime	prime	ADJ
ejpam-5166	185	9	numbers	number	NOUN
ejpam-5166	185	10	,	,	PUNCT
ejpam-5166	185	11	then	then	ADV
ejpam-5166	185	12	w	w	PROPN
ejpam-5166	185	13	(	(	PUNCT
ejpam-5166	185	14	pg(zpq	pg(zpq	PROPN
ejpam-5166	185	15	)	)	PUNCT
ejpam-5166	185	16	)	)	PUNCT
ejpam-5166	186	1	=	=	PUNCT
ejpam-5166	187	1	p2q2	p2q2	ADP
ejpam-5166	187	2	−	−	NOUN
ejpam-5166	187	3	3pq	3pq	NOUN
ejpam-5166	187	4	+	+	CCONJ
ejpam-5166	187	5	p+	p+	NOUN
ejpam-5166	187	6	q.	q.	NOUN
ejpam-5166	187	7	proof	proof	NOUN
ejpam-5166	187	8	.	.	PUNCT
ejpam-5166	188	1	for	for	ADP
ejpam-5166	188	2	every	every	DET
ejpam-5166	188	3	prime	prime	ADJ
ejpam-5166	188	4	number	number	NOUN
ejpam-5166	188	5	p	p	NOUN
ejpam-5166	188	6	,	,	PUNCT
ejpam-5166	188	7	q	q	X
ejpam-5166	188	8	,	,	PUNCT
ejpam-5166	188	9	the	the	DET
ejpam-5166	188	10	ring	ring	NOUN
ejpam-5166	188	11	zpq	zpq	NOUN
ejpam-5166	188	12	has	have	VERB
ejpam-5166	188	13	u	u	NOUN
ejpam-5166	188	14	=	=	PUNCT
ejpam-5166	188	15	(	(	PUNCT
ejpam-5166	188	16	p	p	X
ejpam-5166	188	17	−	−	PROPN
ejpam-5166	188	18	1)(q	1)(q	NUM
ejpam-5166	188	19	−	−	NOUN
ejpam-5166	188	20	1	1	NUM
ejpam-5166	188	21	)	)	PUNCT
ejpam-5166	188	22	units	unit	NOUN
ejpam-5166	188	23	and	and	CCONJ
ejpam-5166	188	24	p+	p+	NOUN
ejpam-5166	188	25	q	q	NOUN
ejpam-5166	188	26	−	−	PROPN
ejpam-5166	188	27	2	2	NUM
ejpam-5166	188	28	nontrivial	nontrivial	NOUN
ejpam-5166	188	29	zero	zero	NUM
ejpam-5166	188	30	divisors	divisor	NOUN
ejpam-5166	188	31	.	.	PUNCT
ejpam-5166	189	1	next	next	ADJ
ejpam-5166	189	2	,	,	PUNCT
ejpam-5166	189	3	we	we	PRON
ejpam-5166	189	4	partition	partition	VERB
ejpam-5166	189	5	zpq	zpq	VERB
ejpam-5166	189	6	into	into	ADP
ejpam-5166	189	7	three	three	NUM
ejpam-5166	189	8	sets	set	NOUN
ejpam-5166	189	9	,	,	PUNCT
ejpam-5166	189	10	namely	namely	ADV
ejpam-5166	189	11	the	the	DET
ejpam-5166	189	12	zero	zero	NUM
ejpam-5166	189	13	set	set	VERB
ejpam-5166	189	14	o	o	X
ejpam-5166	189	15	=	=	PUNCT
ejpam-5166	189	16	{	{	PUNCT
ejpam-5166	189	17	0	0	NUM
ejpam-5166	189	18	}	}	PUNCT
ejpam-5166	189	19	,	,	PUNCT
ejpam-5166	189	20	the	the	DET
ejpam-5166	189	21	unit	unit	NOUN
ejpam-5166	189	22	set	set	VERB
ejpam-5166	189	23	u	u	NOUN
ejpam-5166	189	24	=	=	PUNCT
ejpam-5166	189	25	{	{	PUNCT
ejpam-5166	189	26	x	x	SYM
ejpam-5166	189	27	∈	∈	PROPN
ejpam-5166	189	28	zpq|x	zpq|x	PROPN
ejpam-5166	189	29	is	be	AUX
ejpam-5166	189	30	unit	unit	NOUN
ejpam-5166	189	31	in	in	ADP
ejpam-5166	189	32	ring	ring	NOUN
ejpam-5166	189	33	zpq	zpq	PROPN
ejpam-5166	189	34	}	}	PUNCT
ejpam-5166	189	35	,	,	PUNCT
ejpam-5166	189	36	and	and	CCONJ
ejpam-5166	189	37	the	the	DET
ejpam-5166	189	38	set	set	NOUN
ejpam-5166	189	39	of	of	ADP
ejpam-5166	189	40	nontrivial	nontrivial	ADJ
ejpam-5166	189	41	zero	zero	NUM
ejpam-5166	189	42	divisors	divisor	NOUN
ejpam-5166	189	43	zpq	zpq	AUX
ejpam-5166	189	44	are	be	AUX
ejpam-5166	189	45	a	a	DET
ejpam-5166	189	46	=	=	X
ejpam-5166	189	47	{	{	PUNCT
ejpam-5166	189	48	q	q	NOUN
ejpam-5166	189	49	,	,	PUNCT
ejpam-5166	189	50	2q	2q	NUM
ejpam-5166	189	51	,	,	PUNCT
ejpam-5166	189	52	.	.	PUNCT
ejpam-5166	189	53	.	.	PUNCT
ejpam-5166	189	54	.	.	PUNCT
ejpam-5166	190	1	,	,	PUNCT
ejpam-5166	190	2	(	(	PUNCT
ejpam-5166	190	3	p−	p−	NOUN
ejpam-5166	190	4	1)q	1)q	NOUN
ejpam-5166	190	5	}	}	PUNCT
ejpam-5166	190	6	=	=	SYM
ejpam-5166	190	7	⟨q⟩	⟨q⟩	ADV
ejpam-5166	190	8	\	\	NOUN
ejpam-5166	190	9	{	{	PUNCT
ejpam-5166	190	10	0	0	NUM
ejpam-5166	190	11	}	}	PUNCT
ejpam-5166	190	12	,	,	PUNCT
ejpam-5166	190	13	|a|	|a|	PROPN
ejpam-5166	190	14	=	=	NOUN
ejpam-5166	190	15	p−	p−	NOUN
ejpam-5166	190	16	1	1	NUM
ejpam-5166	190	17	,	,	PUNCT
ejpam-5166	190	18	b	b	NOUN
ejpam-5166	190	19	=	=	PRON
ejpam-5166	190	20	{	{	PUNCT
ejpam-5166	190	21	p	p	X
ejpam-5166	190	22	,	,	PUNCT
ejpam-5166	190	23	2p	2p	NUM
ejpam-5166	190	24	,	,	PUNCT
ejpam-5166	190	25	.	.	PUNCT
ejpam-5166	190	26	.	.	PUNCT
ejpam-5166	190	27	.	.	PUNCT
ejpam-5166	191	1	,	,	PUNCT
ejpam-5166	191	2	(	(	PUNCT
ejpam-5166	191	3	q	q	NOUN
ejpam-5166	191	4	−	−	PROPN
ejpam-5166	191	5	1)p	1)p	NUM
ejpam-5166	191	6	}	}	PUNCT
ejpam-5166	191	7	=	=	SYM
ejpam-5166	191	8	⟨p⟩	⟨p⟩	PROPN
ejpam-5166	191	9	\	\	PROPN
ejpam-5166	191	10	{	{	PUNCT
ejpam-5166	191	11	0	0	NUM
ejpam-5166	191	12	}	}	PUNCT
ejpam-5166	191	13	,	,	PUNCT
ejpam-5166	191	14	|b|	|b|	PROPN
ejpam-5166	191	15	=	=	PUNCT
ejpam-5166	191	16	q	q	X
ejpam-5166	192	1	−	−	NOUN
ejpam-5166	192	2	1	1	NUM
ejpam-5166	192	3	.	.	PUNCT
ejpam-5166	192	4	based	base	VERB
ejpam-5166	192	5	on	on	ADP
ejpam-5166	192	6	theorem	theorem	NOUN
ejpam-5166	192	7	1	1	NUM
ejpam-5166	192	8	,	,	PUNCT
ejpam-5166	192	9	the	the	DET
ejpam-5166	192	10	adjacency	adjacency	NOUN
ejpam-5166	192	11	of	of	ADP
ejpam-5166	192	12	every	every	DET
ejpam-5166	192	13	vertex	vertex	NOUN
ejpam-5166	192	14	in	in	ADP
ejpam-5166	192	15	pg(zpq	pg(zpq	PROPN
ejpam-5166	192	16	)	)	PUNCT
ejpam-5166	192	17	is	be	AUX
ejpam-5166	192	18	as	as	SCONJ
ejpam-5166	192	19	follows	follow	VERB
ejpam-5166	192	20	:	:	PUNCT
ejpam-5166	192	21	(	(	PUNCT
ejpam-5166	192	22	i	i	NOUN
ejpam-5166	192	23	)	)	PUNCT
ejpam-5166	192	24	every	every	DET
ejpam-5166	192	25	vertex	vertex	NOUN
ejpam-5166	192	26	in	in	ADP
ejpam-5166	192	27	o	o	PROPN
ejpam-5166	192	28	is	be	AUX
ejpam-5166	192	29	adjacent	adjacent	ADJ
ejpam-5166	192	30	to	to	ADP
ejpam-5166	192	31	every	every	DET
ejpam-5166	192	32	vertex	vertex	NOUN
ejpam-5166	192	33	in	in	ADP
ejpam-5166	192	34	a	a	DET
ejpam-5166	192	35	,	,	PUNCT
ejpam-5166	192	36	b	b	NOUN
ejpam-5166	192	37	,	,	PUNCT
ejpam-5166	192	38	and	and	CCONJ
ejpam-5166	192	39	u	u	PROPN
ejpam-5166	192	40	.	.	PUNCT
ejpam-5166	193	1	n.	n.	PROPN
ejpam-5166	193	2	hidayat	hidayat	PROPN
ejpam-5166	193	3	et	et	PROPN
ejpam-5166	193	4	al	al	PROPN
ejpam-5166	193	5	/	/	PUNCT
ejpam-5166	193	6	eur	eur	PROPN
ejpam-5166	193	7	.	.	PUNCT
ejpam-5166	194	1	j.	j.	PROPN
ejpam-5166	194	2	pure	pure	PROPN
ejpam-5166	194	3	appl	appl	PROPN
ejpam-5166	194	4	.	.	PROPN
ejpam-5166	194	5	math	math	PROPN
ejpam-5166	194	6	,	,	PUNCT
ejpam-5166	194	7	17	17	NUM
ejpam-5166	194	8	(	(	PUNCT
ejpam-5166	194	9	3	3	NUM
ejpam-5166	194	10	)	)	PUNCT
ejpam-5166	194	11	(	(	PUNCT
ejpam-5166	194	12	2024	2024	NUM
ejpam-5166	194	13	)	)	PUNCT
ejpam-5166	194	14	,	,	PUNCT
ejpam-5166	194	15	1659	1659	NUM
ejpam-5166	194	16	-	-	SYM
ejpam-5166	194	17	1673	1673	NUM
ejpam-5166	194	18	1666	1666	NUM
ejpam-5166	194	19	(	(	PUNCT
ejpam-5166	194	20	ii	ii	NOUN
ejpam-5166	194	21	)	)	PUNCT
ejpam-5166	194	22	every	every	DET
ejpam-5166	194	23	vertex	vertex	NOUN
ejpam-5166	194	24	in	in	ADP
ejpam-5166	194	25	a	a	PRON
ejpam-5166	194	26	is	be	AUX
ejpam-5166	194	27	adjacent	adjacent	ADJ
ejpam-5166	194	28	to	to	ADP
ejpam-5166	194	29	every	every	DET
ejpam-5166	194	30	vertex	vertex	NOUN
ejpam-5166	194	31	in	in	ADP
ejpam-5166	194	32	o	o	PROPN
ejpam-5166	194	33	and	and	CCONJ
ejpam-5166	194	34	b.	b.	PROPN
ejpam-5166	194	35	(	(	PUNCT
ejpam-5166	194	36	iii	iii	NOUN
ejpam-5166	194	37	)	)	PUNCT
ejpam-5166	194	38	every	every	DET
ejpam-5166	194	39	vertex	vertex	NOUN
ejpam-5166	194	40	in	in	ADP
ejpam-5166	194	41	b	b	PROPN
ejpam-5166	194	42	is	be	AUX
ejpam-5166	194	43	adjacent	adjacent	ADJ
ejpam-5166	194	44	to	to	ADP
ejpam-5166	194	45	every	every	DET
ejpam-5166	194	46	vertex	vertex	NOUN
ejpam-5166	194	47	in	in	ADP
ejpam-5166	194	48	o	o	PROPN
ejpam-5166	194	49	and	and	CCONJ
ejpam-5166	194	50	b.	b.	PROPN
ejpam-5166	194	51	(	(	PUNCT
ejpam-5166	194	52	iv	iv	X
ejpam-5166	194	53	)	)	PUNCT
ejpam-5166	194	54	every	every	DET
ejpam-5166	194	55	vertex	vertex	NOUN
ejpam-5166	194	56	in	in	ADP
ejpam-5166	194	57	u	u	NOUN
ejpam-5166	194	58	is	be	AUX
ejpam-5166	194	59	only	only	ADV
ejpam-5166	194	60	adjacent	adjacent	ADJ
ejpam-5166	194	61	to	to	ADP
ejpam-5166	194	62	every	every	DET
ejpam-5166	194	63	vertex	vertex	NOUN
ejpam-5166	194	64	in	in	ADP
ejpam-5166	194	65	o.	o.	NOUN
ejpam-5166	194	66	then	then	ADV
ejpam-5166	194	67	,	,	PUNCT
ejpam-5166	194	68	the	the	DET
ejpam-5166	194	69	distance	distance	NOUN
ejpam-5166	194	70	matrix	matrix	NOUN
ejpam-5166	194	71	of	of	ADP
ejpam-5166	194	72	pg(zpq	pg(zpq	PROPN
ejpam-5166	194	73	)	)	PUNCT
ejpam-5166	194	74	is	be	AUX
ejpam-5166	194	75	d(pg(zpq	d(pg(zpq	NOUN
ejpam-5166	194	76	)	)	PUNCT
ejpam-5166	194	77	)	)	PUNCT
ejpam-5166	195	1	=	=	PUNCT
ejpam-5166	195	2			NOUN
ejpam-5166	195	3	o	o	NOUN
ejpam-5166	195	4	a	a	PRON
ejpam-5166	195	5	b	b	X
ejpam-5166	195	6	u	u	NOUN
ejpam-5166	195	7	o	o	PROPN
ejpam-5166	195	8	0	0	NUM
ejpam-5166	195	9	11×(p−1	11×(p−1	NUM
ejpam-5166	195	10	)	)	PUNCT
ejpam-5166	195	11	11×(q−1	11×(q−1	NUM
ejpam-5166	195	12	)	)	PUNCT
ejpam-5166	196	1	11×u	11×u	NUM
ejpam-5166	196	2	a	a	DET
ejpam-5166	196	3	1(p−1)×1	1(p−1)×1	NUM
ejpam-5166	196	4	2(jp−1	2(jp−1	NUM
ejpam-5166	196	5	−	−	NOUN
ejpam-5166	196	6	ip−1	ip−1	NOUN
ejpam-5166	196	7	)	)	PUNCT
ejpam-5166	196	8	1(p−1)×(q−1	1(p−1)×(q−1	NUM
ejpam-5166	196	9	)	)	PUNCT
ejpam-5166	196	10	2(p−1)×u	2(p−1)×u	NUM
ejpam-5166	196	11	b	b	SYM
ejpam-5166	196	12	1(q−1)×1	1(q−1)×1	NUM
ejpam-5166	196	13	1(q−1)×(p−1	1(q−1)×(p−1	NUM
ejpam-5166	196	14	)	)	PUNCT
ejpam-5166	197	1	2(jq−1	2(jq−1	NUM
ejpam-5166	197	2	−	−	PROPN
ejpam-5166	197	3	iq−1	iq−1	NOUN
ejpam-5166	197	4	)	)	PUNCT
ejpam-5166	197	5	2(q−1)×u	2(q−1)×u	NUM
ejpam-5166	197	6	u	u	NOUN
ejpam-5166	197	7	1u×1	1u×1	NUM
ejpam-5166	197	8	2u×(p−1	2u×(p−1	NUM
ejpam-5166	197	9	)	)	PUNCT
ejpam-5166	197	10	2u×(q−1	2u×(q−1	NUM
ejpam-5166	197	11	)	)	PUNCT
ejpam-5166	197	12	2(ju	2(ju	PROPN
ejpam-5166	197	13	−	−	PROPN
ejpam-5166	197	14	iu	iu	NOUN
ejpam-5166	197	15	)	)	PUNCT
ejpam-5166	197	16			NOUN
ejpam-5166	197	17	,	,	PUNCT
ejpam-5166	197	18	where	where	SCONJ
ejpam-5166	197	19	1m×n	1m×n	NOUN
ejpam-5166	197	20	is	be	AUX
ejpam-5166	197	21	a	a	DET
ejpam-5166	197	22	matrix	matrix	NOUN
ejpam-5166	197	23	of	of	ADP
ejpam-5166	197	24	order	order	NOUN
ejpam-5166	197	25	m	m	VERB
ejpam-5166	197	26	×	×	NOUN
ejpam-5166	197	27	n	n	INTJ
ejpam-5166	197	28	with	with	ADP
ejpam-5166	197	29	all	all	DET
ejpam-5166	197	30	entries	entry	NOUN
ejpam-5166	197	31	1	1	NUM
ejpam-5166	197	32	,	,	PUNCT
ejpam-5166	197	33	2m×n	2m×n	NUM
ejpam-5166	197	34	is	be	AUX
ejpam-5166	197	35	a	a	DET
ejpam-5166	197	36	matrix	matrix	NOUN
ejpam-5166	197	37	of	of	ADP
ejpam-5166	197	38	order	order	NOUN
ejpam-5166	197	39	m	m	VERB
ejpam-5166	197	40	×	×	NOUN
ejpam-5166	197	41	n	n	INTJ
ejpam-5166	197	42	with	with	ADP
ejpam-5166	197	43	all	all	DET
ejpam-5166	197	44	entries	entry	NOUN
ejpam-5166	197	45	2	2	NUM
ejpam-5166	197	46	,	,	PUNCT
ejpam-5166	197	47	and	and	CCONJ
ejpam-5166	197	48	jn	jn	PROPN
ejpam-5166	197	49	=	=	PROPN
ejpam-5166	198	1	1n×n	1n×n	PROPN
ejpam-5166	198	2	.	.	PUNCT
ejpam-5166	199	1	a	a	DET
ejpam-5166	199	2	half	half	NOUN
ejpam-5166	199	3	of	of	ADP
ejpam-5166	199	4	the	the	DET
ejpam-5166	199	5	sum	sum	NOUN
ejpam-5166	199	6	of	of	ADP
ejpam-5166	199	7	all	all	DET
ejpam-5166	199	8	entries	entry	NOUN
ejpam-5166	199	9	in	in	ADP
ejpam-5166	199	10	the	the	DET
ejpam-5166	199	11	matrix	matrix	NOUN
ejpam-5166	199	12	d(pg(zpq	d(pg(zpq	NOUN
ejpam-5166	199	13	)	)	PUNCT
ejpam-5166	199	14	)	)	PUNCT
ejpam-5166	199	15	is	be	AUX
ejpam-5166	199	16	w	w	PROPN
ejpam-5166	199	17	(	(	PUNCT
ejpam-5166	199	18	pg(zpq	pg(zpq	PROPN
ejpam-5166	199	19	)	)	PUNCT
ejpam-5166	199	20	)	)	PUNCT
ejpam-5166	200	1	=	=	SYM
ejpam-5166	200	2	1	1	NUM
ejpam-5166	200	3	2	2	NUM
ejpam-5166	200	4	(	(	PUNCT
ejpam-5166	200	5	2p2q2	2p2q2	NUM
ejpam-5166	200	6	−	−	ADP
ejpam-5166	200	7	2pq	2pq	NOUN
ejpam-5166	200	8	−	−	PROPN
ejpam-5166	200	9	2(pq	2(pq	NOUN
ejpam-5166	200	10	−	−	PROPN
ejpam-5166	200	11	1)−	1)−	PROPN
ejpam-5166	200	12	2(p−	2(p−	NUM
ejpam-5166	200	13	1)(q	1)(q	NUM
ejpam-5166	200	14	−	−	NOUN
ejpam-5166	200	15	1	1	NUM
ejpam-5166	200	16	)	)	PUNCT
ejpam-5166	200	17	)	)	PUNCT
ejpam-5166	201	1	=	=	NOUN
ejpam-5166	201	2	p2q2	p2q2	ADP
ejpam-5166	201	3	−	−	PROPN
ejpam-5166	201	4	3pq	3pq	NOUN
ejpam-5166	201	5	+	+	CCONJ
ejpam-5166	201	6	p+	p+	PROPN
ejpam-5166	201	7	q.	q.	NOUN
ejpam-5166	201	8	thus	thus	ADV
ejpam-5166	201	9	,	,	PUNCT
ejpam-5166	201	10	we	we	PRON
ejpam-5166	201	11	obtain	obtain	VERB
ejpam-5166	201	12	w	w	ADP
ejpam-5166	201	13	(	(	PUNCT
ejpam-5166	201	14	pg(zpq	pg(zpq	PROPN
ejpam-5166	201	15	)	)	PUNCT
ejpam-5166	201	16	)	)	PUNCT
ejpam-5166	202	1	=	=	PUNCT
ejpam-5166	203	1	p2q2	p2q2	ADP
ejpam-5166	203	2	−	−	NOUN
ejpam-5166	203	3	3pq	3pq	NOUN
ejpam-5166	203	4	+	+	CCONJ
ejpam-5166	203	5	p+	p+	PROPN
ejpam-5166	203	6	q.	q.	PROPN
ejpam-5166	203	7	theorem	theorem	VERB
ejpam-5166	203	8	9	9	NUM
ejpam-5166	203	9	.	.	PUNCT
ejpam-5166	204	1	if	if	SCONJ
ejpam-5166	204	2	p	p	X
ejpam-5166	204	3	,	,	PUNCT
ejpam-5166	204	4	q	q	X
ejpam-5166	204	5	,	,	PUNCT
ejpam-5166	204	6	and	and	CCONJ
ejpam-5166	204	7	r	r	NOUN
ejpam-5166	204	8	are	be	AUX
ejpam-5166	204	9	distinct	distinct	ADJ
ejpam-5166	204	10	prime	prime	ADJ
ejpam-5166	204	11	numbers	number	NOUN
ejpam-5166	204	12	,	,	PUNCT
ejpam-5166	204	13	then	then	ADV
ejpam-5166	204	14	w	w	PROPN
ejpam-5166	204	15	(	(	PUNCT
ejpam-5166	204	16	pg(zpqr	pg(zpqr	PROPN
ejpam-5166	204	17	)	)	PUNCT
ejpam-5166	204	18	)	)	PUNCT
ejpam-5166	205	1	=	=	PUNCT
ejpam-5166	205	2	p2q2r2	p2q2r2	NOUN
ejpam-5166	205	3	−	−	X
ejpam-5166	205	4	5pqr	5pqr	PROPN
ejpam-5166	205	5	+	+	NUM
ejpam-5166	205	6	2(pq	2(pq	NOUN
ejpam-5166	205	7	+	+	CCONJ
ejpam-5166	205	8	qr	qr	NOUN
ejpam-5166	205	9	+	+	CCONJ
ejpam-5166	205	10	pr)−	pr)−	PROPN
ejpam-5166	205	11	(	(	PUNCT
ejpam-5166	205	12	p+	p+	NOUN
ejpam-5166	205	13	q	q	X
ejpam-5166	205	14	+	+	CCONJ
ejpam-5166	205	15	r	r	NOUN
ejpam-5166	205	16	)	)	PUNCT
ejpam-5166	205	17	+	+	NOUN
ejpam-5166	205	18	1	1	X
ejpam-5166	205	19	.	.	X
ejpam-5166	205	20	proof	proof	NOUN
ejpam-5166	205	21	.	.	PUNCT
ejpam-5166	206	1	for	for	ADP
ejpam-5166	206	2	every	every	DET
ejpam-5166	206	3	three	three	NUM
ejpam-5166	206	4	distinct	distinct	ADJ
ejpam-5166	206	5	prime	prime	ADJ
ejpam-5166	206	6	numbers	number	NOUN
ejpam-5166	206	7	p	p	X
ejpam-5166	206	8	,	,	PUNCT
ejpam-5166	206	9	q	q	ADJ
ejpam-5166	206	10	,	,	PUNCT
ejpam-5166	206	11	and	and	CCONJ
ejpam-5166	206	12	r	r	NOUN
ejpam-5166	206	13	,	,	PUNCT
ejpam-5166	206	14	the	the	DET
ejpam-5166	206	15	ring	ring	NOUN
ejpam-5166	206	16	zpqr	zpqr	NOUN
ejpam-5166	206	17	has	have	VERB
ejpam-5166	206	18	u	u	NOUN
ejpam-5166	206	19	=	=	PUNCT
ejpam-5166	206	20	(	(	PUNCT
ejpam-5166	206	21	p−	p−	NOUN
ejpam-5166	206	22	1)(q−	1)(q−	NUM
ejpam-5166	206	23	1)(r−	1)(r−	NUM
ejpam-5166	206	24	1	1	NUM
ejpam-5166	206	25	)	)	PUNCT
ejpam-5166	206	26	=	=	SYM
ejpam-5166	207	1	pqr−	pqr−	PROPN
ejpam-5166	207	2	pq−	pq−	PROPN
ejpam-5166	207	3	qr−	qr−	PROPN
ejpam-5166	207	4	pr+	pr+	PROPN
ejpam-5166	207	5	p+	p+	PROPN
ejpam-5166	207	6	q+	q+	PUNCT
ejpam-5166	207	7	r−	r−	PROPN
ejpam-5166	207	8	1	1	NUM
ejpam-5166	207	9	units	unit	NOUN
ejpam-5166	207	10	and	and	CCONJ
ejpam-5166	207	11	pq+	pq+	NOUN
ejpam-5166	207	12	qr+	qr+	NOUN
ejpam-5166	207	13	pr−	pr−	PUNCT
ejpam-5166	208	1	p−	p−	NOUN
ejpam-5166	208	2	q−	q−	PROPN
ejpam-5166	208	3	r	r	NOUN
ejpam-5166	208	4	nontrivial	nontrivial	NOUN
ejpam-5166	208	5	zero	zero	NUM
ejpam-5166	208	6	divisors	divisor	NOUN
ejpam-5166	208	7	.	.	PUNCT
ejpam-5166	209	1	the	the	DET
ejpam-5166	209	2	nontrivial	nontrivial	ADJ
ejpam-5166	209	3	zero	zero	NUM
ejpam-5166	209	4	divisor	divisor	NOUN
ejpam-5166	209	5	of	of	ADP
ejpam-5166	209	6	zpqr	zpqr	NOUN
ejpam-5166	209	7	is	be	AUX
ejpam-5166	209	8	z	z	NOUN
ejpam-5166	209	9	=	=	SYM
ejpam-5166	209	10	(	(	PUNCT
ejpam-5166	209	11	⟨p⟩	⟨p⟩	PROPN
ejpam-5166	209	12	∪	∪	VERB
ejpam-5166	209	13	⟨q⟩	⟨q⟩	ADP
ejpam-5166	209	14	∪	∪	ADJ
ejpam-5166	209	15	⟨r⟩	⟨r⟩	PROPN
ejpam-5166	209	16	)	)	PUNCT
ejpam-5166	209	17	\	\	NOUN
ejpam-5166	209	18	{	{	PUNCT
ejpam-5166	209	19	0	0	NUM
ejpam-5166	209	20	}	}	PUNCT
ejpam-5166	209	21	.	.	PUNCT
ejpam-5166	210	1	next	next	ADV
ejpam-5166	210	2	,	,	PUNCT
ejpam-5166	210	3	we	we	PRON
ejpam-5166	210	4	partition	partition	VERB
ejpam-5166	210	5	zpqr	zpqr	NOUN
ejpam-5166	210	6	into	into	ADP
ejpam-5166	210	7	three	three	NUM
ejpam-5166	210	8	sets	set	NOUN
ejpam-5166	210	9	,	,	PUNCT
ejpam-5166	210	10	namely	namely	ADV
ejpam-5166	210	11	the	the	DET
ejpam-5166	210	12	zero	zero	NUM
ejpam-5166	210	13	set	set	VERB
ejpam-5166	210	14	o	o	X
ejpam-5166	210	15	=	=	PUNCT
ejpam-5166	210	16	{	{	PUNCT
ejpam-5166	210	17	0	0	NUM
ejpam-5166	210	18	}	}	PUNCT
ejpam-5166	210	19	,	,	PUNCT
ejpam-5166	210	20	the	the	DET
ejpam-5166	210	21	unit	unit	NOUN
ejpam-5166	210	22	set	set	VERB
ejpam-5166	210	23	u	u	NOUN
ejpam-5166	210	24	=	=	PUNCT
ejpam-5166	210	25	{	{	PUNCT
ejpam-5166	210	26	x	x	SYM
ejpam-5166	210	27	∈	∈	PROPN
ejpam-5166	210	28	zpqr|x	zpqr|x	X
ejpam-5166	210	29	is	be	AUX
ejpam-5166	210	30	unit	unit	NOUN
ejpam-5166	210	31	in	in	ADP
ejpam-5166	210	32	ring	ring	PROPN
ejpam-5166	210	33	zpqr	zpqr	PROPN
ejpam-5166	210	34	}	}	PUNCT
ejpam-5166	210	35	,	,	PUNCT
ejpam-5166	210	36	and	and	CCONJ
ejpam-5166	210	37	the	the	DET
ejpam-5166	210	38	set	set	NOUN
ejpam-5166	210	39	of	of	ADP
ejpam-5166	210	40	nontrivial	nontrivial	ADJ
ejpam-5166	210	41	zero	zero	NUM
ejpam-5166	210	42	divisors	divisor	NOUN
ejpam-5166	210	43	zpqr	zpqr	NOUN
ejpam-5166	210	44	are	be	AUX
ejpam-5166	210	45	a	a	DET
ejpam-5166	210	46	=	=	NOUN
ejpam-5166	210	47	⟨qr⟩	⟨qr⟩	X
ejpam-5166	210	48	\	\	PUNCT
ejpam-5166	210	49	{	{	PUNCT
ejpam-5166	210	50	0	0	NUM
ejpam-5166	210	51	}	}	PUNCT
ejpam-5166	210	52	,	,	PUNCT
ejpam-5166	210	53	|a|	|a|	PROPN
ejpam-5166	210	54	=	=	NOUN
ejpam-5166	210	55	p−	p−	NOUN
ejpam-5166	210	56	1	1	NUM
ejpam-5166	210	57	=	=	SYM
ejpam-5166	210	58	a	a	PROPN
ejpam-5166	210	59	,	,	PUNCT
ejpam-5166	210	60	b	b	NOUN
ejpam-5166	210	61	=	=	SYM
ejpam-5166	210	62	⟨pr⟩	⟨pr⟩	PROPN
ejpam-5166	210	63	\	\	NOUN
ejpam-5166	210	64	{	{	PUNCT
ejpam-5166	210	65	0	0	NUM
ejpam-5166	210	66	}	}	PUNCT
ejpam-5166	210	67	,	,	PUNCT
ejpam-5166	210	68	|b|	|b|	PROPN
ejpam-5166	210	69	=	=	PUNCT
ejpam-5166	210	70	q	q	X
ejpam-5166	210	71	−	−	PROPN
ejpam-5166	210	72	1	1	NUM
ejpam-5166	210	73	=	=	SYM
ejpam-5166	210	74	b	b	NOUN
ejpam-5166	210	75	,	,	PUNCT
ejpam-5166	210	76	c	c	NOUN
ejpam-5166	210	77	=	=	SYM
ejpam-5166	210	78	⟨pq⟩	⟨pq⟩	PROPN
ejpam-5166	210	79	\	\	X
ejpam-5166	210	80	{	{	PUNCT
ejpam-5166	210	81	0	0	NUM
ejpam-5166	210	82	}	}	PUNCT
ejpam-5166	210	83	,	,	PUNCT
ejpam-5166	210	84	|c|	|c|	PROPN
ejpam-5166	210	85	=	=	SYM
ejpam-5166	211	1	r	r	NOUN
ejpam-5166	211	2	−	−	PROPN
ejpam-5166	211	3	1	1	NUM
ejpam-5166	211	4	=	=	SYM
ejpam-5166	211	5	c	c	NOUN
ejpam-5166	211	6	,	,	PUNCT
ejpam-5166	211	7	d	d	NOUN
ejpam-5166	211	8	=	=	SYM
ejpam-5166	211	9	⟨p⟩	⟨p⟩	PROPN
ejpam-5166	211	10	\	\	PROPN
ejpam-5166	211	11	(	(	PUNCT
ejpam-5166	211	12	⟨pq⟩	⟨pq⟩	PROPN
ejpam-5166	211	13	∪	∪	ADP
ejpam-5166	211	14	⟨pr⟩	⟨pr⟩	PROPN
ejpam-5166	211	15	)	)	PUNCT
ejpam-5166	211	16	,	,	PUNCT
ejpam-5166	211	17	|d|	|d|	PROPN
ejpam-5166	211	18	=	=	SYM
ejpam-5166	211	19	qr	qr	PROPN
ejpam-5166	211	20	−	−	PROPN
ejpam-5166	211	21	(	(	PUNCT
ejpam-5166	211	22	q	q	PROPN
ejpam-5166	212	1	+	+	PUNCT
ejpam-5166	212	2	r	r	NOUN
ejpam-5166	212	3	−	−	NOUN
ejpam-5166	212	4	1	1	NUM
ejpam-5166	212	5	)	)	PUNCT
ejpam-5166	213	1	=	=	SYM
ejpam-5166	213	2	d	d	PROPN
ejpam-5166	213	3	,	,	PUNCT
ejpam-5166	213	4	e	e	X
ejpam-5166	213	5	=	=	PUNCT
ejpam-5166	213	6	⟨q⟩	⟨q⟩	PUNCT
ejpam-5166	213	7	\	\	NOUN
ejpam-5166	214	1	(	(	PUNCT
ejpam-5166	214	2	⟨pq⟩	⟨pq⟩	X
ejpam-5166	214	3	∪	∪	ADP
ejpam-5166	214	4	⟨qr⟩	⟨qr⟩	NOUN
ejpam-5166	214	5	)	)	PUNCT
ejpam-5166	214	6	,	,	PUNCT
ejpam-5166	214	7	|e|	|e|	PRON
ejpam-5166	214	8	=	=	PUNCT
ejpam-5166	214	9	pr	pr	NOUN
ejpam-5166	214	10	−	−	PROPN
ejpam-5166	214	11	(	(	PUNCT
ejpam-5166	214	12	p+	p+	NOUN
ejpam-5166	214	13	r	r	NOUN
ejpam-5166	214	14	−	−	NOUN
ejpam-5166	214	15	1	1	NUM
ejpam-5166	214	16	)	)	PUNCT
ejpam-5166	214	17	=	=	SYM
ejpam-5166	214	18	e	e	X
ejpam-5166	214	19	,	,	PUNCT
ejpam-5166	214	20	f	f	X
ejpam-5166	214	21	=	=	SYM
ejpam-5166	214	22	⟨r⟩	⟨r⟩	PROPN
ejpam-5166	214	23	\	\	PROPN
ejpam-5166	214	24	(	(	PUNCT
ejpam-5166	214	25	⟨pr⟩	⟨pr⟩	NOUN
ejpam-5166	214	26	∪	∪	VERB
ejpam-5166	214	27	⟨qr⟩	⟨qr⟩	NOUN
ejpam-5166	214	28	)	)	PUNCT
ejpam-5166	214	29	,	,	PUNCT
ejpam-5166	214	30	|f	|f	PUNCT
ejpam-5166	215	1	|	|	NOUN
ejpam-5166	215	2	=	=	SYM
ejpam-5166	215	3	pq	pq	NOUN
ejpam-5166	215	4	−	−	PROPN
ejpam-5166	215	5	(	(	PUNCT
ejpam-5166	215	6	p+	p+	NOUN
ejpam-5166	215	7	q	q	X
ejpam-5166	215	8	−	−	PROPN
ejpam-5166	215	9	1	1	NUM
ejpam-5166	215	10	)	)	PUNCT
ejpam-5166	215	11	=	=	SYM
ejpam-5166	216	1	f.	f.	PROPN
ejpam-5166	216	2	based	base	VERB
ejpam-5166	216	3	on	on	ADP
ejpam-5166	216	4	theorem	theorem	NOUN
ejpam-5166	216	5	1	1	NUM
ejpam-5166	216	6	,	,	PUNCT
ejpam-5166	216	7	the	the	DET
ejpam-5166	216	8	adjacency	adjacency	NOUN
ejpam-5166	216	9	of	of	ADP
ejpam-5166	216	10	every	every	DET
ejpam-5166	216	11	vertex	vertex	NOUN
ejpam-5166	216	12	in	in	ADP
ejpam-5166	216	13	pg(zpqr	pg(zpqr	PROPN
ejpam-5166	216	14	)	)	PUNCT
ejpam-5166	216	15	is	be	AUX
ejpam-5166	216	16	as	as	SCONJ
ejpam-5166	216	17	follows	follow	VERB
ejpam-5166	216	18	:	:	PUNCT
ejpam-5166	217	1	n.	n.	PROPN
ejpam-5166	217	2	hidayat	hidayat	PROPN
ejpam-5166	217	3	et	et	PROPN
ejpam-5166	217	4	al	al	PROPN
ejpam-5166	217	5	/	/	PUNCT
ejpam-5166	217	6	eur	eur	PROPN
ejpam-5166	217	7	.	.	PUNCT
ejpam-5166	218	1	j.	j.	PROPN
ejpam-5166	218	2	pure	pure	PROPN
ejpam-5166	218	3	appl	appl	PROPN
ejpam-5166	218	4	.	.	PROPN
ejpam-5166	218	5	math	math	PROPN
ejpam-5166	218	6	,	,	PUNCT
ejpam-5166	218	7	17	17	NUM
ejpam-5166	218	8	(	(	PUNCT
ejpam-5166	218	9	3	3	NUM
ejpam-5166	218	10	)	)	PUNCT
ejpam-5166	218	11	(	(	PUNCT
ejpam-5166	218	12	2024	2024	NUM
ejpam-5166	218	13	)	)	PUNCT
ejpam-5166	218	14	,	,	PUNCT
ejpam-5166	218	15	1659	1659	NUM
ejpam-5166	218	16	-	-	SYM
ejpam-5166	218	17	1673	1673	NUM
ejpam-5166	218	18	1667	1667	NUM
ejpam-5166	218	19	(	(	PUNCT
ejpam-5166	218	20	i	i	NOUN
ejpam-5166	218	21	)	)	PUNCT
ejpam-5166	218	22	every	every	DET
ejpam-5166	218	23	vertex	vertex	NOUN
ejpam-5166	218	24	in	in	ADP
ejpam-5166	218	25	o	o	PROPN
ejpam-5166	218	26	is	be	AUX
ejpam-5166	218	27	adjacent	adjacent	ADJ
ejpam-5166	218	28	to	to	ADP
ejpam-5166	218	29	every	every	DET
ejpam-5166	218	30	vertex	vertex	NOUN
ejpam-5166	218	31	in	in	ADP
ejpam-5166	218	32	a	a	DET
ejpam-5166	218	33	,	,	PUNCT
ejpam-5166	218	34	b	b	NOUN
ejpam-5166	218	35	,	,	PUNCT
ejpam-5166	218	36	c	c	NOUN
ejpam-5166	218	37	,	,	PUNCT
ejpam-5166	218	38	d	d	NOUN
ejpam-5166	218	39	,	,	PUNCT
ejpam-5166	218	40	e	e	NOUN
ejpam-5166	218	41	,	,	PUNCT
ejpam-5166	218	42	f	f	X
ejpam-5166	218	43	,	,	PUNCT
ejpam-5166	218	44	and	and	CCONJ
ejpam-5166	218	45	u	u	INTJ
ejpam-5166	218	46	.	.	PUNCT
ejpam-5166	219	1	(	(	PUNCT
ejpam-5166	219	2	ii	ii	NOUN
ejpam-5166	219	3	)	)	PUNCT
ejpam-5166	219	4	every	every	DET
ejpam-5166	219	5	vertex	vertex	NOUN
ejpam-5166	219	6	in	in	ADP
ejpam-5166	219	7	a	a	PRON
ejpam-5166	219	8	is	be	AUX
ejpam-5166	219	9	adjacent	adjacent	ADJ
ejpam-5166	219	10	to	to	ADP
ejpam-5166	219	11	every	every	DET
ejpam-5166	219	12	vertex	vertex	NOUN
ejpam-5166	219	13	in	in	ADP
ejpam-5166	219	14	o	o	PROPN
ejpam-5166	219	15	,	,	PUNCT
ejpam-5166	219	16	b	b	PROPN
ejpam-5166	219	17	,	,	PUNCT
ejpam-5166	219	18	c	c	NOUN
ejpam-5166	219	19	,	,	PUNCT
ejpam-5166	219	20	and	and	CCONJ
ejpam-5166	219	21	d.	d.	PROPN
ejpam-5166	219	22	(	(	PUNCT
ejpam-5166	219	23	iii	iii	NOUN
ejpam-5166	219	24	)	)	PUNCT
ejpam-5166	219	25	every	every	DET
ejpam-5166	219	26	vertex	vertex	NOUN
ejpam-5166	219	27	in	in	ADP
ejpam-5166	219	28	b	b	PROPN
ejpam-5166	219	29	is	be	AUX
ejpam-5166	219	30	adjacent	adjacent	ADJ
ejpam-5166	219	31	to	to	ADP
ejpam-5166	219	32	every	every	DET
ejpam-5166	219	33	vertex	vertex	NOUN
ejpam-5166	219	34	in	in	ADP
ejpam-5166	219	35	o	o	PROPN
ejpam-5166	219	36	,	,	PUNCT
ejpam-5166	219	37	a	a	PRON
ejpam-5166	219	38	,	,	PUNCT
ejpam-5166	219	39	c	c	NOUN
ejpam-5166	219	40	,	,	PUNCT
ejpam-5166	219	41	and	and	CCONJ
ejpam-5166	219	42	e.	e.	PROPN
ejpam-5166	219	43	(	(	PUNCT
ejpam-5166	219	44	iv	iv	X
ejpam-5166	219	45	)	)	PUNCT
ejpam-5166	219	46	every	every	DET
ejpam-5166	219	47	vertex	vertex	NOUN
ejpam-5166	219	48	in	in	ADP
ejpam-5166	219	49	c	c	PROPN
ejpam-5166	219	50	is	be	AUX
ejpam-5166	219	51	adjacent	adjacent	ADJ
ejpam-5166	219	52	to	to	ADP
ejpam-5166	219	53	every	every	DET
ejpam-5166	219	54	vertex	vertex	NOUN
ejpam-5166	219	55	in	in	ADP
ejpam-5166	219	56	o	o	PROPN
ejpam-5166	219	57	,	,	PUNCT
ejpam-5166	219	58	a	a	DET
ejpam-5166	219	59	,	,	PUNCT
ejpam-5166	219	60	b	b	NOUN
ejpam-5166	219	61	,	,	PUNCT
ejpam-5166	219	62	and	and	CCONJ
ejpam-5166	219	63	f	f	X
ejpam-5166	219	64	.	.	PUNCT
ejpam-5166	220	1	(	(	PUNCT
ejpam-5166	220	2	v	v	NOUN
ejpam-5166	220	3	)	)	PUNCT
ejpam-5166	220	4	every	every	DET
ejpam-5166	220	5	vertex	vertex	NOUN
ejpam-5166	220	6	in	in	ADP
ejpam-5166	220	7	d	d	PROPN
ejpam-5166	220	8	is	be	AUX
ejpam-5166	220	9	adjacent	adjacent	ADJ
ejpam-5166	220	10	to	to	ADP
ejpam-5166	220	11	every	every	DET
ejpam-5166	220	12	vertex	vertex	NOUN
ejpam-5166	220	13	in	in	ADP
ejpam-5166	220	14	o	o	PROPN
ejpam-5166	220	15	and	and	CCONJ
ejpam-5166	220	16	a.	a.	NOUN
ejpam-5166	220	17	(	(	PUNCT
ejpam-5166	220	18	vi	vi	NOUN
ejpam-5166	220	19	)	)	PUNCT
ejpam-5166	220	20	every	every	DET
ejpam-5166	220	21	vertex	vertex	NOUN
ejpam-5166	220	22	in	in	ADP
ejpam-5166	220	23	e	e	PROPN
ejpam-5166	220	24	is	be	AUX
ejpam-5166	220	25	adjacent	adjacent	ADJ
ejpam-5166	220	26	to	to	ADP
ejpam-5166	220	27	every	every	DET
ejpam-5166	220	28	vertex	vertex	NOUN
ejpam-5166	220	29	in	in	ADP
ejpam-5166	220	30	o	o	PROPN
ejpam-5166	220	31	and	and	CCONJ
ejpam-5166	220	32	b.	b.	PROPN
ejpam-5166	220	33	(	(	PUNCT
ejpam-5166	220	34	vii	vii	PROPN
ejpam-5166	220	35	)	)	PUNCT
ejpam-5166	220	36	every	every	DET
ejpam-5166	220	37	vertex	vertex	NOUN
ejpam-5166	220	38	in	in	ADP
ejpam-5166	220	39	f	f	PROPN
ejpam-5166	220	40	is	be	AUX
ejpam-5166	220	41	adjacent	adjacent	ADJ
ejpam-5166	220	42	to	to	ADP
ejpam-5166	220	43	every	every	DET
ejpam-5166	220	44	vertex	vertex	NOUN
ejpam-5166	220	45	in	in	ADP
ejpam-5166	220	46	o	o	PROPN
ejpam-5166	220	47	and	and	CCONJ
ejpam-5166	220	48	c.	c.	PROPN
ejpam-5166	220	49	(	(	PUNCT
ejpam-5166	220	50	viii	viii	PROPN
ejpam-5166	220	51	)	)	PUNCT
ejpam-5166	220	52	every	every	DET
ejpam-5166	220	53	vertex	vertex	NOUN
ejpam-5166	220	54	in	in	ADP
ejpam-5166	220	55	u	u	NOUN
ejpam-5166	220	56	is	be	AUX
ejpam-5166	220	57	only	only	ADV
ejpam-5166	220	58	adjacent	adjacent	ADJ
ejpam-5166	220	59	to	to	ADP
ejpam-5166	220	60	every	every	DET
ejpam-5166	220	61	vertex	vertex	NOUN
ejpam-5166	220	62	in	in	ADP
ejpam-5166	220	63	o.	o.	PROPN
ejpam-5166	220	64	the	the	DET
ejpam-5166	220	65	distance	distance	NOUN
ejpam-5166	220	66	matrix	matrix	NOUN
ejpam-5166	220	67	d(pg(zpqr	d(pg(zpqr	NUM
ejpam-5166	220	68	)	)	PUNCT
ejpam-5166	220	69	)	)	PUNCT
ejpam-5166	220	70	can	can	AUX
ejpam-5166	220	71	then	then	ADV
ejpam-5166	220	72	be	be	AUX
ejpam-5166	220	73	written	write	VERB
ejpam-5166	220	74	as	as	ADP
ejpam-5166	220	75			ADJ
ejpam-5166	220	76	o	o	NOUN
ejpam-5166	220	77	a	a	DET
ejpam-5166	220	78	b	b	NOUN
ejpam-5166	220	79	c	c	NOUN
ejpam-5166	220	80	d	d	X
ejpam-5166	220	81	e	e	X
ejpam-5166	220	82	f	f	PROPN
ejpam-5166	220	83	u	u	NOUN
ejpam-5166	220	84	o	o	NOUN
ejpam-5166	220	85	0	0	PROPN
ejpam-5166	221	1	11×a	11×a	NUM
ejpam-5166	221	2	11×b	11×b	NUM
ejpam-5166	221	3	11×c	11×c	NUM
ejpam-5166	221	4	11×d	11×d	NUM
ejpam-5166	221	5	11×e	11×e	NUM
ejpam-5166	221	6	11×f	11×f	NUM
ejpam-5166	221	7	11×u	11×u	NUM
ejpam-5166	221	8	a	a	DET
ejpam-5166	221	9	1a×1	1a×1	NUM
ejpam-5166	221	10	2(ja	2(ja	NUM
ejpam-5166	221	11	−	−	PROPN
ejpam-5166	221	12	ia	ia	PROPN
ejpam-5166	221	13	)	)	PUNCT
ejpam-5166	221	14	1a×b	1a×b	PROPN
ejpam-5166	221	15	1a×c	1a×c	NUM
ejpam-5166	221	16	1a×d	1a×d	NUM
ejpam-5166	221	17	2a×e	2a×e	NUM
ejpam-5166	222	1	2a×f	2a×f	NUM
ejpam-5166	223	1	2a×u	2a×u	NUM
ejpam-5166	223	2	b	b	SYM
ejpam-5166	223	3	1b×1	1b×1	NUM
ejpam-5166	223	4	1b×a	1b×a	NOUN
ejpam-5166	223	5	2(jb	2(jb	NUM
ejpam-5166	223	6	−	−	ADP
ejpam-5166	223	7	ib	ib	NOUN
ejpam-5166	223	8	)	)	PUNCT
ejpam-5166	223	9	1b×c	1b×c	PROPN
ejpam-5166	224	1	2b×d	2b×d	NUM
ejpam-5166	225	1	1b×e	1b×e	NUM
ejpam-5166	225	2	2b×f	2b×f	NUM
ejpam-5166	226	1	2b×u	2b×u	NUM
ejpam-5166	226	2	c	c	NOUN
ejpam-5166	226	3	1c×1	1c×1	NUM
ejpam-5166	226	4	1c×a	1c×a	NUM
ejpam-5166	226	5	1c×b	1c×b	NUM
ejpam-5166	227	1	2(jc	2(jc	NUM
ejpam-5166	227	2	−	−	NOUN
ejpam-5166	227	3	ic	ic	NUM
ejpam-5166	227	4	)	)	PUNCT
ejpam-5166	228	1	2c×d	2c×d	NUM
ejpam-5166	228	2	2c×e	2c×e	NUM
ejpam-5166	228	3	1c×f	1c×f	NUM
ejpam-5166	228	4	2c×u	2c×u	NUM
ejpam-5166	229	1	d	d	SYM
ejpam-5166	229	2	1d×1	1d×1	NUM
ejpam-5166	229	3	1d×a	1d×a	NUM
ejpam-5166	229	4	2d×b	2d×b	NUM
ejpam-5166	229	5	2d×c	2d×c	NUM
ejpam-5166	229	6	2(jd	2(jd	NUM
ejpam-5166	229	7	−	−	PUNCT
ejpam-5166	229	8	i	i	PROPN
ejpam-5166	229	9	d	d	PROPN
ejpam-5166	229	10	)	)	PUNCT
ejpam-5166	229	11	2d×e	2d×e	NOUN
ejpam-5166	229	12	2d×f	2d×f	NUM
ejpam-5166	230	1	2d×u	2d×u	NUM
ejpam-5166	231	1	e	e	X
ejpam-5166	231	2	1e×1	1e×1	NUM
ejpam-5166	231	3	2e×a	2e×a	NUM
ejpam-5166	231	4	1e×b	1e×b	NUM
ejpam-5166	231	5	2e×c	2e×c	PROPN
ejpam-5166	232	1	2e×d	2e×d	NUM
ejpam-5166	232	2	2(je	2(je	NOUN
ejpam-5166	232	3	−	−	NOUN
ejpam-5166	232	4	ie	ie	ADJ
ejpam-5166	232	5	)	)	PUNCT
ejpam-5166	232	6	2e×f	2e×f	NOUN
ejpam-5166	232	7	2e×u	2e×u	NUM
ejpam-5166	232	8	f	f	X
ejpam-5166	233	1	1f×1	1f×1	NUM
ejpam-5166	233	2	2f×a	2f×a	NUM
ejpam-5166	234	1	2f×b	2f×b	NUM
ejpam-5166	235	1	1f×c	1f×c	NUM
ejpam-5166	235	2	2f×d	2f×d	NUM
ejpam-5166	236	1	2f×e	2f×e	NUM
ejpam-5166	237	1	2(jf	2(jf	NUM
ejpam-5166	238	1	−	−	NOUN
ejpam-5166	239	1	if	if	SCONJ
ejpam-5166	239	2	)	)	PUNCT
ejpam-5166	239	3	2f×u	2f×u	NUM
ejpam-5166	239	4	u	u	NOUN
ejpam-5166	239	5	1u×1	1u×1	NUM
ejpam-5166	239	6	2u×a	2u×a	PROPN
ejpam-5166	239	7	2u×b	2u×b	NUM
ejpam-5166	239	8	2u×c	2u×c	NUM
ejpam-5166	239	9	2u×d	2u×d	NUM
ejpam-5166	239	10	2u×e	2u×e	NUM
ejpam-5166	239	11	2u×f	2u×f	NOUN
ejpam-5166	239	12	2(ju	2(ju	NUM
ejpam-5166	239	13	−	−	PROPN
ejpam-5166	239	14	iu	iu	NOUN
ejpam-5166	239	15	)	)	PUNCT
ejpam-5166	239	16			NOUN
ejpam-5166	239	17	,	,	PUNCT
ejpam-5166	239	18	where	where	SCONJ
ejpam-5166	239	19	1m×n	1m×n	NOUN
ejpam-5166	239	20	is	be	AUX
ejpam-5166	239	21	a	a	DET
ejpam-5166	239	22	matrix	matrix	NOUN
ejpam-5166	239	23	of	of	ADP
ejpam-5166	239	24	order	order	NOUN
ejpam-5166	239	25	m	m	VERB
ejpam-5166	239	26	×	×	NOUN
ejpam-5166	239	27	n	n	INTJ
ejpam-5166	239	28	with	with	ADP
ejpam-5166	239	29	all	all	DET
ejpam-5166	239	30	entries	entry	NOUN
ejpam-5166	239	31	1	1	NUM
ejpam-5166	239	32	,	,	PUNCT
ejpam-5166	239	33	2m×n	2m×n	NUM
ejpam-5166	239	34	is	be	AUX
ejpam-5166	239	35	a	a	DET
ejpam-5166	239	36	matrix	matrix	NOUN
ejpam-5166	239	37	of	of	ADP
ejpam-5166	239	38	order	order	NOUN
ejpam-5166	239	39	m	m	VERB
ejpam-5166	239	40	×	×	NOUN
ejpam-5166	239	41	n	n	INTJ
ejpam-5166	239	42	with	with	ADP
ejpam-5166	239	43	all	all	DET
ejpam-5166	239	44	entries	entry	NOUN
ejpam-5166	239	45	2	2	NUM
ejpam-5166	239	46	,	,	PUNCT
ejpam-5166	239	47	and	and	CCONJ
ejpam-5166	239	48	jn	jn	PROPN
ejpam-5166	239	49	=	=	PROPN
ejpam-5166	240	1	1n×n	1n×n	PROPN
ejpam-5166	240	2	.	.	PUNCT
ejpam-5166	241	1	a	a	DET
ejpam-5166	241	2	half	half	NOUN
ejpam-5166	241	3	of	of	ADP
ejpam-5166	241	4	the	the	DET
ejpam-5166	241	5	sum	sum	NOUN
ejpam-5166	241	6	of	of	ADP
ejpam-5166	241	7	all	all	DET
ejpam-5166	241	8	entries	entry	NOUN
ejpam-5166	241	9	in	in	ADP
ejpam-5166	241	10	the	the	DET
ejpam-5166	241	11	matrix	matrix	NOUN
ejpam-5166	241	12	d(pg(zpqr	d(pg(zpqr	NUM
ejpam-5166	241	13	)	)	PUNCT
ejpam-5166	241	14	)	)	PUNCT
ejpam-5166	241	15	is	be	AUX
ejpam-5166	241	16	w	w	PROPN
ejpam-5166	241	17	(	(	PUNCT
ejpam-5166	241	18	pg(zpqr	pg(zpqr	PROPN
ejpam-5166	241	19	)	)	PUNCT
ejpam-5166	241	20	)	)	PUNCT
ejpam-5166	242	1	=	=	SYM
ejpam-5166	243	1	1	1	NUM
ejpam-5166	243	2	2	2	NUM
ejpam-5166	243	3	(	(	PUNCT
ejpam-5166	243	4	2p2q2r2	2p2q2r2	NUM
ejpam-5166	243	5	−	−	NUM
ejpam-5166	243	6	2pqr	2pqr	NUM
ejpam-5166	243	7	−	−	NOUN
ejpam-5166	243	8	2(pqr	2(pqr	NUM
ejpam-5166	243	9	−	−	PROPN
ejpam-5166	243	10	1)−	1)−	PROPN
ejpam-5166	243	11	2(p−	2(p−	NUM
ejpam-5166	243	12	1)(qr	1)(qr	NUM
ejpam-5166	243	13	−	−	PROPN
ejpam-5166	243	14	1)−	1)−	NUM
ejpam-5166	243	15	2(q	2(q	NUM
ejpam-5166	243	16	−	−	PROPN
ejpam-5166	243	17	1)(pr	1)(pr	NUM
ejpam-5166	243	18	−	−	PROPN
ejpam-5166	243	19	p	p	NOUN
ejpam-5166	243	20	)	)	PUNCT
ejpam-5166	243	21	)	)	PUNCT
ejpam-5166	244	1	−	−	PROPN
ejpam-5166	244	2	2(r	2(r	NUM
ejpam-5166	244	3	−	−	NUM
ejpam-5166	244	4	1)(pq	1)(pq	NUM
ejpam-5166	244	5	−	−	NOUN
ejpam-5166	245	1	p−	p−	NOUN
ejpam-5166	245	2	q	q	NOUN
ejpam-5166	246	1	+	+	NOUN
ejpam-5166	246	2	1	1	X
ejpam-5166	246	3	)	)	PUNCT
ejpam-5166	247	1	=	=	NOUN
ejpam-5166	247	2	p2q2r2	p2q2r2	NOUN
ejpam-5166	247	3	−	−	X
ejpam-5166	247	4	5pqr	5pqr	PROPN
ejpam-5166	247	5	+	+	NUM
ejpam-5166	247	6	2(pq	2(pq	NOUN
ejpam-5166	247	7	+	+	CCONJ
ejpam-5166	247	8	qr	qr	NOUN
ejpam-5166	247	9	+	+	CCONJ
ejpam-5166	247	10	pr)−	pr)−	PROPN
ejpam-5166	247	11	(	(	PUNCT
ejpam-5166	247	12	p+	p+	NOUN
ejpam-5166	247	13	q	q	X
ejpam-5166	247	14	+	+	CCONJ
ejpam-5166	247	15	r	r	NOUN
ejpam-5166	247	16	)	)	PUNCT
ejpam-5166	247	17	+	+	NOUN
ejpam-5166	247	18	1	1	X
ejpam-5166	247	19	.	.	PUNCT
ejpam-5166	247	20	thus	thus	ADV
ejpam-5166	247	21	,	,	PUNCT
ejpam-5166	247	22	we	we	PRON
ejpam-5166	247	23	obtain	obtain	VERB
ejpam-5166	247	24	w	w	ADP
ejpam-5166	247	25	(	(	PUNCT
ejpam-5166	247	26	pg(zpqr	pg(zpqr	PROPN
ejpam-5166	247	27	)	)	PUNCT
ejpam-5166	247	28	)	)	PUNCT
ejpam-5166	248	1	=	=	PUNCT
ejpam-5166	248	2	p2q2r2	p2q2r2	NOUN
ejpam-5166	248	3	−	−	X
ejpam-5166	248	4	5pqr	5pqr	PROPN
ejpam-5166	248	5	+	+	NUM
ejpam-5166	248	6	2(pq	2(pq	NOUN
ejpam-5166	248	7	+	+	CCONJ
ejpam-5166	248	8	qr	qr	NOUN
ejpam-5166	248	9	+	+	CCONJ
ejpam-5166	248	10	pr)−	pr)−	PROPN
ejpam-5166	248	11	(	(	PUNCT
ejpam-5166	248	12	p+	p+	NOUN
ejpam-5166	248	13	q	q	X
ejpam-5166	248	14	+	+	CCONJ
ejpam-5166	248	15	r	r	NOUN
ejpam-5166	248	16	)	)	PUNCT
ejpam-5166	248	17	+	+	NOUN
ejpam-5166	248	18	1	1	X
ejpam-5166	248	19	.	.	X
ejpam-5166	248	20	theorem	theorem	VERB
ejpam-5166	248	21	10	10	NUM
ejpam-5166	248	22	.	.	PUNCT
ejpam-5166	249	1	if	if	SCONJ
ejpam-5166	249	2	p	p	X
ejpam-5166	249	3	,	,	PUNCT
ejpam-5166	249	4	q	q	X
ejpam-5166	249	5	are	be	AUX
ejpam-5166	249	6	two	two	NUM
ejpam-5166	249	7	distinct	distinct	ADJ
ejpam-5166	249	8	prime	prime	ADJ
ejpam-5166	249	9	numbers	number	NOUN
ejpam-5166	249	10	,	,	PUNCT
ejpam-5166	249	11	then	then	ADV
ejpam-5166	249	12	w	w	PROPN
ejpam-5166	249	13	(	(	PUNCT
ejpam-5166	249	14	pg(zp2q	pg(zp2q	NOUN
ejpam-5166	249	15	)	)	PUNCT
ejpam-5166	249	16	)	)	PUNCT
ejpam-5166	250	1	=	=	SYM
ejpam-5166	250	2	2p4q2	2p4q2	NUM
ejpam-5166	250	3	−	−	NOUN
ejpam-5166	250	4	8p2q	8p2q	NOUN
ejpam-5166	250	5	+	+	CCONJ
ejpam-5166	250	6	3p2	3p2	NUM
ejpam-5166	250	7	+	+	CCONJ
ejpam-5166	250	8	4pq	4pq	ADJ
ejpam-5166	250	9	−	−	PROPN
ejpam-5166	250	10	p	p	NOUN
ejpam-5166	250	11	2	2	NUM
ejpam-5166	250	12	.	.	PUNCT
ejpam-5166	251	1	n.	n.	PROPN
ejpam-5166	251	2	hidayat	hidayat	PROPN
ejpam-5166	251	3	et	et	PROPN
ejpam-5166	251	4	al	al	PROPN
ejpam-5166	251	5	/	/	PUNCT
ejpam-5166	251	6	eur	eur	PROPN
ejpam-5166	251	7	.	.	PUNCT
ejpam-5166	252	1	j.	j.	PROPN
ejpam-5166	252	2	pure	pure	PROPN
ejpam-5166	252	3	appl	appl	PROPN
ejpam-5166	252	4	.	.	PROPN
ejpam-5166	252	5	math	math	PROPN
ejpam-5166	252	6	,	,	PUNCT
ejpam-5166	252	7	17	17	NUM
ejpam-5166	252	8	(	(	PUNCT
ejpam-5166	252	9	3	3	NUM
ejpam-5166	252	10	)	)	PUNCT
ejpam-5166	252	11	(	(	PUNCT
ejpam-5166	252	12	2024	2024	NUM
ejpam-5166	252	13	)	)	PUNCT
ejpam-5166	252	14	,	,	PUNCT
ejpam-5166	252	15	1659	1659	NUM
ejpam-5166	252	16	-	-	SYM
ejpam-5166	252	17	1673	1673	NUM
ejpam-5166	252	18	1668	1668	NUM
ejpam-5166	252	19	proof	proof	NOUN
ejpam-5166	252	20	.	.	PUNCT
ejpam-5166	253	1	for	for	ADP
ejpam-5166	253	2	every	every	DET
ejpam-5166	253	3	two	two	NUM
ejpam-5166	253	4	distinct	distinct	ADJ
ejpam-5166	253	5	prime	prime	ADJ
ejpam-5166	253	6	numbers	number	NOUN
ejpam-5166	253	7	p	p	NOUN
ejpam-5166	253	8	and	and	CCONJ
ejpam-5166	253	9	q	q	NOUN
ejpam-5166	253	10	,	,	PUNCT
ejpam-5166	253	11	the	the	DET
ejpam-5166	253	12	ring	ring	NOUN
ejpam-5166	253	13	zp2q	zp2q	PROPN
ejpam-5166	253	14	has	have	VERB
ejpam-5166	253	15	u	u	NOUN
ejpam-5166	253	16	=	=	NOUN
ejpam-5166	253	17	p(p	p(p	ADV
ejpam-5166	253	18	−	−	PROPN
ejpam-5166	254	1	1)(q	1)(q	NUM
ejpam-5166	254	2	−	−	NOUN
ejpam-5166	254	3	1	1	NUM
ejpam-5166	254	4	)	)	PUNCT
ejpam-5166	254	5	=	=	SYM
ejpam-5166	254	6	p2q	p2q	NOUN
ejpam-5166	254	7	−	−	PROPN
ejpam-5166	254	8	pq	pq	NOUN
ejpam-5166	254	9	−	−	NOUN
ejpam-5166	254	10	p2	p2	PROPN
ejpam-5166	254	11	+	+	CCONJ
ejpam-5166	254	12	p	p	NOUN
ejpam-5166	254	13	units	unit	NOUN
ejpam-5166	254	14	and	and	CCONJ
ejpam-5166	254	15	pq	pq	NOUN
ejpam-5166	254	16	+	+	CCONJ
ejpam-5166	254	17	p2	p2	PROPN
ejpam-5166	254	18	−	−	PROPN
ejpam-5166	254	19	p	p	NOUN
ejpam-5166	254	20	−	−	PROPN
ejpam-5166	254	21	1	1	NUM
ejpam-5166	254	22	nontrivial	nontrivial	ADJ
ejpam-5166	254	23	zero	zero	NUM
ejpam-5166	254	24	divisors	divisor	NOUN
ejpam-5166	254	25	.	.	PUNCT
ejpam-5166	255	1	next	next	ADJ
ejpam-5166	255	2	,	,	PUNCT
ejpam-5166	255	3	we	we	PRON
ejpam-5166	255	4	partition	partition	VERB
ejpam-5166	255	5	zp2q	zp2q	VERB
ejpam-5166	255	6	into	into	ADP
ejpam-5166	255	7	three	three	NUM
ejpam-5166	255	8	sets	set	NOUN
ejpam-5166	255	9	,	,	PUNCT
ejpam-5166	255	10	namely	namely	ADV
ejpam-5166	255	11	the	the	DET
ejpam-5166	255	12	zero	zero	NUM
ejpam-5166	255	13	set	set	VERB
ejpam-5166	255	14	o	o	X
ejpam-5166	255	15	=	=	PUNCT
ejpam-5166	255	16	{	{	PUNCT
ejpam-5166	255	17	0	0	NUM
ejpam-5166	255	18	}	}	PUNCT
ejpam-5166	255	19	,	,	PUNCT
ejpam-5166	255	20	the	the	DET
ejpam-5166	255	21	unit	unit	NOUN
ejpam-5166	255	22	set	set	VERB
ejpam-5166	255	23	u	u	NOUN
ejpam-5166	255	24	=	=	PUNCT
ejpam-5166	255	25	{	{	PUNCT
ejpam-5166	255	26	x	x	SYM
ejpam-5166	255	27	∈	∈	PROPN
ejpam-5166	255	28	zp2q|x	zp2q|x	PROPN
ejpam-5166	255	29	is	be	AUX
ejpam-5166	255	30	unit	unit	NOUN
ejpam-5166	255	31	in	in	ADP
ejpam-5166	255	32	ring	ring	NOUN
ejpam-5166	255	33	zp2q	zp2q	PROPN
ejpam-5166	255	34	}	}	PUNCT
ejpam-5166	255	35	,	,	PUNCT
ejpam-5166	255	36	and	and	CCONJ
ejpam-5166	255	37	the	the	DET
ejpam-5166	255	38	set	set	NOUN
ejpam-5166	255	39	of	of	ADP
ejpam-5166	255	40	nontrivial	nontrivial	ADJ
ejpam-5166	255	41	zero	zero	NUM
ejpam-5166	255	42	divisors	divisor	NOUN
ejpam-5166	255	43	zp2q	zp2q	VERB
ejpam-5166	255	44	are	be	AUX
ejpam-5166	255	45	a	a	PRON
ejpam-5166	255	46	=	=	X
ejpam-5166	255	47	{	{	PUNCT
ejpam-5166	255	48	pq	pq	INTJ
ejpam-5166	255	49	,	,	PUNCT
ejpam-5166	255	50	2pq	2pq	NOUN
ejpam-5166	255	51	,	,	PUNCT
ejpam-5166	255	52	.	.	PUNCT
ejpam-5166	255	53	.	.	PUNCT
ejpam-5166	255	54	.	.	PUNCT
ejpam-5166	256	1	,	,	PUNCT
ejpam-5166	256	2	(	(	PUNCT
ejpam-5166	256	3	p−	p−	NOUN
ejpam-5166	256	4	1)pq	1)pq	NOUN
ejpam-5166	256	5	}	}	PUNCT
ejpam-5166	256	6	=	=	SYM
ejpam-5166	256	7	⟨pq⟩	⟨pq⟩	PROPN
ejpam-5166	256	8	\	\	X
ejpam-5166	256	9	{	{	PUNCT
ejpam-5166	256	10	0	0	NUM
ejpam-5166	256	11	}	}	PUNCT
ejpam-5166	256	12	,	,	PUNCT
ejpam-5166	256	13	|a|	|a|	PROPN
ejpam-5166	256	14	=	=	NOUN
ejpam-5166	256	15	p−	p−	NOUN
ejpam-5166	256	16	1	1	NUM
ejpam-5166	256	17	,	,	PUNCT
ejpam-5166	256	18	b	b	NOUN
ejpam-5166	256	19	=	=	PUNCT
ejpam-5166	256	20	{	{	PUNCT
ejpam-5166	256	21	p2	p2	NOUN
ejpam-5166	256	22	,	,	PUNCT
ejpam-5166	256	23	2p2	2p2	NUM
ejpam-5166	256	24	,	,	PUNCT
ejpam-5166	256	25	.	.	PUNCT
ejpam-5166	256	26	.	.	PUNCT
ejpam-5166	256	27	.	.	PUNCT
ejpam-5166	257	1	,	,	PUNCT
ejpam-5166	257	2	(	(	PUNCT
ejpam-5166	257	3	q	q	NOUN
ejpam-5166	257	4	−	−	PROPN
ejpam-5166	257	5	1)p2	1)p2	NUM
ejpam-5166	257	6	}	}	PUNCT
ejpam-5166	257	7	=	=	SYM
ejpam-5166	257	8	⟨p2⟩	⟨p2⟩	X
ejpam-5166	257	9	\	\	PUNCT
ejpam-5166	257	10	{	{	PUNCT
ejpam-5166	257	11	0	0	NUM
ejpam-5166	257	12	}	}	PUNCT
ejpam-5166	257	13	,	,	PUNCT
ejpam-5166	257	14	|b|	|b|	PROPN
ejpam-5166	257	15	=	=	PUNCT
ejpam-5166	257	16	q	q	X
ejpam-5166	258	1	−	−	PROPN
ejpam-5166	258	2	1	1	NUM
ejpam-5166	258	3	,	,	PUNCT
ejpam-5166	258	4	c	c	NOUN
ejpam-5166	258	5	=	=	SYM
ejpam-5166	258	6	⟨q⟩	⟨q⟩	ADJ
ejpam-5166	258	7	\	\	NOUN
ejpam-5166	258	8	⟨pq⟩	⟨pq⟩	PROPN
ejpam-5166	258	9	,	,	PUNCT
ejpam-5166	258	10	|c|	|c|	PROPN
ejpam-5166	258	11	=	=	PUNCT
ejpam-5166	258	12	(	(	PUNCT
ejpam-5166	258	13	p2	p2	PROPN
ejpam-5166	258	14	−	−	PROPN
ejpam-5166	258	15	1)−	1)−	PROPN
ejpam-5166	258	16	(	(	PUNCT
ejpam-5166	258	17	p−	p−	NOUN
ejpam-5166	258	18	1	1	NUM
ejpam-5166	258	19	)	)	PUNCT
ejpam-5166	259	1	=	=	PUNCT
ejpam-5166	259	2	p2	p2	PROPN
ejpam-5166	259	3	−	−	PROPN
ejpam-5166	259	4	p	p	NOUN
ejpam-5166	259	5	,	,	PUNCT
ejpam-5166	259	6	d	d	PROPN
ejpam-5166	259	7	=	=	SYM
ejpam-5166	259	8	⟨p⟩	⟨p⟩	PROPN
ejpam-5166	259	9	\	\	PROPN
ejpam-5166	259	10	(	(	PUNCT
ejpam-5166	259	11	⟨pq⟩	⟨pq⟩	PROPN
ejpam-5166	259	12	∪	∪	ADP
ejpam-5166	259	13	⟨p2⟩	⟨p2⟩	NOUN
ejpam-5166	259	14	)	)	PUNCT
ejpam-5166	259	15	,	,	PUNCT
ejpam-5166	259	16	|d|	|d|	PROPN
ejpam-5166	259	17	=	=	PUNCT
ejpam-5166	259	18	(	(	PUNCT
ejpam-5166	259	19	pq	pq	INTJ
ejpam-5166	259	20	−	−	PROPN
ejpam-5166	259	21	1)−	1)−	PROPN
ejpam-5166	259	22	(	(	PUNCT
ejpam-5166	259	23	p+	p+	NOUN
ejpam-5166	259	24	q	q	X
ejpam-5166	259	25	−	−	PROPN
ejpam-5166	259	26	2	2	NUM
ejpam-5166	259	27	)	)	PUNCT
ejpam-5166	260	1	=	=	NOUN
ejpam-5166	260	2	pq	pq	NOUN
ejpam-5166	260	3	−	−	NOUN
ejpam-5166	261	1	p−	p−	NOUN
ejpam-5166	261	2	q	q	NOUN
ejpam-5166	262	1	+	+	NUM
ejpam-5166	262	2	1	1	X
ejpam-5166	262	3	=	=	SYM
ejpam-5166	262	4	d.	d.	NOUN
ejpam-5166	262	5	based	base	VERB
ejpam-5166	262	6	on	on	ADP
ejpam-5166	262	7	theorem	theorem	NOUN
ejpam-5166	262	8	1	1	NUM
ejpam-5166	262	9	,	,	PUNCT
ejpam-5166	262	10	the	the	DET
ejpam-5166	262	11	adjacency	adjacency	NOUN
ejpam-5166	262	12	of	of	ADP
ejpam-5166	262	13	every	every	DET
ejpam-5166	262	14	vertex	vertex	NOUN
ejpam-5166	262	15	in	in	ADP
ejpam-5166	262	16	pg(zp2q	pg(zp2q	NOUN
ejpam-5166	262	17	)	)	PUNCT
ejpam-5166	262	18	is	be	AUX
ejpam-5166	262	19	as	as	SCONJ
ejpam-5166	262	20	follows	follow	VERB
ejpam-5166	262	21	:	:	PUNCT
ejpam-5166	262	22	(	(	PUNCT
ejpam-5166	262	23	i	i	NOUN
ejpam-5166	262	24	)	)	PUNCT
ejpam-5166	262	25	every	every	DET
ejpam-5166	262	26	vertex	vertex	NOUN
ejpam-5166	262	27	in	in	ADP
ejpam-5166	262	28	o	o	PROPN
ejpam-5166	262	29	is	be	AUX
ejpam-5166	262	30	adjacent	adjacent	ADJ
ejpam-5166	262	31	to	to	ADP
ejpam-5166	262	32	every	every	DET
ejpam-5166	262	33	vertex	vertex	NOUN
ejpam-5166	262	34	in	in	ADP
ejpam-5166	262	35	a	a	DET
ejpam-5166	262	36	,	,	PUNCT
ejpam-5166	262	37	b	b	NOUN
ejpam-5166	262	38	,	,	PUNCT
ejpam-5166	262	39	c	c	NOUN
ejpam-5166	262	40	,	,	PUNCT
ejpam-5166	262	41	d	d	NOUN
ejpam-5166	262	42	,	,	PUNCT
ejpam-5166	262	43	and	and	CCONJ
ejpam-5166	262	44	u	u	INTJ
ejpam-5166	262	45	.	.	PUNCT
ejpam-5166	263	1	(	(	PUNCT
ejpam-5166	263	2	ii	ii	NOUN
ejpam-5166	263	3	)	)	PUNCT
ejpam-5166	263	4	every	every	DET
ejpam-5166	263	5	vertex	vertex	NOUN
ejpam-5166	263	6	in	in	ADP
ejpam-5166	263	7	a	a	PRON
ejpam-5166	263	8	is	be	AUX
ejpam-5166	263	9	adjacent	adjacent	ADJ
ejpam-5166	263	10	to	to	ADP
ejpam-5166	263	11	every	every	DET
ejpam-5166	263	12	vertex	vertex	NOUN
ejpam-5166	263	13	in	in	ADP
ejpam-5166	263	14	o	o	PROPN
ejpam-5166	263	15	,	,	PUNCT
ejpam-5166	263	16	a	a	DET
ejpam-5166	263	17	,	,	PUNCT
ejpam-5166	263	18	b	b	NOUN
ejpam-5166	263	19	,	,	PUNCT
ejpam-5166	263	20	and	and	CCONJ
ejpam-5166	263	21	d.	d.	PROPN
ejpam-5166	263	22	(	(	PUNCT
ejpam-5166	263	23	iii	iii	NOUN
ejpam-5166	263	24	)	)	PUNCT
ejpam-5166	263	25	every	every	DET
ejpam-5166	263	26	vertex	vertex	NOUN
ejpam-5166	263	27	in	in	ADP
ejpam-5166	263	28	b	b	PROPN
ejpam-5166	263	29	is	be	AUX
ejpam-5166	263	30	adjacent	adjacent	ADJ
ejpam-5166	263	31	to	to	ADP
ejpam-5166	263	32	every	every	DET
ejpam-5166	263	33	vertex	vertex	NOUN
ejpam-5166	263	34	in	in	ADP
ejpam-5166	263	35	o	o	PROPN
ejpam-5166	263	36	,	,	PUNCT
ejpam-5166	263	37	a	a	PRON
ejpam-5166	263	38	and	and	CCONJ
ejpam-5166	263	39	c.	c.	NOUN
ejpam-5166	263	40	(	(	PUNCT
ejpam-5166	263	41	iv	iv	X
ejpam-5166	263	42	)	)	PUNCT
ejpam-5166	263	43	every	every	DET
ejpam-5166	263	44	vertex	vertex	NOUN
ejpam-5166	263	45	in	in	ADP
ejpam-5166	263	46	c	c	PROPN
ejpam-5166	263	47	is	be	AUX
ejpam-5166	263	48	adjacent	adjacent	ADJ
ejpam-5166	263	49	to	to	ADP
ejpam-5166	263	50	every	every	DET
ejpam-5166	263	51	vertex	vertex	NOUN
ejpam-5166	263	52	in	in	ADP
ejpam-5166	263	53	o	o	PROPN
ejpam-5166	263	54	and	and	CCONJ
ejpam-5166	263	55	b.	b.	PROPN
ejpam-5166	263	56	(	(	PUNCT
ejpam-5166	263	57	v	v	NOUN
ejpam-5166	263	58	)	)	PUNCT
ejpam-5166	263	59	every	every	DET
ejpam-5166	263	60	vertex	vertex	NOUN
ejpam-5166	263	61	in	in	ADP
ejpam-5166	263	62	d	d	PROPN
ejpam-5166	263	63	is	be	AUX
ejpam-5166	263	64	adjacent	adjacent	ADJ
ejpam-5166	263	65	to	to	ADP
ejpam-5166	263	66	every	every	DET
ejpam-5166	263	67	vertex	vertex	NOUN
ejpam-5166	263	68	in	in	ADP
ejpam-5166	263	69	o	o	PROPN
ejpam-5166	263	70	and	and	CCONJ
ejpam-5166	263	71	a.	a.	NOUN
ejpam-5166	263	72	(	(	PUNCT
ejpam-5166	263	73	vi	vi	NOUN
ejpam-5166	263	74	)	)	PUNCT
ejpam-5166	263	75	every	every	DET
ejpam-5166	263	76	vertex	vertex	NOUN
ejpam-5166	263	77	in	in	ADP
ejpam-5166	263	78	u	u	NOUN
ejpam-5166	263	79	is	be	AUX
ejpam-5166	263	80	only	only	ADV
ejpam-5166	263	81	adjacent	adjacent	ADJ
ejpam-5166	263	82	to	to	ADP
ejpam-5166	263	83	every	every	DET
ejpam-5166	263	84	vertex	vertex	NOUN
ejpam-5166	263	85	in	in	ADP
ejpam-5166	263	86	o.	o.	PROPN
ejpam-5166	263	87	the	the	DET
ejpam-5166	263	88	distance	distance	NOUN
ejpam-5166	263	89	matrix	matrix	NOUN
ejpam-5166	263	90	d(pg(zp2q	d(pg(zp2q	NOUN
ejpam-5166	263	91	)	)	PUNCT
ejpam-5166	263	92	)	)	PUNCT
ejpam-5166	263	93	can	can	AUX
ejpam-5166	263	94	then	then	ADV
ejpam-5166	263	95	be	be	AUX
ejpam-5166	263	96	written	write	VERB
ejpam-5166	263	97	as	as	ADP
ejpam-5166	263	98			NOUN
ejpam-5166	263	99	0	0	NUM
ejpam-5166	263	100	a	a	DET
ejpam-5166	263	101	b	b	NOUN
ejpam-5166	263	102	c	c	NOUN
ejpam-5166	263	103	d	d	X
ejpam-5166	263	104	u	u	NOUN
ejpam-5166	263	105	0	0	NUM
ejpam-5166	263	106	0	0	NUM
ejpam-5166	263	107	11×(p−1	11×(p−1	NUM
ejpam-5166	263	108	)	)	PUNCT
ejpam-5166	263	109	11×(q−1	11×(q−1	NUM
ejpam-5166	263	110	)	)	PUNCT
ejpam-5166	263	111	11×(p2−p	11×(p2−p	NUM
ejpam-5166	263	112	)	)	PUNCT
ejpam-5166	264	1	11×d	11×d	NUM
ejpam-5166	264	2	11×u	11×u	NUM
ejpam-5166	264	3	a	a	DET
ejpam-5166	264	4	1(p−1)×1	1(p−1)×1	NUM
ejpam-5166	264	5	jp−1	jp−1	PROPN
ejpam-5166	264	6	−	−	PROPN
ejpam-5166	264	7	ip−1	ip−1	PROPN
ejpam-5166	264	8	1(p−1)×(q−1	1(p−1)×(q−1	NUM
ejpam-5166	264	9	)	)	PUNCT
ejpam-5166	264	10	2(p−1)×(p2−p	2(p−1)×(p2−p	X
ejpam-5166	264	11	)	)	PUNCT
ejpam-5166	264	12	1(p−1)×d	1(p−1)×d	NUM
ejpam-5166	264	13	2(p−1)×u	2(p−1)×u	NUM
ejpam-5166	264	14	b	b	SYM
ejpam-5166	264	15	1(q−1)×1	1(q−1)×1	NUM
ejpam-5166	264	16	1(q−1)×(p−1	1(q−1)×(p−1	NUM
ejpam-5166	264	17	)	)	PUNCT
ejpam-5166	265	1	2(jq−1	2(jq−1	NUM
ejpam-5166	265	2	−	−	PROPN
ejpam-5166	265	3	iq−1	iq−1	NOUN
ejpam-5166	265	4	)	)	PUNCT
ejpam-5166	265	5	1(q−1)×(p2−p	1(q−1)×(p2−p	PROPN
ejpam-5166	265	6	)	)	PUNCT
ejpam-5166	265	7	2(q−1)×d	2(q−1)×d	NUM
ejpam-5166	265	8	2(q−1)×u	2(q−1)×u	NUM
ejpam-5166	265	9	c	c	PROPN
ejpam-5166	265	10	1(p2−p)×1	1(p2−p)×1	PROPN
ejpam-5166	265	11	2(p2−p)×(p−1	2(p2−p)×(p−1	NUM
ejpam-5166	265	12	)	)	PUNCT
ejpam-5166	265	13	1(p2−p)×(q−1	1(p2−p)×(q−1	NUM
ejpam-5166	265	14	)	)	PUNCT
ejpam-5166	265	15	2(jp2−p	2(jp2−p	NUM
ejpam-5166	266	1	−	−	PROPN
ejpam-5166	266	2	ip2−p	ip2−p	PROPN
ejpam-5166	266	3	)	)	PUNCT
ejpam-5166	267	1	2(p2−p)×d	2(p2−p)×d	NUM
ejpam-5166	268	1	2(p2−p)×u	2(p2−p)×u	NUM
ejpam-5166	268	2	d	d	SYM
ejpam-5166	268	3	1d×1	1d×1	NUM
ejpam-5166	268	4	1d×(p−1	1d×(p−1	NUM
ejpam-5166	268	5	)	)	PUNCT
ejpam-5166	268	6	2d×(q−1	2d×(q−1	NUM
ejpam-5166	268	7	)	)	PUNCT
ejpam-5166	268	8	2d×(p2−p	2d×(p2−p	NUM
ejpam-5166	268	9	)	)	PUNCT
ejpam-5166	268	10	2(jd	2(jd	NUM
ejpam-5166	268	11	−	−	PROPN
ejpam-5166	268	12	i	i	PROPN
ejpam-5166	268	13	d	d	PROPN
ejpam-5166	268	14	)	)	PUNCT
ejpam-5166	269	1	2d×u	2d×u	NUM
ejpam-5166	269	2	u	u	NOUN
ejpam-5166	269	3	1u×1	1u×1	NUM
ejpam-5166	269	4	2u×(p−1	2u×(p−1	NUM
ejpam-5166	269	5	)	)	PUNCT
ejpam-5166	269	6	2u×(q−1	2u×(q−1	NUM
ejpam-5166	269	7	)	)	PUNCT
ejpam-5166	269	8	2u×(p2−p	2u×(p2−p	NUM
ejpam-5166	269	9	)	)	PUNCT
ejpam-5166	270	1	2u×d	2u×d	NUM
ejpam-5166	270	2	2(ju	2(ju	PROPN
ejpam-5166	270	3	−	−	PROPN
ejpam-5166	270	4	iu	iu	NOUN
ejpam-5166	270	5	)	)	PUNCT
ejpam-5166	270	6			PROPN
ejpam-5166	270	7	,	,	PUNCT
ejpam-5166	270	8	where	where	SCONJ
ejpam-5166	270	9	1m×n	1m×n	NOUN
ejpam-5166	270	10	is	be	AUX
ejpam-5166	270	11	a	a	DET
ejpam-5166	270	12	matrix	matrix	NOUN
ejpam-5166	270	13	of	of	ADP
ejpam-5166	270	14	order	order	NOUN
ejpam-5166	270	15	m	m	VERB
ejpam-5166	270	16	×	×	NOUN
ejpam-5166	270	17	n	n	INTJ
ejpam-5166	270	18	with	with	ADP
ejpam-5166	270	19	all	all	DET
ejpam-5166	270	20	entries	entry	NOUN
ejpam-5166	270	21	1	1	NUM
ejpam-5166	270	22	,	,	PUNCT
ejpam-5166	270	23	2m×n	2m×n	NUM
ejpam-5166	270	24	is	be	AUX
ejpam-5166	270	25	a	a	DET
ejpam-5166	270	26	matrix	matrix	NOUN
ejpam-5166	270	27	of	of	ADP
ejpam-5166	270	28	order	order	NOUN
ejpam-5166	270	29	m	m	VERB
ejpam-5166	270	30	×	×	NOUN
ejpam-5166	270	31	n	n	INTJ
ejpam-5166	270	32	with	with	ADP
ejpam-5166	270	33	all	all	DET
ejpam-5166	270	34	entries	entry	NOUN
ejpam-5166	270	35	2	2	NUM
ejpam-5166	270	36	,	,	PUNCT
ejpam-5166	270	37	and	and	CCONJ
ejpam-5166	270	38	jn	jn	PROPN
ejpam-5166	270	39	=	=	PROPN
ejpam-5166	271	1	1n×n	1n×n	PROPN
ejpam-5166	271	2	.	.	PUNCT
ejpam-5166	272	1	a	a	DET
ejpam-5166	272	2	half	half	NOUN
ejpam-5166	272	3	of	of	ADP
ejpam-5166	272	4	the	the	DET
ejpam-5166	272	5	sum	sum	NOUN
ejpam-5166	272	6	of	of	ADP
ejpam-5166	272	7	all	all	DET
ejpam-5166	272	8	entries	entry	NOUN
ejpam-5166	272	9	in	in	ADP
ejpam-5166	272	10	the	the	DET
ejpam-5166	272	11	matrix	matrix	NOUN
ejpam-5166	272	12	d(pg(zp2q	d(pg(zp2q	NOUN
ejpam-5166	272	13	)	)	PUNCT
ejpam-5166	272	14	)	)	PUNCT
ejpam-5166	272	15	is	be	AUX
ejpam-5166	272	16	w	w	PROPN
ejpam-5166	272	17	(	(	PUNCT
ejpam-5166	272	18	pg(zp2q	pg(zp2q	NOUN
ejpam-5166	272	19	)	)	PUNCT
ejpam-5166	272	20	)	)	PUNCT
ejpam-5166	273	1	=	=	SYM
ejpam-5166	273	2	1	1	NUM
ejpam-5166	273	3	2	2	NUM
ejpam-5166	273	4	(	(	PUNCT
ejpam-5166	273	5	2p4q2	2p4q2	NUM
ejpam-5166	273	6	−	−	NOUN
ejpam-5166	273	7	2p2q	2p2q	NUM
ejpam-5166	273	8	−	−	NOUN
ejpam-5166	273	9	2(p2q	2(p2q	NOUN
ejpam-5166	273	10	−	−	PROPN
ejpam-5166	274	1	1)−	1)−	NUM
ejpam-5166	274	2	(	(	PUNCT
ejpam-5166	274	3	p−	p−	NOUN
ejpam-5166	274	4	1)2	1)2	NUM
ejpam-5166	274	5	+	+	CCONJ
ejpam-5166	274	6	(	(	PUNCT
ejpam-5166	274	7	p−	p−	PROPN
ejpam-5166	274	8	1)−	1)−	PROPN
ejpam-5166	274	9	2(p−	2(p−	NUM
ejpam-5166	274	10	1)(pq	1)(pq	NUM
ejpam-5166	274	11	−	−	PROPN
ejpam-5166	274	12	p	p	X
ejpam-5166	274	13	)	)	PUNCT
ejpam-5166	274	14	−	−	PROPN
ejpam-5166	274	15	2(p2	2(p2	NUM
ejpam-5166	274	16	−	−	NOUN
ejpam-5166	274	17	p)(q	p)(q	NOUN
ejpam-5166	274	18	−	−	NOUN
ejpam-5166	274	19	1	1	NUM
ejpam-5166	274	20	)	)	PUNCT
ejpam-5166	274	21	)	)	PUNCT
ejpam-5166	275	1	=	=	SYM
ejpam-5166	275	2	2p4q2	2p4q2	NUM
ejpam-5166	275	3	−	−	NOUN
ejpam-5166	275	4	8p2q	8p2q	NOUN
ejpam-5166	275	5	+	+	CCONJ
ejpam-5166	275	6	3p2	3p2	NUM
ejpam-5166	275	7	+	+	CCONJ
ejpam-5166	275	8	4pq	4pq	ADJ
ejpam-5166	275	9	−	−	PROPN
ejpam-5166	275	10	p	p	NOUN
ejpam-5166	275	11	2	2	NUM
ejpam-5166	275	12	.	.	PUNCT
ejpam-5166	276	1	thus	thus	ADV
ejpam-5166	276	2	,	,	PUNCT
ejpam-5166	276	3	we	we	PRON
ejpam-5166	276	4	obtain	obtain	VERB
ejpam-5166	276	5	w	w	ADP
ejpam-5166	276	6	(	(	PUNCT
ejpam-5166	276	7	pg(zp2q	pg(zp2q	NOUN
ejpam-5166	276	8	)	)	PUNCT
ejpam-5166	276	9	)	)	PUNCT
ejpam-5166	277	1	=	=	SYM
ejpam-5166	277	2	2p4q2	2p4q2	NUM
ejpam-5166	277	3	−	−	NOUN
ejpam-5166	277	4	8p2q	8p2q	NOUN
ejpam-5166	277	5	+	+	CCONJ
ejpam-5166	277	6	3p2	3p2	NUM
ejpam-5166	277	7	+	+	CCONJ
ejpam-5166	277	8	4pq	4pq	ADJ
ejpam-5166	277	9	−	−	PROPN
ejpam-5166	277	10	p	p	NOUN
ejpam-5166	277	11	2	2	NUM
ejpam-5166	277	12	.	.	PUNCT
ejpam-5166	278	1	n.	n.	PROPN
ejpam-5166	278	2	hidayat	hidayat	PROPN
ejpam-5166	278	3	et	et	PROPN
ejpam-5166	278	4	al	al	PROPN
ejpam-5166	278	5	/	/	PUNCT
ejpam-5166	278	6	eur	eur	PROPN
ejpam-5166	278	7	.	.	PUNCT
ejpam-5166	279	1	j.	j.	PROPN
ejpam-5166	279	2	pure	pure	PROPN
ejpam-5166	279	3	appl	appl	PROPN
ejpam-5166	279	4	.	.	PROPN
ejpam-5166	279	5	math	math	PROPN
ejpam-5166	279	6	,	,	PUNCT
ejpam-5166	279	7	17	17	NUM
ejpam-5166	279	8	(	(	PUNCT
ejpam-5166	279	9	3	3	NUM
ejpam-5166	279	10	)	)	PUNCT
ejpam-5166	279	11	(	(	PUNCT
ejpam-5166	279	12	2024	2024	NUM
ejpam-5166	279	13	)	)	PUNCT
ejpam-5166	279	14	,	,	PUNCT
ejpam-5166	279	15	1659	1659	NUM
ejpam-5166	279	16	-	-	SYM
ejpam-5166	279	17	1673	1673	NUM
ejpam-5166	279	18	1669	1669	NUM
ejpam-5166	279	19	theorem	theorem	VERB
ejpam-5166	279	20	11	11	NUM
ejpam-5166	279	21	.	.	PUNCT
ejpam-5166	280	1	if	if	SCONJ
ejpam-5166	280	2	p	p	X
ejpam-5166	280	3	,	,	PUNCT
ejpam-5166	280	4	q	q	X
ejpam-5166	280	5	are	be	AUX
ejpam-5166	280	6	two	two	NUM
ejpam-5166	280	7	distinct	distinct	ADJ
ejpam-5166	280	8	prime	prime	ADJ
ejpam-5166	280	9	numbers	number	NOUN
ejpam-5166	280	10	,	,	PUNCT
ejpam-5166	280	11	then	then	ADV
ejpam-5166	280	12	w	w	PROPN
ejpam-5166	280	13	(	(	PUNCT
ejpam-5166	280	14	pg(zp2q2	pg(zp2q2	NOUN
ejpam-5166	280	15	)	)	PUNCT
ejpam-5166	280	16	)	)	PUNCT
ejpam-5166	281	1	=	=	SYM
ejpam-5166	282	1	2p4q4	2p4q4	NUM
ejpam-5166	282	2	−	−	NOUN
ejpam-5166	282	3	11p2q2	11p2q2	NOUN
ejpam-5166	282	4	+	+	CCONJ
ejpam-5166	282	5	6p2q	6p2q	NOUN
ejpam-5166	282	6	+	+	X
ejpam-5166	282	7	6pq2	6pq2	NUM
ejpam-5166	282	8	−	−	ADP
ejpam-5166	282	9	3pq	3pq	NOUN
ejpam-5166	282	10	2	2	NUM
ejpam-5166	282	11	.	.	PUNCT
ejpam-5166	283	1	proof	proof	NOUN
ejpam-5166	283	2	.	.	PUNCT
ejpam-5166	284	1	for	for	ADP
ejpam-5166	284	2	every	every	DET
ejpam-5166	284	3	two	two	NUM
ejpam-5166	284	4	distinct	distinct	ADJ
ejpam-5166	284	5	prime	prime	ADJ
ejpam-5166	284	6	numbers	number	NOUN
ejpam-5166	284	7	p	p	NOUN
ejpam-5166	284	8	and	and	CCONJ
ejpam-5166	284	9	q	q	NOUN
ejpam-5166	284	10	,	,	PUNCT
ejpam-5166	284	11	the	the	DET
ejpam-5166	284	12	ring	ring	NOUN
ejpam-5166	284	13	zp2q2	zp2q2	PROPN
ejpam-5166	284	14	has	have	VERB
ejpam-5166	284	15	u	u	NOUN
ejpam-5166	284	16	=	=	NOUN
ejpam-5166	284	17	p(p	p(p	ADV
ejpam-5166	284	18	−	−	PROPN
ejpam-5166	284	19	1)q(q	1)q(q	NUM
ejpam-5166	284	20	−	−	NOUN
ejpam-5166	284	21	1	1	NUM
ejpam-5166	284	22	)	)	PUNCT
ejpam-5166	284	23	=	=	PUNCT
ejpam-5166	285	1	p2q2	p2q2	ADP
ejpam-5166	285	2	−	−	NOUN
ejpam-5166	285	3	pq2	pq2	NOUN
ejpam-5166	285	4	−	−	NOUN
ejpam-5166	285	5	p2q	p2q	NOUN
ejpam-5166	285	6	+	+	CCONJ
ejpam-5166	285	7	pq	pq	NOUN
ejpam-5166	285	8	units	unit	NOUN
ejpam-5166	285	9	and	and	CCONJ
ejpam-5166	285	10	pq2	pq2	NOUN
ejpam-5166	285	11	+	+	CCONJ
ejpam-5166	285	12	p2q	p2q	NOUN
ejpam-5166	285	13	−	−	PROPN
ejpam-5166	285	14	pq	pq	NOUN
ejpam-5166	285	15	−	−	NOUN
ejpam-5166	285	16	1	1	NUM
ejpam-5166	285	17	nontrivial	nontrivial	ADJ
ejpam-5166	285	18	zero	zero	NUM
ejpam-5166	285	19	divisors	divisor	NOUN
ejpam-5166	285	20	.	.	PUNCT
ejpam-5166	286	1	the	the	DET
ejpam-5166	286	2	nontrivial	nontrivial	ADJ
ejpam-5166	286	3	zero	zero	NUM
ejpam-5166	286	4	divisor	divisor	NOUN
ejpam-5166	286	5	of	of	ADP
ejpam-5166	286	6	zp2q2	zp2q2	PROPN
ejpam-5166	286	7	is	be	AUX
ejpam-5166	286	8	z	z	NOUN
ejpam-5166	286	9	=	=	SYM
ejpam-5166	286	10	(	(	PUNCT
ejpam-5166	286	11	⟨p⟩	⟨p⟩	PROPN
ejpam-5166	286	12	∪	∪	VERB
ejpam-5166	286	13	⟨q⟩	⟨q⟩	ADV
ejpam-5166	286	14	)	)	PUNCT
ejpam-5166	286	15	\	\	PROPN
ejpam-5166	287	1	⟨0⟩.	⟨0⟩.	NOUN
ejpam-5166	287	2	next	next	ADV
ejpam-5166	287	3	,	,	PUNCT
ejpam-5166	287	4	we	we	PRON
ejpam-5166	287	5	partition	partition	VERB
ejpam-5166	287	6	we	we	PRON
ejpam-5166	287	7	partition	partition	VERB
ejpam-5166	287	8	zp2q2	zp2q2	PROPN
ejpam-5166	287	9	into	into	ADP
ejpam-5166	287	10	three	three	NUM
ejpam-5166	287	11	sets	set	NOUN
ejpam-5166	287	12	,	,	PUNCT
ejpam-5166	287	13	namely	namely	ADV
ejpam-5166	287	14	the	the	DET
ejpam-5166	287	15	zero	zero	NUM
ejpam-5166	287	16	set	set	VERB
ejpam-5166	287	17	o	o	X
ejpam-5166	287	18	=	=	PUNCT
ejpam-5166	287	19	{	{	PUNCT
ejpam-5166	287	20	0	0	NUM
ejpam-5166	287	21	}	}	PUNCT
ejpam-5166	287	22	,	,	PUNCT
ejpam-5166	287	23	the	the	DET
ejpam-5166	287	24	unit	unit	NOUN
ejpam-5166	287	25	set	set	VERB
ejpam-5166	287	26	u	u	NOUN
ejpam-5166	287	27	=	=	PUNCT
ejpam-5166	287	28	{	{	PUNCT
ejpam-5166	287	29	x	x	SYM
ejpam-5166	287	30	∈	∈	PROPN
ejpam-5166	287	31	zp2q2	zp2q2	PROPN
ejpam-5166	287	32	|x	|x	NOUN
ejpam-5166	287	33	is	be	AUX
ejpam-5166	287	34	unit	unit	NOUN
ejpam-5166	287	35	in	in	ADP
ejpam-5166	287	36	ring	re	VERB
ejpam-5166	287	37	zp2q2	zp2q2	PROPN
ejpam-5166	287	38	}	}	PUNCT
ejpam-5166	287	39	,	,	PUNCT
ejpam-5166	287	40	and	and	CCONJ
ejpam-5166	287	41	the	the	DET
ejpam-5166	287	42	set	set	NOUN
ejpam-5166	287	43	of	of	ADP
ejpam-5166	287	44	nontrivial	nontrivial	ADJ
ejpam-5166	287	45	zero	zero	NUM
ejpam-5166	287	46	divisors	divisor	NOUN
ejpam-5166	287	47	zp2q2	zp2q2	NOUN
ejpam-5166	287	48	are	be	AUX
ejpam-5166	288	1	a	a	DET
ejpam-5166	288	2	=	=	PUNCT
ejpam-5166	288	3	⟨pq2⟩	⟨pq2⟩	NOUN
ejpam-5166	288	4	\	\	PROPN
ejpam-5166	288	5	{	{	PUNCT
ejpam-5166	288	6	0	0	NUM
ejpam-5166	288	7	}	}	PUNCT
ejpam-5166	288	8	,	,	PUNCT
ejpam-5166	288	9	|a|	|a|	PROPN
ejpam-5166	288	10	=	=	NOUN
ejpam-5166	288	11	p−	p−	NOUN
ejpam-5166	288	12	1	1	NUM
ejpam-5166	288	13	=	=	SYM
ejpam-5166	288	14	a	a	PROPN
ejpam-5166	288	15	,	,	PUNCT
ejpam-5166	288	16	b	b	X
ejpam-5166	288	17	=	=	PUNCT
ejpam-5166	288	18	⟨p2q⟩	⟨p2q⟩	NOUN
ejpam-5166	288	19	\	\	PROPN
ejpam-5166	288	20	{	{	PUNCT
ejpam-5166	288	21	0	0	NUM
ejpam-5166	288	22	}	}	PUNCT
ejpam-5166	288	23	,	,	PUNCT
ejpam-5166	288	24	|b|	|b|	PROPN
ejpam-5166	288	25	=	=	PUNCT
ejpam-5166	288	26	q	q	X
ejpam-5166	289	1	−	−	PROPN
ejpam-5166	289	2	1	1	NUM
ejpam-5166	289	3	=	=	SYM
ejpam-5166	289	4	b	b	NOUN
ejpam-5166	289	5	,	,	PUNCT
ejpam-5166	289	6	c	c	NOUN
ejpam-5166	289	7	=	=	SYM
ejpam-5166	289	8	⟨q2⟩	⟨q2⟩	NOUN
ejpam-5166	289	9	\	\	X
ejpam-5166	289	10	⟨pq2⟩	⟨pq2⟩	PROPN
ejpam-5166	289	11	,	,	PUNCT
ejpam-5166	289	12	|c|	|c|	PROPN
ejpam-5166	289	13	=	=	PUNCT
ejpam-5166	289	14	p2	p2	PROPN
ejpam-5166	289	15	−	−	PROPN
ejpam-5166	289	16	p	p	NOUN
ejpam-5166	289	17	=	=	SYM
ejpam-5166	289	18	c	c	NOUN
ejpam-5166	289	19	,	,	PUNCT
ejpam-5166	289	20	d	d	X
ejpam-5166	289	21	=	=	SYM
ejpam-5166	289	22	⟨p2⟩	⟨p2⟩	PROPN
ejpam-5166	289	23	\	\	PROPN
ejpam-5166	289	24	⟨p2q⟩	⟨p2q⟩	PROPN
ejpam-5166	289	25	,	,	PUNCT
ejpam-5166	289	26	|d|	|d|	PROPN
ejpam-5166	289	27	=	=	SYM
ejpam-5166	289	28	q2	q2	PROPN
ejpam-5166	289	29	−	−	PROPN
ejpam-5166	289	30	q	q	PROPN
ejpam-5166	290	1	=	=	SYM
ejpam-5166	290	2	d	d	PROPN
ejpam-5166	290	3	,	,	PUNCT
ejpam-5166	290	4	e	e	X
ejpam-5166	290	5	=	=	SYM
ejpam-5166	290	6	⟨pq⟩	⟨pq⟩	PROPN
ejpam-5166	290	7	\	\	PROPN
ejpam-5166	290	8	(	(	PUNCT
ejpam-5166	290	9	⟨pq2⟩	⟨pq2⟩	ADV
ejpam-5166	290	10	∪	∪	ADJ
ejpam-5166	290	11	⟨p2q⟩	⟨p2q⟩	NOUN
ejpam-5166	290	12	)	)	PUNCT
ejpam-5166	290	13	,	,	PUNCT
ejpam-5166	290	14	|e|	|e|	PROPN
ejpam-5166	290	15	=	=	SYM
ejpam-5166	290	16	pq	pq	NOUN
ejpam-5166	290	17	−	−	NOUN
ejpam-5166	291	1	p−	p−	NOUN
ejpam-5166	291	2	q	q	NOUN
ejpam-5166	292	1	+	+	NUM
ejpam-5166	292	2	1	1	NUM
ejpam-5166	292	3	=	=	SYM
ejpam-5166	292	4	e	e	NOUN
ejpam-5166	292	5	,	,	PUNCT
ejpam-5166	292	6	f	f	PROPN
ejpam-5166	292	7	=	=	SYM
ejpam-5166	292	8	⟨p⟩	⟨p⟩	PROPN
ejpam-5166	292	9	\	\	PROPN
ejpam-5166	292	10	(	(	PUNCT
ejpam-5166	292	11	⟨pq⟩	⟨pq⟩	PROPN
ejpam-5166	292	12	∪	∪	ADP
ejpam-5166	292	13	⟨p2⟩	⟨p2⟩	NOUN
ejpam-5166	292	14	)	)	PUNCT
ejpam-5166	292	15	,	,	PUNCT
ejpam-5166	292	16	|f	|f	PUNCT
ejpam-5166	293	1	|	|	NOUN
ejpam-5166	293	2	=	=	PUNCT
ejpam-5166	294	1	pq2	pq2	NOUN
ejpam-5166	294	2	−	−	PROPN
ejpam-5166	294	3	q2	q2	NOUN
ejpam-5166	294	4	−	−	PROPN
ejpam-5166	295	1	pq	pq	PROPN
ejpam-5166	296	1	+	+	CCONJ
ejpam-5166	296	2	q	q	NOUN
ejpam-5166	296	3	=	=	SYM
ejpam-5166	296	4	f	f	NOUN
ejpam-5166	296	5	,	,	PUNCT
ejpam-5166	296	6	g	g	PROPN
ejpam-5166	296	7	=	=	PUNCT
ejpam-5166	296	8	⟨q⟩	⟨q⟩	PUNCT
ejpam-5166	296	9	\	\	NOUN
ejpam-5166	296	10	(	(	PUNCT
ejpam-5166	296	11	⟨pq⟩	⟨pq⟩	X
ejpam-5166	296	12	∪	∪	VERB
ejpam-5166	296	13	⟨q2⟩	⟨q2⟩	NOUN
ejpam-5166	296	14	)	)	PUNCT
ejpam-5166	296	15	,	,	PUNCT
ejpam-5166	296	16	|g|	|g|	PROPN
ejpam-5166	296	17	=	=	PUNCT
ejpam-5166	296	18	p2q	p2q	NOUN
ejpam-5166	296	19	−	−	NOUN
ejpam-5166	296	20	p2	p2	PROPN
ejpam-5166	296	21	−	−	PROPN
ejpam-5166	296	22	pq	pq	NOUN
ejpam-5166	297	1	+	+	CCONJ
ejpam-5166	297	2	p	p	NOUN
ejpam-5166	297	3	=	=	PUNCT
ejpam-5166	297	4	g.	g.	NOUN
ejpam-5166	297	5	based	base	VERB
ejpam-5166	297	6	on	on	ADP
ejpam-5166	297	7	theorem	theorem	NOUN
ejpam-5166	297	8	1	1	NUM
ejpam-5166	297	9	,	,	PUNCT
ejpam-5166	297	10	the	the	DET
ejpam-5166	297	11	adjacency	adjacency	NOUN
ejpam-5166	297	12	of	of	ADP
ejpam-5166	297	13	every	every	DET
ejpam-5166	297	14	vertex	vertex	NOUN
ejpam-5166	297	15	in	in	ADP
ejpam-5166	297	16	pg(zp2q2	pg(zp2q2	NOUN
ejpam-5166	297	17	)	)	PUNCT
ejpam-5166	297	18	is	be	AUX
ejpam-5166	297	19	as	as	SCONJ
ejpam-5166	297	20	follows	follow	VERB
ejpam-5166	297	21	:	:	PUNCT
ejpam-5166	297	22	(	(	PUNCT
ejpam-5166	297	23	i	i	NOUN
ejpam-5166	297	24	)	)	PUNCT
ejpam-5166	297	25	every	every	DET
ejpam-5166	297	26	vertex	vertex	NOUN
ejpam-5166	297	27	in	in	ADP
ejpam-5166	297	28	o	o	PROPN
ejpam-5166	297	29	is	be	AUX
ejpam-5166	297	30	adjacent	adjacent	ADJ
ejpam-5166	297	31	to	to	ADP
ejpam-5166	297	32	every	every	DET
ejpam-5166	297	33	vertex	vertex	NOUN
ejpam-5166	297	34	in	in	ADP
ejpam-5166	297	35	a	a	DET
ejpam-5166	297	36	,	,	PUNCT
ejpam-5166	297	37	b	b	NOUN
ejpam-5166	297	38	,	,	PUNCT
ejpam-5166	297	39	c	c	NOUN
ejpam-5166	297	40	,	,	PUNCT
ejpam-5166	297	41	d	d	NOUN
ejpam-5166	297	42	,	,	PUNCT
ejpam-5166	297	43	e	e	NOUN
ejpam-5166	297	44	,	,	PUNCT
ejpam-5166	297	45	f	f	X
ejpam-5166	297	46	,	,	PUNCT
ejpam-5166	297	47	g	g	PROPN
ejpam-5166	297	48	,	,	PUNCT
ejpam-5166	297	49	and	and	CCONJ
ejpam-5166	297	50	u	u	NOUN
ejpam-5166	297	51	.	.	PUNCT
ejpam-5166	298	1	(	(	PUNCT
ejpam-5166	298	2	ii	ii	NOUN
ejpam-5166	298	3	)	)	PUNCT
ejpam-5166	298	4	every	every	DET
ejpam-5166	298	5	vertex	vertex	NOUN
ejpam-5166	298	6	in	in	ADP
ejpam-5166	298	7	a	a	PRON
ejpam-5166	298	8	is	be	AUX
ejpam-5166	298	9	adjacent	adjacent	ADJ
ejpam-5166	298	10	to	to	ADP
ejpam-5166	298	11	every	every	DET
ejpam-5166	298	12	vertex	vertex	NOUN
ejpam-5166	298	13	in	in	ADP
ejpam-5166	298	14	o	o	PROPN
ejpam-5166	298	15	,	,	PUNCT
ejpam-5166	298	16	a	a	PRON
ejpam-5166	298	17	,	,	PUNCT
ejpam-5166	298	18	b	b	NOUN
ejpam-5166	298	19	,	,	PUNCT
ejpam-5166	298	20	d	d	PROPN
ejpam-5166	298	21	,	,	PUNCT
ejpam-5166	298	22	e	e	NOUN
ejpam-5166	298	23	,	,	PUNCT
ejpam-5166	298	24	and	and	CCONJ
ejpam-5166	298	25	f	f	X
ejpam-5166	298	26	.	.	PUNCT
ejpam-5166	299	1	(	(	PUNCT
ejpam-5166	299	2	iii	iii	NOUN
ejpam-5166	299	3	)	)	PUNCT
ejpam-5166	299	4	every	every	DET
ejpam-5166	299	5	vertex	vertex	NOUN
ejpam-5166	299	6	in	in	ADP
ejpam-5166	299	7	b	b	PROPN
ejpam-5166	299	8	is	be	AUX
ejpam-5166	299	9	adjacent	adjacent	ADJ
ejpam-5166	299	10	to	to	ADP
ejpam-5166	299	11	every	every	DET
ejpam-5166	299	12	vertex	vertex	NOUN
ejpam-5166	299	13	in	in	ADP
ejpam-5166	299	14	o	o	PROPN
ejpam-5166	299	15	,	,	PUNCT
ejpam-5166	299	16	a	a	DET
ejpam-5166	299	17	,	,	PUNCT
ejpam-5166	299	18	b	b	NOUN
ejpam-5166	299	19	,	,	PUNCT
ejpam-5166	299	20	c	c	X
ejpam-5166	299	21	,	,	PUNCT
ejpam-5166	299	22	e	e	NOUN
ejpam-5166	299	23	,	,	PUNCT
ejpam-5166	299	24	and	and	CCONJ
ejpam-5166	299	25	g.	g.	PROPN
ejpam-5166	299	26	(	(	PUNCT
ejpam-5166	299	27	iv	iv	X
ejpam-5166	299	28	)	)	PUNCT
ejpam-5166	299	29	every	every	DET
ejpam-5166	299	30	vertex	vertex	NOUN
ejpam-5166	299	31	in	in	ADP
ejpam-5166	299	32	c	c	PROPN
ejpam-5166	299	33	is	be	AUX
ejpam-5166	299	34	adjacent	adjacent	ADJ
ejpam-5166	299	35	to	to	ADP
ejpam-5166	299	36	every	every	DET
ejpam-5166	299	37	vertex	vertex	NOUN
ejpam-5166	299	38	in	in	ADP
ejpam-5166	299	39	o	o	PROPN
ejpam-5166	299	40	,	,	PUNCT
ejpam-5166	299	41	b	b	PROPN
ejpam-5166	299	42	and	and	CCONJ
ejpam-5166	299	43	d.	d.	PROPN
ejpam-5166	299	44	(	(	PUNCT
ejpam-5166	299	45	v	v	NOUN
ejpam-5166	299	46	)	)	PUNCT
ejpam-5166	299	47	every	every	DET
ejpam-5166	299	48	vertex	vertex	NOUN
ejpam-5166	299	49	in	in	ADP
ejpam-5166	299	50	d	d	PROPN
ejpam-5166	299	51	is	be	AUX
ejpam-5166	299	52	adjacent	adjacent	ADJ
ejpam-5166	299	53	to	to	ADP
ejpam-5166	299	54	every	every	DET
ejpam-5166	299	55	vertex	vertex	NOUN
ejpam-5166	299	56	in	in	ADP
ejpam-5166	299	57	o	o	PROPN
ejpam-5166	299	58	,	,	PUNCT
ejpam-5166	299	59	a	a	PRON
ejpam-5166	299	60	and	and	CCONJ
ejpam-5166	299	61	c.	c.	NOUN
ejpam-5166	299	62	(	(	PUNCT
ejpam-5166	299	63	vi	vi	PROPN
ejpam-5166	299	64	)	)	PUNCT
ejpam-5166	299	65	every	every	DET
ejpam-5166	299	66	vertex	vertex	NOUN
ejpam-5166	299	67	in	in	ADP
ejpam-5166	299	68	e	e	PROPN
ejpam-5166	299	69	is	be	AUX
ejpam-5166	299	70	adjacent	adjacent	ADJ
ejpam-5166	299	71	to	to	ADP
ejpam-5166	299	72	every	every	DET
ejpam-5166	299	73	vertex	vertex	NOUN
ejpam-5166	299	74	in	in	ADP
ejpam-5166	299	75	o	o	PROPN
ejpam-5166	299	76	,	,	PUNCT
ejpam-5166	299	77	a	a	DET
ejpam-5166	299	78	,	,	PUNCT
ejpam-5166	299	79	b	b	NOUN
ejpam-5166	299	80	,	,	PUNCT
ejpam-5166	299	81	and	and	CCONJ
ejpam-5166	299	82	e.	e.	PROPN
ejpam-5166	299	83	(	(	PUNCT
ejpam-5166	299	84	vii	vii	PROPN
ejpam-5166	299	85	)	)	PUNCT
ejpam-5166	299	86	every	every	DET
ejpam-5166	299	87	vertex	vertex	NOUN
ejpam-5166	299	88	in	in	ADP
ejpam-5166	299	89	f	f	PROPN
ejpam-5166	299	90	is	be	AUX
ejpam-5166	299	91	adjacent	adjacent	ADJ
ejpam-5166	299	92	to	to	ADP
ejpam-5166	299	93	every	every	DET
ejpam-5166	299	94	vertex	vertex	NOUN
ejpam-5166	299	95	in	in	ADP
ejpam-5166	299	96	o	o	PROPN
ejpam-5166	299	97	and	and	CCONJ
ejpam-5166	299	98	a.	a.	NOUN
ejpam-5166	299	99	(	(	PUNCT
ejpam-5166	299	100	viii	viii	PROPN
ejpam-5166	299	101	)	)	PUNCT
ejpam-5166	299	102	every	every	DET
ejpam-5166	299	103	vertex	vertex	NOUN
ejpam-5166	299	104	in	in	ADP
ejpam-5166	299	105	g	g	PROPN
ejpam-5166	299	106	is	be	AUX
ejpam-5166	299	107	adjacent	adjacent	ADJ
ejpam-5166	299	108	to	to	ADP
ejpam-5166	299	109	every	every	DET
ejpam-5166	299	110	vertex	vertex	NOUN
ejpam-5166	299	111	in	in	ADP
ejpam-5166	299	112	o	o	PROPN
ejpam-5166	299	113	and	and	CCONJ
ejpam-5166	299	114	b.	b.	PROPN
ejpam-5166	299	115	(	(	PUNCT
ejpam-5166	299	116	ix	ix	PROPN
ejpam-5166	299	117	)	)	PUNCT
ejpam-5166	299	118	every	every	DET
ejpam-5166	299	119	vertex	vertex	NOUN
ejpam-5166	299	120	in	in	ADP
ejpam-5166	299	121	u	u	NOUN
ejpam-5166	299	122	is	be	AUX
ejpam-5166	299	123	only	only	ADV
ejpam-5166	299	124	adjacent	adjacent	ADJ
ejpam-5166	299	125	to	to	ADP
ejpam-5166	299	126	every	every	DET
ejpam-5166	299	127	vertex	vertex	NOUN
ejpam-5166	299	128	in	in	ADP
ejpam-5166	299	129	o.	o.	PROPN
ejpam-5166	299	130	n.	n.	PROPN
ejpam-5166	299	131	hidayat	hidayat	PROPN
ejpam-5166	299	132	et	et	PROPN
ejpam-5166	299	133	al	al	PROPN
ejpam-5166	299	134	/	/	PUNCT
ejpam-5166	299	135	eur	eur	PROPN
ejpam-5166	299	136	.	.	PUNCT
ejpam-5166	300	1	j.	j.	PROPN
ejpam-5166	300	2	pure	pure	PROPN
ejpam-5166	300	3	appl	appl	PROPN
ejpam-5166	300	4	.	.	PROPN
ejpam-5166	300	5	math	math	PROPN
ejpam-5166	300	6	,	,	PUNCT
ejpam-5166	300	7	17	17	NUM
ejpam-5166	300	8	(	(	PUNCT
ejpam-5166	300	9	3	3	NUM
ejpam-5166	300	10	)	)	PUNCT
ejpam-5166	300	11	(	(	PUNCT
ejpam-5166	300	12	2024	2024	NUM
ejpam-5166	300	13	)	)	PUNCT
ejpam-5166	300	14	,	,	PUNCT
ejpam-5166	300	15	1659	1659	NUM
ejpam-5166	300	16	-	-	SYM
ejpam-5166	300	17	1673	1673	NUM
ejpam-5166	300	18	1670	1670	NUM
ejpam-5166	300	19	the	the	DET
ejpam-5166	300	20	distance	distance	NOUN
ejpam-5166	300	21	matrix	matrix	NOUN
ejpam-5166	300	22	of	of	ADP
ejpam-5166	300	23	d(pg(zp2q2	d(pg(zp2q2	NOUN
ejpam-5166	300	24	)	)	PUNCT
ejpam-5166	300	25	)	)	PUNCT
ejpam-5166	300	26	can	can	AUX
ejpam-5166	300	27	then	then	ADV
ejpam-5166	300	28	be	be	AUX
ejpam-5166	300	29	written	write	VERB
ejpam-5166	300	30	as	as	ADP
ejpam-5166	300	31			NOUN
ejpam-5166	300	32	0	0	NUM
ejpam-5166	301	1	a	a	DET
ejpam-5166	301	2	b	b	NOUN
ejpam-5166	301	3	c	c	NOUN
ejpam-5166	301	4	d	d	X
ejpam-5166	301	5	e	e	X
ejpam-5166	301	6	f	f	PROPN
ejpam-5166	301	7	g	g	PROPN
ejpam-5166	301	8	u	u	NOUN
ejpam-5166	301	9	0	0	PROPN
ejpam-5166	301	10	0	0	NUM
ejpam-5166	301	11	11×a	11×a	NUM
ejpam-5166	301	12	11×b	11×b	NUM
ejpam-5166	301	13	11×c	11×c	NUM
ejpam-5166	301	14	11×d	11×d	NUM
ejpam-5166	301	15	11×e	11×e	NUM
ejpam-5166	301	16	11×f	11×f	NUM
ejpam-5166	301	17	11×g	11×g	NUM
ejpam-5166	301	18	11×u	11×u	NUM
ejpam-5166	301	19	a	a	DET
ejpam-5166	301	20	1a×1	1a×1	NUM
ejpam-5166	301	21	ja	ja	PROPN
ejpam-5166	301	22	−	−	PROPN
ejpam-5166	301	23	ia	ia	PROPN
ejpam-5166	301	24	1a×b	1a×b	PROPN
ejpam-5166	301	25	2a×c	2a×c	NUM
ejpam-5166	301	26	1a×d	1a×d	NUM
ejpam-5166	301	27	1a×e	1a×e	NUM
ejpam-5166	301	28	1a×f	1a×f	NOUN
ejpam-5166	302	1	2a×g	2a×g	NUM
ejpam-5166	303	1	2a×u	2a×u	PROPN
ejpam-5166	303	2	b	b	X
ejpam-5166	303	3	1b×1	1b×1	NUM
ejpam-5166	304	1	1b×a	1b×a	NOUN
ejpam-5166	304	2	jb	jb	PROPN
ejpam-5166	304	3	−	−	PROPN
ejpam-5166	305	1	ib	ib	INTJ
ejpam-5166	305	2	1b×c	1b×c	PROPN
ejpam-5166	306	1	2b×d	2b×d	NUM
ejpam-5166	306	2	1b×e	1b×e	NUM
ejpam-5166	306	3	2b×f	2b×f	NUM
ejpam-5166	306	4	1b×g	1b×g	NUM
ejpam-5166	307	1	2b×u	2b×u	NUM
ejpam-5166	307	2	c	c	PROPN
ejpam-5166	307	3	1c×1	1c×1	NUM
ejpam-5166	307	4	2c×a	2c×a	NUM
ejpam-5166	308	1	1c×b	1c×b	NUM
ejpam-5166	309	1	2(jc	2(jc	NUM
ejpam-5166	309	2	−	−	NOUN
ejpam-5166	309	3	ic	ic	NUM
ejpam-5166	309	4	)	)	PUNCT
ejpam-5166	310	1	1c×d	1c×d	PROPN
ejpam-5166	311	1	2c×e	2c×e	NUM
ejpam-5166	311	2	2c×f	2c×f	NUM
ejpam-5166	312	1	2c×g	2c×g	NUM
ejpam-5166	312	2	2c×u	2c×u	NUM
ejpam-5166	313	1	d	d	NOUN
ejpam-5166	313	2	1d×1	1d×1	NUM
ejpam-5166	313	3	1d×a	1d×a	NUM
ejpam-5166	313	4	2d×b	2d×b	NUM
ejpam-5166	313	5	1d×c	1d×c	NUM
ejpam-5166	313	6	2(jd	2(jd	NUM
ejpam-5166	313	7	−	−	PUNCT
ejpam-5166	313	8	i	i	PROPN
ejpam-5166	313	9	d	d	PROPN
ejpam-5166	313	10	)	)	PUNCT
ejpam-5166	313	11	2d×e	2d×e	NOUN
ejpam-5166	314	1	2d×f	2d×f	NUM
ejpam-5166	314	2	2d×g	2d×g	NUM
ejpam-5166	315	1	2d×u	2d×u	NUM
ejpam-5166	315	2	e	e	X
ejpam-5166	315	3	1e×1	1e×1	NUM
ejpam-5166	315	4	1e×a	1e×a	NUM
ejpam-5166	315	5	1e×b	1e×b	NUM
ejpam-5166	315	6	2e×c	2e×c	PROPN
ejpam-5166	315	7	2e×d	2e×d	NUM
ejpam-5166	315	8	je	je	X
ejpam-5166	315	9	−	−	X
ejpam-5166	315	10	ie	ie	X
ejpam-5166	315	11	2e×f	2e×f	PROPN
ejpam-5166	316	1	2e×g	2e×g	PROPN
ejpam-5166	317	1	2e×u	2e×u	NUM
ejpam-5166	317	2	f	f	X
ejpam-5166	318	1	1f×1	1f×1	NUM
ejpam-5166	318	2	1f×a	1f×a	NUM
ejpam-5166	319	1	2f×b	2f×b	NUM
ejpam-5166	320	1	2f×c	2f×c	NUM
ejpam-5166	320	2	2f×d	2f×d	NUM
ejpam-5166	321	1	2f×e	2f×e	NUM
ejpam-5166	321	2	2(jf	2(jf	NUM
ejpam-5166	322	1	−	−	NOUN
ejpam-5166	322	2	if	if	SCONJ
ejpam-5166	322	3	)	)	PUNCT
ejpam-5166	322	4	2f×g	2f×g	PROPN
ejpam-5166	322	5	2f×u	2f×u	NUM
ejpam-5166	322	6	g	g	ADP
ejpam-5166	322	7	1g×1	1g×1	NUM
ejpam-5166	323	1	2g×a	2g×a	NUM
ejpam-5166	323	2	1g×b	1g×b	NUM
ejpam-5166	324	1	2g×c	2g×c	NUM
ejpam-5166	324	2	2g×d	2g×d	NOUN
ejpam-5166	325	1	2g×e	2g×e	NUM
ejpam-5166	325	2	2g×f	2g×f	NUM
ejpam-5166	325	3	2(jg	2(jg	NUM
ejpam-5166	325	4	−	−	PROPN
ejpam-5166	325	5	ig	ig	PROPN
ejpam-5166	325	6	)	)	PUNCT
ejpam-5166	325	7	2g×u	2g×u	NUM
ejpam-5166	325	8	u	u	NOUN
ejpam-5166	325	9	1u×1	1u×1	NUM
ejpam-5166	325	10	2u×a	2u×a	PROPN
ejpam-5166	325	11	2u×b	2u×b	NUM
ejpam-5166	325	12	2u×c	2u×c	NUM
ejpam-5166	325	13	2u×d	2u×d	NUM
ejpam-5166	325	14	2u×e	2u×e	NUM
ejpam-5166	325	15	2u×f	2u×f	NOUN
ejpam-5166	326	1	2u×g	2u×g	NUM
ejpam-5166	326	2	2(ju	2(ju	PROPN
ejpam-5166	326	3	−	−	PROPN
ejpam-5166	326	4	iu	iu	NOUN
ejpam-5166	326	5	)	)	PUNCT
ejpam-5166	326	6			NOUN
ejpam-5166	326	7	,	,	PUNCT
ejpam-5166	326	8	where	where	SCONJ
ejpam-5166	326	9	1m×n	1m×n	NOUN
ejpam-5166	326	10	is	be	AUX
ejpam-5166	326	11	a	a	DET
ejpam-5166	326	12	matrix	matrix	NOUN
ejpam-5166	326	13	of	of	ADP
ejpam-5166	326	14	order	order	NOUN
ejpam-5166	326	15	m	m	VERB
ejpam-5166	326	16	×	×	NOUN
ejpam-5166	326	17	n	n	INTJ
ejpam-5166	326	18	with	with	ADP
ejpam-5166	326	19	all	all	DET
ejpam-5166	326	20	entries	entry	NOUN
ejpam-5166	326	21	1	1	NUM
ejpam-5166	326	22	,	,	PUNCT
ejpam-5166	326	23	2m×n	2m×n	NUM
ejpam-5166	326	24	is	be	AUX
ejpam-5166	326	25	a	a	DET
ejpam-5166	326	26	matrix	matrix	NOUN
ejpam-5166	326	27	of	of	ADP
ejpam-5166	326	28	order	order	NOUN
ejpam-5166	326	29	m	m	VERB
ejpam-5166	326	30	×	×	NOUN
ejpam-5166	326	31	n	n	INTJ
ejpam-5166	326	32	with	with	ADP
ejpam-5166	326	33	all	all	DET
ejpam-5166	326	34	entries	entry	NOUN
ejpam-5166	326	35	2	2	NUM
ejpam-5166	326	36	,	,	PUNCT
ejpam-5166	326	37	and	and	CCONJ
ejpam-5166	326	38	jn	jn	PROPN
ejpam-5166	326	39	=	=	PROPN
ejpam-5166	327	1	1n×n	1n×n	PROPN
ejpam-5166	327	2	.	.	PUNCT
ejpam-5166	328	1	a	a	DET
ejpam-5166	328	2	half	half	NOUN
ejpam-5166	328	3	of	of	ADP
ejpam-5166	328	4	the	the	DET
ejpam-5166	328	5	sum	sum	NOUN
ejpam-5166	328	6	of	of	ADP
ejpam-5166	328	7	all	all	DET
ejpam-5166	328	8	entries	entry	NOUN
ejpam-5166	328	9	in	in	ADP
ejpam-5166	328	10	the	the	DET
ejpam-5166	328	11	matrix	matrix	NOUN
ejpam-5166	328	12	d(pg(zp2q2	d(pg(zp2q2	NOUN
ejpam-5166	328	13	)	)	PUNCT
ejpam-5166	328	14	)	)	PUNCT
ejpam-5166	328	15	is	be	AUX
ejpam-5166	328	16	w	w	NOUN
ejpam-5166	328	17	(	(	PUNCT
ejpam-5166	328	18	pg(zp2q2	pg(zp2q2	NOUN
ejpam-5166	328	19	)	)	PUNCT
ejpam-5166	328	20	)	)	PUNCT
ejpam-5166	329	1	=	=	SYM
ejpam-5166	329	2	1	1	NUM
ejpam-5166	329	3	2	2	NUM
ejpam-5166	329	4	(	(	PUNCT
ejpam-5166	329	5	2p4q4	2p4q4	NUM
ejpam-5166	329	6	−	−	NUM
ejpam-5166	329	7	2p2q2	2p2q2	NUM
ejpam-5166	329	8	−	−	PROPN
ejpam-5166	329	9	2(p2q2	2(p2q2	NUM
ejpam-5166	330	1	−	−	PROPN
ejpam-5166	331	1	1)−	1)−	NUM
ejpam-5166	331	2	(	(	PUNCT
ejpam-5166	331	3	p−	p−	NOUN
ejpam-5166	331	4	1)2	1)2	NUM
ejpam-5166	331	5	+	+	CCONJ
ejpam-5166	331	6	(	(	PUNCT
ejpam-5166	331	7	p−	p−	PROPN
ejpam-5166	331	8	1)−	1)−	PROPN
ejpam-5166	331	9	2(p−	2(p−	NUM
ejpam-5166	331	10	1)(pq2	1)(pq2	NUM
ejpam-5166	331	11	−	−	PROPN
ejpam-5166	331	12	p	p	NOUN
ejpam-5166	331	13	)	)	PUNCT
ejpam-5166	331	14	−	−	PROPN
ejpam-5166	331	15	(	(	PUNCT
ejpam-5166	331	16	q	q	NOUN
ejpam-5166	331	17	−	−	PROPN
ejpam-5166	331	18	1)2	1)2	NUM
ejpam-5166	331	19	+	+	CCONJ
ejpam-5166	331	20	(	(	PUNCT
ejpam-5166	331	21	q	q	PROPN
ejpam-5166	331	22	−	−	PROPN
ejpam-5166	332	1	1)−	1)−	PROPN
ejpam-5166	332	2	2(q	2(q	NUM
ejpam-5166	333	1	−	−	ADP
ejpam-5166	333	2	1)(p2q	1)(p2q	NUM
ejpam-5166	333	3	−	−	NOUN
ejpam-5166	333	4	p−	p−	NOUN
ejpam-5166	333	5	q	q	NOUN
ejpam-5166	334	1	+	+	NOUN
ejpam-5166	334	2	1	1	NUM
ejpam-5166	334	3	)	)	PUNCT
ejpam-5166	334	4	−	−	PROPN
ejpam-5166	334	5	2(p2	2(p2	NUM
ejpam-5166	334	6	−	−	PROPN
ejpam-5166	334	7	p)(q2	p)(q2	PROPN
ejpam-5166	335	1	−	−	PROPN
ejpam-5166	335	2	q)−	q)−	PROPN
ejpam-5166	335	3	(	(	PUNCT
ejpam-5166	335	4	pq	pq	INTJ
ejpam-5166	335	5	−	−	NOUN
ejpam-5166	336	1	p−	p−	NOUN
ejpam-5166	336	2	q	q	NOUN
ejpam-5166	337	1	+	+	CCONJ
ejpam-5166	337	2	1)2	1)2	NUM
ejpam-5166	337	3	+	+	CCONJ
ejpam-5166	337	4	(	(	PUNCT
ejpam-5166	337	5	pq	pq	INTJ
ejpam-5166	337	6	−	−	NOUN
ejpam-5166	338	1	p−	p−	NOUN
ejpam-5166	338	2	q	q	NOUN
ejpam-5166	339	1	+	+	NOUN
ejpam-5166	339	2	1	1	NUM
ejpam-5166	339	3	)	)	PUNCT
ejpam-5166	339	4	)	)	PUNCT
ejpam-5166	340	1	=	=	SYM
ejpam-5166	341	1	2p4q4	2p4q4	NUM
ejpam-5166	341	2	−	−	NOUN
ejpam-5166	341	3	11p2q2	11p2q2	NOUN
ejpam-5166	341	4	+	+	CCONJ
ejpam-5166	341	5	6p2q	6p2q	NOUN
ejpam-5166	341	6	+	+	X
ejpam-5166	341	7	6pq2	6pq2	NUM
ejpam-5166	341	8	−	−	ADP
ejpam-5166	341	9	3pq	3pq	NOUN
ejpam-5166	341	10	2	2	NUM
ejpam-5166	341	11	.	.	PUNCT
ejpam-5166	342	1	thus	thus	ADV
ejpam-5166	342	2	,	,	PUNCT
ejpam-5166	342	3	we	we	PRON
ejpam-5166	342	4	obtain	obtain	VERB
ejpam-5166	342	5	w	w	ADP
ejpam-5166	342	6	(	(	PUNCT
ejpam-5166	342	7	pg(zp2q2	pg(zp2q2	NOUN
ejpam-5166	342	8	)	)	PUNCT
ejpam-5166	342	9	)	)	PUNCT
ejpam-5166	343	1	=	=	SYM
ejpam-5166	344	1	2p4q4	2p4q4	NUM
ejpam-5166	344	2	−	−	NOUN
ejpam-5166	344	3	11p2q2	11p2q2	NOUN
ejpam-5166	344	4	+	+	CCONJ
ejpam-5166	344	5	6p2q	6p2q	NOUN
ejpam-5166	344	6	+	+	X
ejpam-5166	344	7	6pq2	6pq2	NUM
ejpam-5166	344	8	−	−	ADP
ejpam-5166	344	9	3pq	3pq	NOUN
ejpam-5166	344	10	2	2	NUM
ejpam-5166	344	11	.	.	PUNCT
ejpam-5166	345	1	4	4	X
ejpam-5166	345	2	.	.	X
ejpam-5166	345	3	conclusion	conclusion	NOUN
ejpam-5166	345	4	based	base	VERB
ejpam-5166	345	5	on	on	ADP
ejpam-5166	345	6	the	the	DET
ejpam-5166	345	7	results	result	NOUN
ejpam-5166	345	8	and	and	CCONJ
ejpam-5166	345	9	discussion	discussion	NOUN
ejpam-5166	345	10	above	above	ADV
ejpam-5166	345	11	,	,	PUNCT
ejpam-5166	345	12	we	we	PRON
ejpam-5166	345	13	obtain	obtain	VERB
ejpam-5166	345	14	the	the	DET
ejpam-5166	345	15	wiener	wiener	NOUN
ejpam-5166	345	16	index	index	NOUN
ejpam-5166	345	17	formulas	formula	NOUN
ejpam-5166	345	18	for	for	ADP
ejpam-5166	345	19	prime	prime	ADJ
ejpam-5166	345	20	graphs	graph	NOUN
ejpam-5166	345	21	of	of	ADP
ejpam-5166	345	22	the	the	DET
ejpam-5166	345	23	ring	ring	NOUN
ejpam-5166	345	24	zn	zn	PROPN
ejpam-5166	345	25	where	where	SCONJ
ejpam-5166	345	26	n	n	NOUN
ejpam-5166	345	27	=	=	SYM
ejpam-5166	345	28	p	p	NOUN
ejpam-5166	345	29	,	,	PUNCT
ejpam-5166	345	30	p2	p2	NOUN
ejpam-5166	345	31	,	,	PUNCT
ejpam-5166	345	32	p3	p3	PROPN
ejpam-5166	345	33	,	,	PUNCT
ejpam-5166	345	34	pq	pq	NOUN
ejpam-5166	345	35	,	,	PUNCT
ejpam-5166	345	36	p2q	p2q	NOUN
ejpam-5166	345	37	,	,	PUNCT
ejpam-5166	345	38	p2q2	p2q2	NOUN
ejpam-5166	345	39	,	,	PUNCT
ejpam-5166	345	40	pqr	pqr	NOUN
ejpam-5166	345	41	for	for	ADP
ejpam-5166	345	42	distinct	distinct	ADJ
ejpam-5166	345	43	prime	prime	ADJ
ejpam-5166	345	44	numbers	number	NOUN
ejpam-5166	345	45	p	p	X
ejpam-5166	345	46	,	,	PUNCT
ejpam-5166	345	47	q	q	X
ejpam-5166	345	48	,	,	PUNCT
ejpam-5166	345	49	and	and	CCONJ
ejpam-5166	345	50	r.	r.	VERB
ejpam-5166	345	51	the	the	DET
ejpam-5166	345	52	distance	distance	NOUN
ejpam-5166	345	53	matrix	matrix	NOUN
ejpam-5166	345	54	is	be	AUX
ejpam-5166	345	55	formed	form	VERB
ejpam-5166	345	56	by	by	ADP
ejpam-5166	345	57	partitioning	partition	VERB
ejpam-5166	345	58	the	the	DET
ejpam-5166	345	59	ring	ring	NOUN
ejpam-5166	345	60	zn	zn	PROPN
ejpam-5166	345	61	into	into	ADP
ejpam-5166	345	62	a	a	DET
ejpam-5166	345	63	zero	zero	NUM
ejpam-5166	345	64	set	set	NOUN
ejpam-5166	345	65	,	,	PUNCT
ejpam-5166	345	66	a	a	DET
ejpam-5166	345	67	nontrivial	nontrivial	ADJ
ejpam-5166	345	68	zero	zero	NUM
ejpam-5166	345	69	divisor	divisor	NOUN
ejpam-5166	345	70	set	set	NOUN
ejpam-5166	345	71	,	,	PUNCT
ejpam-5166	345	72	and	and	CCONJ
ejpam-5166	345	73	a	a	DET
ejpam-5166	345	74	unit	unit	NOUN
ejpam-5166	345	75	set	set	NOUN
ejpam-5166	345	76	.	.	PUNCT
ejpam-5166	346	1	next	next	ADV
ejpam-5166	346	2	,	,	PUNCT
ejpam-5166	346	3	the	the	DET
ejpam-5166	346	4	adjacency	adjacency	NOUN
ejpam-5166	346	5	between	between	ADP
ejpam-5166	346	6	the	the	DET
ejpam-5166	346	7	vertices	vertex	NOUN
ejpam-5166	346	8	of	of	ADP
ejpam-5166	346	9	each	each	DET
ejpam-5166	346	10	set	set	NOUN
ejpam-5166	346	11	is	be	AUX
ejpam-5166	346	12	determined	determine	VERB
ejpam-5166	346	13	,	,	PUNCT
ejpam-5166	346	14	so	so	SCONJ
ejpam-5166	346	15	that	that	SCONJ
ejpam-5166	346	16	the	the	DET
ejpam-5166	346	17	distance	distance	NOUN
ejpam-5166	346	18	between	between	ADP
ejpam-5166	346	19	the	the	DET
ejpam-5166	346	20	vertices	vertex	NOUN
ejpam-5166	346	21	of	of	ADP
ejpam-5166	346	22	zn	zn	PROPN
ejpam-5166	346	23	is	be	AUX
ejpam-5166	346	24	obtained	obtain	VERB
ejpam-5166	346	25	.	.	PUNCT
ejpam-5166	347	1	based	base	VERB
ejpam-5166	347	2	on	on	ADP
ejpam-5166	347	3	these	these	DET
ejpam-5166	347	4	results	result	NOUN
ejpam-5166	347	5	,	,	PUNCT
ejpam-5166	347	6	for	for	ADP
ejpam-5166	347	7	the	the	DET
ejpam-5166	347	8	next	next	ADJ
ejpam-5166	347	9	reseraches	reserache	NOUN
ejpam-5166	347	10	,	,	PUNCT
ejpam-5166	347	11	we	we	PRON
ejpam-5166	347	12	give	give	VERB
ejpam-5166	347	13	some	some	PRON
ejpam-5166	347	14	of	of	ADP
ejpam-5166	347	15	the	the	DET
ejpam-5166	347	16	following	following	ADJ
ejpam-5166	347	17	open	open	ADJ
ejpam-5166	347	18	problems	problem	NOUN
ejpam-5166	347	19	:	:	PUNCT
ejpam-5166	347	20	(	(	PUNCT
ejpam-5166	347	21	i	i	NOUN
ejpam-5166	347	22	)	)	PUNCT
ejpam-5166	347	23	w	w	PROPN
ejpam-5166	347	24	(	(	PUNCT
ejpam-5166	347	25	pg(zpk	pg(zpk	NOUN
ejpam-5166	347	26	)	)	PUNCT
ejpam-5166	347	27	)	)	PUNCT
ejpam-5166	347	28	,	,	PUNCT
ejpam-5166	347	29	with	with	ADP
ejpam-5166	347	30	prime	prime	ADJ
ejpam-5166	347	31	number	number	NOUN
ejpam-5166	347	32	p	p	NOUN
ejpam-5166	347	33	and	and	CCONJ
ejpam-5166	347	34	natural	natural	ADJ
ejpam-5166	347	35	number	number	NOUN
ejpam-5166	347	36	k	k	PROPN
ejpam-5166	347	37	>	>	X
ejpam-5166	347	38	3	3	X
ejpam-5166	347	39	.	.	PUNCT
ejpam-5166	347	40	(	(	PUNCT
ejpam-5166	347	41	ii	ii	NOUN
ejpam-5166	347	42	)	)	PUNCT
ejpam-5166	347	43	w	w	PROPN
ejpam-5166	347	44	(	(	PUNCT
ejpam-5166	347	45	pg(zpkq	pg(zpkq	PROPN
ejpam-5166	347	46	)	)	PUNCT
ejpam-5166	347	47	)	)	PUNCT
ejpam-5166	347	48	,	,	PUNCT
ejpam-5166	347	49	with	with	ADP
ejpam-5166	347	50	distinct	distinct	ADJ
ejpam-5166	347	51	prime	prime	ADJ
ejpam-5166	347	52	numbers	number	NOUN
ejpam-5166	347	53	p	p	NOUN
ejpam-5166	347	54	,	,	PUNCT
ejpam-5166	347	55	q	q	NOUN
ejpam-5166	347	56	and	and	CCONJ
ejpam-5166	347	57	natural	natural	ADJ
ejpam-5166	347	58	number	number	NOUN
ejpam-5166	347	59	k	k	PROPN
ejpam-5166	347	60	>	>	X
ejpam-5166	347	61	2	2	X
ejpam-5166	347	62	.	.	PUNCT
ejpam-5166	347	63	(	(	PUNCT
ejpam-5166	347	64	iii	iii	NOUN
ejpam-5166	347	65	)	)	PUNCT
ejpam-5166	347	66	w	w	PROPN
ejpam-5166	347	67	(	(	PUNCT
ejpam-5166	347	68	pg(zpkqh	pg(zpkqh	PROPN
ejpam-5166	347	69	)	)	PUNCT
ejpam-5166	347	70	)	)	PUNCT
ejpam-5166	347	71	,	,	PUNCT
ejpam-5166	347	72	with	with	ADP
ejpam-5166	347	73	distinct	distinct	ADJ
ejpam-5166	347	74	prime	prime	ADJ
ejpam-5166	347	75	numbers	number	NOUN
ejpam-5166	347	76	p	p	NOUN
ejpam-5166	347	77	,	,	PUNCT
ejpam-5166	347	78	q	q	NOUN
ejpam-5166	347	79	and	and	CCONJ
ejpam-5166	347	80	natural	natural	ADJ
ejpam-5166	347	81	numbers	number	NOUN
ejpam-5166	347	82	k	k	PROPN
ejpam-5166	347	83	,	,	PUNCT
ejpam-5166	347	84	h	h	PROPN
ejpam-5166	347	85	>	>	X
ejpam-5166	347	86	2	2	X
ejpam-5166	347	87	.	.	PUNCT
ejpam-5166	347	88	(	(	PUNCT
ejpam-5166	347	89	iv	iv	X
ejpam-5166	347	90	)	)	PUNCT
ejpam-5166	347	91	w	w	PROPN
ejpam-5166	347	92	(	(	PUNCT
ejpam-5166	347	93	pg(zp1p2	pg(zp1p2	NUM
ejpam-5166	347	94	...	...	PUNCT
ejpam-5166	347	95	pn	pn	NOUN
ejpam-5166	347	96	)	)	PUNCT
ejpam-5166	347	97	)	)	PUNCT
ejpam-5166	347	98	,	,	PUNCT
ejpam-5166	347	99	with	with	ADP
ejpam-5166	347	100	distinct	distinct	ADJ
ejpam-5166	347	101	prime	prime	ADJ
ejpam-5166	347	102	numbers	number	NOUN
ejpam-5166	347	103	p1	p1	PROPN
ejpam-5166	347	104	,	,	PUNCT
ejpam-5166	347	105	.	.	PUNCT
ejpam-5166	347	106	.	.	PUNCT
ejpam-5166	348	1	.	.	PUNCT
ejpam-5166	349	1	,	,	PUNCT
ejpam-5166	349	2	pn	pn	PROPN
ejpam-5166	349	3	.	.	PROPN
ejpam-5166	349	4	references	reference	NOUN
ejpam-5166	349	5	1671	1671	NUM
ejpam-5166	349	6	acknowledgements	acknowledgement	NOUN
ejpam-5166	349	7	this	this	DET
ejpam-5166	349	8	research	research	NOUN
ejpam-5166	349	9	was	be	AUX
ejpam-5166	349	10	funded	fund	VERB
ejpam-5166	349	11	by	by	ADP
ejpam-5166	349	12	a	a	DET
ejpam-5166	349	13	”	"	PUNCT
ejpam-5166	349	14	lector	lector	NOUN
ejpam-5166	349	15	-	-	PUNCT
ejpam-5166	349	16	head	head	NOUN
ejpam-5166	349	17	doctoral	doctoral	ADJ
ejpam-5166	349	18	grant	grant	NOUN
ejpam-5166	349	19	”	"	PUNCT
ejpam-5166	349	20	from	from	ADP
ejpam-5166	349	21	faculty	faculty	NOUN
ejpam-5166	349	22	of	of	ADP
ejpam-5166	349	23	mathematics	mathematic	NOUN
ejpam-5166	349	24	and	and	CCONJ
ejpam-5166	349	25	natural	natural	ADJ
ejpam-5166	349	26	sciences	sciences	PROPN
ejpam-5166	349	27	university	university	PROPN
ejpam-5166	349	28	of	of	ADP
ejpam-5166	349	29	brawijaya	brawijaya	NOUN
ejpam-5166	349	30	with	with	ADP
ejpam-5166	349	31	contract	contract	NOUN
ejpam-5166	349	32	agreement	agreement	NOUN
ejpam-5166	349	33	letter	letter	NOUN
ejpam-5166	350	1	no	no	PRON
ejpam-5166	350	2	:	:	PUNCT
ejpam-5166	350	3	4160.7	4160.7	NUM
ejpam-5166	350	4	/	/	SYM
ejpam-5166	350	5	un10.f09	un10.f09	NOUN
ejpam-5166	350	6	/	/	SYM
ejpam-5166	350	7	pn/2023	pn/2023	NOUN
ejpam-5166	350	8	.	.	PUNCT
ejpam-5166	351	1	references	reference	NOUN
ejpam-5166	351	2	[	[	X
ejpam-5166	351	3	1	1	NUM
ejpam-5166	351	4	]	]	X
ejpam-5166	351	5	m	m	VERB
ejpam-5166	351	6	h	h	NOUN
ejpam-5166	351	7	aftab	aftab	PROPN
ejpam-5166	351	8	,	,	PUNCT
ejpam-5166	351	9	a	a	DET
ejpam-5166	351	10	akgül	akgül	PROPN
ejpam-5166	351	11	,	,	PUNCT
ejpam-5166	351	12	m	m	PROPN
ejpam-5166	351	13	b	b	NOUN
ejpam-5166	351	14	riaz	riaz	PROPN
ejpam-5166	351	15	,	,	PUNCT
ejpam-5166	351	16	m	m	PROPN
ejpam-5166	351	17	hussain	hussain	PROPN
ejpam-5166	351	18	,	,	PUNCT
ejpam-5166	351	19	k	k	PROPN
ejpam-5166	351	20	jebreen	jebreen	PROPN
ejpam-5166	351	21	,	,	PUNCT
ejpam-5166	351	22	and	and	CCONJ
ejpam-5166	351	23	h	h	PROPN
ejpam-5166	351	24	kanj	kanj	PROPN
ejpam-5166	351	25	.	.	PUNCT
ejpam-5166	352	1	measuring	measure	VERB
ejpam-5166	352	2	the	the	DET
ejpam-5166	352	3	energy	energy	NOUN
ejpam-5166	352	4	for	for	ADP
ejpam-5166	352	5	the	the	DET
ejpam-5166	352	6	molecular	molecular	ADJ
ejpam-5166	352	7	graphs	graph	NOUN
ejpam-5166	352	8	of	of	ADP
ejpam-5166	352	9	antiviral	antiviral	ADJ
ejpam-5166	352	10	agents	agent	NOUN
ejpam-5166	352	11	:	:	PUNCT
ejpam-5166	352	12	hydroxychloroquine	hydroxychloroquine	PROPN
ejpam-5166	352	13	,	,	PUNCT
ejpam-5166	352	14	chloroquine	chloroquine	NOUN
ejpam-5166	352	15	and	and	CCONJ
ejpam-5166	352	16	remdesivir	remdesivir	NOUN
ejpam-5166	352	17	.	.	PUNCT
ejpam-5166	353	1	south	south	ADJ
ejpam-5166	353	2	african	african	ADJ
ejpam-5166	353	3	journal	journal	PROPN
ejpam-5166	353	4	of	of	ADP
ejpam-5166	353	5	chemical	chemical	PROPN
ejpam-5166	353	6	engineering	engineering	NOUN
ejpam-5166	353	7	,	,	PUNCT
ejpam-5166	353	8	47:333–337	47:333–337	NUM
ejpam-5166	353	9	,	,	PUNCT
ejpam-5166	353	10	2024	2024	NUM
ejpam-5166	353	11	.	.	PUNCT
ejpam-5166	354	1	[	[	X
ejpam-5166	354	2	2	2	NUM
ejpam-5166	354	3	]	]	PUNCT
ejpam-5166	354	4	m	m	VERB
ejpam-5166	354	5	h	h	NOUN
ejpam-5166	354	6	aftab	aftab	PROPN
ejpam-5166	354	7	,	,	PUNCT
ejpam-5166	354	8	i	i	PRON
ejpam-5166	354	9	siddique	siddique	VERB
ejpam-5166	354	10	,	,	PUNCT
ejpam-5166	354	11	j	j	PROPN
ejpam-5166	354	12	k	k	PROPN
ejpam-5166	354	13	k	k	PROPN
ejpam-5166	355	1	asamoah	asamoah	PROPN
ejpam-5166	355	2	,	,	PUNCT
ejpam-5166	355	3	h	h	NOUN
ejpam-5166	355	4	a	a	X
ejpam-5166	355	5	e	e	X
ejpam-5166	355	6	w	w	NOUN
ejpam-5166	355	7	khalifa	khalifa	PROPN
ejpam-5166	355	8	,	,	PUNCT
ejpam-5166	355	9	and	and	CCONJ
ejpam-5166	355	10	m	m	PROPN
ejpam-5166	355	11	hussain	hussain	PROPN
ejpam-5166	355	12	.	.	PUNCT
ejpam-5166	356	1	multiplicative	multiplicative	ADJ
ejpam-5166	356	2	attributes	attribute	NOUN
ejpam-5166	356	3	derived	derive	VERB
ejpam-5166	356	4	from	from	ADP
ejpam-5166	356	5	graph	graph	NOUN
ejpam-5166	356	6	invariants	invariant	NOUN
ejpam-5166	356	7	for	for	ADP
ejpam-5166	356	8	saztec4	saztec4	NOUN
ejpam-5166	356	9	diamond	diamond	NOUN
ejpam-5166	356	10	.	.	PUNCT
ejpam-5166	357	1	hindawi	hindawi	ADJ
ejpam-5166	357	2	journal	journal	PROPN
ejpam-5166	357	3	of	of	ADP
ejpam-5166	357	4	mathematics	mathematic	NOUN
ejpam-5166	357	5	,	,	PUNCT
ejpam-5166	357	6	2022:1–7	2022:1–7	NUM
ejpam-5166	357	7	,	,	PUNCT
ejpam-5166	357	8	2022	2022	NUM
ejpam-5166	357	9	.	.	PUNCT
ejpam-5166	358	1	[	[	X
ejpam-5166	358	2	3	3	X
ejpam-5166	358	3	]	]	X
ejpam-5166	358	4	m	m	VERB
ejpam-5166	358	5	r	r	NOUN
ejpam-5166	358	6	ahmadi	ahmadi	NOUN
ejpam-5166	358	7	and	and	CCONJ
ejpam-5166	358	8	r	r	PROPN
ejpam-5166	358	9	nezhad	nezhad	VERB
ejpam-5166	358	10	.	.	PUNCT
ejpam-5166	359	1	energy	energy	NOUN
ejpam-5166	359	2	and	and	CCONJ
ejpam-5166	359	3	wiener	wiener	NOUN
ejpam-5166	359	4	index	index	NOUN
ejpam-5166	359	5	of	of	ADP
ejpam-5166	359	6	zero	zero	NUM
ejpam-5166	359	7	-	-	PUNCT
ejpam-5166	359	8	divisor	divisor	NOUN
ejpam-5166	359	9	graphs	graph	NOUN
ejpam-5166	359	10	.	.	PUNCT
ejpam-5166	360	1	iran	iran	PROPN
ejpam-5166	360	2	.	.	PUNCT
ejpam-5166	361	1	j.	j.	PROPN
ejpam-5166	361	2	math	math	PROPN
ejpam-5166	361	3	.	.	PUNCT
ejpam-5166	362	1	chem	chem	PROPN
ejpam-5166	362	2	.	.	PUNCT
ejpam-5166	362	3	,	,	PUNCT
ejpam-5166	362	4	2(1):45–51	2(1):45–51	NUM
ejpam-5166	362	5	,	,	PUNCT
ejpam-5166	362	6	2011	2011	NUM
ejpam-5166	362	7	.	.	PUNCT
ejpam-5166	363	1	[	[	X
ejpam-5166	363	2	4	4	NUM
ejpam-5166	363	3	]	]	X
ejpam-5166	363	4	s	s	PART
ejpam-5166	363	5	akbari	akbari	PROPN
ejpam-5166	363	6	and	and	CCONJ
ejpam-5166	363	7	a	a	DET
ejpam-5166	363	8	mohammadian	mohammadian	NOUN
ejpam-5166	363	9	.	.	PUNCT
ejpam-5166	364	1	on	on	ADP
ejpam-5166	364	2	zero	zero	NUM
ejpam-5166	364	3	-	-	PUNCT
ejpam-5166	364	4	divisor	divisor	NOUN
ejpam-5166	364	5	graphs	graph	NOUN
ejpam-5166	364	6	of	of	ADP
ejpam-5166	364	7	finite	finite	ADJ
ejpam-5166	364	8	rings	ring	NOUN
ejpam-5166	364	9	.	.	PUNCT
ejpam-5166	365	1	journal	journal	PROPN
ejpam-5166	365	2	of	of	ADP
ejpam-5166	365	3	algebra	algebra	PROPN
ejpam-5166	365	4	,	,	PUNCT
ejpam-5166	365	5	314:168–184	314:168–184	NUM
ejpam-5166	365	6	,	,	PUNCT
ejpam-5166	365	7	2007	2007	NUM
ejpam-5166	365	8	.	.	PUNCT
ejpam-5166	366	1	[	[	X
ejpam-5166	366	2	5	5	NUM
ejpam-5166	366	3	]	]	X
ejpam-5166	366	4	d	d	X
ejpam-5166	366	5	f	f	PROPN
ejpam-5166	366	6	anderson	anderson	PROPN
ejpam-5166	366	7	,	,	PUNCT
ejpam-5166	366	8	m	m	PROPN
ejpam-5166	366	9	c	c	PROPN
ejpam-5166	366	10	axtell	axtell	PROPN
ejpam-5166	366	11	,	,	PUNCT
ejpam-5166	366	12	and	and	CCONJ
ejpam-5166	366	13	j	j	X
ejpam-5166	366	14	a	a	DET
ejpam-5166	366	15	stickles	stickle	NOUN
ejpam-5166	366	16	.	.	PUNCT
ejpam-5166	367	1	zero	zero	NUM
ejpam-5166	367	2	-	-	PUNCT
ejpam-5166	367	3	divisor	divisor	NOUN
ejpam-5166	367	4	graphs	graph	NOUN
ejpam-5166	367	5	in	in	ADP
ejpam-5166	367	6	commutative	commutative	ADJ
ejpam-5166	367	7	rings	ring	NOUN
ejpam-5166	367	8	.	.	PUNCT
ejpam-5166	368	1	commutative	commutative	ADJ
ejpam-5166	368	2	algebra	algebra	NOUN
ejpam-5166	368	3	:	:	PUNCT
ejpam-5166	368	4	noetherian	noetherian	ADJ
ejpam-5166	368	5	and	and	CCONJ
ejpam-5166	368	6	non	non	ADJ
ejpam-5166	368	7	-	-	ADJ
ejpam-5166	368	8	noetherian	noetherian	ADJ
ejpam-5166	368	9	perspectives	perspective	NOUN
ejpam-5166	368	10	,	,	PUNCT
ejpam-5166	368	11	pages	page	NOUN
ejpam-5166	368	12	23	23	NUM
ejpam-5166	368	13	–	–	PUNCT
ejpam-5166	368	14	46	46	NUM
ejpam-5166	368	15	,	,	PUNCT
ejpam-5166	368	16	2011	2011	NUM
ejpam-5166	368	17	.	.	PUNCT
ejpam-5166	369	1	[	[	X
ejpam-5166	369	2	6	6	NUM
ejpam-5166	369	3	]	]	PUNCT
ejpam-5166	369	4	d	d	X
ejpam-5166	369	5	f	f	PROPN
ejpam-5166	369	6	anderson	anderson	PROPN
ejpam-5166	369	7	and	and	CCONJ
ejpam-5166	369	8	a	a	DET
ejpam-5166	369	9	badawi	badawi	NOUN
ejpam-5166	369	10	.	.	PUNCT
ejpam-5166	370	1	the	the	DET
ejpam-5166	370	2	total	total	ADJ
ejpam-5166	370	3	graph	graph	NOUN
ejpam-5166	370	4	of	of	ADP
ejpam-5166	370	5	a	a	DET
ejpam-5166	370	6	commutative	commutative	ADJ
ejpam-5166	370	7	ring	ring	NOUN
ejpam-5166	370	8	.	.	PUNCT
ejpam-5166	371	1	journal	journal	PROPN
ejpam-5166	371	2	of	of	ADP
ejpam-5166	371	3	algebra	algebra	PROPN
ejpam-5166	371	4	,	,	PUNCT
ejpam-5166	371	5	320:2706–2719	320:2706–2719	NUM
ejpam-5166	371	6	,	,	PUNCT
ejpam-5166	371	7	2008	2008	NUM
ejpam-5166	371	8	.	.	PUNCT
ejpam-5166	372	1	[	[	X
ejpam-5166	372	2	7	7	X
ejpam-5166	372	3	]	]	X
ejpam-5166	372	4	n	n	CCONJ
ejpam-5166	372	5	ashrafi	ashrafi	NOUN
ejpam-5166	372	6	,	,	PUNCT
ejpam-5166	372	7	h	h	NOUN
ejpam-5166	372	8	r	r	NOUN
ejpam-5166	372	9	maimani	maimani	NOUN
ejpam-5166	372	10	,	,	PUNCT
ejpam-5166	372	11	m	m	NOUN
ejpam-5166	372	12	r	r	NOUN
ejpam-5166	372	13	pournaki	pournaki	NOUN
ejpam-5166	372	14	,	,	PUNCT
ejpam-5166	372	15	and	and	CCONJ
ejpam-5166	372	16	s	s	NOUN
ejpam-5166	372	17	yassemi	yassemi	NOUN
ejpam-5166	372	18	.	.	PUNCT
ejpam-5166	373	1	unit	unit	NOUN
ejpam-5166	373	2	graphs	graph	NOUN
ejpam-5166	373	3	associated	associate	VERB
ejpam-5166	373	4	with	with	ADP
ejpam-5166	373	5	rings	ring	NOUN
ejpam-5166	373	6	.	.	PUNCT
ejpam-5166	374	1	communications	communication	NOUN
ejpam-5166	374	2	in	in	ADP
ejpam-5166	374	3	algebra	algebra	NOUN
ejpam-5166	374	4	,	,	PUNCT
ejpam-5166	374	5	38(8):2851–2871	38(8):2851–2871	NUM
ejpam-5166	374	6	,	,	PUNCT
ejpam-5166	374	7	2010	2010	NUM
ejpam-5166	374	8	.	.	PUNCT
ejpam-5166	375	1	[	[	X
ejpam-5166	375	2	8	8	NUM
ejpam-5166	375	3	]	]	PUNCT
ejpam-5166	375	4	t	t	PROPN
ejpam-5166	375	5	asir	asir	PROPN
ejpam-5166	375	6	and	and	CCONJ
ejpam-5166	375	7	v	v	NUM
ejpam-5166	375	8	rabikka	rabikka	NOUN
ejpam-5166	375	9	.	.	PUNCT
ejpam-5166	376	1	the	the	DET
ejpam-5166	376	2	wiener	wiener	NOUN
ejpam-5166	376	3	index	index	NOUN
ejpam-5166	376	4	of	of	ADP
ejpam-5166	376	5	the	the	DET
ejpam-5166	376	6	zero	zero	NUM
ejpam-5166	376	7	-	-	PUNCT
ejpam-5166	376	8	divisor	divisor	NOUN
ejpam-5166	376	9	graph	graph	NOUN
ejpam-5166	376	10	of	of	ADP
ejpam-5166	376	11	zn	zn	PROPN
ejpam-5166	376	12	.	.	PUNCT
ejpam-5166	376	13	discrete	discrete	ADJ
ejpam-5166	376	14	appl	appl	PROPN
ejpam-5166	376	15	.	.	PUNCT
ejpam-5166	376	16	math	math	PROPN
ejpam-5166	376	17	.	.	PUNCT
ejpam-5166	376	18	,	,	PUNCT
ejpam-5166	376	19	319:461–471	319:461–471	NUM
ejpam-5166	376	20	,	,	PUNCT
ejpam-5166	376	21	2022	2022	NUM
ejpam-5166	376	22	.	.	PUNCT
ejpam-5166	377	1	[	[	X
ejpam-5166	377	2	9	9	NUM
ejpam-5166	377	3	]	]	PUNCT
ejpam-5166	377	4	t	t	PROPN
ejpam-5166	377	5	asir	asir	PROPN
ejpam-5166	377	6	,	,	PUNCT
ejpam-5166	377	7	v	v	NUM
ejpam-5166	377	8	rabikka	rabikka	NOUN
ejpam-5166	377	9	,	,	PUNCT
ejpam-5166	377	10	m	m	VERB
ejpam-5166	377	11	anto	anto	PROPN
ejpam-5166	377	12	,	,	PUNCT
ejpam-5166	377	13	and	and	CCONJ
ejpam-5166	377	14	n	n	NUM
ejpam-5166	377	15	shunmugapriya	shunmugapriya	NOUN
ejpam-5166	377	16	.	.	PUNCT
ejpam-5166	378	1	wiener	wiener	NOUN
ejpam-5166	378	2	index	index	NOUN
ejpam-5166	378	3	of	of	ADP
ejpam-5166	378	4	graphs	graph	NOUN
ejpam-5166	378	5	over	over	ADP
ejpam-5166	378	6	rings	ring	NOUN
ejpam-5166	378	7	:	:	PUNCT
ejpam-5166	378	8	a	a	DET
ejpam-5166	378	9	survey	survey	NOUN
ejpam-5166	378	10	.	.	PUNCT
ejpam-5166	379	1	akce	akce	PROPN
ejpam-5166	379	2	international	international	PROPN
ejpam-5166	379	3	journal	journal	NOUN
ejpam-5166	379	4	of	of	ADP
ejpam-5166	379	5	graphs	graph	NOUN
ejpam-5166	379	6	and	and	CCONJ
ejpam-5166	379	7	combinatorics	combinatoric	NOUN
ejpam-5166	379	8	,	,	PUNCT
ejpam-5166	379	9	19(3):316–324	19(3):316–324	NUM
ejpam-5166	379	10	,	,	PUNCT
ejpam-5166	379	11	2022	2022	NUM
ejpam-5166	379	12	.	.	PUNCT
ejpam-5166	380	1	[	[	X
ejpam-5166	380	2	10	10	NUM
ejpam-5166	380	3	]	]	X
ejpam-5166	380	4	t	t	PROPN
ejpam-5166	380	5	asir	asir	PROPN
ejpam-5166	380	6	,	,	PUNCT
ejpam-5166	380	7	v	v	NUM
ejpam-5166	380	8	rabikka	rabikka	NOUN
ejpam-5166	380	9	,	,	PUNCT
ejpam-5166	380	10	and	and	CCONJ
ejpam-5166	380	11	h	h	PROPN
ejpam-5166	380	12	su	su	PROPN
ejpam-5166	380	13	.	.	PROPN
ejpam-5166	381	1	on	on	ADP
ejpam-5166	381	2	wiener	wiener	NOUN
ejpam-5166	381	3	index	index	NOUN
ejpam-5166	381	4	of	of	ADP
ejpam-5166	381	5	unit	unit	NOUN
ejpam-5166	381	6	graph	graph	NOUN
ejpam-5166	381	7	associated	associate	VERB
ejpam-5166	381	8	with	with	ADP
ejpam-5166	381	9	a	a	DET
ejpam-5166	381	10	commutative	commutative	ADJ
ejpam-5166	381	11	ring	ring	NOUN
ejpam-5166	381	12	.	.	PUNCT
ejpam-5166	382	1	algebra	algebra	PROPN
ejpam-5166	382	2	colloq	colloq	PROPN
ejpam-5166	382	3	.	.	PUNCT
ejpam-5166	382	4	,	,	PUNCT
ejpam-5166	382	5	29(2):221–230	29(2):221–230	PROPN
ejpam-5166	382	6	,	,	PUNCT
ejpam-5166	382	7	2022	2022	NUM
ejpam-5166	382	8	.	.	PUNCT
ejpam-5166	383	1	[	[	X
ejpam-5166	383	2	11	11	NUM
ejpam-5166	383	3	]	]	X
ejpam-5166	383	4	i	i	PROPN
ejpam-5166	383	5	beck	beck	PROPN
ejpam-5166	383	6	.	.	PUNCT
ejpam-5166	384	1	coloring	coloring	NOUN
ejpam-5166	384	2	of	of	ADP
ejpam-5166	384	3	commutative	commutative	ADJ
ejpam-5166	384	4	rings	ring	NOUN
ejpam-5166	384	5	.	.	PUNCT
ejpam-5166	385	1	journal	journal	PROPN
ejpam-5166	385	2	of	of	ADP
ejpam-5166	385	3	algebra	algebra	PROPN
ejpam-5166	385	4	,	,	PUNCT
ejpam-5166	385	5	116(1):208–226	116(1):208–226	NUM
ejpam-5166	385	6	,	,	PUNCT
ejpam-5166	385	7	1988	1988	NUM
ejpam-5166	385	8	.	.	PUNCT
ejpam-5166	386	1	[	[	X
ejpam-5166	386	2	12	12	NUM
ejpam-5166	386	3	]	]	PUNCT
ejpam-5166	386	4	s	s	VERB
ejpam-5166	386	5	bhavanari	bhavanari	NOUN
ejpam-5166	386	6	,	,	PUNCT
ejpam-5166	386	7	s	s	VERB
ejpam-5166	386	8	kuncham	kuncham	NOUN
ejpam-5166	386	9	,	,	PUNCT
ejpam-5166	386	10	and	and	CCONJ
ejpam-5166	386	11	n	n	PRON
ejpam-5166	386	12	dasari	dasari	NOUN
ejpam-5166	386	13	.	.	PUNCT
ejpam-5166	387	1	prime	prime	ADJ
ejpam-5166	387	2	graph	graph	NOUN
ejpam-5166	387	3	of	of	ADP
ejpam-5166	387	4	a	a	DET
ejpam-5166	387	5	ring	ring	NOUN
ejpam-5166	387	6	.	.	PUNCT
ejpam-5166	388	1	journal	journal	PROPN
ejpam-5166	388	2	of	of	ADP
ejpam-5166	388	3	combinatorics	combinatorics	PROPN
ejpam-5166	388	4	,	,	PUNCT
ejpam-5166	388	5	information	information	NOUN
ejpam-5166	388	6	&	&	CCONJ
ejpam-5166	388	7	system	system	NOUN
ejpam-5166	388	8	sciences	sciences	PROPN
ejpam-5166	388	9	,	,	PUNCT
ejpam-5166	388	10	35(1	35(1	NOUN
ejpam-5166	388	11	-	-	PUNCT
ejpam-5166	388	12	2):27–42	2):27–42	NUM
ejpam-5166	388	13	,	,	PUNCT
ejpam-5166	388	14	2010	2010	NUM
ejpam-5166	388	15	.	.	PUNCT
ejpam-5166	389	1	references	reference	NOUN
ejpam-5166	389	2	1672	1672	NUM
ejpam-5166	390	1	[	[	X
ejpam-5166	390	2	13	13	NUM
ejpam-5166	390	3	]	]	X
ejpam-5166	390	4	s	s	PART
ejpam-5166	390	5	brezovnik	brezovnik	NOUN
ejpam-5166	390	6	,	,	PUNCT
ejpam-5166	390	7	n	n	PRON
ejpam-5166	390	8	tratnik	tratnik	NOUN
ejpam-5166	390	9	,	,	PUNCT
ejpam-5166	390	10	and	and	CCONJ
ejpam-5166	390	11	p	p	NOUN
ejpam-5166	390	12	z	z	PROPN
ejpam-5166	390	13	pletersek	pletersek	PROPN
ejpam-5166	390	14	.	.	PUNCT
ejpam-5166	391	1	weighted	weight	VERB
ejpam-5166	391	2	wiener	wiener	NOUN
ejpam-5166	391	3	indices	index	NOUN
ejpam-5166	391	4	of	of	ADP
ejpam-5166	391	5	molecular	molecular	ADJ
ejpam-5166	391	6	graphs	graph	NOUN
ejpam-5166	391	7	with	with	ADP
ejpam-5166	391	8	application	application	NOUN
ejpam-5166	391	9	to	to	ADP
ejpam-5166	391	10	alkenes	alkene	NOUN
ejpam-5166	391	11	and	and	CCONJ
ejpam-5166	391	12	alkadienes	alkadiene	NOUN
ejpam-5166	391	13	.	.	PUNCT
ejpam-5166	392	1	mathematics	mathematic	NOUN
ejpam-5166	392	2	,	,	PUNCT
ejpam-5166	392	3	9(153):2–16	9(153):2–16	NUM
ejpam-5166	392	4	,	,	PUNCT
ejpam-5166	392	5	2021	2021	NUM
ejpam-5166	392	6	.	.	PUNCT
ejpam-5166	393	1	[	[	X
ejpam-5166	393	2	14	14	NUM
ejpam-5166	393	3	]	]	X
ejpam-5166	393	4	g	g	PROPN
ejpam-5166	393	5	chartrand	chartrand	NOUN
ejpam-5166	393	6	,	,	PUNCT
ejpam-5166	393	7	l	l	PROPN
ejpam-5166	393	8	lesniak	lesniak	PROPN
ejpam-5166	393	9	,	,	PUNCT
ejpam-5166	393	10	and	and	CCONJ
ejpam-5166	393	11	p	p	PROPN
ejpam-5166	393	12	zhang	zhang	PROPN
ejpam-5166	393	13	.	.	PUNCT
ejpam-5166	393	14	graphs	graph	NOUN
ejpam-5166	393	15	and	and	CCONJ
ejpam-5166	393	16	digraphs	digraph	NOUN
ejpam-5166	393	17	.	.	PUNCT
ejpam-5166	394	1	crc	crc	PROPN
ejpam-5166	394	2	press	press	PROPN
ejpam-5166	394	3	,	,	PUNCT
ejpam-5166	394	4	2016	2016	NUM
ejpam-5166	394	5	.	.	PUNCT
ejpam-5166	395	1	[	[	X
ejpam-5166	395	2	15	15	NUM
ejpam-5166	395	3	]	]	X
ejpam-5166	395	4	s	s	VERB
ejpam-5166	395	5	derrible	derrible	NOUN
ejpam-5166	395	6	and	and	CCONJ
ejpam-5166	395	7	c	c	PROPN
ejpam-5166	395	8	kennedy	kennedy	PROPN
ejpam-5166	395	9	.	.	PUNCT
ejpam-5166	396	1	applications	application	NOUN
ejpam-5166	396	2	of	of	ADP
ejpam-5166	396	3	graph	graph	NOUN
ejpam-5166	396	4	theory	theory	NOUN
ejpam-5166	396	5	and	and	CCONJ
ejpam-5166	396	6	network	network	NOUN
ejpam-5166	396	7	science	science	NOUN
ejpam-5166	396	8	to	to	ADP
ejpam-5166	396	9	transit	transit	NOUN
ejpam-5166	396	10	network	network	NOUN
ejpam-5166	396	11	design	design	NOUN
ejpam-5166	396	12	.	.	PUNCT
ejpam-5166	397	1	transp	transp	PROPN
ejpam-5166	397	2	rev	rev	PROPN
ejpam-5166	397	3	,	,	PUNCT
ejpam-5166	397	4	31(4):495–519	31(4):495–519	PROPN
ejpam-5166	397	5	,	,	PUNCT
ejpam-5166	397	6	2011	2011	NUM
ejpam-5166	397	7	.	.	PUNCT
ejpam-5166	398	1	[	[	X
ejpam-5166	398	2	16	16	NUM
ejpam-5166	398	3	]	]	X
ejpam-5166	398	4	j	j	PROPN
ejpam-5166	398	5	a	a	DET
ejpam-5166	398	6	gallian	gallian	PROPN
ejpam-5166	398	7	.	.	PUNCT
ejpam-5166	399	1	contemporary	contemporary	ADJ
ejpam-5166	399	2	abstract	abstract	ADJ
ejpam-5166	399	3	algebra	algebra	PROPN
ejpam-5166	399	4	.	.	PUNCT
ejpam-5166	400	1	chapman	chapman	PROPN
ejpam-5166	400	2	hall	hall	PROPN
ejpam-5166	400	3	/	/	SYM
ejpam-5166	400	4	crc	crc	PROPN
ejpam-5166	400	5	,	,	PUNCT
ejpam-5166	400	6	2021	2021	NUM
ejpam-5166	400	7	.	.	PUNCT
ejpam-5166	401	1	[	[	X
ejpam-5166	401	2	17	17	NUM
ejpam-5166	401	3	]	]	X
ejpam-5166	401	4	h	h	NOUN
ejpam-5166	401	5	hosoya	hosoya	PROPN
ejpam-5166	401	6	.	.	PUNCT
ejpam-5166	402	1	topological	topological	ADJ
ejpam-5166	402	2	index	index	NOUN
ejpam-5166	402	3	:	:	PUNCT
ejpam-5166	402	4	a	a	DET
ejpam-5166	402	5	newly	newly	ADV
ejpam-5166	402	6	proposed	propose	VERB
ejpam-5166	402	7	quantity	quantity	NOUN
ejpam-5166	402	8	characterizing	characterize	VERB
ejpam-5166	402	9	the	the	DET
ejpam-5166	402	10	topological	topological	ADJ
ejpam-5166	402	11	nature	nature	NOUN
ejpam-5166	402	12	of	of	ADP
ejpam-5166	402	13	structural	structural	ADJ
ejpam-5166	402	14	isomers	isomer	NOUN
ejpam-5166	402	15	of	of	ADP
ejpam-5166	402	16	saturated	saturated	ADJ
ejpam-5166	402	17	hydrocarbons	hydrocarbon	NOUN
ejpam-5166	402	18	.	.	PUNCT
ejpam-5166	403	1	bcsj	bcsj	NOUN
ejpam-5166	403	2	,	,	PUNCT
ejpam-5166	403	3	19(3):2332–2339	19(3):2332–2339	NUM
ejpam-5166	403	4	,	,	PUNCT
ejpam-5166	403	5	1971	1971	NUM
ejpam-5166	403	6	.	.	PUNCT
ejpam-5166	404	1	[	[	X
ejpam-5166	404	2	18	18	NUM
ejpam-5166	404	3	]	]	SYM
ejpam-5166	404	4	s	s	PART
ejpam-5166	404	5	s	s	X
ejpam-5166	404	6	joshi	joshi	PROPN
ejpam-5166	404	7	and	and	CCONJ
ejpam-5166	404	8	k	k	PROPN
ejpam-5166	404	9	f	f	PROPN
ejpam-5166	404	10	pawar	pawar	PROPN
ejpam-5166	404	11	.	.	PUNCT
ejpam-5166	405	1	energy	energy	NOUN
ejpam-5166	405	2	,	,	PUNCT
ejpam-5166	405	3	wiener	wiener	NOUN
ejpam-5166	405	4	index	index	NOUN
ejpam-5166	405	5	and	and	CCONJ
ejpam-5166	405	6	line	line	NOUN
ejpam-5166	405	7	graph	graph	NOUN
ejpam-5166	405	8	of	of	ADP
ejpam-5166	405	9	prime	prime	ADJ
ejpam-5166	405	10	graph	graph	NOUN
ejpam-5166	405	11	of	of	ADP
ejpam-5166	405	12	a	a	DET
ejpam-5166	405	13	ring	ring	NOUN
ejpam-5166	405	14	.	.	PUNCT
ejpam-5166	406	1	international	international	ADJ
ejpam-5166	406	2	j.	j.	PROPN
ejpam-5166	406	3	math	math	PROPN
ejpam-5166	406	4	.	.	PUNCT
ejpam-5166	407	1	combin	combin	NOUN
ejpam-5166	407	2	,	,	PUNCT
ejpam-5166	407	3	3:74–80	3:74–80	NUM
ejpam-5166	407	4	,	,	PUNCT
ejpam-5166	407	5	2018	2018	NUM
ejpam-5166	407	6	.	.	PUNCT
ejpam-5166	408	1	[	[	X
ejpam-5166	408	2	19	19	NUM
ejpam-5166	408	3	]	]	SYM
ejpam-5166	408	4	s	s	PART
ejpam-5166	408	5	s	s	X
ejpam-5166	408	6	joshi	joshi	PROPN
ejpam-5166	408	7	and	and	CCONJ
ejpam-5166	408	8	k	k	PROPN
ejpam-5166	408	9	f	f	PROPN
ejpam-5166	408	10	pawar	pawar	PROPN
ejpam-5166	408	11	.	.	PUNCT
ejpam-5166	409	1	on	on	ADP
ejpam-5166	409	2	prime	prime	ADJ
ejpam-5166	409	3	graph	graph	NOUN
ejpam-5166	409	4	pg2(r	pg2(r	NOUN
ejpam-5166	409	5	)	)	PUNCT
ejpam-5166	409	6	of	of	ADP
ejpam-5166	409	7	a	a	DET
ejpam-5166	409	8	ring	ring	NOUN
ejpam-5166	409	9	.	.	PUNCT
ejpam-5166	410	1	international	international	ADJ
ejpam-5166	410	2	journal	journal	PROPN
ejpam-5166	410	3	of	of	ADP
ejpam-5166	410	4	mathematical	mathematical	ADJ
ejpam-5166	410	5	combinatorics	combinatoric	NOUN
ejpam-5166	410	6	,	,	PUNCT
ejpam-5166	410	7	30:11–22	30:11–22	NUM
ejpam-5166	410	8	,	,	PUNCT
ejpam-5166	410	9	2019	2019	NUM
ejpam-5166	410	10	.	.	PUNCT
ejpam-5166	411	1	[	[	X
ejpam-5166	411	2	20	20	NUM
ejpam-5166	411	3	]	]	SYM
ejpam-5166	411	4	s	s	PART
ejpam-5166	411	5	s	s	X
ejpam-5166	411	6	joshi	joshi	PROPN
ejpam-5166	411	7	and	and	CCONJ
ejpam-5166	411	8	k	k	PROPN
ejpam-5166	411	9	f	f	PROPN
ejpam-5166	411	10	pawar	pawar	PROPN
ejpam-5166	411	11	.	.	PUNCT
ejpam-5166	412	1	coloring	coloring	NOUN
ejpam-5166	412	2	of	of	ADP
ejpam-5166	412	3	prime	prime	ADJ
ejpam-5166	412	4	graph	graph	NOUN
ejpam-5166	412	5	pg1(r	pg1(r	NOUN
ejpam-5166	412	6	)	)	PUNCT
ejpam-5166	412	7	and	and	CCONJ
ejpam-5166	412	8	pg2(r	pg2(r	PROPN
ejpam-5166	412	9	)	)	PUNCT
ejpam-5166	412	10	of	of	ADP
ejpam-5166	412	11	a	a	DET
ejpam-5166	412	12	ring	ring	NOUN
ejpam-5166	412	13	.	.	PUNCT
ejpam-5166	413	1	palestine	palestine	PROPN
ejpam-5166	413	2	journal	journal	PROPN
ejpam-5166	413	3	of	of	ADP
ejpam-5166	413	4	mathematics	mathematics	PROPN
ejpam-5166	413	5	,	,	PUNCT
ejpam-5166	413	6	9(1):97–104	9(1):97–104	NOUN
ejpam-5166	413	7	,	,	PUNCT
ejpam-5166	413	8	2020	2020	NUM
ejpam-5166	413	9	.	.	PUNCT
ejpam-5166	414	1	[	[	X
ejpam-5166	414	2	21	21	NUM
ejpam-5166	414	3	]	]	X
ejpam-5166	414	4	h	h	PROPN
ejpam-5166	414	5	kanj	kanj	PROPN
ejpam-5166	414	6	,	,	PUNCT
ejpam-5166	414	7	h	h	PROPN
ejpam-5166	414	8	iqbal	iqbal	PROPN
ejpam-5166	414	9	,	,	PUNCT
ejpam-5166	414	10	m	m	VERB
ejpam-5166	414	11	h	h	NOUN
ejpam-5166	414	12	aftab	aftab	PROPN
ejpam-5166	414	13	,	,	PUNCT
ejpam-5166	414	14	h	h	NOUN
ejpam-5166	414	15	raza	raza	PROPN
ejpam-5166	414	16	,	,	PUNCT
ejpam-5166	414	17	k	k	PROPN
ejpam-5166	414	18	jebreen	jebreen	PROPN
ejpam-5166	414	19	,	,	PUNCT
ejpam-5166	414	20	and	and	CCONJ
ejpam-5166	414	21	m	m	VERB
ejpam-5166	414	22	i	i	NOUN
ejpam-5166	414	23	sowaity	sowaity	NOUN
ejpam-5166	414	24	.	.	PUNCT
ejpam-5166	415	1	topological	topological	ADJ
ejpam-5166	415	2	characterization	characterization	NOUN
ejpam-5166	415	3	of	of	ADP
ejpam-5166	415	4	hexagonal	hexagonal	ADJ
ejpam-5166	415	5	network	network	NOUN
ejpam-5166	415	6	and	and	CCONJ
ejpam-5166	415	7	non	non	ADJ
ejpam-5166	415	8	-	-	ADJ
ejpam-5166	415	9	kekulean	kekulean	ADJ
ejpam-5166	415	10	benzenoid	benzenoid	NOUN
ejpam-5166	415	11	hydrocarbon	hydrocarbon	NOUN
ejpam-5166	415	12	.	.	PUNCT
ejpam-5166	416	1	european	european	PROPN
ejpam-5166	416	2	journal	journal	PROPN
ejpam-5166	416	3	of	of	ADP
ejpam-5166	416	4	pure	pure	ADJ
ejpam-5166	416	5	and	and	CCONJ
ejpam-5166	416	6	applied	applied	ADJ
ejpam-5166	416	7	mathematics	mathematic	NOUN
ejpam-5166	416	8	,	,	PUNCT
ejpam-5166	416	9	16(4):2187–2197	16(4):2187–2197	NUM
ejpam-5166	416	10	,	,	PUNCT
ejpam-5166	416	11	2023	2023	NUM
ejpam-5166	416	12	.	.	PUNCT
ejpam-5166	417	1	[	[	X
ejpam-5166	417	2	22	22	NUM
ejpam-5166	417	3	]	]	PUNCT
ejpam-5166	417	4	a	a	DET
ejpam-5166	417	5	kumar	kumar	PROPN
ejpam-5166	417	6	and	and	CCONJ
ejpam-5166	417	7	v	v	ADP
ejpam-5166	417	8	kumar	kumar	PROPN
ejpam-5166	417	9	.	.	PUNCT
ejpam-5166	418	1	application	application	NOUN
ejpam-5166	418	2	of	of	ADP
ejpam-5166	418	3	graph	graph	NOUN
ejpam-5166	418	4	labeling	labeling	NOUN
ejpam-5166	418	5	in	in	ADP
ejpam-5166	418	6	crystallography	crystallography	NOUN
ejpam-5166	418	7	.	.	PUNCT
ejpam-5166	419	1	mater	mater	NOUN
ejpam-5166	419	2	today	today	NOUN
ejpam-5166	419	3	proc	proc	NOUN
ejpam-5166	419	4	,	,	PUNCT
ejpam-5166	419	5	2020	2020	NUM
ejpam-5166	419	6	.	.	PUNCT
ejpam-5166	420	1	[	[	X
ejpam-5166	420	2	23	23	NUM
ejpam-5166	420	3	]	]	X
ejpam-5166	420	4	r	r	NOUN
ejpam-5166	420	5	likaj	likaj	NOUN
ejpam-5166	420	6	,	,	PUNCT
ejpam-5166	420	7	a	a	DET
ejpam-5166	420	8	shala	shala	NOUN
ejpam-5166	420	9	,	,	PUNCT
ejpam-5166	420	10	mmehmetaj	mmehmetaj	NOUN
ejpam-5166	420	11	,	,	PUNCT
ejpam-5166	420	12	p	p	NOUN
ejpam-5166	420	13	hyseni	hyseni	ADJ
ejpam-5166	420	14	,	,	PUNCT
ejpam-5166	420	15	and	and	CCONJ
ejpam-5166	420	16	x	x	NOUN
ejpam-5166	420	17	bajrami	bajrami	NOUN
ejpam-5166	420	18	.	.	PUNCT
ejpam-5166	421	1	application	application	NOUN
ejpam-5166	421	2	of	of	ADP
ejpam-5166	421	3	graph	graph	NOUN
ejpam-5166	421	4	theory	theory	NOUN
ejpam-5166	421	5	to	to	PART
ejpam-5166	421	6	find	find	VERB
ejpam-5166	421	7	optimal	optimal	ADJ
ejpam-5166	421	8	paths	path	NOUN
ejpam-5166	421	9	for	for	ADP
ejpam-5166	421	10	the	the	DET
ejpam-5166	421	11	transportation	transportation	NOUN
ejpam-5166	421	12	problem	problem	NOUN
ejpam-5166	421	13	.	.	PUNCT
ejpam-5166	422	1	ifac	ifac	NOUN
ejpam-5166	422	2	proceedings	proceeding	NOUN
ejpam-5166	422	3	volumes	volume	NOUN
ejpam-5166	422	4	,	,	PUNCT
ejpam-5166	422	5	46(8):235–240	46(8):235–240	NOUN
ejpam-5166	422	6	,	,	PUNCT
ejpam-5166	422	7	2013	2013	NUM
ejpam-5166	422	8	.	.	PUNCT
ejpam-5166	423	1	[	[	X
ejpam-5166	423	2	24	24	NUM
ejpam-5166	423	3	]	]	SYM
ejpam-5166	423	4	b	b	PROPN
ejpam-5166	423	5	molnar	molnar	PROPN
ejpam-5166	423	6	and	and	CCONJ
ejpam-5166	423	7	a	a	DET
ejpam-5166	423	8	benczur	benczur	NOUN
ejpam-5166	423	9	.	.	PUNCT
ejpam-5166	424	1	the	the	DET
ejpam-5166	424	2	application	application	NOUN
ejpam-5166	424	3	of	of	ADP
ejpam-5166	424	4	directed	direct	VERB
ejpam-5166	424	5	hyper	hyper	NOUN
ejpam-5166	424	6	-	-	NOUN
ejpam-5166	424	7	graphs	graph	NOUN
ejpam-5166	424	8	for	for	ADP
ejpam-5166	424	9	analysis	analysis	NOUN
ejpam-5166	424	10	of	of	ADP
ejpam-5166	424	11	models	model	NOUN
ejpam-5166	424	12	of	of	ADP
ejpam-5166	424	13	information	information	NOUN
ejpam-5166	424	14	systems	system	NOUN
ejpam-5166	424	15	.	.	PUNCT
ejpam-5166	425	1	mathematics	mathematic	NOUN
ejpam-5166	425	2	,	,	PUNCT
ejpam-5166	425	3	10(5):759–769	10(5):759–769	NOUN
ejpam-5166	425	4	,	,	PUNCT
ejpam-5166	425	5	2022	2022	NUM
ejpam-5166	425	6	.	.	PUNCT
ejpam-5166	426	1	[	[	X
ejpam-5166	426	2	25	25	NUM
ejpam-5166	426	3	]	]	X
ejpam-5166	426	4	m	m	VERB
ejpam-5166	426	5	p	p	NOUN
ejpam-5166	426	6	nayaki	nayaki	ADV
ejpam-5166	426	7	and	and	CCONJ
ejpam-5166	426	8	e	e	PROPN
ejpam-5166	426	9	simon	simon	PROPN
ejpam-5166	426	10	-	-	PUNCT
ejpam-5166	426	11	raj	raj	PROPN
ejpam-5166	426	12	.	.	PUNCT
ejpam-5166	427	1	the	the	DET
ejpam-5166	427	2	physical	physical	ADJ
ejpam-5166	427	3	chemical	chemical	PROPN
ejpam-5166	427	4	characteristics	characteristic	NOUN
ejpam-5166	427	5	of	of	ADP
ejpam-5166	427	6	alkanes	alkane	NOUN
ejpam-5166	427	7	and	and	CCONJ
ejpam-5166	427	8	wiener	wiener	NOUN
ejpam-5166	427	9	indices	index	NOUN
ejpam-5166	427	10	.	.	PUNCT
ejpam-5166	428	1	journal	journal	NOUN
ejpam-5166	428	2	of	of	ADP
ejpam-5166	428	3	algebraic	algebraic	PROPN
ejpam-5166	428	4	statistics	statistic	NOUN
ejpam-5166	428	5	,	,	PUNCT
ejpam-5166	428	6	13(2):3338–3345	13(2):3338–3345	NUM
ejpam-5166	428	7	,	,	PUNCT
ejpam-5166	428	8	22	22	NUM
ejpam-5166	428	9	.	.	PUNCT
ejpam-5166	429	1	[	[	X
ejpam-5166	429	2	26	26	NUM
ejpam-5166	429	3	]	]	X
ejpam-5166	429	4	k	k	PROPN
ejpam-5166	429	5	patra	patra	PROPN
ejpam-5166	429	6	and	and	CCONJ
ejpam-5166	429	7	s	s	PROPN
ejpam-5166	429	8	kalita	kalita	PROPN
ejpam-5166	429	9	.	.	PUNCT
ejpam-5166	430	1	prime	prime	ADJ
ejpam-5166	430	2	graph	graph	NOUN
ejpam-5166	430	3	of	of	ADP
ejpam-5166	430	4	the	the	DET
ejpam-5166	430	5	commutative	commutative	ADJ
ejpam-5166	430	6	ring	ring	PROPN
ejpam-5166	430	7	zn	zn	PROPN
ejpam-5166	430	8	.	.	PUNCT
ejpam-5166	430	9	matematika	matematika	PROPN
ejpam-5166	430	10	:	:	PUNCT
ejpam-5166	430	11	malaysian	malaysian	ADJ
ejpam-5166	430	12	journal	journal	PROPN
ejpam-5166	430	13	of	of	ADP
ejpam-5166	430	14	industrial	industrial	ADJ
ejpam-5166	430	15	and	and	CCONJ
ejpam-5166	430	16	applied	apply	VERB
ejpam-5166	430	17	mathematics	mathematic	NOUN
ejpam-5166	430	18	,	,	PUNCT
ejpam-5166	430	19	30(1):59–67	30(1):59–67	NUM
ejpam-5166	430	20	,	,	PUNCT
ejpam-5166	430	21	2014	2014	NUM
ejpam-5166	430	22	.	.	PUNCT
ejpam-5166	431	1	[	[	X
ejpam-5166	431	2	27	27	NUM
ejpam-5166	431	3	]	]	X
ejpam-5166	431	4	k	k	PROPN
ejpam-5166	431	5	f	f	PROPN
ejpam-5166	431	6	pawar	pawar	PROPN
ejpam-5166	431	7	and	and	CCONJ
ejpam-5166	431	8	s	s	PROPN
ejpam-5166	431	9	s	s	PROPN
ejpam-5166	431	10	joshi	joshi	PROPN
ejpam-5166	431	11	.	.	PUNCT
ejpam-5166	432	1	the	the	DET
ejpam-5166	432	2	prime	prime	ADJ
ejpam-5166	432	3	graph	graph	NOUN
ejpam-5166	432	4	pg1(r	pg1(r	NOUN
ejpam-5166	432	5	)	)	PUNCT
ejpam-5166	432	6	of	of	ADP
ejpam-5166	432	7	a	a	DET
ejpam-5166	432	8	ring	ring	NOUN
ejpam-5166	432	9	.	.	PUNCT
ejpam-5166	433	1	palestine	palestine	PROPN
ejpam-5166	433	2	journal	journal	PROPN
ejpam-5166	433	3	of	of	ADP
ejpam-5166	433	4	mathematics	mathematic	NOUN
ejpam-5166	433	5	,	,	PUNCT
ejpam-5166	433	6	6(1):153–158	6(1):153–158	NUM
ejpam-5166	433	7	,	,	PUNCT
ejpam-5166	433	8	2017	2017	NUM
ejpam-5166	433	9	.	.	PUNCT
ejpam-5166	434	1	[	[	X
ejpam-5166	434	2	28	28	NUM
ejpam-5166	434	3	]	]	X
ejpam-5166	434	4	s	s	PART
ejpam-5166	434	5	pirzada	pirzada	PROPN
ejpam-5166	434	6	,	,	PUNCT
ejpam-5166	434	7	m	m	PROPN
ejpam-5166	434	8	aijaz	aijaz	ADJ
ejpam-5166	434	9	,	,	PUNCT
ejpam-5166	434	10	and	and	CCONJ
ejpam-5166	434	11	m	m	VERB
ejpam-5166	434	12	i	i	PROPN
ejpam-5166	434	13	bhat	bhat	PROPN
ejpam-5166	434	14	.	.	PUNCT
ejpam-5166	435	1	on	on	ADP
ejpam-5166	435	2	zero	zero	NUM
ejpam-5166	435	3	-	-	PUNCT
ejpam-5166	435	4	divisor	divisor	NOUN
ejpam-5166	435	5	graphs	graph	NOUN
ejpam-5166	435	6	of	of	ADP
ejpam-5166	435	7	the	the	DET
ejpam-5166	435	8	rings	ring	NOUN
ejpam-5166	435	9	zn	zn	PROPN
ejpam-5166	435	10	.	.	PUNCT
ejpam-5166	435	11	afr	afr	PROPN
ejpam-5166	435	12	.	.	PUNCT
ejpam-5166	435	13	math	math	PROPN
ejpam-5166	435	14	.	.	PUNCT
ejpam-5166	435	15	,	,	PUNCT
ejpam-5166	435	16	31:727–737	31:727–737	NUM
ejpam-5166	435	17	,	,	PUNCT
ejpam-5166	435	18	2020	2020	NUM
ejpam-5166	435	19	.	.	PUNCT
ejpam-5166	436	1	references	reference	NOUN
ejpam-5166	436	2	1673	1673	NUM
ejpam-5166	436	3	[	[	X
ejpam-5166	436	4	29	29	NUM
ejpam-5166	436	5	]	]	SYM
ejpam-5166	436	6	n	n	NUM
ejpam-5166	436	7	l	l	NOUN
ejpam-5166	436	8	prasanna	prasanna	PROPN
ejpam-5166	436	9	,	,	PUNCT
ejpam-5166	436	10	k	k	PROPN
ejpam-5166	436	11	sravanthi	sravanthi	X
ejpam-5166	436	12	,	,	PUNCT
ejpam-5166	436	13	and	and	CCONJ
ejpam-5166	437	1	n	n	DET
ejpam-5166	437	2	sudhakar	sudhakar	NOUN
ejpam-5166	437	3	.	.	PUNCT
ejpam-5166	438	1	applications	application	NOUN
ejpam-5166	438	2	of	of	ADP
ejpam-5166	438	3	graph	graph	NOUN
ejpam-5166	438	4	labeling	labeling	NOUN
ejpam-5166	438	5	in	in	ADP
ejpam-5166	438	6	communication	communication	NOUN
ejpam-5166	438	7	networks	network	NOUN
ejpam-5166	438	8	.	.	PUNCT
ejpam-5166	439	1	oriental	oriental	ADJ
ejpam-5166	439	2	journal	journal	PROPN
ejpam-5166	439	3	of	of	ADP
ejpam-5166	439	4	computer	computer	NOUN
ejpam-5166	439	5	science	science	NOUN
ejpam-5166	439	6	and	and	CCONJ
ejpam-5166	439	7	technology	technology	NOUN
ejpam-5166	439	8	,	,	PUNCT
ejpam-5166	439	9	7(1):139–145	7(1):139–145	NUM
ejpam-5166	439	10	,	,	PUNCT
ejpam-5166	439	11	2014	2014	NUM
ejpam-5166	439	12	.	.	PUNCT
ejpam-5166	440	1	[	[	X
ejpam-5166	440	2	30	30	NUM
ejpam-5166	440	3	]	]	X
ejpam-5166	440	4	a	a	DET
ejpam-5166	440	5	prathik	prathik	NOUN
ejpam-5166	440	6	,	,	PUNCT
ejpam-5166	440	7	k	k	PROPN
ejpam-5166	440	8	uma	uma	PROPN
ejpam-5166	440	9	,	,	PUNCT
ejpam-5166	440	10	and	and	CCONJ
ejpam-5166	440	11	j	j	PROPN
ejpam-5166	440	12	anuradha	anuradha	PROPN
ejpam-5166	440	13	.	.	PUNCT
ejpam-5166	441	1	an	an	DET
ejpam-5166	441	2	overview	overview	NOUN
ejpam-5166	441	3	of	of	ADP
ejpam-5166	441	4	application	application	NOUN
ejpam-5166	441	5	of	of	ADP
ejpam-5166	441	6	graph	graph	NOUN
ejpam-5166	441	7	theory	theory	NOUN
ejpam-5166	441	8	.	.	PUNCT
ejpam-5166	442	1	international	international	ADJ
ejpam-5166	442	2	journal	journal	NOUN
ejpam-5166	442	3	of	of	ADP
ejpam-5166	442	4	chemtech	chemtech	PROPN
ejpam-5166	442	5	research	research	NOUN
ejpam-5166	442	6	,	,	PUNCT
ejpam-5166	442	7	9(2):242–248	9(2):242–248	NUM
ejpam-5166	442	8	,	,	PUNCT
ejpam-5166	442	9	2019	2019	NUM
ejpam-5166	442	10	.	.	PUNCT
ejpam-5166	443	1	[	[	X
ejpam-5166	443	2	31	31	NUM
ejpam-5166	443	3	]	]	X
ejpam-5166	443	4	g	g	NOUN
ejpam-5166	443	5	raeisi	raeisi	VERB
ejpam-5166	443	6	and	and	CCONJ
ejpam-5166	443	7	m	m	VERB
ejpam-5166	443	8	gholami	gholami	ADJ
ejpam-5166	443	9	.	.	PUNCT
ejpam-5166	444	1	edge	edge	NOUN
ejpam-5166	444	2	coloring	coloring	NOUN
ejpam-5166	444	3	of	of	ADP
ejpam-5166	444	4	graphs	graph	NOUN
ejpam-5166	444	5	with	with	ADP
ejpam-5166	444	6	applications	application	NOUN
ejpam-5166	444	7	in	in	ADP
ejpam-5166	444	8	coding	code	VERB
ejpam-5166	444	9	theory	theory	NOUN
ejpam-5166	444	10	.	.	PUNCT
ejpam-5166	445	1	china	china	PROPN
ejpam-5166	445	2	communications	communications	PROPN
ejpam-5166	445	3	,	,	PUNCT
ejpam-5166	445	4	18(1):181–195	18(1):181–195	PROPN
ejpam-5166	445	5	,	,	PUNCT
ejpam-5166	445	6	2021	2021	NUM
ejpam-5166	445	7	.	.	PUNCT
ejpam-5166	446	1	[	[	X
ejpam-5166	446	2	32	32	NUM
ejpam-5166	446	3	]	]	SYM
ejpam-5166	446	4	h	h	PROPN
ejpam-5166	446	5	s	s	PROPN
ejpam-5166	446	6	ramane	ramane	PROPN
ejpam-5166	446	7	,	,	PUNCT
ejpam-5166	446	8	d	d	PROPN
ejpam-5166	446	9	s	s	X
ejpam-5166	446	10	revankar	revankar	NOUN
ejpam-5166	446	11	,	,	PUNCT
ejpam-5166	446	12	and	and	CCONJ
ejpam-5166	446	13	a	a	DET
ejpam-5166	446	14	b	b	NOUN
ejpam-5166	446	15	ganagi	ganagi	NOUN
ejpam-5166	446	16	.	.	PUNCT
ejpam-5166	447	1	on	on	ADP
ejpam-5166	447	2	the	the	DET
ejpam-5166	447	3	wiener	wiener	NOUN
ejpam-5166	447	4	index	index	NOUN
ejpam-5166	447	5	of	of	ADP
ejpam-5166	447	6	a	a	DET
ejpam-5166	447	7	graph	graph	NOUN
ejpam-5166	447	8	.	.	PUNCT
ejpam-5166	447	9	journal	journal	NOUN
ejpam-5166	447	10	of	of	ADP
ejpam-5166	447	11	the	the	DET
ejpam-5166	447	12	indonesian	indonesian	PROPN
ejpam-5166	447	13	mathematical	mathematical	ADJ
ejpam-5166	447	14	society	society	NOUN
ejpam-5166	447	15	,	,	PUNCT
ejpam-5166	447	16	18(1):57–66	18(1):57–66	NUM
ejpam-5166	447	17	,	,	PUNCT
ejpam-5166	447	18	2012	2012	NUM
ejpam-5166	447	19	.	.	PUNCT
ejpam-5166	448	1	[	[	X
ejpam-5166	448	2	33	33	NUM
ejpam-5166	448	3	]	]	SYM
ejpam-5166	448	4	b	b	PROPN
ejpam-5166	448	5	s	s	VERB
ejpam-5166	448	6	reddy	reddy	NOUN
ejpam-5166	448	7	,	,	PUNCT
ejpam-5166	448	8	r	r	NOUN
ejpam-5166	448	9	jain	jain	NOUN
ejpam-5166	448	10	,	,	PUNCT
ejpam-5166	448	11	and	and	CCONJ
ejpam-5166	448	12	n	n	PRON
ejpam-5166	448	13	laxmikanth	laxmikanth	ADJ
ejpam-5166	448	14	.	.	PUNCT
ejpam-5166	449	1	eigenvalues	eigenvalue	NOUN
ejpam-5166	449	2	and	and	CCONJ
ejpam-5166	449	3	wiener	wiener	NOUN
ejpam-5166	449	4	index	index	NOUN
ejpam-5166	449	5	of	of	ADP
ejpam-5166	449	6	the	the	DET
ejpam-5166	449	7	zero	zero	NUM
ejpam-5166	449	8	divisor	divisor	NOUN
ejpam-5166	449	9	graph	graph	NOUN
ejpam-5166	449	10	γ(zn	γ(zn	PROPN
ejpam-5166	449	11	)	)	PUNCT
ejpam-5166	449	12	.	.	PUNCT
ejpam-5166	450	1	arxiv:1707.05083	arxiv:1707.05083	PROPN
ejpam-5166	450	2	,	,	PUNCT
ejpam-5166	450	3	2017	2017	NUM
ejpam-5166	450	4	.	.	PUNCT
ejpam-5166	451	1	[	[	X
ejpam-5166	451	2	34	34	NUM
ejpam-5166	451	3	]	]	X
ejpam-5166	451	4	k	k	PROPN
ejpam-5166	451	5	selvakumar	selvakumar	PROPN
ejpam-5166	451	6	,	,	PUNCT
ejpam-5166	451	7	p	p	PROPN
ejpam-5166	451	8	gangaeswari	gangaeswari	PROPN
ejpam-5166	451	9	,	,	PUNCT
ejpam-5166	451	10	and	and	CCONJ
ejpam-5166	451	11	g	g	PROPN
ejpam-5166	451	12	arunkumar	arunkumar	PROPN
ejpam-5166	451	13	.	.	PUNCT
ejpam-5166	452	1	the	the	DET
ejpam-5166	452	2	wiener	wiener	NOUN
ejpam-5166	452	3	index	index	NOUN
ejpam-5166	452	4	of	of	ADP
ejpam-5166	452	5	the	the	DET
ejpam-5166	452	6	zerodivisor	zerodivisor	NOUN
ejpam-5166	452	7	graph	graph	NOUN
ejpam-5166	452	8	of	of	ADP
ejpam-5166	452	9	a	a	DET
ejpam-5166	452	10	finite	finite	ADJ
ejpam-5166	452	11	commutative	commutative	ADJ
ejpam-5166	452	12	ring	ring	NOUN
ejpam-5166	452	13	with	with	ADP
ejpam-5166	452	14	unity	unity	NOUN
ejpam-5166	452	15	.	.	PUNCT
ejpam-5166	453	1	discrete	discrete	ADJ
ejpam-5166	453	2	applied	apply	VERB
ejpam-5166	453	3	mathematics	mathematic	NOUN
ejpam-5166	453	4	,	,	PUNCT
ejpam-5166	453	5	311:72–84	311:72–84	NUM
ejpam-5166	453	6	,	,	PUNCT
ejpam-5166	453	7	2022	2022	NUM
ejpam-5166	453	8	.	.	PUNCT
ejpam-5166	454	1	[	[	X
ejpam-5166	454	2	35	35	NUM
ejpam-5166	454	3	]	]	X
ejpam-5166	454	4	d	d	X
ejpam-5166	454	5	sensarma	sensarma	NOUN
ejpam-5166	454	6	and	and	CCONJ
ejpam-5166	454	7	s	s	NOUN
ejpam-5166	454	8	s	s	NOUN
ejpam-5166	454	9	sarma	sarma	NOUN
ejpam-5166	454	10	.	.	PUNCT
ejpam-5166	455	1	application	application	NOUN
ejpam-5166	455	2	of	of	ADP
ejpam-5166	455	3	graphs	graph	NOUN
ejpam-5166	455	4	in	in	ADP
ejpam-5166	455	5	security	security	NOUN
ejpam-5166	455	6	.	.	PUNCT
ejpam-5166	456	1	international	international	ADJ
ejpam-5166	456	2	journal	journal	NOUN
ejpam-5166	456	3	of	of	ADP
ejpam-5166	456	4	innovative	innovative	ADJ
ejpam-5166	456	5	technology	technology	NOUN
ejpam-5166	456	6	and	and	CCONJ
ejpam-5166	456	7	exploring	explore	VERB
ejpam-5166	456	8	engineering	engineering	NOUN
ejpam-5166	456	9	,	,	PUNCT
ejpam-5166	456	10	8(10):2273–2279	8(10):2273–2279	NUM
ejpam-5166	456	11	,	,	PUNCT
ejpam-5166	456	12	2019	2019	NUM
ejpam-5166	456	13	.	.	PUNCT
ejpam-5166	457	1	[	[	X
ejpam-5166	457	2	36	36	NUM
ejpam-5166	457	3	]	]	X
ejpam-5166	457	4	p	p	X
ejpam-5166	457	5	singh	singh	PROPN
ejpam-5166	457	6	and	and	CCONJ
ejpam-5166	457	7	v	v	ADP
ejpam-5166	457	8	k	k	PROPN
ejpam-5166	457	9	bhat	bhat	PROPN
ejpam-5166	457	10	.	.	PUNCT
ejpam-5166	458	1	adjacency	adjacency	PROPN
ejpam-5166	458	2	matrix	matrix	NOUN
ejpam-5166	458	3	and	and	CCONJ
ejpam-5166	458	4	wiener	wiener	NOUN
ejpam-5166	458	5	index	index	NOUN
ejpam-5166	458	6	of	of	ADP
ejpam-5166	458	7	zero	zero	NUM
ejpam-5166	458	8	divisor	divisor	NOUN
ejpam-5166	458	9	graph	graph	NOUN
ejpam-5166	458	10	γ(zn	γ(zn	PROPN
ejpam-5166	458	11	)	)	PUNCT
ejpam-5166	458	12	.	.	PUNCT
ejpam-5166	459	1	journal	journal	PROPN
ejpam-5166	459	2	of	of	ADP
ejpam-5166	459	3	applied	apply	VERB
ejpam-5166	459	4	mathematics	mathematic	NOUN
ejpam-5166	459	5	and	and	CCONJ
ejpam-5166	459	6	computing	computing	NOUN
ejpam-5166	459	7	,	,	PUNCT
ejpam-5166	459	8	66:717–732	66:717–732	PROPN
ejpam-5166	459	9	,	,	PUNCT
ejpam-5166	459	10	2021	2021	NUM
ejpam-5166	459	11	.	.	PUNCT
ejpam-5166	460	1	[	[	X
ejpam-5166	460	2	37	37	NUM
ejpam-5166	460	3	]	]	X
ejpam-5166	460	4	m	m	VERB
ejpam-5166	460	5	j	j	NOUN
ejpam-5166	460	6	subhakar	subhakar	NOUN
ejpam-5166	460	7	.	.	PUNCT
ejpam-5166	461	1	associate	associate	ADJ
ejpam-5166	461	2	ring	ring	NOUN
ejpam-5166	461	3	graphs	graph	NOUN
ejpam-5166	461	4	.	.	PUNCT
ejpam-5166	462	1	mapana	mapana	PROPN
ejpam-5166	462	2	journal	journal	PROPN
ejpam-5166	462	3	of	of	ADP
ejpam-5166	462	4	sciences	sciences	PROPN
ejpam-5166	462	5	,	,	PUNCT
ejpam-5166	462	6	9(1):31–40	9(1):31–40	NUM
ejpam-5166	462	7	,	,	PUNCT
ejpam-5166	462	8	2010	2010	NUM
ejpam-5166	462	9	.	.	PUNCT
ejpam-5166	463	1	[	[	X
ejpam-5166	463	2	38	38	NUM
ejpam-5166	463	3	]	]	SYM
ejpam-5166	463	4	s	s	VERB
ejpam-5166	463	5	suthar	suthar	NOUN
ejpam-5166	463	6	and	and	CCONJ
ejpam-5166	463	7	o	o	PROPN
ejpam-5166	463	8	prakash	prakash	PROPN
ejpam-5166	463	9	.	.	PUNCT
ejpam-5166	463	10	energy	energy	PROPN
ejpam-5166	463	11	and	and	CCONJ
ejpam-5166	463	12	wiener	wiener	NOUN
ejpam-5166	463	13	index	index	NOUN
ejpam-5166	463	14	of	of	ADP
ejpam-5166	463	15	total	total	ADJ
ejpam-5166	463	16	graph	graph	NOUN
ejpam-5166	463	17	over	over	ADP
ejpam-5166	463	18	ring	ring	PROPN
ejpam-5166	463	19	zn	zn	PROPN
ejpam-5166	463	20	.	.	PUNCT
ejpam-5166	463	21	electric	electric	ADJ
ejpam-5166	463	22	notes	note	NOUN
ejpam-5166	463	23	in	in	ADP
ejpam-5166	463	24	discrite	discrite	ADJ
ejpam-5166	463	25	mathematics	mathematic	NOUN
ejpam-5166	463	26	,	,	PUNCT
ejpam-5166	463	27	63:485–495	63:485–495	NUM
ejpam-5166	463	28	,	,	PUNCT
ejpam-5166	463	29	2017	2017	NUM
ejpam-5166	463	30	.	.	PUNCT
ejpam-5166	464	1	[	[	X
ejpam-5166	464	2	39	39	NUM
ejpam-5166	464	3	]	]	PUNCT
ejpam-5166	464	4	m	m	VERB
ejpam-5166	464	5	s	s	NOUN
ejpam-5166	464	6	vinutha	vinutha	NOUN
ejpam-5166	464	7	and	and	CCONJ
ejpam-5166	464	8	p	p	PROPN
ejpam-5166	464	9	arathi	arathi	PROPN
ejpam-5166	464	10	.	.	PUNCT
ejpam-5166	465	1	applications	application	NOUN
ejpam-5166	465	2	of	of	ADP
ejpam-5166	465	3	graph	graph	NOUN
ejpam-5166	465	4	coloring	coloring	NOUN
ejpam-5166	465	5	and	and	CCONJ
ejpam-5166	465	6	labeling	labeling	NOUN
ejpam-5166	465	7	in	in	ADP
ejpam-5166	465	8	computer	computer	NOUN
ejpam-5166	465	9	science	science	NOUN
ejpam-5166	465	10	.	.	PUNCT
ejpam-5166	466	1	international	international	ADJ
ejpam-5166	466	2	journal	journal	PROPN
ejpam-5166	466	3	on	on	ADP
ejpam-5166	466	4	future	future	ADJ
ejpam-5166	466	5	revolution	revolution	NOUN
ejpam-5166	466	6	in	in	ADP
ejpam-5166	466	7	computer	computer	NOUN
ejpam-5166	466	8	science	science	NOUN
ejpam-5166	466	9	and	and	CCONJ
ejpam-5166	466	10	communication	communication	NOUN
ejpam-5166	466	11	engineering	engineering	NOUN
ejpam-5166	466	12	,	,	PUNCT
ejpam-5166	466	13	3(8):14–16	3(8):14–16	NUM
ejpam-5166	466	14	,	,	PUNCT
ejpam-5166	466	15	2017	2017	NUM
ejpam-5166	466	16	.	.	PUNCT
ejpam-5166	467	1	[	[	X
ejpam-5166	467	2	40	40	NUM
ejpam-5166	467	3	]	]	PUNCT
ejpam-5166	467	4	h	h	NOUN
ejpam-5166	467	5	wiener	wiener	NOUN
ejpam-5166	467	6	.	.	PUNCT
ejpam-5166	468	1	structural	structural	ADJ
ejpam-5166	468	2	determination	determination	NOUN
ejpam-5166	468	3	of	of	ADP
ejpam-5166	468	4	paraffin	paraffin	NOUN
ejpam-5166	468	5	boiling	boiling	NOUN
ejpam-5166	468	6	points	point	NOUN
ejpam-5166	468	7	.	.	PUNCT
ejpam-5166	469	1	contributions	contribution	NOUN
ejpam-5166	469	2	from	from	ADP
ejpam-5166	469	3	departement	departement	NOUN
ejpam-5166	469	4	of	of	ADP
ejpam-5166	469	5	chemistry	chemistry	NOUN
ejpam-5166	469	6	,	,	PUNCT
ejpam-5166	469	7	69:17–20	69:17–20	NUM
ejpam-5166	469	8	,	,	PUNCT
ejpam-5166	469	9	1947	1947	NUM
ejpam-5166	469	10	.	.	PUNCT