id	sid	tid	token	lemma	pos
ejpam-5971	1	1	european	european	PROPN
ejpam-5971	1	2	journal	journal	PROPN
ejpam-5971	1	3	of	of	ADP
ejpam-5971	1	4	pure	pure	ADJ
ejpam-5971	1	5	and	and	CCONJ
ejpam-5971	1	6	applied	applied	ADJ
ejpam-5971	1	7	mathematics	mathematic	NOUN
ejpam-5971	1	8	2025	2025	NUM
ejpam-5971	1	9	,	,	PUNCT
ejpam-5971	1	10	vol	vol	NOUN
ejpam-5971	1	11	.	.	PROPN
ejpam-5971	1	12	18	18	NUM
ejpam-5971	1	13	,	,	PUNCT
ejpam-5971	1	14	issue	issue	NOUN
ejpam-5971	1	15	2	2	NUM
ejpam-5971	1	16	,	,	PUNCT
ejpam-5971	1	17	article	article	NOUN
ejpam-5971	1	18	number	number	NOUN
ejpam-5971	1	19	5971	5971	NUM
ejpam-5971	1	20	issn	issn	PROPN
ejpam-5971	1	21	1307	1307	NUM
ejpam-5971	1	22	-	-	SYM
ejpam-5971	1	23	5543	5543	NUM
ejpam-5971	1	24	–	–	PUNCT
ejpam-5971	1	25	ejpam.com	ejpam.com	X
ejpam-5971	1	26	published	publish	VERB
ejpam-5971	1	27	by	by	ADP
ejpam-5971	1	28	new	new	PROPN
ejpam-5971	1	29	york	york	PROPN
ejpam-5971	1	30	business	business	PROPN
ejpam-5971	1	31	global	global	ADJ
ejpam-5971	1	32	bounds	bound	NOUN
ejpam-5971	1	33	on	on	ADP
ejpam-5971	1	34	the	the	DET
ejpam-5971	1	35	energy	energy	NOUN
ejpam-5971	1	36	of	of	ADP
ejpam-5971	1	37	zero	zero	NUM
ejpam-5971	1	38	-	-	PUNCT
ejpam-5971	1	39	divisor	divisor	NOUN
ejpam-5971	1	40	graph	graph	NOUN
ejpam-5971	1	41	of	of	ADP
ejpam-5971	1	42	quotient	quotient	NOUN
ejpam-5971	1	43	ring	ring	NOUN
ejpam-5971	1	44	and	and	CCONJ
ejpam-5971	1	45	its	its	PRON
ejpam-5971	1	46	topological	topological	ADJ
ejpam-5971	1	47	indices	index	NOUN
ejpam-5971	1	48	vira	vira	PROPN
ejpam-5971	1	49	hari	hari	PROPN
ejpam-5971	1	50	krisnawati1	krisnawati1	PROPN
ejpam-5971	1	51	,	,	PUNCT
ejpam-5971	1	52	,	,	PUNCT
ejpam-5971	1	53	noor	noor	PROPN
ejpam-5971	1	54	hidayat1	hidayat1	PROPN
ejpam-5971	1	55	,	,	PUNCT
ejpam-5971	1	56	ayunda	ayunda	ADP
ejpam-5971	1	57	faizatul	faizatul	PROPN
ejpam-5971	1	58	musyarrofah∗1	musyarrofah∗1	PROPN
ejpam-5971	1	59	1	1	NUM
ejpam-5971	1	60	department	department	NOUN
ejpam-5971	1	61	of	of	ADP
ejpam-5971	1	62	mathematics	mathematic	NOUN
ejpam-5971	1	63	,	,	PUNCT
ejpam-5971	1	64	faculty	faculty	NOUN
ejpam-5971	1	65	of	of	ADP
ejpam-5971	1	66	mathematics	mathematic	NOUN
ejpam-5971	1	67	and	and	CCONJ
ejpam-5971	1	68	natural	natural	ADJ
ejpam-5971	1	69	sciences	science	NOUN
ejpam-5971	1	70	,	,	PUNCT
ejpam-5971	1	71	university	university	NOUN
ejpam-5971	1	72	of	of	ADP
ejpam-5971	1	73	brawijaya	brawijaya	PROPN
ejpam-5971	1	74	,	,	PUNCT
ejpam-5971	1	75	malang	malang	PROPN
ejpam-5971	1	76	,	,	PUNCT
ejpam-5971	1	77	east	east	PROPN
ejpam-5971	1	78	java	java	PROPN
ejpam-5971	1	79	,	,	PUNCT
ejpam-5971	1	80	indonesia	indonesia	PROPN
ejpam-5971	1	81	abstract	abstract	NOUN
ejpam-5971	1	82	.	.	PUNCT
ejpam-5971	2	1	in	in	ADP
ejpam-5971	2	2	this	this	DET
ejpam-5971	2	3	paper	paper	NOUN
ejpam-5971	2	4	,	,	PUNCT
ejpam-5971	2	5	we	we	PRON
ejpam-5971	2	6	study	study	VERB
ejpam-5971	2	7	the	the	DET
ejpam-5971	2	8	zero	zero	NUM
ejpam-5971	2	9	-	-	PUNCT
ejpam-5971	2	10	divisor	divisor	NOUN
ejpam-5971	2	11	graph	graph	NOUN
ejpam-5971	2	12	of	of	ADP
ejpam-5971	2	13	z℘[x]/⟨x5⟩	z℘[x]/⟨x5⟩	PROPN
ejpam-5971	2	14	for	for	ADP
ejpam-5971	2	15	prime	prime	ADJ
ejpam-5971	2	16	number	number	NOUN
ejpam-5971	2	17	℘	℘	PROPN
ejpam-5971	2	18	,	,	PUNCT
ejpam-5971	2	19	denoted	denote	VERB
ejpam-5971	2	20	as	as	ADP
ejpam-5971	2	21	γ(z℘[x]/⟨x5⟩	γ(z℘[x]/⟨x5⟩	PROPN
ejpam-5971	2	22	)	)	PUNCT
ejpam-5971	2	23	,	,	PUNCT
ejpam-5971	2	24	including	include	VERB
ejpam-5971	2	25	its	its	PRON
ejpam-5971	2	26	energy	energy	NOUN
ejpam-5971	2	27	and	and	CCONJ
ejpam-5971	2	28	topological	topological	ADJ
ejpam-5971	2	29	indices	index	NOUN
ejpam-5971	2	30	.	.	PUNCT
ejpam-5971	3	1	specifically	specifically	ADV
ejpam-5971	3	2	,	,	PUNCT
ejpam-5971	3	3	we	we	PRON
ejpam-5971	3	4	provide	provide	VERB
ejpam-5971	3	5	bounds	bound	NOUN
ejpam-5971	3	6	of	of	ADP
ejpam-5971	3	7	the	the	DET
ejpam-5971	3	8	energy	energy	NOUN
ejpam-5971	3	9	for	for	ADP
ejpam-5971	3	10	γ(z℘[x]/⟨x5⟩	γ(z℘[x]/⟨x5⟩	NUM
ejpam-5971	3	11	)	)	PUNCT
ejpam-5971	3	12	and	and	CCONJ
ejpam-5971	3	13	show	show	VERB
ejpam-5971	3	14	that	that	SCONJ
ejpam-5971	3	15	these	these	DET
ejpam-5971	3	16	bounds	bound	NOUN
ejpam-5971	3	17	are	be	AUX
ejpam-5971	3	18	numerically	numerically	ADV
ejpam-5971	3	19	close	close	ADJ
ejpam-5971	3	20	to	to	ADP
ejpam-5971	3	21	the	the	DET
ejpam-5971	3	22	actual	actual	ADJ
ejpam-5971	3	23	energy	energy	NOUN
ejpam-5971	3	24	value	value	NOUN
ejpam-5971	3	25	.	.	PUNCT
ejpam-5971	4	1	furthermore	furthermore	ADV
ejpam-5971	4	2	,	,	PUNCT
ejpam-5971	4	3	we	we	PRON
ejpam-5971	4	4	determine	determine	VERB
ejpam-5971	4	5	the	the	DET
ejpam-5971	4	6	topological	topological	ADJ
ejpam-5971	4	7	indices	index	NOUN
ejpam-5971	4	8	of	of	ADP
ejpam-5971	4	9	γ(z℘[x]/⟨x5⟩	γ(z℘[x]/⟨x5⟩	NUM
ejpam-5971	4	10	)	)	PUNCT
ejpam-5971	4	11	,	,	PUNCT
ejpam-5971	4	12	including	include	VERB
ejpam-5971	4	13	the	the	DET
ejpam-5971	4	14	topological	topological	ADJ
ejpam-5971	4	15	indices	index	NOUN
ejpam-5971	4	16	based	base	VERB
ejpam-5971	4	17	on	on	ADP
ejpam-5971	4	18	distance	distance	NOUN
ejpam-5971	4	19	and	and	CCONJ
ejpam-5971	4	20	degree	degree	NOUN
ejpam-5971	4	21	.	.	PUNCT
ejpam-5971	5	1	we	we	PRON
ejpam-5971	5	2	also	also	ADV
ejpam-5971	5	3	perform	perform	VERB
ejpam-5971	5	4	numerical	numerical	ADJ
ejpam-5971	5	5	simulations	simulation	NOUN
ejpam-5971	5	6	of	of	ADP
ejpam-5971	5	7	the	the	DET
ejpam-5971	5	8	topological	topological	ADJ
ejpam-5971	5	9	indices	index	NOUN
ejpam-5971	5	10	for	for	ADP
ejpam-5971	5	11	various	various	ADJ
ejpam-5971	5	12	prime	prime	ADJ
ejpam-5971	5	13	numbers	number	NOUN
ejpam-5971	5	14	℘.	℘.	PROPN
ejpam-5971	5	15	2020	2020	NUM
ejpam-5971	5	16	mathematics	mathematic	NOUN
ejpam-5971	5	17	subject	subject	NOUN
ejpam-5971	5	18	classifications	classification	NOUN
ejpam-5971	5	19	:	:	PUNCT
ejpam-5971	5	20	13a70	13a70	NUM
ejpam-5971	5	21	,	,	PUNCT
ejpam-5971	5	22	05c50	05c50	NUM
ejpam-5971	5	23	,	,	PUNCT
ejpam-5971	5	24	05c09	05c09	DET
ejpam-5971	5	25	key	key	ADJ
ejpam-5971	5	26	words	word	NOUN
ejpam-5971	5	27	and	and	CCONJ
ejpam-5971	5	28	phrases	phrase	NOUN
ejpam-5971	5	29	:	:	PUNCT
ejpam-5971	5	30	zero	zero	NUM
ejpam-5971	5	31	-	-	PUNCT
ejpam-5971	5	32	divisor	divisor	NOUN
ejpam-5971	5	33	graph	graph	NOUN
ejpam-5971	5	34	,	,	PUNCT
ejpam-5971	5	35	graph	graph	NOUN
ejpam-5971	5	36	energy	energy	NOUN
ejpam-5971	5	37	,	,	PUNCT
ejpam-5971	5	38	distance	distance	NOUN
ejpam-5971	5	39	-	-	PUNCT
ejpam-5971	5	40	based	base	VERB
ejpam-5971	5	41	topological	topological	ADJ
ejpam-5971	5	42	indices	index	NOUN
ejpam-5971	5	43	,	,	PUNCT
ejpam-5971	5	44	degree	degree	NOUN
ejpam-5971	5	45	-	-	PUNCT
ejpam-5971	5	46	based	base	VERB
ejpam-5971	5	47	topological	topological	ADJ
ejpam-5971	5	48	indices	index	NOUN
ejpam-5971	5	49	1	1	NUM
ejpam-5971	5	50	.	.	PUNCT
ejpam-5971	6	1	introduction	introduction	NOUN
ejpam-5971	6	2	the	the	DET
ejpam-5971	6	3	concept	concept	NOUN
ejpam-5971	6	4	of	of	ADP
ejpam-5971	6	5	graphs	graph	NOUN
ejpam-5971	6	6	regarding	regard	VERB
ejpam-5971	6	7	different	different	ADJ
ejpam-5971	6	8	algebraic	algebraic	ADJ
ejpam-5971	6	9	structures	structure	NOUN
ejpam-5971	6	10	is	be	AUX
ejpam-5971	6	11	interesting	interesting	ADJ
ejpam-5971	6	12	to	to	PART
ejpam-5971	6	13	investigate	investigate	VERB
ejpam-5971	6	14	because	because	SCONJ
ejpam-5971	6	15	it	it	PRON
ejpam-5971	6	16	enables	enable	VERB
ejpam-5971	6	17	us	we	PRON
ejpam-5971	6	18	to	to	PART
ejpam-5971	6	19	explore	explore	VERB
ejpam-5971	6	20	algebraic	algebraic	ADJ
ejpam-5971	6	21	properties	property	NOUN
ejpam-5971	6	22	using	use	VERB
ejpam-5971	6	23	graph	graph	NOUN
ejpam-5971	6	24	theory	theory	NOUN
ejpam-5971	6	25	.	.	PUNCT
ejpam-5971	7	1	one	one	NUM
ejpam-5971	7	2	notable	notable	ADJ
ejpam-5971	7	3	example	example	NOUN
ejpam-5971	7	4	is	be	AUX
ejpam-5971	7	5	the	the	DET
ejpam-5971	7	6	zero	zero	NUM
ejpam-5971	7	7	-	-	PUNCT
ejpam-5971	7	8	divisor	divisor	NOUN
ejpam-5971	7	9	graph	graph	NOUN
ejpam-5971	7	10	that	that	PRON
ejpam-5971	7	11	came	come	VERB
ejpam-5971	7	12	from	from	ADP
ejpam-5971	7	13	the	the	DET
ejpam-5971	7	14	work	work	NOUN
ejpam-5971	7	15	done	do	VERB
ejpam-5971	7	16	by	by	ADP
ejpam-5971	7	17	beck	beck	NOUN
ejpam-5971	7	18	in	in	ADP
ejpam-5971	7	19	1988	1988	NUM
ejpam-5971	7	20	[	[	X
ejpam-5971	7	21	1	1	NUM
ejpam-5971	7	22	]	]	PUNCT
ejpam-5971	7	23	.	.	PUNCT
ejpam-5971	8	1	he	he	PRON
ejpam-5971	8	2	defined	define	VERB
ejpam-5971	8	3	the	the	DET
ejpam-5971	8	4	vertex	vertex	NOUN
ejpam-5971	8	5	set	set	VERB
ejpam-5971	8	6	as	as	ADP
ejpam-5971	8	7	zero	zero	NUM
ejpam-5971	8	8	divisors	divisor	NOUN
ejpam-5971	8	9	,	,	PUNCT
ejpam-5971	8	10	including	include	VERB
ejpam-5971	8	11	zero	zero	NUM
ejpam-5971	8	12	.	.	PUNCT
ejpam-5971	9	1	in	in	ADP
ejpam-5971	9	2	1999	1999	NUM
ejpam-5971	9	3	,	,	PUNCT
ejpam-5971	9	4	anderson	anderson	PROPN
ejpam-5971	9	5	and	and	CCONJ
ejpam-5971	9	6	livingston	livingston	PROPN
ejpam-5971	9	7	revised	revise	VERB
ejpam-5971	9	8	the	the	DET
ejpam-5971	9	9	definition	definition	NOUN
ejpam-5971	9	10	by	by	ADP
ejpam-5971	9	11	focusing	focus	VERB
ejpam-5971	9	12	on	on	ADP
ejpam-5971	9	13	only	only	ADV
ejpam-5971	9	14	non	non	ADJ
ejpam-5971	9	15	-	-	ADJ
ejpam-5971	9	16	zero	zero	ADJ
ejpam-5971	9	17	zero	zero	NUM
ejpam-5971	9	18	divisors	divisor	NOUN
ejpam-5971	9	19	as	as	ADP
ejpam-5971	9	20	its	its	PRON
ejpam-5971	9	21	vertices	vertex	NOUN
ejpam-5971	9	22	,	,	PUNCT
ejpam-5971	9	23	denoted	denote	VERB
ejpam-5971	9	24	as	as	ADP
ejpam-5971	9	25	γ(r	γ(r	PROPN
ejpam-5971	9	26	)	)	PUNCT
ejpam-5971	9	27	for	for	ADP
ejpam-5971	9	28	commutative	commutative	ADJ
ejpam-5971	9	29	ring	ring	NOUN
ejpam-5971	9	30	r	r	NOUN
ejpam-5971	9	31	[	[	X
ejpam-5971	9	32	2	2	NUM
ejpam-5971	9	33	]	]	PUNCT
ejpam-5971	9	34	.	.	PUNCT
ejpam-5971	10	1	since	since	SCONJ
ejpam-5971	10	2	then	then	ADV
ejpam-5971	10	3	,	,	PUNCT
ejpam-5971	10	4	the	the	DET
ejpam-5971	10	5	zero	zero	NUM
ejpam-5971	10	6	-	-	PUNCT
ejpam-5971	10	7	divisor	divisor	NOUN
ejpam-5971	10	8	graph	graph	NOUN
ejpam-5971	10	9	has	have	AUX
ejpam-5971	10	10	been	be	AUX
ejpam-5971	10	11	a	a	DET
ejpam-5971	10	12	fastdeveloping	fastdevelope	VERB
ejpam-5971	10	13	area	area	NOUN
ejpam-5971	10	14	and	and	CCONJ
ejpam-5971	10	15	widely	widely	ADV
ejpam-5971	10	16	applied	apply	VERB
ejpam-5971	10	17	in	in	ADP
ejpam-5971	10	18	various	various	ADJ
ejpam-5971	10	19	fields	field	NOUN
ejpam-5971	10	20	,	,	PUNCT
ejpam-5971	10	21	including	include	VERB
ejpam-5971	10	22	algebraic	algebraic	ADJ
ejpam-5971	10	23	cryptography	cryptography	NOUN
ejpam-5971	11	1	[	[	X
ejpam-5971	11	2	3	3	NUM
ejpam-5971	11	3	,	,	PUNCT
ejpam-5971	11	4	4	4	NUM
ejpam-5971	11	5	]	]	PUNCT
ejpam-5971	11	6	and	and	CCONJ
ejpam-5971	12	1	coding	code	VERB
ejpam-5971	12	2	theory	theory	NOUN
ejpam-5971	12	3	[	[	X
ejpam-5971	12	4	5	5	NUM
ejpam-5971	12	5	,	,	PUNCT
ejpam-5971	12	6	6	6	NUM
ejpam-5971	12	7	]	]	PUNCT
ejpam-5971	12	8	.	.	PUNCT
ejpam-5971	13	1	for	for	ADP
ejpam-5971	13	2	further	further	ADJ
ejpam-5971	13	3	literature	literature	NOUN
ejpam-5971	13	4	on	on	ADP
ejpam-5971	13	5	this	this	DET
ejpam-5971	13	6	topic	topic	NOUN
ejpam-5971	13	7	,	,	PUNCT
ejpam-5971	13	8	see	see	VERB
ejpam-5971	13	9	[	[	X
ejpam-5971	13	10	7–12	7–12	X
ejpam-5971	13	11	]	]	X
ejpam-5971	13	12	.	.	PUNCT
ejpam-5971	14	1	besides	besides	SCONJ
ejpam-5971	14	2	its	its	PRON
ejpam-5971	14	3	importance	importance	NOUN
ejpam-5971	14	4	in	in	ADP
ejpam-5971	14	5	algebra	algebra	NOUN
ejpam-5971	14	6	,	,	PUNCT
ejpam-5971	14	7	graph	graph	NOUN
ejpam-5971	14	8	theory	theory	NOUN
ejpam-5971	14	9	has	have	AUX
ejpam-5971	14	10	also	also	ADV
ejpam-5971	14	11	seen	see	VERB
ejpam-5971	14	12	rapid	rapid	ADJ
ejpam-5971	14	13	development	development	NOUN
ejpam-5971	14	14	in	in	ADP
ejpam-5971	14	15	its	its	PRON
ejpam-5971	14	16	applications	application	NOUN
ejpam-5971	14	17	to	to	ADP
ejpam-5971	14	18	chemistry	chemistry	NOUN
ejpam-5971	14	19	,	,	PUNCT
ejpam-5971	14	20	particularly	particularly	ADV
ejpam-5971	14	21	through	through	ADP
ejpam-5971	14	22	the	the	DET
ejpam-5971	14	23	study	study	NOUN
ejpam-5971	14	24	of	of	ADP
ejpam-5971	14	25	graph	graph	NOUN
ejpam-5971	14	26	energy	energy	NOUN
ejpam-5971	14	27	.	.	PUNCT
ejpam-5971	15	1	in	in	ADP
ejpam-5971	15	2	1978	1978	NUM
ejpam-5971	15	3	,	,	PUNCT
ejpam-5971	15	4	gutman	gutman	NOUN
ejpam-5971	15	5	first	first	ADV
ejpam-5971	15	6	defined	define	VERB
ejpam-5971	15	7	the	the	DET
ejpam-5971	15	8	graph	graph	NOUN
ejpam-5971	15	9	energy	energy	NOUN
ejpam-5971	15	10	as	as	SCONJ
ejpam-5971	15	11	the	the	DET
ejpam-5971	15	12	total	total	NOUN
ejpam-5971	15	13	of	of	ADP
ejpam-5971	15	14	the	the	DET
ejpam-5971	15	15	absolute	absolute	ADJ
ejpam-5971	15	16	values	value	NOUN
ejpam-5971	15	17	of	of	ADP
ejpam-5971	15	18	its	its	PRON
ejpam-5971	15	19	adjacency	adjacency	NOUN
ejpam-5971	15	20	matrix	matrix	NOUN
ejpam-5971	15	21	’s	’s	PART
ejpam-5971	15	22	eigenvalues	eigenvalue	VERB
ejpam-5971	15	23	[	[	X
ejpam-5971	15	24	13	13	NUM
ejpam-5971	15	25	]	]	PUNCT
ejpam-5971	15	26	.	.	PUNCT
ejpam-5971	16	1	this	this	DET
ejpam-5971	16	2	concept	concept	NOUN
ejpam-5971	16	3	arose	arise	VERB
ejpam-5971	16	4	when	when	SCONJ
ejpam-5971	16	5	erich	erich	PROPN
ejpam-5971	16	6	huckel	huckel	NOUN
ejpam-5971	16	7	developed	develop	VERB
ejpam-5971	16	8	huckel	huckel	NOUN
ejpam-5971	16	9	molecular	molecular	ADJ
ejpam-5971	16	10	orbital	orbital	ADJ
ejpam-5971	16	11	theory	theory	NOUN
ejpam-5971	16	12	to	to	PART
ejpam-5971	16	13	estimate	estimate	VERB
ejpam-5971	16	14	the	the	DET
ejpam-5971	16	15	π	π	PROPN
ejpam-5971	16	16	-	-	NOUN
ejpam-5971	16	17	electron	electron	NOUN
ejpam-5971	16	18	energy	energy	NOUN
ejpam-5971	16	19	[	[	X
ejpam-5971	16	20	14	14	NUM
ejpam-5971	16	21	]	]	PUNCT
ejpam-5971	16	22	.	.	PUNCT
ejpam-5971	17	1	beyond	beyond	ADP
ejpam-5971	17	2	graph	graph	NOUN
ejpam-5971	17	3	energy	energy	NOUN
ejpam-5971	17	4	,	,	PUNCT
ejpam-5971	17	5	∗corresponding	∗corresponde	VERB
ejpam-5971	17	6	author	author	NOUN
ejpam-5971	17	7	.	.	PUNCT
ejpam-5971	18	1	doi	doi	NOUN
ejpam-5971	18	2	:	:	PUNCT
ejpam-5971	18	3	https://doi.org/10.29020/nybg.ejpam.v18i2.5971	https://doi.org/10.29020/nybg.ejpam.v18i2.5971	SYM
ejpam-5971	18	4	email	email	NOUN
ejpam-5971	18	5	addresses	address	NOUN
ejpam-5971	18	6	:	:	PUNCT
ejpam-5971	18	7	virahari@ub.ac.id	virahari@ub.ac.id	PROPN
ejpam-5971	18	8	(	(	PUNCT
ejpam-5971	18	9	v.	v.	ADP
ejpam-5971	18	10	h.	h.	PROPN
ejpam-5971	18	11	krisnawati	krisnawati	PROPN
ejpam-5971	18	12	)	)	PUNCT
ejpam-5971	18	13	,	,	PUNCT
ejpam-5971	18	14	noorh@ub.ac.id	noorh@ub.ac.id	PROPN
ejpam-5971	18	15	(	(	PUNCT
ejpam-5971	18	16	n.	n.	PROPN
ejpam-5971	18	17	hidayat	hidayat	PROPN
ejpam-5971	18	18	)	)	PUNCT
ejpam-5971	18	19	,	,	PUNCT
ejpam-5971	18	20	ayundafaiza02@gmail.com	ayundafaiza02@gmail.com	X
ejpam-5971	18	21	(	(	PUNCT
ejpam-5971	18	22	a.	a.	PROPN
ejpam-5971	18	23	f.	f.	PROPN
ejpam-5971	18	24	musyarrofah	musyarrofah	PROPN
ejpam-5971	18	25	)	)	PUNCT
ejpam-5971	18	26	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-5971	18	27	1	1	NUM
ejpam-5971	18	28	copyright	copyright	NOUN
ejpam-5971	18	29	:	:	PUNCT
ejpam-5971	19	1	©	©	PROPN
ejpam-5971	19	2	2025	2025	NUM
ejpam-5971	19	3	the	the	DET
ejpam-5971	19	4	author(s	author(s	NOUN
ejpam-5971	19	5	)	)	PUNCT
ejpam-5971	19	6	.	.	PUNCT
ejpam-5971	20	1	(	(	PUNCT
ejpam-5971	20	2	cc	cc	NOUN
ejpam-5971	20	3	by	by	ADP
ejpam-5971	20	4	-	-	PUNCT
ejpam-5971	20	5	nc	nc	PROPN
ejpam-5971	20	6	4.0	4.0	NUM
ejpam-5971	20	7	)	)	PUNCT
ejpam-5971	20	8	v.h	v.h	PROPN
ejpam-5971	20	9	.	.	PROPN
ejpam-5971	20	10	krisnawati	krisnawati	PROPN
ejpam-5971	20	11	,	,	PUNCT
ejpam-5971	20	12	n.	n.	PROPN
ejpam-5971	20	13	hidayat	hidayat	PROPN
ejpam-5971	20	14	,	,	PUNCT
ejpam-5971	20	15	a.f	a.f	PROPN
ejpam-5971	20	16	.	.	PROPN
ejpam-5971	20	17	musyarrofah	musyarrofah	PROPN
ejpam-5971	20	18	/	/	SYM
ejpam-5971	20	19	eur	eur	PROPN
ejpam-5971	20	20	.	.	PUNCT
ejpam-5971	21	1	j.	j.	PROPN
ejpam-5971	21	2	pure	pure	PROPN
ejpam-5971	21	3	appl	appl	PROPN
ejpam-5971	21	4	.	.	PROPN
ejpam-5971	21	5	math	math	PROPN
ejpam-5971	21	6	,	,	PUNCT
ejpam-5971	21	7	18	18	NUM
ejpam-5971	21	8	(	(	PUNCT
ejpam-5971	21	9	2	2	NUM
ejpam-5971	21	10	)	)	PUNCT
ejpam-5971	21	11	(	(	PUNCT
ejpam-5971	21	12	2025	2025	NUM
ejpam-5971	21	13	)	)	PUNCT
ejpam-5971	21	14	,	,	PUNCT
ejpam-5971	21	15	5971	5971	NUM
ejpam-5971	21	16	2	2	NUM
ejpam-5971	21	17	of	of	ADP
ejpam-5971	21	18	19	19	NUM
ejpam-5971	21	19	topological	topological	ADJ
ejpam-5971	21	20	indices	index	NOUN
ejpam-5971	21	21	are	be	AUX
ejpam-5971	21	22	also	also	ADV
ejpam-5971	21	23	important	important	ADJ
ejpam-5971	21	24	parameters	parameter	NOUN
ejpam-5971	21	25	for	for	ADP
ejpam-5971	21	26	analyzing	analyze	VERB
ejpam-5971	21	27	molecular	molecular	ADJ
ejpam-5971	21	28	structures	structure	NOUN
ejpam-5971	21	29	and	and	CCONJ
ejpam-5971	21	30	predicting	predict	VERB
ejpam-5971	21	31	chemical	chemical	NOUN
ejpam-5971	21	32	properties	property	NOUN
ejpam-5971	21	33	.	.	PUNCT
ejpam-5971	22	1	most	most	ADJ
ejpam-5971	22	2	of	of	ADP
ejpam-5971	22	3	the	the	DET
ejpam-5971	22	4	studies	study	NOUN
ejpam-5971	22	5	of	of	ADP
ejpam-5971	22	6	topological	topological	ADJ
ejpam-5971	22	7	indices	index	NOUN
ejpam-5971	22	8	currently	currently	ADV
ejpam-5971	22	9	are	be	AUX
ejpam-5971	22	10	based	base	VERB
ejpam-5971	22	11	on	on	ADP
ejpam-5971	22	12	distance	distance	NOUN
ejpam-5971	22	13	or	or	CCONJ
ejpam-5971	22	14	degree	degree	NOUN
ejpam-5971	22	15	.	.	PUNCT
ejpam-5971	23	1	the	the	DET
ejpam-5971	23	2	wiener	wiener	NOUN
ejpam-5971	23	3	index	index	NOUN
ejpam-5971	23	4	,	,	PUNCT
ejpam-5971	23	5	proposed	propose	VERB
ejpam-5971	23	6	by	by	ADP
ejpam-5971	23	7	wiener	wiener	NOUN
ejpam-5971	23	8	[	[	X
ejpam-5971	23	9	15	15	NUM
ejpam-5971	23	10	]	]	X
ejpam-5971	23	11	in	in	ADP
ejpam-5971	23	12	1947	1947	NUM
ejpam-5971	23	13	,	,	PUNCT
ejpam-5971	23	14	is	be	AUX
ejpam-5971	23	15	the	the	DET
ejpam-5971	23	16	earliest	early	ADJ
ejpam-5971	23	17	distance	distance	NOUN
ejpam-5971	23	18	-	-	PUNCT
ejpam-5971	23	19	based	base	VERB
ejpam-5971	23	20	topological	topological	ADJ
ejpam-5971	23	21	indices	index	NOUN
ejpam-5971	23	22	and	and	CCONJ
ejpam-5971	23	23	is	be	AUX
ejpam-5971	23	24	used	use	VERB
ejpam-5971	23	25	to	to	PART
ejpam-5971	23	26	approximate	approximate	VERB
ejpam-5971	23	27	the	the	DET
ejpam-5971	23	28	boiling	boiling	NOUN
ejpam-5971	23	29	points	point	NOUN
ejpam-5971	23	30	of	of	ADP
ejpam-5971	23	31	alkanes	alkane	NOUN
ejpam-5971	23	32	.	.	PUNCT
ejpam-5971	24	1	in	in	ADP
ejpam-5971	24	2	1993	1993	NUM
ejpam-5971	24	3	,	,	PUNCT
ejpam-5971	24	4	randic	randic	ADJ
ejpam-5971	24	5	[	[	X
ejpam-5971	24	6	16	16	NUM
ejpam-5971	24	7	]	]	PUNCT
ejpam-5971	24	8	proposed	propose	VERB
ejpam-5971	24	9	the	the	DET
ejpam-5971	24	10	hyper	hyper	ADJ
ejpam-5971	24	11	-	-	ADJ
ejpam-5971	24	12	wiener	wiener	NOUN
ejpam-5971	24	13	index	index	NOUN
ejpam-5971	24	14	applied	apply	VERB
ejpam-5971	24	15	for	for	ADP
ejpam-5971	24	16	analyzing	analyze	VERB
ejpam-5971	24	17	the	the	DET
ejpam-5971	24	18	physicochemical	physicochemical	ADJ
ejpam-5971	24	19	properties	property	NOUN
ejpam-5971	24	20	of	of	ADP
ejpam-5971	24	21	organic	organic	ADJ
ejpam-5971	24	22	compounds	compound	NOUN
ejpam-5971	24	23	.	.	PUNCT
ejpam-5971	25	1	meanwhile	meanwhile	ADV
ejpam-5971	25	2	,	,	PUNCT
ejpam-5971	25	3	first	first	ADJ
ejpam-5971	25	4	degree	degree	NOUN
ejpam-5971	25	5	-	-	PUNCT
ejpam-5971	25	6	based	base	VERB
ejpam-5971	25	7	topological	topological	ADJ
ejpam-5971	25	8	indices	index	NOUN
ejpam-5971	25	9	were	be	AUX
ejpam-5971	25	10	proposed	propose	VERB
ejpam-5971	25	11	in	in	ADP
ejpam-5971	25	12	1970s	1970s	NUM
ejpam-5971	25	13	by	by	ADP
ejpam-5971	25	14	gutman	gutman	NOUN
ejpam-5971	25	15	and	and	CCONJ
ejpam-5971	25	16	trinajstic	trinajstic	ADJ
ejpam-5971	25	17	[	[	X
ejpam-5971	25	18	17	17	NUM
ejpam-5971	25	19	]	]	PUNCT
ejpam-5971	25	20	.	.	PUNCT
ejpam-5971	26	1	there	there	PRON
ejpam-5971	26	2	are	be	VERB
ejpam-5971	26	3	the	the	DET
ejpam-5971	26	4	first	first	ADJ
ejpam-5971	26	5	and	and	CCONJ
ejpam-5971	26	6	second	second	ADJ
ejpam-5971	26	7	zagreb	zagreb	PROPN
ejpam-5971	26	8	indices	index	NOUN
ejpam-5971	26	9	that	that	PRON
ejpam-5971	26	10	are	be	AUX
ejpam-5971	26	11	used	use	VERB
ejpam-5971	26	12	for	for	ADP
ejpam-5971	26	13	analyzing	analyze	VERB
ejpam-5971	26	14	the	the	DET
ejpam-5971	26	15	thermodynamic	thermodynamic	ADJ
ejpam-5971	26	16	stability	stability	NOUN
ejpam-5971	26	17	and	and	CCONJ
ejpam-5971	26	18	reactivity	reactivity	NOUN
ejpam-5971	26	19	of	of	ADP
ejpam-5971	26	20	unsaturated	unsaturated	ADJ
ejpam-5971	26	21	molecules	molecule	NOUN
ejpam-5971	26	22	.	.	PUNCT
ejpam-5971	27	1	furthermore	furthermore	ADV
ejpam-5971	27	2	,	,	PUNCT
ejpam-5971	27	3	in	in	ADP
ejpam-5971	27	4	1984	1984	NUM
ejpam-5971	27	5	,	,	PUNCT
ejpam-5971	27	6	narumi	narumi	PROPN
ejpam-5971	27	7	and	and	CCONJ
ejpam-5971	27	8	katayama	katayama	PROPN
ejpam-5971	27	9	proposed	propose	VERB
ejpam-5971	27	10	the	the	DET
ejpam-5971	27	11	narumi	narumi	PROPN
ejpam-5971	27	12	-	-	PUNCT
ejpam-5971	27	13	katayama	katayama	PROPN
ejpam-5971	27	14	index	index	NOUN
ejpam-5971	27	15	,	,	PUNCT
ejpam-5971	27	16	a	a	DET
ejpam-5971	27	17	simpler	simple	ADJ
ejpam-5971	27	18	degree	degree	NOUN
ejpam-5971	27	19	-	-	PUNCT
ejpam-5971	27	20	based	base	VERB
ejpam-5971	27	21	topological	topological	ADJ
ejpam-5971	27	22	index	index	NOUN
ejpam-5971	27	23	used	use	VERB
ejpam-5971	27	24	to	to	PART
ejpam-5971	27	25	examine	examine	VERB
ejpam-5971	27	26	the	the	DET
ejpam-5971	27	27	branching	branch	VERB
ejpam-5971	27	28	structures	structure	NOUN
ejpam-5971	27	29	of	of	ADP
ejpam-5971	27	30	saturated	saturate	VERB
ejpam-5971	27	31	hydrocarbons[18	hydrocarbons[18	NOUN
ejpam-5971	27	32	]	]	PUNCT
ejpam-5971	27	33	.	.	PUNCT
ejpam-5971	28	1	in	in	ADP
ejpam-5971	28	2	addition	addition	NOUN
ejpam-5971	28	3	some	some	DET
ejpam-5971	28	4	researchers	researcher	NOUN
ejpam-5971	28	5	have	have	AUX
ejpam-5971	28	6	extended	extend	VERB
ejpam-5971	28	7	their	their	PRON
ejpam-5971	28	8	study	study	NOUN
ejpam-5971	28	9	to	to	ADP
ejpam-5971	28	10	various	various	ADJ
ejpam-5971	28	11	algebraic	algebraic	ADJ
ejpam-5971	28	12	graph	graph	NOUN
ejpam-5971	28	13	structures	structure	NOUN
ejpam-5971	28	14	,	,	PUNCT
ejpam-5971	28	15	including	include	VERB
ejpam-5971	28	16	zero	zero	NUM
ejpam-5971	28	17	-	-	PUNCT
ejpam-5971	28	18	divisor	divisor	NOUN
ejpam-5971	28	19	graph	graph	NOUN
ejpam-5971	28	20	.	.	PUNCT
ejpam-5971	29	1	in	in	ADP
ejpam-5971	29	2	2011	2011	NUM
ejpam-5971	29	3	,	,	PUNCT
ejpam-5971	29	4	ahmadi	ahmadi	PROPN
ejpam-5971	29	5	and	and	CCONJ
ejpam-5971	29	6	jahani	jahani	PROPN
ejpam-5971	29	7	-	-	PUNCT
ejpam-5971	29	8	nezhad	nezhad	NOUN
ejpam-5971	29	9	pioneered	pioneer	VERB
ejpam-5971	29	10	the	the	DET
ejpam-5971	29	11	examination	examination	NOUN
ejpam-5971	29	12	of	of	ADP
ejpam-5971	29	13	the	the	DET
ejpam-5971	29	14	energy	energy	NOUN
ejpam-5971	29	15	and	and	CCONJ
ejpam-5971	29	16	wiener	wiener	NOUN
ejpam-5971	29	17	index	index	NOUN
ejpam-5971	29	18	of	of	ADP
ejpam-5971	29	19	γ(zpq	γ(zpq	PROPN
ejpam-5971	29	20	)	)	PUNCT
ejpam-5971	29	21	and	and	CCONJ
ejpam-5971	29	22	γ(zp2q	γ(zp2q	NOUN
ejpam-5971	29	23	)	)	PUNCT
ejpam-5971	29	24	for	for	ADP
ejpam-5971	29	25	every	every	DET
ejpam-5971	29	26	distinct	distinct	ADJ
ejpam-5971	29	27	prime	prime	NOUN
ejpam-5971	29	28	p	p	NOUN
ejpam-5971	29	29	,	,	PUNCT
ejpam-5971	29	30	q	q	X
ejpam-5971	30	1	[	[	X
ejpam-5971	30	2	19	19	NUM
ejpam-5971	30	3	]	]	PUNCT
ejpam-5971	30	4	.	.	PUNCT
ejpam-5971	31	1	later	later	ADV
ejpam-5971	31	2	,	,	PUNCT
ejpam-5971	31	3	johnson	johnson	PROPN
ejpam-5971	31	4	and	and	CCONJ
ejpam-5971	31	5	sankar	sankar	NOUN
ejpam-5971	31	6	in	in	ADP
ejpam-5971	31	7	2023	2023	NUM
ejpam-5971	31	8	studied	study	VERB
ejpam-5971	31	9	the	the	DET
ejpam-5971	31	10	energy	energy	NOUN
ejpam-5971	31	11	and	and	CCONJ
ejpam-5971	31	12	topological	topological	ADJ
ejpam-5971	31	13	indices	index	NOUN
ejpam-5971	31	14	of	of	ADP
ejpam-5971	31	15	γ(zp[x]/⟨x4⟩	γ(zp[x]/⟨x4⟩	PROPN
ejpam-5971	31	16	)	)	PUNCT
ejpam-5971	31	17	for	for	ADP
ejpam-5971	31	18	prime	prime	ADJ
ejpam-5971	31	19	number	number	NOUN
ejpam-5971	31	20	p	p	PROPN
ejpam-5971	32	1	[	[	X
ejpam-5971	32	2	20	20	NUM
ejpam-5971	32	3	]	]	PUNCT
ejpam-5971	32	4	.	.	PUNCT
ejpam-5971	33	1	however	however	ADV
ejpam-5971	33	2	,	,	PUNCT
ejpam-5971	33	3	rather	rather	ADV
ejpam-5971	33	4	[	[	X
ejpam-5971	33	5	21	21	NUM
ejpam-5971	33	6	]	]	PUNCT
ejpam-5971	33	7	revised	revise	VERB
ejpam-5971	33	8	their	their	PRON
ejpam-5971	33	9	results	result	NOUN
ejpam-5971	33	10	on	on	ADP
ejpam-5971	33	11	the	the	DET
ejpam-5971	33	12	energy	energy	NOUN
ejpam-5971	33	13	and	and	CCONJ
ejpam-5971	33	14	second	second	ADJ
ejpam-5971	33	15	zagreb	zagreb	PROPN
ejpam-5971	33	16	index	index	NOUN
ejpam-5971	33	17	formula	formula	NOUN
ejpam-5971	33	18	.	.	PUNCT
ejpam-5971	34	1	rayer	rayer	PROPN
ejpam-5971	34	2	and	and	CCONJ
ejpam-5971	34	3	jeyaraj	jeyaraj	PROPN
ejpam-5971	34	4	in	in	ADP
ejpam-5971	34	5	2023	2023	NUM
ejpam-5971	34	6	studied	study	VERB
ejpam-5971	34	7	the	the	DET
ejpam-5971	34	8	topological	topological	ADJ
ejpam-5971	34	9	indices	index	NOUN
ejpam-5971	34	10	of	of	ADP
ejpam-5971	34	11	γ(zp2	γ(zp2	PROPN
ejpam-5971	35	1	[	[	X
ejpam-5971	35	2	x]/⟨x2⟩	x]/⟨x2⟩	X
ejpam-5971	35	3	)	)	PUNCT
ejpam-5971	35	4	for	for	ADP
ejpam-5971	35	5	every	every	DET
ejpam-5971	35	6	prime	prime	ADJ
ejpam-5971	35	7	q	q	X
ejpam-5971	35	8	≥	≥	NUM
ejpam-5971	35	9	3	3	NUM
ejpam-5971	35	10	and	and	CCONJ
ejpam-5971	35	11	γ(zpq[x]/⟨x2⟩	γ(zpq[x]/⟨x2⟩	NUM
ejpam-5971	35	12	)	)	PUNCT
ejpam-5971	35	13	for	for	ADP
ejpam-5971	35	14	every	every	DET
ejpam-5971	35	15	prime	prime	ADJ
ejpam-5971	35	16	2	2	NUM
ejpam-5971	35	17	<	<	X
ejpam-5971	35	18	p	p	X
ejpam-5971	35	19	<	<	X
ejpam-5971	35	20	q	q	X
ejpam-5971	36	1	[	[	X
ejpam-5971	36	2	22	22	NUM
ejpam-5971	36	3	]	]	PUNCT
ejpam-5971	36	4	,	,	PUNCT
ejpam-5971	36	5	and	and	CCONJ
ejpam-5971	36	6	further	far	ADV
ejpam-5971	36	7	investigated	investigate	VERB
ejpam-5971	36	8	the	the	DET
ejpam-5971	36	9	energy	energy	NOUN
ejpam-5971	36	10	of	of	ADP
ejpam-5971	36	11	γ(zp2	γ(zp2	PROPN
ejpam-5971	37	1	[	[	X
ejpam-5971	37	2	x]/⟨x2⟩	x]/⟨x2⟩	X
ejpam-5971	37	3	)	)	PUNCT
ejpam-5971	37	4	in	in	ADP
ejpam-5971	37	5	2024	2024	NUM
ejpam-5971	37	6	[	[	X
ejpam-5971	37	7	23	23	NUM
ejpam-5971	37	8	]	]	PUNCT
ejpam-5971	37	9	.	.	PUNCT
ejpam-5971	38	1	previous	previous	ADJ
ejpam-5971	38	2	research	research	NOUN
ejpam-5971	38	3	has	have	AUX
ejpam-5971	38	4	primarily	primarily	ADV
ejpam-5971	38	5	focused	focus	VERB
ejpam-5971	38	6	on	on	ADP
ejpam-5971	38	7	determining	determine	VERB
ejpam-5971	38	8	the	the	DET
ejpam-5971	38	9	energy	energy	NOUN
ejpam-5971	38	10	and	and	CCONJ
ejpam-5971	38	11	topological	topological	ADJ
ejpam-5971	38	12	indices	index	NOUN
ejpam-5971	38	13	of	of	ADP
ejpam-5971	38	14	the	the	DET
ejpam-5971	38	15	zero	zero	NUM
ejpam-5971	38	16	-	-	PUNCT
ejpam-5971	38	17	divisor	divisor	NOUN
ejpam-5971	38	18	graph	graph	NOUN
ejpam-5971	38	19	in	in	ADP
ejpam-5971	38	20	quotient	quotient	NOUN
ejpam-5971	38	21	rings	ring	NOUN
ejpam-5971	38	22	with	with	ADP
ejpam-5971	38	23	principal	principal	ADJ
ejpam-5971	38	24	ideals	ideal	NOUN
ejpam-5971	38	25	⟨x2⟩	⟨x2⟩	PART
ejpam-5971	38	26	and	and	CCONJ
ejpam-5971	38	27	⟨x4⟩.	⟨x4⟩.	PROPN
ejpam-5971	38	28	recently	recently	ADV
ejpam-5971	38	29	,	,	PUNCT
ejpam-5971	38	30	musyarrofah	musyarrofah	PROPN
ejpam-5971	38	31	et	et	PROPN
ejpam-5971	38	32	al	al	PROPN
ejpam-5971	38	33	.	.	PUNCT
ejpam-5971	39	1	[	[	X
ejpam-5971	39	2	24	24	NUM
ejpam-5971	39	3	]	]	PUNCT
ejpam-5971	39	4	explored	explore	VERB
ejpam-5971	39	5	a	a	DET
ejpam-5971	39	6	different	different	ADJ
ejpam-5971	39	7	type	type	NOUN
ejpam-5971	39	8	of	of	ADP
ejpam-5971	39	9	quotient	quotient	NOUN
ejpam-5971	39	10	ring	ring	NOUN
ejpam-5971	39	11	structure	structure	NOUN
ejpam-5971	39	12	,	,	PUNCT
ejpam-5971	39	13	specifically	specifically	ADV
ejpam-5971	39	14	γ(z℘[x]/⟨x5⟩	γ(z℘[x]/⟨x5⟩	NUM
ejpam-5971	39	15	)	)	PUNCT
ejpam-5971	39	16	for	for	ADP
ejpam-5971	39	17	a	a	DET
ejpam-5971	39	18	prime	prime	ADJ
ejpam-5971	39	19	number	number	NOUN
ejpam-5971	39	20	℘	℘	NOUN
ejpam-5971	39	21	,	,	PUNCT
ejpam-5971	39	22	focusing	focus	VERB
ejpam-5971	39	23	on	on	ADP
ejpam-5971	39	24	the	the	DET
ejpam-5971	39	25	fundamental	fundamental	ADJ
ejpam-5971	39	26	properties	property	NOUN
ejpam-5971	39	27	of	of	ADP
ejpam-5971	39	28	the	the	DET
ejpam-5971	39	29	graph	graph	NOUN
ejpam-5971	39	30	.	.	PUNCT
ejpam-5971	40	1	however	however	ADV
ejpam-5971	40	2	,	,	PUNCT
ejpam-5971	40	3	their	their	PRON
ejpam-5971	40	4	study	study	NOUN
ejpam-5971	40	5	did	do	AUX
ejpam-5971	40	6	not	not	PART
ejpam-5971	40	7	examine	examine	VERB
ejpam-5971	40	8	its	its	PRON
ejpam-5971	40	9	energy	energy	NOUN
ejpam-5971	40	10	or	or	CCONJ
ejpam-5971	40	11	topological	topological	ADJ
ejpam-5971	40	12	indices	index	NOUN
ejpam-5971	40	13	in	in	ADP
ejpam-5971	40	14	detail	detail	NOUN
ejpam-5971	40	15	.	.	PUNCT
ejpam-5971	41	1	in	in	ADP
ejpam-5971	41	2	this	this	DET
ejpam-5971	41	3	paper	paper	NOUN
ejpam-5971	41	4	,	,	PUNCT
ejpam-5971	41	5	we	we	PRON
ejpam-5971	41	6	address	address	VERB
ejpam-5971	41	7	this	this	DET
ejpam-5971	41	8	gap	gap	NOUN
ejpam-5971	41	9	by	by	ADP
ejpam-5971	41	10	analyzing	analyze	VERB
ejpam-5971	41	11	the	the	DET
ejpam-5971	41	12	energy	energy	NOUN
ejpam-5971	41	13	and	and	CCONJ
ejpam-5971	41	14	topological	topological	ADJ
ejpam-5971	41	15	indices	index	NOUN
ejpam-5971	41	16	of	of	ADP
ejpam-5971	41	17	γ(z℘[x]/⟨x5⟩	γ(z℘[x]/⟨x5⟩	NUM
ejpam-5971	41	18	)	)	PUNCT
ejpam-5971	41	19	for	for	ADP
ejpam-5971	41	20	prime	prime	ADJ
ejpam-5971	41	21	number	number	NOUN
ejpam-5971	41	22	℘.	℘.	PROPN
ejpam-5971	41	23	specifically	specifically	ADV
ejpam-5971	41	24	,	,	PUNCT
ejpam-5971	41	25	we	we	PRON
ejpam-5971	41	26	obtain	obtain	VERB
ejpam-5971	41	27	the	the	DET
ejpam-5971	41	28	lower	low	ADJ
ejpam-5971	41	29	and	and	CCONJ
ejpam-5971	41	30	upper	upper	ADJ
ejpam-5971	41	31	bounds	bound	NOUN
ejpam-5971	41	32	of	of	ADP
ejpam-5971	41	33	the	the	DET
ejpam-5971	41	34	energy	energy	NOUN
ejpam-5971	41	35	for	for	ADP
ejpam-5971	41	36	the	the	DET
ejpam-5971	41	37	graph	graph	NOUN
ejpam-5971	41	38	and	and	CCONJ
ejpam-5971	41	39	these	these	DET
ejpam-5971	41	40	bounds	bound	NOUN
ejpam-5971	41	41	are	be	AUX
ejpam-5971	41	42	numerically	numerically	ADV
ejpam-5971	41	43	close	close	ADJ
ejpam-5971	41	44	to	to	ADP
ejpam-5971	41	45	the	the	DET
ejpam-5971	41	46	actual	actual	ADJ
ejpam-5971	41	47	energy	energy	NOUN
ejpam-5971	41	48	value	value	NOUN
ejpam-5971	41	49	.	.	PUNCT
ejpam-5971	42	1	this	this	PRON
ejpam-5971	42	2	provides	provide	VERB
ejpam-5971	42	3	a	a	DET
ejpam-5971	42	4	reliable	reliable	ADJ
ejpam-5971	42	5	method	method	NOUN
ejpam-5971	42	6	for	for	ADP
ejpam-5971	42	7	estimating	estimate	VERB
ejpam-5971	42	8	the	the	DET
ejpam-5971	42	9	energy	energy	NOUN
ejpam-5971	42	10	of	of	ADP
ejpam-5971	42	11	the	the	DET
ejpam-5971	42	12	graph	graph	NOUN
ejpam-5971	42	13	in	in	ADP
ejpam-5971	42	14	similar	similar	ADJ
ejpam-5971	42	15	cases	case	NOUN
ejpam-5971	42	16	.	.	PUNCT
ejpam-5971	43	1	furthermore	furthermore	ADV
ejpam-5971	43	2	,	,	PUNCT
ejpam-5971	43	3	we	we	PRON
ejpam-5971	43	4	investigate	investigate	VERB
ejpam-5971	43	5	topological	topological	ADJ
ejpam-5971	43	6	indices	index	NOUN
ejpam-5971	43	7	,	,	PUNCT
ejpam-5971	43	8	including	include	VERB
ejpam-5971	43	9	distance	distance	NOUN
ejpam-5971	43	10	-	-	PUNCT
ejpam-5971	43	11	based	base	VERB
ejpam-5971	43	12	topological	topological	ADJ
ejpam-5971	43	13	indices	index	NOUN
ejpam-5971	43	14	such	such	ADJ
ejpam-5971	43	15	as	as	ADP
ejpam-5971	43	16	the	the	DET
ejpam-5971	43	17	wiener	wiener	NOUN
ejpam-5971	43	18	and	and	CCONJ
ejpam-5971	43	19	hyper	hyper	NOUN
ejpam-5971	43	20	-	-	ADJ
ejpam-5971	43	21	wiener	wiener	NOUN
ejpam-5971	43	22	indices	index	NOUN
ejpam-5971	43	23	,	,	PUNCT
ejpam-5971	43	24	as	as	ADV
ejpam-5971	43	25	well	well	ADV
ejpam-5971	43	26	as	as	ADP
ejpam-5971	43	27	degree	degree	NOUN
ejpam-5971	43	28	-	-	PUNCT
ejpam-5971	43	29	based	base	VERB
ejpam-5971	43	30	topological	topological	ADJ
ejpam-5971	43	31	indices	index	NOUN
ejpam-5971	43	32	such	such	ADJ
ejpam-5971	43	33	as	as	ADP
ejpam-5971	43	34	the	the	DET
ejpam-5971	43	35	first	first	ADJ
ejpam-5971	43	36	,	,	PUNCT
ejpam-5971	43	37	second	second	ADJ
ejpam-5971	43	38	zagreb	zagreb	PROPN
ejpam-5971	43	39	,	,	PUNCT
ejpam-5971	43	40	and	and	CCONJ
ejpam-5971	43	41	narumi	narumi	PROPN
ejpam-5971	43	42	-	-	PUNCT
ejpam-5971	43	43	katayama	katayama	NOUN
ejpam-5971	43	44	indices	index	NOUN
ejpam-5971	43	45	.	.	PUNCT
ejpam-5971	44	1	to	to	PART
ejpam-5971	44	2	validate	validate	VERB
ejpam-5971	44	3	our	our	PRON
ejpam-5971	44	4	theoretical	theoretical	ADJ
ejpam-5971	44	5	results	result	NOUN
ejpam-5971	44	6	,	,	PUNCT
ejpam-5971	44	7	we	we	PRON
ejpam-5971	44	8	conduct	conduct	VERB
ejpam-5971	44	9	numerical	numerical	ADJ
ejpam-5971	44	10	simulations	simulation	NOUN
ejpam-5971	44	11	using	use	VERB
ejpam-5971	44	12	a	a	DET
ejpam-5971	44	13	computer	computer	NOUN
ejpam-5971	44	14	software	software	NOUN
ejpam-5971	44	15	matlab	matlab	PROPN
ejpam-5971	44	16	,	,	PUNCT
ejpam-5971	44	17	comparing	compare	VERB
ejpam-5971	44	18	the	the	DET
ejpam-5971	44	19	computed	compute	VERB
ejpam-5971	44	20	graph	graph	NOUN
ejpam-5971	44	21	energy	energy	NOUN
ejpam-5971	44	22	with	with	ADP
ejpam-5971	44	23	its	its	PRON
ejpam-5971	44	24	theoretical	theoretical	ADJ
ejpam-5971	44	25	bounds	bound	NOUN
ejpam-5971	44	26	and	and	CCONJ
ejpam-5971	44	27	analyzing	analyze	VERB
ejpam-5971	44	28	the	the	DET
ejpam-5971	44	29	growth	growth	NOUN
ejpam-5971	44	30	patterns	pattern	NOUN
ejpam-5971	44	31	of	of	ADP
ejpam-5971	44	32	various	various	ADJ
ejpam-5971	44	33	topological	topological	ADJ
ejpam-5971	44	34	indices	index	NOUN
ejpam-5971	44	35	.	.	PUNCT
ejpam-5971	45	1	2	2	X
ejpam-5971	45	2	.	.	X
ejpam-5971	45	3	preliminaries	preliminary	NOUN
ejpam-5971	45	4	in	in	ADP
ejpam-5971	45	5	this	this	DET
ejpam-5971	45	6	section	section	NOUN
ejpam-5971	45	7	presents	present	VERB
ejpam-5971	45	8	basic	basic	ADJ
ejpam-5971	45	9	concepts	concept	NOUN
ejpam-5971	45	10	,	,	PUNCT
ejpam-5971	45	11	notations	notation	NOUN
ejpam-5971	45	12	,	,	PUNCT
ejpam-5971	45	13	and	and	CCONJ
ejpam-5971	45	14	preliminaries	preliminary	NOUN
ejpam-5971	45	15	relevant	relevant	ADJ
ejpam-5971	45	16	to	to	ADP
ejpam-5971	45	17	this	this	DET
ejpam-5971	45	18	paper	paper	NOUN
ejpam-5971	45	19	.	.	PUNCT
ejpam-5971	46	1	all	all	PRON
ejpam-5971	46	2	of	of	ADP
ejpam-5971	46	3	the	the	DET
ejpam-5971	46	4	graphs	graph	NOUN
ejpam-5971	46	5	mentioned	mention	VERB
ejpam-5971	46	6	are	be	AUX
ejpam-5971	46	7	simple	simple	ADJ
ejpam-5971	46	8	graphs	graph	NOUN
ejpam-5971	46	9	,	,	PUNCT
ejpam-5971	46	10	meaning	mean	VERB
ejpam-5971	46	11	that	that	SCONJ
ejpam-5971	46	12	they	they	PRON
ejpam-5971	46	13	are	be	AUX
ejpam-5971	46	14	undirected	undirected	ADJ
ejpam-5971	46	15	,	,	PUNCT
ejpam-5971	46	16	do	do	AUX
ejpam-5971	46	17	not	not	PART
ejpam-5971	46	18	have	have	VERB
ejpam-5971	46	19	loops	loop	NOUN
ejpam-5971	46	20	,	,	PUNCT
ejpam-5971	46	21	and	and	CCONJ
ejpam-5971	46	22	do	do	AUX
ejpam-5971	46	23	not	not	PART
ejpam-5971	46	24	contain	contain	VERB
ejpam-5971	46	25	multiple	multiple	ADJ
ejpam-5971	46	26	edges	edge	NOUN
ejpam-5971	46	27	.	.	PUNCT
ejpam-5971	47	1	the	the	DET
ejpam-5971	47	2	fundamental	fundamental	ADJ
ejpam-5971	47	3	concepts	concept	NOUN
ejpam-5971	47	4	of	of	ADP
ejpam-5971	47	5	graph	graph	NOUN
ejpam-5971	47	6	theory	theory	NOUN
ejpam-5971	47	7	discussed	discuss	VERB
ejpam-5971	47	8	in	in	ADP
ejpam-5971	47	9	this	this	DET
ejpam-5971	47	10	article	article	NOUN
ejpam-5971	47	11	are	be	AUX
ejpam-5971	47	12	referenced	reference	VERB
ejpam-5971	47	13	in	in	ADP
ejpam-5971	47	14	[	[	X
ejpam-5971	47	15	25	25	NUM
ejpam-5971	47	16	]	]	PUNCT
ejpam-5971	47	17	.	.	PUNCT
ejpam-5971	48	1	let	let	VERB
ejpam-5971	48	2	g	g	PRON
ejpam-5971	48	3	be	be	AUX
ejpam-5971	48	4	a	a	DET
ejpam-5971	48	5	graph	graph	NOUN
ejpam-5971	48	6	with	with	ADP
ejpam-5971	48	7	vertex	vertex	NOUN
ejpam-5971	48	8	set	set	VERB
ejpam-5971	48	9	v	v	NOUN
ejpam-5971	48	10	(	(	PUNCT
ejpam-5971	48	11	g	g	NOUN
ejpam-5971	48	12	)	)	PUNCT
ejpam-5971	48	13	=	=	SYM
ejpam-5971	48	14	{	{	PUNCT
ejpam-5971	48	15	v1	v1	PROPN
ejpam-5971	48	16	,	,	PUNCT
ejpam-5971	48	17	v2	v2	PROPN
ejpam-5971	48	18	,	,	PUNCT
ejpam-5971	48	19	v3	v3	PROPN
ejpam-5971	48	20	,	,	PUNCT
ejpam-5971	48	21	.	.	PUNCT
ejpam-5971	48	22	.	.	PUNCT
ejpam-5971	49	1	.	.	PUNCT
ejpam-5971	50	1	,	,	PUNCT
ejpam-5971	50	2	vn	vn	PROPN
ejpam-5971	50	3	}	}	PUNCT
ejpam-5971	50	4	.	.	PUNCT
ejpam-5971	51	1	the	the	DET
ejpam-5971	51	2	adjacency	adjacency	NOUN
ejpam-5971	51	3	matrix	matrix	NOUN
ejpam-5971	51	4	of	of	ADP
ejpam-5971	51	5	g	g	NOUN
ejpam-5971	51	6	,	,	PUNCT
ejpam-5971	51	7	a(g	a(g	PROPN
ejpam-5971	51	8	)	)	PUNCT
ejpam-5971	51	9	=	=	PUNCT
ejpam-5971	52	1	[	[	X
ejpam-5971	52	2	aij	aij	X
ejpam-5971	52	3	]	]	PUNCT
ejpam-5971	52	4	is	be	AUX
ejpam-5971	52	5	a	a	DET
ejpam-5971	52	6	(	(	PUNCT
ejpam-5971	52	7	0	0	NUM
ejpam-5971	52	8	,	,	PUNCT
ejpam-5971	52	9	1)-symmetric	1)-symmetric	NUM
ejpam-5971	52	10	v.h	v.h	PROPN
ejpam-5971	52	11	.	.	PROPN
ejpam-5971	52	12	krisnawati	krisnawati	PROPN
ejpam-5971	52	13	,	,	PUNCT
ejpam-5971	52	14	n.	n.	PROPN
ejpam-5971	52	15	hidayat	hidayat	PROPN
ejpam-5971	52	16	,	,	PUNCT
ejpam-5971	52	17	a.f	a.f	PROPN
ejpam-5971	52	18	.	.	PROPN
ejpam-5971	52	19	musyarrofah	musyarrofah	PROPN
ejpam-5971	52	20	/	/	SYM
ejpam-5971	52	21	eur	eur	PROPN
ejpam-5971	52	22	.	.	PUNCT
ejpam-5971	53	1	j.	j.	PROPN
ejpam-5971	53	2	pure	pure	PROPN
ejpam-5971	53	3	appl	appl	PROPN
ejpam-5971	53	4	.	.	PROPN
ejpam-5971	53	5	math	math	PROPN
ejpam-5971	53	6	,	,	PUNCT
ejpam-5971	53	7	18	18	NUM
ejpam-5971	53	8	(	(	PUNCT
ejpam-5971	53	9	2	2	NUM
ejpam-5971	53	10	)	)	PUNCT
ejpam-5971	53	11	(	(	PUNCT
ejpam-5971	53	12	2025	2025	NUM
ejpam-5971	53	13	)	)	PUNCT
ejpam-5971	53	14	,	,	PUNCT
ejpam-5971	53	15	5971	5971	NUM
ejpam-5971	53	16	3	3	NUM
ejpam-5971	53	17	of	of	ADP
ejpam-5971	53	18	19	19	NUM
ejpam-5971	53	19	matrix	matrix	NOUN
ejpam-5971	53	20	with	with	ADP
ejpam-5971	53	21	entries	entry	NOUN
ejpam-5971	53	22	aij	aij	PROPN
ejpam-5971	53	23	equal	equal	ADJ
ejpam-5971	53	24	to	to	ADP
ejpam-5971	53	25	1	1	NUM
ejpam-5971	53	26	if	if	SCONJ
ejpam-5971	53	27	vi	vi	PROPN
ejpam-5971	53	28	is	be	AUX
ejpam-5971	53	29	adjacent	adjacent	ADJ
ejpam-5971	53	30	to	to	ADP
ejpam-5971	53	31	vj	vj	PROPN
ejpam-5971	53	32	and	and	CCONJ
ejpam-5971	53	33	equal	equal	ADJ
ejpam-5971	53	34	to	to	ADP
ejpam-5971	53	35	0	0	NUM
ejpam-5971	53	36	otherwise	otherwise	ADV
ejpam-5971	53	37	.	.	PUNCT
ejpam-5971	54	1	the	the	DET
ejpam-5971	54	2	degree	degree	NOUN
ejpam-5971	54	3	of	of	ADP
ejpam-5971	54	4	a	a	DET
ejpam-5971	54	5	vertex	vertex	NOUN
ejpam-5971	54	6	v	v	ADP
ejpam-5971	54	7	∈	∈	NOUN
ejpam-5971	54	8	v	v	NOUN
ejpam-5971	54	9	(	(	PUNCT
ejpam-5971	54	10	g	g	NOUN
ejpam-5971	54	11	)	)	PUNCT
ejpam-5971	54	12	,	,	PUNCT
ejpam-5971	54	13	deg(v	deg(v	PROPN
ejpam-5971	54	14	)	)	PUNCT
ejpam-5971	54	15	,	,	PUNCT
ejpam-5971	54	16	indicates	indicate	VERB
ejpam-5971	54	17	the	the	DET
ejpam-5971	54	18	number	number	NOUN
ejpam-5971	54	19	of	of	ADP
ejpam-5971	54	20	vertices	vertex	NOUN
ejpam-5971	54	21	that	that	PRON
ejpam-5971	54	22	are	be	AUX
ejpam-5971	54	23	adjacent	adjacent	ADJ
ejpam-5971	54	24	to	to	ADP
ejpam-5971	54	25	v	v	NOUN
ejpam-5971	54	26	and	and	CCONJ
ejpam-5971	54	27	the	the	DET
ejpam-5971	54	28	distance	distance	NOUN
ejpam-5971	54	29	d(v	d(v	PROPN
ejpam-5971	54	30	,	,	PUNCT
ejpam-5971	54	31	w	w	NOUN
ejpam-5971	54	32	)	)	PUNCT
ejpam-5971	54	33	indicates	indicate	VERB
ejpam-5971	54	34	the	the	DET
ejpam-5971	54	35	shortest	short	ADJ
ejpam-5971	54	36	path	path	NOUN
ejpam-5971	54	37	between	between	ADP
ejpam-5971	54	38	the	the	DET
ejpam-5971	54	39	vertices	vertex	NOUN
ejpam-5971	54	40	v	v	NOUN
ejpam-5971	54	41	and	and	CCONJ
ejpam-5971	54	42	w.	w.	NOUN
ejpam-5971	54	43	the	the	DET
ejpam-5971	54	44	distance	distance	NOUN
ejpam-5971	54	45	matrix	matrix	NOUN
ejpam-5971	54	46	of	of	ADP
ejpam-5971	54	47	g	g	NOUN
ejpam-5971	54	48	,	,	PUNCT
ejpam-5971	54	49	d(g	d(g	PROPN
ejpam-5971	54	50	)	)	PUNCT
ejpam-5971	54	51	=	=	PUNCT
ejpam-5971	55	1	[	[	X
ejpam-5971	55	2	dij	dij	X
ejpam-5971	55	3	]	]	X
ejpam-5971	55	4	is	be	AUX
ejpam-5971	55	5	a	a	DET
ejpam-5971	55	6	symmetric	symmetric	ADJ
ejpam-5971	55	7	matrix	matrix	NOUN
ejpam-5971	55	8	,	,	PUNCT
ejpam-5971	55	9	where	where	SCONJ
ejpam-5971	55	10	dij	dij	PROPN
ejpam-5971	55	11	denotes	denote	VERB
ejpam-5971	55	12	the	the	DET
ejpam-5971	55	13	distance	distance	NOUN
ejpam-5971	55	14	between	between	ADP
ejpam-5971	55	15	two	two	NUM
ejpam-5971	55	16	distinct	distinct	ADJ
ejpam-5971	55	17	vertices	vertex	NOUN
ejpam-5971	55	18	vi	vi	NOUN
ejpam-5971	55	19	and	and	CCONJ
ejpam-5971	55	20	vj	vj	INTJ
ejpam-5971	55	21	.	.	PUNCT
ejpam-5971	56	1	zero	zero	NUM
ejpam-5971	56	2	-	-	PUNCT
ejpam-5971	56	3	divisor	divisor	NOUN
ejpam-5971	56	4	graph	graph	NOUN
ejpam-5971	56	5	is	be	AUX
ejpam-5971	56	6	the	the	DET
ejpam-5971	56	7	subject	subject	NOUN
ejpam-5971	56	8	in	in	ADP
ejpam-5971	56	9	this	this	DET
ejpam-5971	56	10	investigation	investigation	NOUN
ejpam-5971	56	11	,	,	PUNCT
ejpam-5971	56	12	where	where	SCONJ
ejpam-5971	56	13	the	the	DET
ejpam-5971	56	14	definition	definition	NOUN
ejpam-5971	56	15	used	use	VERB
ejpam-5971	56	16	follows	follow	VERB
ejpam-5971	56	17	anderson	anderson	PROPN
ejpam-5971	56	18	and	and	CCONJ
ejpam-5971	56	19	livingston	livingston	PROPN
ejpam-5971	57	1	[	[	X
ejpam-5971	57	2	2	2	NUM
ejpam-5971	57	3	]	]	PUNCT
ejpam-5971	57	4	.	.	PUNCT
ejpam-5971	58	1	suppose	suppose	VERB
ejpam-5971	58	2	r	r	NOUN
ejpam-5971	58	3	is	be	AUX
ejpam-5971	58	4	a	a	DET
ejpam-5971	58	5	commutative	commutative	ADJ
ejpam-5971	58	6	ring	ring	NOUN
ejpam-5971	58	7	,	,	PUNCT
ejpam-5971	58	8	with	with	ADP
ejpam-5971	58	9	z(r	z(r	NOUN
ejpam-5971	58	10	)	)	PUNCT
ejpam-5971	58	11	being	be	AUX
ejpam-5971	58	12	the	the	DET
ejpam-5971	58	13	set	set	NOUN
ejpam-5971	58	14	of	of	ADP
ejpam-5971	58	15	zero	zero	NUM
ejpam-5971	58	16	-	-	PUNCT
ejpam-5971	58	17	divisors	divisor	NOUN
ejpam-5971	58	18	of	of	ADP
ejpam-5971	58	19	r.	r.	PROPN
ejpam-5971	58	20	the	the	DET
ejpam-5971	58	21	zero	zero	NUM
ejpam-5971	58	22	-	-	PUNCT
ejpam-5971	58	23	divisor	divisor	NOUN
ejpam-5971	58	24	graph	graph	NOUN
ejpam-5971	58	25	of	of	ADP
ejpam-5971	58	26	r	r	NOUN
ejpam-5971	58	27	,	,	PUNCT
ejpam-5971	58	28	γ(r	γ(r	PROPN
ejpam-5971	58	29	)	)	PUNCT
ejpam-5971	58	30	is	be	AUX
ejpam-5971	58	31	the	the	DET
ejpam-5971	58	32	graph	graph	NOUN
ejpam-5971	58	33	with	with	ADP
ejpam-5971	58	34	the	the	DET
ejpam-5971	58	35	set	set	NOUN
ejpam-5971	58	36	of	of	ADP
ejpam-5971	58	37	vertex	vertex	NOUN
ejpam-5971	58	38	consisting	consist	VERB
ejpam-5971	58	39	of	of	ADP
ejpam-5971	58	40	the	the	DET
ejpam-5971	58	41	elements	element	NOUN
ejpam-5971	58	42	of	of	ADP
ejpam-5971	58	43	z∗(r	z∗(r	NUM
ejpam-5971	58	44	)	)	PUNCT
ejpam-5971	59	1	=	=	SYM
ejpam-5971	59	2	z(r	z(r	PROPN
ejpam-5971	59	3	)	)	PUNCT
ejpam-5971	59	4	\	\	NOUN
ejpam-5971	59	5	{	{	PUNCT
ejpam-5971	59	6	0	0	NUM
ejpam-5971	59	7	}	}	PUNCT
ejpam-5971	59	8	and	and	CCONJ
ejpam-5971	59	9	the	the	DET
ejpam-5971	59	10	set	set	NOUN
ejpam-5971	59	11	of	of	ADP
ejpam-5971	59	12	edges	edge	NOUN
ejpam-5971	59	13	e(γ(r	e(γ(r	PROPN
ejpam-5971	59	14	)	)	PUNCT
ejpam-5971	59	15	)	)	PUNCT
ejpam-5971	60	1	=	=	PRON
ejpam-5971	60	2	{	{	PUNCT
ejpam-5971	60	3	xy	xy	INTJ
ejpam-5971	60	4	|	|	ADV
ejpam-5971	60	5	xy	xy	NOUN
ejpam-5971	60	6	=	=	SYM
ejpam-5971	60	7	0	0	PROPN
ejpam-5971	60	8	,	,	PUNCT
ejpam-5971	60	9	∀x	∀x	X
ejpam-5971	60	10	,	,	PUNCT
ejpam-5971	60	11	y	y	PROPN
ejpam-5971	60	12	∈	∈	PROPN
ejpam-5971	60	13	z∗(r	z∗(r	PROPN
ejpam-5971	60	14	)	)	PUNCT
ejpam-5971	60	15	}	}	PUNCT
ejpam-5971	60	16	.	.	PUNCT
ejpam-5971	61	1	furthermore	furthermore	ADV
ejpam-5971	61	2	,	,	PUNCT
ejpam-5971	61	3	we	we	PRON
ejpam-5971	61	4	present	present	VERB
ejpam-5971	61	5	several	several	ADJ
ejpam-5971	61	6	results	result	NOUN
ejpam-5971	61	7	related	relate	VERB
ejpam-5971	61	8	to	to	PART
ejpam-5971	61	9	block	block	VERB
ejpam-5971	61	10	and	and	CCONJ
ejpam-5971	61	11	circulant	circulant	ADJ
ejpam-5971	61	12	matrices	matrix	NOUN
ejpam-5971	61	13	that	that	PRON
ejpam-5971	61	14	are	be	AUX
ejpam-5971	61	15	utilized	utilize	VERB
ejpam-5971	61	16	.	.	PUNCT
ejpam-5971	62	1	these	these	DET
ejpam-5971	62	2	results	result	NOUN
ejpam-5971	62	3	are	be	AUX
ejpam-5971	62	4	used	use	VERB
ejpam-5971	62	5	to	to	PART
ejpam-5971	62	6	calculate	calculate	VERB
ejpam-5971	62	7	the	the	DET
ejpam-5971	62	8	eigenvalues	eigenvalue	NOUN
ejpam-5971	62	9	and	and	CCONJ
ejpam-5971	62	10	determinants	determinant	NOUN
ejpam-5971	62	11	of	of	ADP
ejpam-5971	62	12	the	the	DET
ejpam-5971	62	13	adjacency	adjacency	NOUN
ejpam-5971	62	14	matrix	matrix	NOUN
ejpam-5971	62	15	.	.	PUNCT
ejpam-5971	63	1	lemma	lemma	PROPN
ejpam-5971	63	2	1	1	NUM
ejpam-5971	63	3	.	.	PUNCT
ejpam-5971	64	1	[	[	X
ejpam-5971	64	2	26	26	NUM
ejpam-5971	64	3	]	]	PUNCT
ejpam-5971	64	4	let	let	VERB
ejpam-5971	64	5	p	p	PRON
ejpam-5971	64	6	,	,	PUNCT
ejpam-5971	64	7	q	q	ADJ
ejpam-5971	64	8	,	,	PUNCT
ejpam-5971	64	9	r	r	NOUN
ejpam-5971	64	10	,	,	PUNCT
ejpam-5971	64	11	s	s	VERB
ejpam-5971	64	12	be	be	AUX
ejpam-5971	64	13	matrices	matrix	NOUN
ejpam-5971	64	14	and	and	CCONJ
ejpam-5971	64	15	suppose	suppose	VERB
ejpam-5971	64	16	that	that	DET
ejpam-5971	64	17	matrix	matrix	NOUN
ejpam-5971	64	18	p	p	NOUN
ejpam-5971	64	19	is	be	AUX
ejpam-5971	64	20	invertible	invertible	ADJ
ejpam-5971	64	21	.	.	PUNCT
ejpam-5971	65	1	if	if	SCONJ
ejpam-5971	65	2	m	m	VERB
ejpam-5971	65	3	=	=	X
ejpam-5971	65	4	[	[	PUNCT
ejpam-5971	65	5	p	p	X
ejpam-5971	65	6	q	q	X
ejpam-5971	65	7	r	r	NOUN
ejpam-5971	65	8	s	s	X
ejpam-5971	65	9	]	]	PUNCT
ejpam-5971	65	10	,	,	PUNCT
ejpam-5971	65	11	then	then	ADV
ejpam-5971	65	12	det(m	det(m	PROPN
ejpam-5971	65	13	)	)	PUNCT
ejpam-5971	65	14	=	=	SYM
ejpam-5971	65	15	det(p	det(p	NOUN
ejpam-5971	65	16	)	)	PUNCT
ejpam-5971	65	17	·	·	PUNCT
ejpam-5971	65	18	det(s	det(s	PROPN
ejpam-5971	66	1	−rp−1q	−rp−1q	PROPN
ejpam-5971	66	2	)	)	PUNCT
ejpam-5971	66	3	.	.	PUNCT
ejpam-5971	67	1	a	a	DET
ejpam-5971	67	2	circulant	circulant	ADJ
ejpam-5971	67	3	matrix	matrix	NOUN
ejpam-5971	67	4	is	be	AUX
ejpam-5971	67	5	a	a	DET
ejpam-5971	67	6	square	square	ADJ
ejpam-5971	67	7	matrix	matrix	NOUN
ejpam-5971	67	8	where	where	SCONJ
ejpam-5971	67	9	each	each	DET
ejpam-5971	67	10	row	row	NOUN
ejpam-5971	67	11	is	be	AUX
ejpam-5971	67	12	generated	generate	VERB
ejpam-5971	67	13	by	by	ADP
ejpam-5971	67	14	moving	move	VERB
ejpam-5971	67	15	the	the	DET
ejpam-5971	67	16	entries	entry	NOUN
ejpam-5971	67	17	of	of	ADP
ejpam-5971	67	18	the	the	DET
ejpam-5971	67	19	previous	previous	ADJ
ejpam-5971	67	20	row	row	NOUN
ejpam-5971	67	21	one	one	NUM
ejpam-5971	67	22	position	position	NOUN
ejpam-5971	67	23	to	to	ADP
ejpam-5971	67	24	the	the	DET
ejpam-5971	67	25	right	right	NOUN
ejpam-5971	67	26	,	,	PUNCT
ejpam-5971	67	27	while	while	SCONJ
ejpam-5971	67	28	the	the	DET
ejpam-5971	67	29	last	last	ADJ
ejpam-5971	67	30	entry	entry	NOUN
ejpam-5971	67	31	moves	move	NOUN
ejpam-5971	67	32	to	to	ADP
ejpam-5971	67	33	the	the	DET
ejpam-5971	67	34	first	first	ADJ
ejpam-5971	67	35	position	position	NOUN
ejpam-5971	67	36	.	.	PUNCT
ejpam-5971	68	1	this	this	DET
ejpam-5971	68	2	matrix	matrix	NOUN
ejpam-5971	68	3	c	c	NOUN
ejpam-5971	68	4	can	can	AUX
ejpam-5971	68	5	be	be	AUX
ejpam-5971	68	6	represented	represent	VERB
ejpam-5971	68	7	by	by	ADP
ejpam-5971	68	8	the	the	DET
ejpam-5971	68	9	vector	vector	NOUN
ejpam-5971	68	10	c	c	NOUN
ejpam-5971	68	11	=	=	PUNCT
ejpam-5971	69	1	[	[	X
ejpam-5971	69	2	c0	c0	X
ejpam-5971	69	3	,	,	PUNCT
ejpam-5971	69	4	c1	c1	PROPN
ejpam-5971	69	5	,	,	PUNCT
ejpam-5971	69	6	c2	c2	PROPN
ejpam-5971	69	7	,	,	PUNCT
ejpam-5971	69	8	.	.	PUNCT
ejpam-5971	69	9	.	.	PUNCT
ejpam-5971	69	10	.	.	PUNCT
ejpam-5971	70	1	,	,	PUNCT
ejpam-5971	70	2	cm−1	cm−1	NOUN
ejpam-5971	70	3	]	]	PUNCT
ejpam-5971	70	4	,	,	PUNCT
ejpam-5971	70	5	where	where	SCONJ
ejpam-5971	70	6	each	each	DET
ejpam-5971	70	7	row	row	NOUN
ejpam-5971	70	8	results	result	VERB
ejpam-5971	70	9	from	from	ADP
ejpam-5971	70	10	a	a	DET
ejpam-5971	70	11	right	right	ADJ
ejpam-5971	70	12	circular	circular	ADJ
ejpam-5971	70	13	shift	shift	NOUN
ejpam-5971	70	14	of	of	ADP
ejpam-5971	70	15	c.	c.	NOUN
ejpam-5971	70	16	the	the	DET
ejpam-5971	70	17	circulant	circulant	ADJ
ejpam-5971	70	18	matrix	matrix	NOUN
ejpam-5971	70	19	of	of	ADP
ejpam-5971	70	20	order	order	NOUN
ejpam-5971	70	21	m×m	m×m	ADJ
ejpam-5971	70	22	with	with	ADP
ejpam-5971	70	23	entries	entry	NOUN
ejpam-5971	70	24	c0	c0	X
ejpam-5971	70	25	,	,	PUNCT
ejpam-5971	70	26	c1	c1	PROPN
ejpam-5971	70	27	∈	∈	PROPN
ejpam-5971	70	28	r	r	NOUN
ejpam-5971	70	29	is	be	AUX
ejpam-5971	70	30	denoted	denote	VERB
ejpam-5971	70	31	as	as	ADP
ejpam-5971	70	32	c(c0,c1,m	c(c0,c1,m	NOUN
ejpam-5971	70	33	)	)	PUNCT
ejpam-5971	70	34	and	and	CCONJ
ejpam-5971	70	35	has	have	VERB
ejpam-5971	70	36	the	the	DET
ejpam-5971	70	37	following	follow	VERB
ejpam-5971	70	38	form	form	NOUN
ejpam-5971	70	39	:	:	PUNCT
ejpam-5971	70	40	c(c0,c1,m	c(c0,c1,m	NOUN
ejpam-5971	70	41	)	)	PUNCT
ejpam-5971	70	42	=	=	SYM
ejpam-5971	70	43			NOUN
ejpam-5971	70	44	c0	c0	PROPN
ejpam-5971	70	45	c1	c1	PROPN
ejpam-5971	70	46	c1	c1	PROPN
ejpam-5971	70	47	.	.	PUNCT
ejpam-5971	70	48	.	.	PUNCT
ejpam-5971	70	49	.	.	PUNCT
ejpam-5971	71	1	c1	c1	PROPN
ejpam-5971	71	2	c1	c1	PROPN
ejpam-5971	71	3	c0	c0	PROPN
ejpam-5971	71	4	c1	c1	PROPN
ejpam-5971	71	5	.	.	PUNCT
ejpam-5971	71	6	.	.	PUNCT
ejpam-5971	71	7	.	.	PUNCT
ejpam-5971	72	1	c1	c1	PROPN
ejpam-5971	72	2	c1	c1	PROPN
ejpam-5971	72	3	c1	c1	PROPN
ejpam-5971	72	4	c0	c0	PROPN
ejpam-5971	72	5	.	.	PUNCT
ejpam-5971	72	6	.	.	PUNCT
ejpam-5971	72	7	.	.	PUNCT
ejpam-5971	73	1	c1	c1	PROPN
ejpam-5971	73	2	...	...	PUNCT
ejpam-5971	73	3	...	...	PUNCT
ejpam-5971	73	4	...	...	PUNCT
ejpam-5971	73	5	.	.	PUNCT
ejpam-5971	73	6	.	.	PUNCT
ejpam-5971	73	7	.	.	PUNCT
ejpam-5971	73	8	...	...	PUNCT
ejpam-5971	74	1	c1	c1	PROPN
ejpam-5971	74	2	c1	c1	PROPN
ejpam-5971	74	3	c1	c1	PROPN
ejpam-5971	74	4	.	.	PUNCT
ejpam-5971	74	5	.	.	PUNCT
ejpam-5971	74	6	.	.	PUNCT
ejpam-5971	75	1	c0	c0	PROPN
ejpam-5971	75	2			PROPN
ejpam-5971	75	3	m×m	m×m	PROPN
ejpam-5971	75	4	.	.	PUNCT
ejpam-5971	76	1	proposition	proposition	NOUN
ejpam-5971	76	2	1	1	NUM
ejpam-5971	76	3	.	.	PUNCT
ejpam-5971	77	1	[	[	X
ejpam-5971	77	2	27	27	NUM
ejpam-5971	77	3	]	]	X
ejpam-5971	77	4	let	let	AUX
ejpam-5971	77	5	c(c0,c1,m	c(c0,c1,m	NOUN
ejpam-5971	77	6	)	)	PUNCT
ejpam-5971	77	7	be	be	AUX
ejpam-5971	77	8	a	a	DET
ejpam-5971	77	9	circulant	circulant	ADJ
ejpam-5971	77	10	matrix	matrix	NOUN
ejpam-5971	77	11	.	.	PUNCT
ejpam-5971	78	1	the	the	DET
ejpam-5971	78	2	determinant	determinant	NOUN
ejpam-5971	78	3	of	of	ADP
ejpam-5971	78	4	c(c0,c1,m	c(c0,c1,m	NOUN
ejpam-5971	78	5	)	)	PUNCT
ejpam-5971	78	6	is	be	AUX
ejpam-5971	78	7	det(c(c0,c1,m	det(c(c0,c1,m	PROPN
ejpam-5971	78	8	)	)	PUNCT
ejpam-5971	78	9	)	)	PUNCT
ejpam-5971	79	1	=	=	PUNCT
ejpam-5971	80	1	[	[	X
ejpam-5971	80	2	c0	c0	X
ejpam-5971	80	3	+	+	CCONJ
ejpam-5971	80	4	(	(	PUNCT
ejpam-5971	80	5	m−	m−	PROPN
ejpam-5971	80	6	1)c1](c0	1)c1](c0	PROPN
ejpam-5971	80	7	−	−	PROPN
ejpam-5971	80	8	c1	c1	PROPN
ejpam-5971	80	9	)	)	PUNCT
ejpam-5971	81	1	m−1	m−1	PROPN
ejpam-5971	81	2	.	.	PUNCT
ejpam-5971	82	1	proposition	proposition	NOUN
ejpam-5971	82	2	2	2	NUM
ejpam-5971	82	3	.	.	PUNCT
ejpam-5971	83	1	[	[	X
ejpam-5971	83	2	27	27	NUM
ejpam-5971	83	3	]	]	X
ejpam-5971	83	4	let	let	AUX
ejpam-5971	83	5	c(c0,c1,m	c(c0,c1,m	NOUN
ejpam-5971	83	6	)	)	PUNCT
ejpam-5971	83	7	be	be	VERB
ejpam-5971	83	8	a	a	DET
ejpam-5971	83	9	nonsingular	nonsingular	ADJ
ejpam-5971	83	10	circulant	circulant	NOUN
ejpam-5971	83	11	matrix	matrix	NOUN
ejpam-5971	83	12	.	.	PUNCT
ejpam-5971	84	1	the	the	DET
ejpam-5971	84	2	inverse	inverse	NOUN
ejpam-5971	84	3	of	of	ADP
ejpam-5971	84	4	c(c0,c1,m	c(c0,c1,m	NOUN
ejpam-5971	84	5	)	)	PUNCT
ejpam-5971	84	6	is	be	AUX
ejpam-5971	84	7	c−1	c−1	PROPN
ejpam-5971	84	8	(	(	PUNCT
ejpam-5971	84	9	c0,c1,m	c0,c1,m	PROPN
ejpam-5971	84	10	)	)	PUNCT
ejpam-5971	84	11	=	=	SYM
ejpam-5971	84	12	1	1	NUM
ejpam-5971	84	13	det(c(c0	det(c(c0	PROPN
ejpam-5971	84	14	,	,	PUNCT
ejpam-5971	84	15	c1,m	c1,m	PROPN
ejpam-5971	84	16	)	)	PUNCT
ejpam-5971	84	17	)	)	PUNCT
ejpam-5971	84	18			VERB
ejpam-5971	84	19	φm−1	φm−1	PROPN
ejpam-5971	84	20	ϑm−1	ϑm−1	PROPN
ejpam-5971	84	21	ϑm−1	ϑm−1	PROPN
ejpam-5971	84	22	.	.	PUNCT
ejpam-5971	84	23	.	.	PUNCT
ejpam-5971	84	24	.	.	PUNCT
ejpam-5971	85	1	ϑm−1	ϑm−1	PROPN
ejpam-5971	85	2	ϑm−1	ϑm−1	PROPN
ejpam-5971	85	3	φm−1	φm−1	PROPN
ejpam-5971	85	4	ϑm−1	ϑm−1	PROPN
ejpam-5971	85	5	.	.	PUNCT
ejpam-5971	85	6	.	.	PUNCT
ejpam-5971	85	7	.	.	PUNCT
ejpam-5971	86	1	ϑm−1	ϑm−1	PROPN
ejpam-5971	86	2	ϑm−1	ϑm−1	PROPN
ejpam-5971	86	3	ϑm−1	ϑm−1	PROPN
ejpam-5971	86	4	φm−1	φm−1	PROPN
ejpam-5971	86	5	.	.	PUNCT
ejpam-5971	86	6	.	.	PUNCT
ejpam-5971	86	7	.	.	PUNCT
ejpam-5971	87	1	ϑm−1	ϑm−1	PROPN
ejpam-5971	87	2	...	...	PUNCT
ejpam-5971	87	3	...	...	PUNCT
ejpam-5971	87	4	...	...	PUNCT
ejpam-5971	87	5	.	.	PUNCT
ejpam-5971	87	6	.	.	PUNCT
ejpam-5971	87	7	.	.	PUNCT
ejpam-5971	88	1	...	...	PUNCT
ejpam-5971	89	1	ϑm−1	ϑm−1	PROPN
ejpam-5971	89	2	ϑm−1	ϑm−1	PROPN
ejpam-5971	89	3	ϑm−1	ϑm−1	PROPN
ejpam-5971	89	4	.	.	PUNCT
ejpam-5971	89	5	.	.	PUNCT
ejpam-5971	89	6	.	.	PUNCT
ejpam-5971	90	1	φm−1	φm−1	PROPN
ejpam-5971	90	2			PUNCT
ejpam-5971	90	3	c−1	c−1	PROPN
ejpam-5971	90	4	(	(	PUNCT
ejpam-5971	90	5	c0,c1,m	c0,c1,m	PROPN
ejpam-5971	90	6	)	)	PUNCT
ejpam-5971	90	7	=	=	SYM
ejpam-5971	90	8	1	1	NUM
ejpam-5971	90	9	det(c(c0	det(c(c0	PROPN
ejpam-5971	90	10	,	,	PUNCT
ejpam-5971	90	11	c1,m	c1,m	PROPN
ejpam-5971	90	12	)	)	PUNCT
ejpam-5971	90	13	)	)	PUNCT
ejpam-5971	90	14	c(φm−1	c(φm−1	NOUN
ejpam-5971	90	15	,	,	PUNCT
ejpam-5971	90	16	ϑm−1,m	ϑm−1,m	NOUN
ejpam-5971	90	17	)	)	PUNCT
ejpam-5971	90	18	,	,	PUNCT
ejpam-5971	90	19	v.h	v.h	PROPN
ejpam-5971	90	20	.	.	PROPN
ejpam-5971	90	21	krisnawati	krisnawati	PROPN
ejpam-5971	90	22	,	,	PUNCT
ejpam-5971	90	23	n.	n.	PROPN
ejpam-5971	90	24	hidayat	hidayat	PROPN
ejpam-5971	90	25	,	,	PUNCT
ejpam-5971	90	26	a.f	a.f	PROPN
ejpam-5971	90	27	.	.	PROPN
ejpam-5971	90	28	musyarrofah	musyarrofah	PROPN
ejpam-5971	90	29	/	/	SYM
ejpam-5971	90	30	eur	eur	PROPN
ejpam-5971	90	31	.	.	PUNCT
ejpam-5971	91	1	j.	j.	PROPN
ejpam-5971	91	2	pure	pure	PROPN
ejpam-5971	91	3	appl	appl	PROPN
ejpam-5971	91	4	.	.	PROPN
ejpam-5971	91	5	math	math	PROPN
ejpam-5971	91	6	,	,	PUNCT
ejpam-5971	91	7	18	18	NUM
ejpam-5971	91	8	(	(	PUNCT
ejpam-5971	91	9	2	2	NUM
ejpam-5971	91	10	)	)	PUNCT
ejpam-5971	91	11	(	(	PUNCT
ejpam-5971	91	12	2025	2025	NUM
ejpam-5971	91	13	)	)	PUNCT
ejpam-5971	91	14	,	,	PUNCT
ejpam-5971	91	15	5971	5971	NUM
ejpam-5971	91	16	4	4	NUM
ejpam-5971	91	17	of	of	ADP
ejpam-5971	91	18	19	19	NUM
ejpam-5971	91	19	where	where	SCONJ
ejpam-5971	91	20	φm−1	φm−1	PROPN
ejpam-5971	91	21	=	=	PROPN
ejpam-5971	92	1	[	[	X
ejpam-5971	92	2	c0	c0	X
ejpam-5971	92	3	+	+	CCONJ
ejpam-5971	92	4	(	(	PUNCT
ejpam-5971	92	5	m−	m−	PROPN
ejpam-5971	92	6	2)c1](c0	2)c1](c0	NOUN
ejpam-5971	92	7	−	−	PROPN
ejpam-5971	92	8	c1	c1	PROPN
ejpam-5971	92	9	)	)	PUNCT
ejpam-5971	92	10	m−2	m−2	PROPN
ejpam-5971	92	11	and	and	CCONJ
ejpam-5971	92	12	ϑm−1	ϑm−1	PROPN
ejpam-5971	92	13	=	=	SYM
ejpam-5971	92	14	−c1(c0	−c1(c0	PROPN
ejpam-5971	92	15	−	−	PROPN
ejpam-5971	92	16	c1	c1	PROPN
ejpam-5971	92	17	)	)	PUNCT
ejpam-5971	92	18	m−2	m−2	PROPN
ejpam-5971	92	19	.	.	PUNCT
ejpam-5971	93	1	the	the	DET
ejpam-5971	93	2	study	study	NOUN
ejpam-5971	93	3	of	of	ADP
ejpam-5971	93	4	graph	graph	NOUN
ejpam-5971	93	5	energy	energy	NOUN
ejpam-5971	93	6	proposed	propose	VERB
ejpam-5971	93	7	by	by	ADP
ejpam-5971	93	8	gutman	gutman	NOUN
ejpam-5971	93	9	in	in	ADP
ejpam-5971	93	10	1978	1978	NUM
ejpam-5971	93	11	[	[	X
ejpam-5971	93	12	13	13	NUM
ejpam-5971	93	13	]	]	PUNCT
ejpam-5971	93	14	,	,	PUNCT
ejpam-5971	93	15	is	be	AUX
ejpam-5971	93	16	defined	define	VERB
ejpam-5971	93	17	as	as	ADP
ejpam-5971	93	18	:	:	PUNCT
ejpam-5971	93	19	en(g	en(g	NUM
ejpam-5971	93	20	)	)	PUNCT
ejpam-5971	94	1	=	=	SYM
ejpam-5971	94	2	n∑	n∑	PROPN
ejpam-5971	94	3	i=1	i=1	PROPN
ejpam-5971	94	4	|λi|	|λi|	PROPN
ejpam-5971	94	5	,	,	PUNCT
ejpam-5971	94	6	where	where	SCONJ
ejpam-5971	94	7	λi	λi	AUX
ejpam-5971	94	8	represents	represent	VERB
ejpam-5971	94	9	the	the	DET
ejpam-5971	94	10	eigenvalues	eigenvalue	NOUN
ejpam-5971	94	11	of	of	ADP
ejpam-5971	94	12	a(g	a(g	PROPN
ejpam-5971	94	13	)	)	PUNCT
ejpam-5971	94	14	.	.	PUNCT
ejpam-5971	95	1	to	to	PART
ejpam-5971	95	2	further	far	ADV
ejpam-5971	95	3	analyze	analyze	VERB
ejpam-5971	95	4	graph	graph	NOUN
ejpam-5971	95	5	energy	energy	NOUN
ejpam-5971	95	6	,	,	PUNCT
ejpam-5971	95	7	the	the	DET
ejpam-5971	95	8	maclaurin	maclaurin	NOUN
ejpam-5971	95	9	symmetric	symmetric	ADJ
ejpam-5971	95	10	mean	mean	NOUN
ejpam-5971	95	11	inequality	inequality	NOUN
ejpam-5971	95	12	is	be	AUX
ejpam-5971	95	13	used	use	VERB
ejpam-5971	95	14	to	to	PART
ejpam-5971	95	15	establish	establish	VERB
ejpam-5971	95	16	lower	low	ADJ
ejpam-5971	95	17	and	and	CCONJ
ejpam-5971	95	18	upper	upper	ADJ
ejpam-5971	95	19	bounds	bound	NOUN
ejpam-5971	95	20	.	.	PUNCT
ejpam-5971	96	1	proposition	proposition	NOUN
ejpam-5971	96	2	3	3	NUM
ejpam-5971	96	3	.	.	PUNCT
ejpam-5971	97	1	[	[	X
ejpam-5971	97	2	28	28	NUM
ejpam-5971	97	3	]	]	X
ejpam-5971	97	4	let	let	VERB
ejpam-5971	97	5	a1	a1	NOUN
ejpam-5971	97	6	,	,	PUNCT
ejpam-5971	97	7	a2	a2	PROPN
ejpam-5971	97	8	,	,	PUNCT
ejpam-5971	97	9	a3	a3	NOUN
ejpam-5971	97	10	,	,	PUNCT
ejpam-5971	97	11	.	.	PUNCT
ejpam-5971	97	12	.	.	PUNCT
ejpam-5971	98	1	.	.	PUNCT
ejpam-5971	99	1	,	,	PUNCT
ejpam-5971	99	2	as	as	SCONJ
ejpam-5971	99	3	be	be	AUX
ejpam-5971	99	4	a	a	DET
ejpam-5971	99	5	positive	positive	ADJ
ejpam-5971	99	6	real	real	ADJ
ejpam-5971	99	7	numbers	number	NOUN
ejpam-5971	99	8	and	and	CCONJ
ejpam-5971	99	9	the	the	DET
ejpam-5971	99	10	average	average	NOUN
ejpam-5971	99	11	of	of	ADP
ejpam-5971	99	12	the	the	DET
ejpam-5971	99	13	product	product	NOUN
ejpam-5971	99	14	of	of	ADP
ejpam-5971	99	15	all	all	DET
ejpam-5971	99	16	subsets	subset	NOUN
ejpam-5971	99	17	of	of	ADP
ejpam-5971	99	18	order	order	NOUN
ejpam-5971	99	19	k	k	PROPN
ejpam-5971	99	20	represented	represent	VERB
ejpam-5971	99	21	by	by	ADP
ejpam-5971	99	22	∏	∏	PROPN
ejpam-5971	99	23	k	k	PROPN
ejpam-5971	99	24	,	,	PUNCT
ejpam-5971	99	25	where	where	SCONJ
ejpam-5971	99	26	the	the	DET
ejpam-5971	99	27	number	number	NOUN
ejpam-5971	99	28	of	of	ADP
ejpam-5971	99	29	such	such	ADJ
ejpam-5971	99	30	subsets	subset	NOUN
ejpam-5971	99	31	is	be	AUX
ejpam-5971	99	32	given	give	VERB
ejpam-5971	99	33	by	by	ADP
ejpam-5971	99	34	the	the	DET
ejpam-5971	99	35	number	number	NOUN
ejpam-5971	99	36	of	of	ADP
ejpam-5971	99	37	ways	way	NOUN
ejpam-5971	99	38	to	to	PART
ejpam-5971	99	39	choose	choose	VERB
ejpam-5971	99	40	k	k	PROPN
ejpam-5971	99	41	elements	element	NOUN
ejpam-5971	99	42	from	from	ADP
ejpam-5971	99	43	s	s	NOUN
ejpam-5971	99	44	elements	element	NOUN
ejpam-5971	99	45	.	.	PUNCT
ejpam-5971	100	1	the	the	DET
ejpam-5971	100	2	values	value	NOUN
ejpam-5971	100	3	of	of	ADP
ejpam-5971	100	4	∏	∏	PROPN
ejpam-5971	100	5	k	k	X
ejpam-5971	100	6	are	be	AUX
ejpam-5971	100	7	defined	define	VERB
ejpam-5971	100	8	as	as	ADP
ejpam-5971	100	9	follows.∏	follows.∏	NOUN
ejpam-5971	100	10	1	1	NUM
ejpam-5971	100	11	=	=	SYM
ejpam-5971	100	12	a1	a1	NOUN
ejpam-5971	100	13	+	+	CCONJ
ejpam-5971	100	14	a2	a2	PROPN
ejpam-5971	100	15	+	+	CCONJ
ejpam-5971	100	16	a3	a3	NOUN
ejpam-5971	100	17	+	+	X
ejpam-5971	100	18	·	·	PUNCT
ejpam-5971	100	19	·	·	PUNCT
ejpam-5971	100	20	·	·	PUNCT
ejpam-5971	101	1	+	+	CCONJ
ejpam-5971	101	2	as	as	ADP
ejpam-5971	101	3	s	s	PRON
ejpam-5971	101	4	,	,	PUNCT
ejpam-5971	101	5	∏	∏	PROPN
ejpam-5971	101	6	2	2	NUM
ejpam-5971	101	7	=	=	SYM
ejpam-5971	101	8	1	1	NUM
ejpam-5971	101	9	s(s−1	s(s−1	NOUN
ejpam-5971	101	10	)	)	PUNCT
ejpam-5971	101	11	2	2	NUM
ejpam-5971	101	12	(	(	PUNCT
ejpam-5971	101	13	a1a2	a1a2	X
ejpam-5971	101	14	+	+	X
ejpam-5971	101	15	a1a3	a1a3	X
ejpam-5971	101	16	+	+	CCONJ
ejpam-5971	101	17	·	·	PUNCT
ejpam-5971	101	18	·	·	PUNCT
ejpam-5971	101	19	·	·	PUNCT
ejpam-5971	101	20	+	+	CCONJ
ejpam-5971	101	21	a1as	a1as	PUNCT
ejpam-5971	102	1	+	+	CCONJ
ejpam-5971	102	2	a2a3	a2a3	VERB
ejpam-5971	102	3	+	+	X
ejpam-5971	102	4	·	·	PUNCT
ejpam-5971	102	5	·	·	PUNCT
ejpam-5971	102	6	·	·	PUNCT
ejpam-5971	102	7	+	+	NUM
ejpam-5971	102	8	as−1as	as−1as	NUM
ejpam-5971	102	9	)	)	PUNCT
ejpam-5971	102	10	,	,	PUNCT
ejpam-5971	102	11	...	...	PUNCT
ejpam-5971	102	12	∏	∏	PROPN
ejpam-5971	102	13	s	s	PART
ejpam-5971	102	14	=	=	VERB
ejpam-5971	102	15	a1a2a3	a1a2a3	VERB
ejpam-5971	102	16	.	.	PUNCT
ejpam-5971	102	17	.	.	PUNCT
ejpam-5971	102	18	.	.	PUNCT
ejpam-5971	103	1	as	as	ADP
ejpam-5971	103	2	.	.	PUNCT
ejpam-5971	104	1	the	the	DET
ejpam-5971	104	2	maclaurin	maclaurin	ADJ
ejpam-5971	104	3	symmetric	symmetric	ADJ
ejpam-5971	104	4	mean	mean	NOUN
ejpam-5971	104	5	inequality	inequality	NOUN
ejpam-5971	104	6	states	state	VERB
ejpam-5971	104	7	that∏	that∏	ADP
ejpam-5971	104	8	1	1	NUM
ejpam-5971	104	9	≥	≥	NOUN
ejpam-5971	104	10	∏	∏	PROPN
ejpam-5971	104	11	2	2	NUM
ejpam-5971	104	12	1/2	1/2	NUM
ejpam-5971	104	13	≥	≥	NOUN
ejpam-5971	104	14	∏	∏	PROPN
ejpam-5971	104	15	3	3	NUM
ejpam-5971	104	16	1/3	1/3	NUM
ejpam-5971	104	17	≥	≥	NOUN
ejpam-5971	104	18	∏	∏	PROPN
ejpam-5971	104	19	4	4	NUM
ejpam-5971	104	20	1/4	1/4	NUM
ejpam-5971	104	21	≥	≥	NOUN
ejpam-5971	104	22	·	·	PUNCT
ejpam-5971	104	23	·	·	PUNCT
ejpam-5971	104	24	·	·	PUNCT
ejpam-5971	104	25	≥	≥	PUNCT
ejpam-5971	104	26	∏	∏	PROPN
ejpam-5971	104	27	s	s	NOUN
ejpam-5971	104	28	1	1	NUM
ejpam-5971	104	29	/	/	SYM
ejpam-5971	104	30	s	s	PROPN
ejpam-5971	104	31	,	,	PUNCT
ejpam-5971	104	32	(	(	PUNCT
ejpam-5971	104	33	1	1	X
ejpam-5971	104	34	)	)	PUNCT
ejpam-5971	104	35	with	with	ADP
ejpam-5971	104	36	equalities	equality	NOUN
ejpam-5971	104	37	holding	hold	VERB
ejpam-5971	104	38	if	if	SCONJ
ejpam-5971	104	39	and	and	CCONJ
ejpam-5971	104	40	only	only	ADV
ejpam-5971	104	41	if	if	SCONJ
ejpam-5971	104	42	a1	a1	NOUN
ejpam-5971	104	43	=	=	SYM
ejpam-5971	104	44	a2	a2	PROPN
ejpam-5971	104	45	=	=	SYM
ejpam-5971	104	46	a3	a3	PROPN
ejpam-5971	104	47	=	=	SYM
ejpam-5971	104	48	·	·	PUNCT
ejpam-5971	104	49	·	·	PUNCT
ejpam-5971	104	50	·	·	PUNCT
ejpam-5971	105	1	=	=	PUNCT
ejpam-5971	105	2	as	as	SCONJ
ejpam-5971	105	3	we	we	PRON
ejpam-5971	105	4	review	review	VERB
ejpam-5971	105	5	several	several	ADJ
ejpam-5971	105	6	topological	topological	ADJ
ejpam-5971	105	7	indices	index	NOUN
ejpam-5971	105	8	of	of	ADP
ejpam-5971	105	9	graph	graph	NOUN
ejpam-5971	105	10	that	that	PRON
ejpam-5971	105	11	are	be	AUX
ejpam-5971	105	12	used	use	VERB
ejpam-5971	105	13	in	in	ADP
ejpam-5971	105	14	this	this	DET
ejpam-5971	105	15	paper	paper	NOUN
ejpam-5971	105	16	.	.	PUNCT
ejpam-5971	106	1	the	the	DET
ejpam-5971	106	2	wiener	wiener	NOUN
ejpam-5971	106	3	index	index	NOUN
ejpam-5971	106	4	[	[	X
ejpam-5971	106	5	15	15	NUM
ejpam-5971	106	6	]	]	PUNCT
ejpam-5971	106	7	can	can	AUX
ejpam-5971	106	8	be	be	AUX
ejpam-5971	106	9	described	describe	VERB
ejpam-5971	106	10	as	as	ADP
ejpam-5971	106	11	the	the	DET
ejpam-5971	106	12	following	follow	VERB
ejpam-5971	106	13	equation	equation	NOUN
ejpam-5971	106	14	.	.	PUNCT
ejpam-5971	107	1	w(g	w(g	PROPN
ejpam-5971	107	2	)	)	PUNCT
ejpam-5971	108	1	=	=	SYM
ejpam-5971	108	2	1	1	NUM
ejpam-5971	108	3	2	2	NUM
ejpam-5971	108	4	n∑	n∑	NOUN
ejpam-5971	108	5	i=1	i=1	PROPN
ejpam-5971	108	6	n∑	n∑	PROPN
ejpam-5971	109	1	j=1	j=1	PROPN
ejpam-5971	109	2	dij	dij	INTJ
ejpam-5971	109	3	.	.	PUNCT
ejpam-5971	110	1	meanwhile	meanwhile	ADV
ejpam-5971	110	2	,	,	PUNCT
ejpam-5971	110	3	the	the	DET
ejpam-5971	110	4	hyper	hyper	ADJ
ejpam-5971	110	5	-	-	ADJ
ejpam-5971	110	6	wiener	wiener	NOUN
ejpam-5971	110	7	index	index	NOUN
ejpam-5971	110	8	[	[	X
ejpam-5971	110	9	16	16	NUM
ejpam-5971	110	10	]	]	PUNCT
ejpam-5971	110	11	is	be	AUX
ejpam-5971	110	12	defined	define	VERB
ejpam-5971	110	13	as	as	ADP
ejpam-5971	110	14	ww(g	ww(g	NOUN
ejpam-5971	110	15	)	)	PUNCT
ejpam-5971	110	16	=	=	SYM
ejpam-5971	110	17	1	1	NUM
ejpam-5971	110	18	2	2	NUM
ejpam-5971	110	19	w(g	w(g	NUM
ejpam-5971	110	20	)	)	PUNCT
ejpam-5971	111	1	+	+	CCONJ
ejpam-5971	111	2	1	1	NUM
ejpam-5971	111	3	4	4	NUM
ejpam-5971	111	4	n∑	n∑	NOUN
ejpam-5971	111	5	i=1	i=1	PROPN
ejpam-5971	111	6	n∑	n∑	PROPN
ejpam-5971	112	1	j=1	j=1	NOUN
ejpam-5971	112	2	(	(	PUNCT
ejpam-5971	112	3	dij	dij	NOUN
ejpam-5971	112	4	)	)	PUNCT
ejpam-5971	112	5	2	2	NUM
ejpam-5971	112	6	.	.	X
ejpam-5971	113	1	v.h	v.h	PROPN
ejpam-5971	113	2	.	.	PROPN
ejpam-5971	113	3	krisnawati	krisnawati	PROPN
ejpam-5971	113	4	,	,	PUNCT
ejpam-5971	113	5	n.	n.	PROPN
ejpam-5971	113	6	hidayat	hidayat	PROPN
ejpam-5971	113	7	,	,	PUNCT
ejpam-5971	113	8	a.f	a.f	PROPN
ejpam-5971	113	9	.	.	PROPN
ejpam-5971	113	10	musyarrofah	musyarrofah	PROPN
ejpam-5971	113	11	/	/	SYM
ejpam-5971	113	12	eur	eur	PROPN
ejpam-5971	113	13	.	.	PUNCT
ejpam-5971	114	1	j.	j.	PROPN
ejpam-5971	114	2	pure	pure	PROPN
ejpam-5971	114	3	appl	appl	PROPN
ejpam-5971	114	4	.	.	PROPN
ejpam-5971	114	5	math	math	PROPN
ejpam-5971	114	6	,	,	PUNCT
ejpam-5971	114	7	18	18	NUM
ejpam-5971	114	8	(	(	PUNCT
ejpam-5971	114	9	2	2	NUM
ejpam-5971	114	10	)	)	PUNCT
ejpam-5971	114	11	(	(	PUNCT
ejpam-5971	114	12	2025	2025	NUM
ejpam-5971	114	13	)	)	PUNCT
ejpam-5971	114	14	,	,	PUNCT
ejpam-5971	114	15	5971	5971	NUM
ejpam-5971	114	16	5	5	NUM
ejpam-5971	114	17	of	of	ADP
ejpam-5971	114	18	19	19	NUM
ejpam-5971	114	19	the	the	DET
ejpam-5971	114	20	first	first	ADJ
ejpam-5971	114	21	zagreb	zagreb	PROPN
ejpam-5971	114	22	index	index	NOUN
ejpam-5971	114	23	and	and	CCONJ
ejpam-5971	114	24	the	the	DET
ejpam-5971	114	25	second	second	ADJ
ejpam-5971	114	26	zagreb	zagreb	PROPN
ejpam-5971	114	27	index	index	NOUN
ejpam-5971	114	28	[	[	X
ejpam-5971	114	29	17	17	NUM
ejpam-5971	114	30	]	]	PUNCT
ejpam-5971	114	31	are	be	AUX
ejpam-5971	114	32	respectively	respectively	ADV
ejpam-5971	114	33	defined	define	VERB
ejpam-5971	114	34	as	as	ADP
ejpam-5971	114	35	m1(g	m1(g	NOUN
ejpam-5971	114	36	)	)	PUNCT
ejpam-5971	114	37	=	=	SYM
ejpam-5971	114	38	∑	∑	PUNCT
ejpam-5971	114	39	vw∈e(g	vw∈e(g	NUM
ejpam-5971	114	40	)	)	PUNCT
ejpam-5971	115	1	[	[	X
ejpam-5971	115	2	deg(v	deg(v	X
ejpam-5971	115	3	)	)	PUNCT
ejpam-5971	115	4	+	+	SYM
ejpam-5971	115	5	deg(w	deg(w	NUM
ejpam-5971	115	6	)	)	PUNCT
ejpam-5971	115	7	]	]	PUNCT
ejpam-5971	115	8	and	and	CCONJ
ejpam-5971	115	9	m2(g	m2(g	NOUN
ejpam-5971	115	10	)	)	PUNCT
ejpam-5971	115	11	=	=	SYM
ejpam-5971	115	12	∑	∑	PUNCT
ejpam-5971	115	13	vw∈e(g	vw∈e(g	NUM
ejpam-5971	115	14	)	)	PUNCT
ejpam-5971	116	1	[	[	X
ejpam-5971	116	2	deg(v	deg(v	X
ejpam-5971	116	3	)	)	PUNCT
ejpam-5971	116	4	deg(w	deg(w	PROPN
ejpam-5971	116	5	)	)	PUNCT
ejpam-5971	116	6	]	]	PUNCT
ejpam-5971	116	7	.	.	PUNCT
ejpam-5971	117	1	the	the	DET
ejpam-5971	117	2	narumi	narumi	PROPN
ejpam-5971	117	3	-	-	PUNCT
ejpam-5971	117	4	katayama	katayama	NOUN
ejpam-5971	117	5	index	index	NOUN
ejpam-5971	117	6	[	[	X
ejpam-5971	117	7	18	18	NUM
ejpam-5971	117	8	]	]	PUNCT
ejpam-5971	117	9	is	be	AUX
ejpam-5971	117	10	defined	define	VERB
ejpam-5971	117	11	as	as	ADP
ejpam-5971	117	12	nk(g	nk(g	NOUN
ejpam-5971	117	13	)	)	PUNCT
ejpam-5971	117	14	=	=	SYM
ejpam-5971	118	1	∏	∏	PROPN
ejpam-5971	118	2	v∈v	v∈v	NOUN
ejpam-5971	118	3	(	(	PUNCT
ejpam-5971	118	4	g	g	NOUN
ejpam-5971	118	5	)	)	PUNCT
ejpam-5971	118	6	deg(v	deg(v	PROPN
ejpam-5971	118	7	)	)	PUNCT
ejpam-5971	118	8	.	.	PUNCT
ejpam-5971	119	1	3	3	X
ejpam-5971	119	2	.	.	X
ejpam-5971	119	3	energy	energy	NOUN
ejpam-5971	119	4	of	of	ADP
ejpam-5971	119	5	zero	zero	NUM
ejpam-5971	119	6	-	-	PUNCT
ejpam-5971	119	7	divisor	divisor	NOUN
ejpam-5971	119	8	graph	graph	NOUN
ejpam-5971	119	9	of	of	ADP
ejpam-5971	119	10	z℘[x]/⟨x5⟩	z℘[x]/⟨x5⟩	PROPN
ejpam-5971	119	11	in	in	ADP
ejpam-5971	119	12	this	this	DET
ejpam-5971	119	13	section	section	NOUN
ejpam-5971	119	14	,	,	PUNCT
ejpam-5971	119	15	we	we	PRON
ejpam-5971	119	16	discuss	discuss	VERB
ejpam-5971	119	17	the	the	DET
ejpam-5971	119	18	energy	energy	NOUN
ejpam-5971	119	19	of	of	ADP
ejpam-5971	119	20	γ(z℘[x]/⟨x5⟩	γ(z℘[x]/⟨x5⟩	NUM
ejpam-5971	119	21	)	)	PUNCT
ejpam-5971	119	22	.	.	PUNCT
ejpam-5971	120	1	to	to	PART
ejpam-5971	120	2	provide	provide	VERB
ejpam-5971	120	3	a	a	DET
ejpam-5971	120	4	comprehensive	comprehensive	ADJ
ejpam-5971	120	5	understanding	understanding	NOUN
ejpam-5971	120	6	,	,	PUNCT
ejpam-5971	120	7	we	we	PRON
ejpam-5971	120	8	first	first	ADV
ejpam-5971	120	9	revisit	revisit	VERB
ejpam-5971	120	10	essential	essential	ADJ
ejpam-5971	120	11	results	result	NOUN
ejpam-5971	120	12	related	relate	VERB
ejpam-5971	120	13	to	to	ADP
ejpam-5971	120	14	the	the	DET
ejpam-5971	120	15	structure	structure	NOUN
ejpam-5971	120	16	of	of	ADP
ejpam-5971	120	17	γ(z℘[x]/⟨x5⟩	γ(z℘[x]/⟨x5⟩	PROPN
ejpam-5971	120	18	)	)	PUNCT
ejpam-5971	120	19	.	.	PUNCT
ejpam-5971	121	1	next	next	ADV
ejpam-5971	121	2	,	,	PUNCT
ejpam-5971	121	3	we	we	PRON
ejpam-5971	121	4	explore	explore	VERB
ejpam-5971	121	5	the	the	DET
ejpam-5971	121	6	calculation	calculation	NOUN
ejpam-5971	121	7	of	of	ADP
ejpam-5971	121	8	eigenvalues	eigenvalue	NOUN
ejpam-5971	121	9	.	.	PUNCT
ejpam-5971	122	1	following	follow	VERB
ejpam-5971	122	2	this	this	PRON
ejpam-5971	122	3	,	,	PUNCT
ejpam-5971	122	4	we	we	PRON
ejpam-5971	122	5	discuss	discuss	VERB
ejpam-5971	122	6	the	the	DET
ejpam-5971	122	7	lower	low	ADJ
ejpam-5971	122	8	and	and	CCONJ
ejpam-5971	122	9	upper	upper	ADJ
ejpam-5971	122	10	bounds	bound	NOUN
ejpam-5971	122	11	for	for	ADP
ejpam-5971	122	12	graph	graph	NOUN
ejpam-5971	122	13	’s	’s	PART
ejpam-5971	122	14	energy	energy	NOUN
ejpam-5971	122	15	.	.	PUNCT
ejpam-5971	123	1	let	let	VERB
ejpam-5971	123	2	z℘[x	z℘[x	NUM
ejpam-5971	123	3	]	]	PUNCT
ejpam-5971	123	4	be	be	AUX
ejpam-5971	123	5	a	a	DET
ejpam-5971	123	6	polynomial	polynomial	ADJ
ejpam-5971	123	7	commutative	commutative	ADJ
ejpam-5971	123	8	ring	ring	NOUN
ejpam-5971	123	9	and	and	CCONJ
ejpam-5971	123	10	⟨x5⟩	⟨x5⟩	PROPN
ejpam-5971	123	11	be	be	AUX
ejpam-5971	123	12	a	a	DET
ejpam-5971	123	13	principal	principal	ADJ
ejpam-5971	123	14	ideal	ideal	NOUN
ejpam-5971	123	15	of	of	ADP
ejpam-5971	123	16	z℘[x	z℘[x	NUM
ejpam-5971	123	17	]	]	PUNCT
ejpam-5971	123	18	.	.	PUNCT
ejpam-5971	124	1	a	a	DET
ejpam-5971	124	2	quotient	quotient	NOUN
ejpam-5971	124	3	ring	ring	NOUN
ejpam-5971	124	4	z℘[x	z℘[x	PROPN
ejpam-5971	124	5	]	]	PUNCT
ejpam-5971	124	6	is	be	AUX
ejpam-5971	124	7	formed	form	VERB
ejpam-5971	124	8	from	from	ADP
ejpam-5971	124	9	the	the	DET
ejpam-5971	124	10	set	set	NOUN
ejpam-5971	124	11	of	of	ADP
ejpam-5971	124	12	all	all	DET
ejpam-5971	124	13	cosets	coset	NOUN
ejpam-5971	124	14	z℘[x]/⟨x5⟩	z℘[x]/⟨x5⟩	PRON
ejpam-5971	124	15	=	=	PUNCT
ejpam-5971	124	16	{	{	PUNCT
ejpam-5971	124	17	kx4	kx4	NOUN
ejpam-5971	124	18	+	+	CCONJ
ejpam-5971	124	19	lx3	lx3	NOUN
ejpam-5971	124	20	+	+	ADJ
ejpam-5971	124	21	mx2	mx2	NOUN
ejpam-5971	124	22	+	+	CCONJ
ejpam-5971	124	23	nx+	nx+	ADJ
ejpam-5971	124	24	o+	o+	NOUN
ejpam-5971	124	25	⟨x5⟩	⟨x5⟩	PROPN
ejpam-5971	125	1	|	|	ADV
ejpam-5971	125	2	k	k	NOUN
ejpam-5971	125	3	,	,	PUNCT
ejpam-5971	125	4	l	l	PROPN
ejpam-5971	125	5	,	,	PUNCT
ejpam-5971	125	6	m	m	PROPN
ejpam-5971	125	7	,	,	PUNCT
ejpam-5971	125	8	n	n	CCONJ
ejpam-5971	125	9	,	,	PUNCT
ejpam-5971	125	10	o	o	PROPN
ejpam-5971	125	11	∈	∈	PROPN
ejpam-5971	125	12	z℘	z℘	ADV
ejpam-5971	125	13	}	}	PUNCT
ejpam-5971	125	14	.	.	PUNCT
ejpam-5971	126	1	further	far	ADV
ejpam-5971	126	2	,	,	PUNCT
ejpam-5971	126	3	we	we	PRON
ejpam-5971	126	4	write	write	VERB
ejpam-5971	126	5	z℘[x]/⟨x5⟩	z℘[x]/⟨x5⟩	PROPN
ejpam-5971	126	6	as	as	ADP
ejpam-5971	126	7	z℘[x]/⟨x5⟩	z℘[x]/⟨x5⟩	PROPN
ejpam-5971	126	8	=	=	PUNCT
ejpam-5971	126	9	{	{	PUNCT
ejpam-5971	126	10	kx4	kx4	NOUN
ejpam-5971	126	11	+	+	CCONJ
ejpam-5971	126	12	lx3	lx3	NOUN
ejpam-5971	126	13	+	+	ADJ
ejpam-5971	126	14	mx2	mx2	NOUN
ejpam-5971	126	15	+	+	CCONJ
ejpam-5971	126	16	nx+	nx+	ADJ
ejpam-5971	126	17	o	o	NOUN
ejpam-5971	127	1	|	|	CCONJ
ejpam-5971	127	2	k	k	NOUN
ejpam-5971	127	3	,	,	PUNCT
ejpam-5971	127	4	l	l	NOUN
ejpam-5971	127	5	,	,	PUNCT
ejpam-5971	127	6	m	m	PROPN
ejpam-5971	127	7	,	,	PUNCT
ejpam-5971	127	8	n	n	CCONJ
ejpam-5971	127	9	,	,	PUNCT
ejpam-5971	127	10	o	o	PROPN
ejpam-5971	127	11	∈	∈	PROPN
ejpam-5971	127	12	z℘	z℘	ADV
ejpam-5971	127	13	}	}	PUNCT
ejpam-5971	127	14	.	.	PUNCT
ejpam-5971	128	1	the	the	DET
ejpam-5971	128	2	graph	graph	NOUN
ejpam-5971	128	3	γ(z℘[x]/⟨x5⟩	γ(z℘[x]/⟨x5⟩	PROPN
ejpam-5971	128	4	)	)	PUNCT
ejpam-5971	128	5	has	have	VERB
ejpam-5971	128	6	℘4−1	℘4−1	PRON
ejpam-5971	128	7	vertices	vertex	NOUN
ejpam-5971	128	8	and	and	CCONJ
ejpam-5971	128	9	1	1	NUM
ejpam-5971	128	10	2(4	2(4	NUM
ejpam-5971	128	11	℘5−5℘4−℘2	℘5−5℘4−℘2	ADJ
ejpam-5971	128	12	+	+	NOUN
ejpam-5971	128	13	2	2	NUM
ejpam-5971	128	14	)	)	PUNCT
ejpam-5971	128	15	edges	edge	NOUN
ejpam-5971	128	16	.	.	PUNCT
ejpam-5971	129	1	the	the	DET
ejpam-5971	129	2	structure	structure	NOUN
ejpam-5971	129	3	of	of	ADP
ejpam-5971	129	4	this	this	DET
ejpam-5971	129	5	graph	graph	NOUN
ejpam-5971	129	6	was	be	AUX
ejpam-5971	129	7	originally	originally	ADV
ejpam-5971	129	8	defined	define	VERB
ejpam-5971	129	9	by	by	ADP
ejpam-5971	129	10	musyarrofah	musyarrofah	PROPN
ejpam-5971	129	11	et	et	PROPN
ejpam-5971	129	12	al	al	PROPN
ejpam-5971	129	13	.	.	PUNCT
ejpam-5971	130	1	in	in	ADP
ejpam-5971	130	2	[	[	X
ejpam-5971	130	3	24	24	NUM
ejpam-5971	130	4	]	]	PUNCT
ejpam-5971	130	5	.	.	PUNCT
ejpam-5971	131	1	the	the	DET
ejpam-5971	131	2	following	follow	VERB
ejpam-5971	131	3	expression	expression	NOUN
ejpam-5971	131	4	represents	represent	VERB
ejpam-5971	131	5	the	the	DET
ejpam-5971	131	6	vertex	vertex	NOUN
ejpam-5971	131	7	set	set	NOUN
ejpam-5971	131	8	of	of	ADP
ejpam-5971	131	9	γ(z℘[x]/⟨x5⟩	γ(z℘[x]/⟨x5⟩	PROPN
ejpam-5971	131	10	)	)	PUNCT
ejpam-5971	131	11	.	.	PUNCT
ejpam-5971	132	1	a	a	DET
ejpam-5971	132	2	=	=	NOUN
ejpam-5971	132	3	{	{	PUNCT
ejpam-5971	132	4	kx4	kx4	NOUN
ejpam-5971	132	5	+	+	CCONJ
ejpam-5971	132	6	lx3	lx3	NOUN
ejpam-5971	132	7	+	+	ADJ
ejpam-5971	132	8	mx2	mx2	NOUN
ejpam-5971	132	9	+	+	CCONJ
ejpam-5971	132	10	nx	nx	NOUN
ejpam-5971	132	11	|	|	ADV
ejpam-5971	132	12	k	k	NOUN
ejpam-5971	132	13	,	,	PUNCT
ejpam-5971	132	14	l	l	NOUN
ejpam-5971	132	15	,	,	PUNCT
ejpam-5971	132	16	m	m	VERB
ejpam-5971	132	17	∈	∈	ADJ
ejpam-5971	132	18	z℘	z℘	PROPN
ejpam-5971	132	19	,	,	PUNCT
ejpam-5971	132	20	n	n	PROPN
ejpam-5971	132	21	∈	∈	PROPN
ejpam-5971	132	22	z℘	z℘	PROPN
ejpam-5971	132	23	\	\	PROPN
ejpam-5971	132	24	{	{	PUNCT
ejpam-5971	132	25	0̄	0̄	PROPN
ejpam-5971	132	26	}	}	PUNCT
ejpam-5971	132	27	}	}	PUNCT
ejpam-5971	132	28	,	,	PUNCT
ejpam-5971	132	29	|a|	|a|	PROPN
ejpam-5971	132	30	=	=	PUNCT
ejpam-5971	132	31	℘4	℘4	PROPN
ejpam-5971	132	32	−	−	PROPN
ejpam-5971	132	33	℘3	℘3	PROPN
ejpam-5971	132	34	,	,	PUNCT
ejpam-5971	132	35	b	b	X
ejpam-5971	132	36	=	=	PRON
ejpam-5971	132	37	{	{	PUNCT
ejpam-5971	132	38	kx4	kx4	NOUN
ejpam-5971	132	39	+	+	CCONJ
ejpam-5971	132	40	lx3	lx3	NOUN
ejpam-5971	132	41	+	+	ADJ
ejpam-5971	132	42	mx2	mx2	NOUN
ejpam-5971	132	43	|	|	ADV
ejpam-5971	132	44	k	k	NOUN
ejpam-5971	132	45	,	,	PUNCT
ejpam-5971	132	46	l	l	PROPN
ejpam-5971	132	47	∈	∈	PROPN
ejpam-5971	132	48	z℘,m	z℘,m	PROPN
ejpam-5971	132	49	∈	∈	PROPN
ejpam-5971	132	50	z℘	z℘	PROPN
ejpam-5971	132	51	\	\	PROPN
ejpam-5971	132	52	{	{	PUNCT
ejpam-5971	132	53	0̄	0̄	PROPN
ejpam-5971	132	54	}	}	PUNCT
ejpam-5971	132	55	}	}	PUNCT
ejpam-5971	132	56	,	,	PUNCT
ejpam-5971	132	57	|b|	|b|	PROPN
ejpam-5971	132	58	=	=	SYM
ejpam-5971	132	59	℘3	℘3	ADJ
ejpam-5971	132	60	−	−	PROPN
ejpam-5971	132	61	℘2	℘2	PROPN
ejpam-5971	132	62	,	,	PUNCT
ejpam-5971	132	63	c	c	NOUN
ejpam-5971	132	64	=	=	PRON
ejpam-5971	132	65	{	{	PUNCT
ejpam-5971	132	66	kx4	kx4	NOUN
ejpam-5971	132	67	+	+	CCONJ
ejpam-5971	132	68	lx3	lx3	NOUN
ejpam-5971	133	1	|	|	ADV
ejpam-5971	133	2	k	k	PROPN
ejpam-5971	133	3	∈	∈	PROPN
ejpam-5971	133	4	z℘	z℘	PROPN
ejpam-5971	133	5	,	,	PUNCT
ejpam-5971	133	6	l	l	PROPN
ejpam-5971	133	7	∈	∈	PROPN
ejpam-5971	133	8	z℘	z℘	PROPN
ejpam-5971	133	9	\	\	PROPN
ejpam-5971	133	10	{	{	PUNCT
ejpam-5971	133	11	0̄	0̄	PROPN
ejpam-5971	133	12	}	}	PUNCT
ejpam-5971	133	13	}	}	PUNCT
ejpam-5971	133	14	,	,	PUNCT
ejpam-5971	133	15	|c|	|c|	PROPN
ejpam-5971	133	16	=	=	SYM
ejpam-5971	133	17	℘2	℘2	PROPN
ejpam-5971	133	18	−	−	PROPN
ejpam-5971	133	19	℘	℘	NOUN
ejpam-5971	133	20	,	,	PUNCT
ejpam-5971	133	21	d	d	NOUN
ejpam-5971	133	22	=	=	PUNCT
ejpam-5971	133	23	{	{	PUNCT
ejpam-5971	133	24	kx4	kx4	NOUN
ejpam-5971	133	25	|	|	ADV
ejpam-5971	133	26	k	k	PROPN
ejpam-5971	133	27	∈	∈	PROPN
ejpam-5971	133	28	z℘	z℘	PROPN
ejpam-5971	133	29	\	\	PROPN
ejpam-5971	133	30	{	{	PUNCT
ejpam-5971	133	31	0̄	0̄	PROPN
ejpam-5971	133	32	}	}	PUNCT
ejpam-5971	133	33	}	}	PUNCT
ejpam-5971	133	34	,	,	PUNCT
ejpam-5971	133	35	|d|	|d|	PROPN
ejpam-5971	133	36	=	=	SYM
ejpam-5971	133	37	℘−	℘−	NOUN
ejpam-5971	133	38	1	1	NUM
ejpam-5971	133	39	.	.	PUNCT
ejpam-5971	134	1	the	the	DET
ejpam-5971	134	2	adjacency	adjacency	PROPN
ejpam-5971	134	3	matrix	matrix	NOUN
ejpam-5971	134	4	of	of	ADP
ejpam-5971	134	5	γ(z℘[x]/⟨x5⟩	γ(z℘[x]/⟨x5⟩	PROPN
ejpam-5971	134	6	)	)	PUNCT
ejpam-5971	134	7	is	be	AUX
ejpam-5971	134	8	provided	provide	VERB
ejpam-5971	134	9	by	by	ADP
ejpam-5971	134	10	the	the	DET
ejpam-5971	134	11	following	follow	VERB
ejpam-5971	134	12	lemma	lemma	PROPN
ejpam-5971	134	13	lemma	lemma	PROPN
ejpam-5971	134	14	2	2	NUM
ejpam-5971	134	15	.	.	PUNCT
ejpam-5971	135	1	[	[	X
ejpam-5971	135	2	24	24	NUM
ejpam-5971	135	3	]	]	PUNCT
ejpam-5971	135	4	adjacency	adjacency	NOUN
ejpam-5971	135	5	matrix	matrix	NOUN
ejpam-5971	135	6	of	of	ADP
ejpam-5971	135	7	graph	graph	NOUN
ejpam-5971	135	8	g	g	PROPN
ejpam-5971	135	9	∼=	∼=	PROPN
ejpam-5971	135	10	γ(z℘[x]/⟨x5⟩	γ(z℘[x]/⟨x5⟩	NUM
ejpam-5971	135	11	)	)	PUNCT
ejpam-5971	135	12	is	be	AUX
ejpam-5971	135	13	a(g	a(g	PROPN
ejpam-5971	135	14	)	)	PUNCT
ejpam-5971	136	1	=	=	SYM
ejpam-5971	136	2			NOUN
ejpam-5971	137	1	a	a	DET
ejpam-5971	137	2	b	b	X
ejpam-5971	137	3	c	c	NOUN
ejpam-5971	137	4	d	d	NOUN
ejpam-5971	137	5	a	a	DET
ejpam-5971	137	6	o℘4−℘3	o℘4−℘3	NUM
ejpam-5971	137	7	o(℘4−℘3)×(℘3−℘2	o(℘4−℘3)×(℘3−℘2	NUM
ejpam-5971	137	8	)	)	PUNCT
ejpam-5971	137	9	o(℘4−℘3)×(℘2−℘	o(℘4−℘3)×(℘2−℘	NOUN
ejpam-5971	137	10	)	)	PUNCT
ejpam-5971	137	11	n(℘4−℘3)×(℘−1	n(℘4−℘3)×(℘−1	PROPN
ejpam-5971	137	12	)	)	PUNCT
ejpam-5971	137	13	b	b	PROPN
ejpam-5971	137	14	o(℘3−℘2)×(℘4−℘3	o(℘3−℘2)×(℘4−℘3	PROPN
ejpam-5971	137	15	)	)	PUNCT
ejpam-5971	137	16	o℘3−℘2	o℘3−℘2	NUM
ejpam-5971	137	17	n(℘3−℘2)×(℘2−℘	n(℘3−℘2)×(℘2−℘	NOUN
ejpam-5971	137	18	)	)	PUNCT
ejpam-5971	137	19	n(℘3−℘2)×(℘−1	n(℘3−℘2)×(℘−1	PROPN
ejpam-5971	137	20	)	)	PUNCT
ejpam-5971	137	21	c	c	PROPN
ejpam-5971	137	22	o(℘2−℘)×(℘4−℘3	o(℘2−℘)×(℘4−℘3	PROPN
ejpam-5971	137	23	)	)	PUNCT
ejpam-5971	137	24	n(℘2−℘)×(℘3−℘2	n(℘2−℘)×(℘3−℘2	PROPN
ejpam-5971	137	25	)	)	PUNCT
ejpam-5971	137	26	n℘2−℘	n℘2−℘	NOUN
ejpam-5971	138	1	−	−	PROPN
ejpam-5971	138	2	i℘2−℘	i℘2−℘	PROPN
ejpam-5971	138	3	n(℘2−℘)×(℘−1	n(℘2−℘)×(℘−1	PROPN
ejpam-5971	138	4	)	)	PUNCT
ejpam-5971	138	5	d	d	NOUN
ejpam-5971	138	6	n(℘−1)×(℘4−℘3	n(℘−1)×(℘4−℘3	NOUN
ejpam-5971	138	7	)	)	PUNCT
ejpam-5971	138	8	n(℘−1)×(℘3−℘2	n(℘−1)×(℘3−℘2	ADJ
ejpam-5971	138	9	)	)	PUNCT
ejpam-5971	138	10	n(℘−1)×(℘2−℘	n(℘−1)×(℘2−℘	NOUN
ejpam-5971	138	11	)	)	PUNCT
ejpam-5971	138	12	n℘−1	n℘−1	PROPN
ejpam-5971	138	13	−	−	PROPN
ejpam-5971	138	14	i℘−1	i℘−1	PROPN
ejpam-5971	138	15	.	.	PROPN
ejpam-5971	138	16	here	here	ADV
ejpam-5971	138	17	o	o	NOUN
ejpam-5971	138	18	represents	represent	VERB
ejpam-5971	138	19	the	the	DET
ejpam-5971	138	20	zero	zero	NUM
ejpam-5971	138	21	matrix	matrix	NOUN
ejpam-5971	138	22	,	,	PUNCT
ejpam-5971	138	23	n	n	PRON
ejpam-5971	138	24	represents	represent	VERB
ejpam-5971	138	25	the	the	DET
ejpam-5971	138	26	matrix	matrix	NOUN
ejpam-5971	138	27	of	of	ADP
ejpam-5971	138	28	ones	one	NOUN
ejpam-5971	138	29	,	,	PUNCT
ejpam-5971	138	30	and	and	CCONJ
ejpam-5971	138	31	i	i	PRON
ejpam-5971	138	32	represents	represent	VERB
ejpam-5971	138	33	the	the	DET
ejpam-5971	138	34	identity	identity	NOUN
ejpam-5971	138	35	matrix	matrix	NOUN
ejpam-5971	138	36	.	.	PUNCT
ejpam-5971	139	1	v.h	v.h	PROPN
ejpam-5971	139	2	.	.	PROPN
ejpam-5971	139	3	krisnawati	krisnawati	PROPN
ejpam-5971	139	4	,	,	PUNCT
ejpam-5971	139	5	n.	n.	PROPN
ejpam-5971	139	6	hidayat	hidayat	PROPN
ejpam-5971	139	7	,	,	PUNCT
ejpam-5971	139	8	a.f	a.f	PROPN
ejpam-5971	139	9	.	.	PROPN
ejpam-5971	139	10	musyarrofah	musyarrofah	PROPN
ejpam-5971	139	11	/	/	SYM
ejpam-5971	139	12	eur	eur	PROPN
ejpam-5971	139	13	.	.	PUNCT
ejpam-5971	140	1	j.	j.	PROPN
ejpam-5971	140	2	pure	pure	PROPN
ejpam-5971	140	3	appl	appl	PROPN
ejpam-5971	140	4	.	.	PROPN
ejpam-5971	140	5	math	math	PROPN
ejpam-5971	140	6	,	,	PUNCT
ejpam-5971	140	7	18	18	NUM
ejpam-5971	140	8	(	(	PUNCT
ejpam-5971	140	9	2	2	NUM
ejpam-5971	140	10	)	)	PUNCT
ejpam-5971	140	11	(	(	PUNCT
ejpam-5971	140	12	2025	2025	NUM
ejpam-5971	140	13	)	)	PUNCT
ejpam-5971	140	14	,	,	PUNCT
ejpam-5971	140	15	5971	5971	NUM
ejpam-5971	140	16	6	6	NUM
ejpam-5971	140	17	of	of	ADP
ejpam-5971	140	18	19	19	NUM
ejpam-5971	140	19	the	the	DET
ejpam-5971	140	20	eigenvalues	eigenvalue	NOUN
ejpam-5971	140	21	of	of	ADP
ejpam-5971	140	22	γ(z℘[x]/⟨x5⟩	γ(z℘[x]/⟨x5⟩	NUM
ejpam-5971	140	23	)	)	PUNCT
ejpam-5971	140	24	are	be	AUX
ejpam-5971	140	25	provided	provide	VERB
ejpam-5971	140	26	by	by	ADP
ejpam-5971	140	27	the	the	DET
ejpam-5971	140	28	following	follow	VERB
ejpam-5971	140	29	theorem	theorem	PROPN
ejpam-5971	140	30	.	.	PUNCT
ejpam-5971	140	31	theorem	theorem	NOUN
ejpam-5971	140	32	1	1	NUM
ejpam-5971	140	33	.	.	PUNCT
ejpam-5971	141	1	let	let	VERB
ejpam-5971	141	2	g	g	PRON
ejpam-5971	141	3	∼=	∼=	PROPN
ejpam-5971	141	4	γ(z℘[x]/⟨x5⟩	γ(z℘[x]/⟨x5⟩	NUM
ejpam-5971	141	5	)	)	PUNCT
ejpam-5971	141	6	.	.	PUNCT
ejpam-5971	142	1	then	then	ADV
ejpam-5971	142	2	the	the	DET
ejpam-5971	142	3	following	follow	VERB
ejpam-5971	142	4	hold	hold	NOUN
ejpam-5971	142	5	for	for	ADP
ejpam-5971	142	6	g.	g.	PROPN
ejpam-5971	142	7	(	(	PUNCT
ejpam-5971	142	8	i	i	NOUN
ejpam-5971	142	9	)	)	PUNCT
ejpam-5971	142	10	the	the	DET
ejpam-5971	142	11	eigenvalues	eigenvalue	NOUN
ejpam-5971	142	12	of	of	ADP
ejpam-5971	142	13	g	g	PROPN
ejpam-5971	142	14	are	be	AUX
ejpam-5971	142	15	0	0	NUM
ejpam-5971	142	16	,	,	PUNCT
ejpam-5971	142	17	with	with	ADP
ejpam-5971	142	18	multiplicity	multiplicity	NOUN
ejpam-5971	142	19	℘4	℘4	NOUN
ejpam-5971	142	20	−	−	NOUN
ejpam-5971	142	21	℘2	℘2	NOUN
ejpam-5971	142	22	−	−	PROPN
ejpam-5971	142	23	2	2	NUM
ejpam-5971	142	24	,	,	PUNCT
ejpam-5971	142	25	and	and	CCONJ
ejpam-5971	142	26	−1	−1	NOUN
ejpam-5971	142	27	,	,	PUNCT
ejpam-5971	142	28	with	with	ADP
ejpam-5971	142	29	multiplicity	multiplicity	NOUN
ejpam-5971	142	30	℘2	℘2	NOUN
ejpam-5971	142	31	−	−	PROPN
ejpam-5971	142	32	3	3	NUM
ejpam-5971	142	33	.	.	PUNCT
ejpam-5971	142	34	(	(	PUNCT
ejpam-5971	142	35	ii	ii	NOUN
ejpam-5971	142	36	)	)	PUNCT
ejpam-5971	142	37	the	the	DET
ejpam-5971	142	38	other	other	ADJ
ejpam-5971	142	39	eigenvalues	eigenvalue	NOUN
ejpam-5971	142	40	of	of	ADP
ejpam-5971	142	41	g	g	PROPN
ejpam-5971	142	42	are	be	AUX
ejpam-5971	142	43	solutions	solution	NOUN
ejpam-5971	142	44	to	to	ADP
ejpam-5971	142	45	the	the	DET
ejpam-5971	142	46	following	follow	VERB
ejpam-5971	142	47	polynomial	polynomial	ADJ
ejpam-5971	142	48	λ4	λ4	PROPN
ejpam-5971	142	49	−	−	PROPN
ejpam-5971	142	50	(	(	PUNCT
ejpam-5971	142	51	℘2	℘2	NOUN
ejpam-5971	142	52	−	−	PROPN
ejpam-5971	142	53	3	3	NUM
ejpam-5971	142	54	)	)	PUNCT
ejpam-5971	142	55	λ3	λ3	PROPN
ejpam-5971	142	56	−	−	PROPN
ejpam-5971	142	57	(	(	PUNCT
ejpam-5971	142	58	2℘5	2℘5	NUM
ejpam-5971	142	59	−	−	NUM
ejpam-5971	142	60	3℘4	3℘4	NUM
ejpam-5971	142	61	+	+	SYM
ejpam-5971	142	62	2℘2	2℘2	NUM
ejpam-5971	142	63	−	−	NUM
ejpam-5971	142	64	2	2	NUM
ejpam-5971	142	65	)	)	PUNCT
ejpam-5971	142	66	λ2	λ2	PROPN
ejpam-5971	142	67	+	+	CCONJ
ejpam-5971	142	68	℘3	℘3	ADJ
ejpam-5971	142	69	(	(	PUNCT
ejpam-5971	142	70	℘3	℘3	ADJ
ejpam-5971	142	71	−	−	PROPN
ejpam-5971	142	72	℘2	℘2	NOUN
ejpam-5971	142	73	−	−	PROPN
ejpam-5971	142	74	2℘−	2℘−	NUM
ejpam-5971	142	75	1	1	NUM
ejpam-5971	142	76	)	)	PUNCT
ejpam-5971	142	77	(	(	PUNCT
ejpam-5971	142	78	℘−	℘−	NOUN
ejpam-5971	142	79	1)2λ+	1)2λ+	NUM
ejpam-5971	142	80	℘6(℘−	℘6(℘−	NOUN
ejpam-5971	142	81	1)4	1)4	NOUN
ejpam-5971	142	82	=	=	SYM
ejpam-5971	142	83	0	0	X
ejpam-5971	142	84	.	.	PUNCT
ejpam-5971	143	1	proof	proof	NOUN
ejpam-5971	143	2	.	.	PUNCT
ejpam-5971	144	1	suppose	suppose	VERB
ejpam-5971	144	2	that	that	SCONJ
ejpam-5971	144	3	λ	λ	NOUN
ejpam-5971	144	4	be	be	VERB
ejpam-5971	144	5	the	the	DET
ejpam-5971	144	6	eigenvalues	eigenvalue	NOUN
ejpam-5971	144	7	of	of	ADP
ejpam-5971	144	8	g	g	NOUN
ejpam-5971	144	9	∼=	∼=	PROPN
ejpam-5971	144	10	γ(z℘[x]/⟨x5⟩	γ(z℘[x]/⟨x5⟩	NUM
ejpam-5971	144	11	)	)	PUNCT
ejpam-5971	144	12	.	.	PUNCT
ejpam-5971	145	1	based	base	VERB
ejpam-5971	145	2	on	on	ADP
ejpam-5971	145	3	lemma	lemma	PROPN
ejpam-5971	145	4	2	2	NUM
ejpam-5971	145	5	has	have	AUX
ejpam-5971	145	6	been	be	AUX
ejpam-5971	145	7	obtained	obtain	VERB
ejpam-5971	145	8	adjacency	adjacency	NOUN
ejpam-5971	145	9	matrix	matrix	NOUN
ejpam-5971	145	10	of	of	ADP
ejpam-5971	145	11	a	a	DET
ejpam-5971	145	12	graph	graph	NOUN
ejpam-5971	145	13	g	g	NOUN
ejpam-5971	145	14	,	,	PUNCT
ejpam-5971	145	15	then	then	ADV
ejpam-5971	145	16	the	the	DET
ejpam-5971	145	17	matrix	matrix	NOUN
ejpam-5971	145	18	a(g	a(g	PROPN
ejpam-5971	145	19	)	)	PUNCT
ejpam-5971	145	20	−	−	PROPN
ejpam-5971	146	1	λi	λi	INTJ
ejpam-5971	146	2	can	can	AUX
ejpam-5971	146	3	be	be	AUX
ejpam-5971	146	4	expressed	express	VERB
ejpam-5971	146	5	as	as	ADP
ejpam-5971	146	6	:	:	PUNCT
ejpam-5971	146	7	a(g)−	a(g)−	NOUN
ejpam-5971	146	8	λi	λi	ADP
ejpam-5971	146	9	=	=	NOUN
ejpam-5971	146	10			NOUN
ejpam-5971	146	11	c(−λ	c(−λ	NOUN
ejpam-5971	146	12	,	,	PUNCT
ejpam-5971	146	13	0,℘4−℘3	0,℘4−℘3	PROPN
ejpam-5971	146	14	)	)	PUNCT
ejpam-5971	146	15	o(℘4−℘3)×(℘3−℘2	o(℘4−℘3)×(℘3−℘2	NUM
ejpam-5971	146	16	)	)	PUNCT
ejpam-5971	146	17	o(℘4−℘3)×(℘2−℘	o(℘4−℘3)×(℘2−℘	NOUN
ejpam-5971	146	18	)	)	PUNCT
ejpam-5971	146	19	n(℘4−℘3)×(℘−1	n(℘4−℘3)×(℘−1	ADJ
ejpam-5971	146	20	)	)	PUNCT
ejpam-5971	146	21	o(℘3−℘2)×(℘4−℘3	o(℘3−℘2)×(℘4−℘3	PROPN
ejpam-5971	146	22	)	)	PUNCT
ejpam-5971	146	23	c(−λ	c(−λ	NOUN
ejpam-5971	146	24	,	,	PUNCT
ejpam-5971	146	25	0,℘3−℘2	0,℘3−℘2	PROPN
ejpam-5971	146	26	)	)	PUNCT
ejpam-5971	146	27	n(℘3−℘2)×(℘2−℘	n(℘3−℘2)×(℘2−℘	NOUN
ejpam-5971	146	28	)	)	PUNCT
ejpam-5971	146	29	n(℘3−℘2)×(℘−1	n(℘3−℘2)×(℘−1	PROPN
ejpam-5971	146	30	)	)	PUNCT
ejpam-5971	146	31	o(℘2−℘)×(℘4−℘3	o(℘2−℘)×(℘4−℘3	PROPN
ejpam-5971	146	32	)	)	PUNCT
ejpam-5971	146	33	n(℘2−℘)×(℘3−℘2	n(℘2−℘)×(℘3−℘2	PROPN
ejpam-5971	146	34	)	)	PUNCT
ejpam-5971	146	35	c(−λ	c(−λ	NOUN
ejpam-5971	146	36	,	,	PUNCT
ejpam-5971	146	37	1,℘2−℘	1,℘2−℘	NUM
ejpam-5971	146	38	)	)	PUNCT
ejpam-5971	146	39	n(℘2−℘)×(℘−1	n(℘2−℘)×(℘−1	PROPN
ejpam-5971	146	40	)	)	PUNCT
ejpam-5971	146	41	n(℘−1)×(℘4−℘3	n(℘−1)×(℘4−℘3	NOUN
ejpam-5971	146	42	)	)	PUNCT
ejpam-5971	146	43	n(℘−1)×(℘3−℘2	n(℘−1)×(℘3−℘2	ADJ
ejpam-5971	146	44	)	)	PUNCT
ejpam-5971	146	45	n(℘−1)×(℘2−℘	n(℘−1)×(℘2−℘	NOUN
ejpam-5971	146	46	)	)	PUNCT
ejpam-5971	146	47	c(−λ	c(−λ	NOUN
ejpam-5971	146	48	,	,	PUNCT
ejpam-5971	146	49	1,℘−1	1,℘−1	NUM
ejpam-5971	146	50	)	)	PUNCT
ejpam-5971	146	51			NOUN
ejpam-5971	146	52	=	=	PUNCT
ejpam-5971	146	53	[	[	PUNCT
ejpam-5971	146	54	p	p	X
ejpam-5971	146	55	q	q	X
ejpam-5971	146	56	r	r	NOUN
ejpam-5971	146	57	s	s	X
ejpam-5971	146	58	]	]	PUNCT
ejpam-5971	146	59	.	.	PUNCT
ejpam-5971	147	1	if	if	SCONJ
ejpam-5971	147	2	λ	λ	PROPN
ejpam-5971	147	3	̸=	̸=	PROPN
ejpam-5971	147	4	0	0	NUM
ejpam-5971	147	5	,	,	PUNCT
ejpam-5971	147	6	then	then	ADV
ejpam-5971	147	7	p	p	NOUN
ejpam-5971	147	8	is	be	AUX
ejpam-5971	147	9	invertible	invertible	ADJ
ejpam-5971	147	10	and	and	CCONJ
ejpam-5971	147	11	according	accord	VERB
ejpam-5971	147	12	to	to	ADP
ejpam-5971	147	13	lemma	lemma	PROPN
ejpam-5971	147	14	1	1	NUM
ejpam-5971	147	15	,	,	PUNCT
ejpam-5971	147	16	the	the	DET
ejpam-5971	147	17	determinant	determinant	NOUN
ejpam-5971	147	18	of	of	ADP
ejpam-5971	147	19	a(g)−	a(g)−	NOUN
ejpam-5971	147	20	λi	λi	VERB
ejpam-5971	147	21	is	be	AUX
ejpam-5971	147	22	given	give	VERB
ejpam-5971	147	23	by	by	ADP
ejpam-5971	147	24	det(a(g)−	det(a(g)−	NOUN
ejpam-5971	147	25	λi	λi	NUM
ejpam-5971	147	26	)	)	PUNCT
ejpam-5971	147	27	=	=	SYM
ejpam-5971	147	28	det(p	det(p	NOUN
ejpam-5971	147	29	)	)	PUNCT
ejpam-5971	147	30	·	·	PUNCT
ejpam-5971	148	1	det(s	det(s	PROPN
ejpam-5971	148	2	−rp−1q	−rp−1q	PROPN
ejpam-5971	148	3	)	)	PUNCT
ejpam-5971	148	4	.	.	PUNCT
ejpam-5971	149	1	since	since	SCONJ
ejpam-5971	149	2	p	p	NOUN
ejpam-5971	149	3	is	be	AUX
ejpam-5971	149	4	a	a	DET
ejpam-5971	149	5	diagonal	diagonal	ADJ
ejpam-5971	149	6	matrix	matrix	NOUN
ejpam-5971	149	7	,	,	PUNCT
ejpam-5971	149	8	its	its	PRON
ejpam-5971	149	9	determinant	determinant	ADJ
ejpam-5971	149	10	is	be	AUX
ejpam-5971	149	11	det(p	det(p	NOUN
ejpam-5971	149	12	)	)	PUNCT
ejpam-5971	150	1	=	=	SYM
ejpam-5971	150	2	(	(	PUNCT
ejpam-5971	150	3	−λ)℘	−λ)℘	X
ejpam-5971	150	4	4−℘2	4−℘2	NOUN
ejpam-5971	150	5	.	.	PUNCT
ejpam-5971	151	1	(	(	PUNCT
ejpam-5971	151	2	2	2	X
ejpam-5971	151	3	)	)	PUNCT
ejpam-5971	151	4	moreover	moreover	ADV
ejpam-5971	151	5	,	,	PUNCT
ejpam-5971	151	6	because	because	SCONJ
ejpam-5971	151	7	p	p	NOUN
ejpam-5971	151	8	can	can	AUX
ejpam-5971	151	9	be	be	AUX
ejpam-5971	151	10	written	write	VERB
ejpam-5971	151	11	as	as	ADP
ejpam-5971	151	12	circulant	circulant	ADJ
ejpam-5971	151	13	matrix	matrix	NOUN
ejpam-5971	151	14	c(−λ	c(−λ	NOUN
ejpam-5971	151	15	,	,	PUNCT
ejpam-5971	151	16	0,℘4−℘2	0,℘4−℘2	PROPN
ejpam-5971	151	17	)	)	PUNCT
ejpam-5971	151	18	,	,	PUNCT
ejpam-5971	151	19	its	its	PRON
ejpam-5971	151	20	inverse	inverse	NOUN
ejpam-5971	151	21	can	can	AUX
ejpam-5971	151	22	be	be	AUX
ejpam-5971	151	23	computed	compute	VERB
ejpam-5971	151	24	using	use	VERB
ejpam-5971	151	25	proposition	proposition	NOUN
ejpam-5971	151	26	2	2	NUM
ejpam-5971	151	27	,	,	PUNCT
ejpam-5971	151	28	that	that	PRON
ejpam-5971	151	29	is	be	AUX
ejpam-5971	151	30	p−1	p−1	PROPN
ejpam-5971	151	31	=	=	SYM
ejpam-5971	151	32	1	1	NUM
ejpam-5971	151	33	(	(	PUNCT
ejpam-5971	151	34	−λ)℘	−λ)℘	X
ejpam-5971	151	35	4−℘2c	4−℘2c	NOUN
ejpam-5971	151	36	(	(	PUNCT
ejpam-5971	151	37	(	(	PUNCT
ejpam-5971	151	38	−λ	−λ	NOUN
ejpam-5971	151	39	)	)	PUNCT
ejpam-5971	151	40	℘4	℘4	NOUN
ejpam-5971	151	41	−℘2	−℘2	PROPN
ejpam-5971	151	42	−1	−1	NOUN
ejpam-5971	151	43	,	,	PUNCT
ejpam-5971	151	44	0,℘4−℘2	0,℘4−℘2	PROPN
ejpam-5971	151	45	)	)	PUNCT
ejpam-5971	152	1	=	=	SYM
ejpam-5971	152	2	(	(	PUNCT
ejpam-5971	152	3	−λ)℘	−λ)℘	X
ejpam-5971	152	4	4−℘2−1	4−℘2−1	PRON
ejpam-5971	152	5	(	(	PUNCT
ejpam-5971	152	6	−λ)℘	−λ)℘	X
ejpam-5971	152	7	4−℘2	4−℘2	NOUN
ejpam-5971	152	8	i℘4−℘2	i℘4−℘2	NUM
ejpam-5971	153	1	=	=	SYM
ejpam-5971	153	2	−	−	PROPN
ejpam-5971	153	3	1	1	NUM
ejpam-5971	153	4	λ	λ	NOUN
ejpam-5971	153	5	i℘4−℘2	i℘4−℘2	NUM
ejpam-5971	153	6	,	,	PUNCT
ejpam-5971	153	7	substituting	substitute	VERB
ejpam-5971	153	8	this	this	DET
ejpam-5971	153	9	inverse	inverse	NOUN
ejpam-5971	153	10	into	into	ADP
ejpam-5971	153	11	rp−1q	rp−1q	PROPN
ejpam-5971	153	12	,	,	PUNCT
ejpam-5971	153	13	we	we	PRON
ejpam-5971	153	14	find	find	VERB
ejpam-5971	153	15	rp−1q	rp−1q	NOUN
ejpam-5971	153	16	=	=	PUNCT
ejpam-5971	153	17	−	−	PROPN
ejpam-5971	153	18	1	1	NUM
ejpam-5971	153	19	λ	λ	PROPN
ejpam-5971	153	20	[	[	PUNCT
ejpam-5971	153	21	(	(	PUNCT
ejpam-5971	153	22	℘3	℘3	ADJ
ejpam-5971	153	23	−	−	NOUN
ejpam-5971	153	24	℘2)n℘2−℘	℘2)n℘2−℘	NOUN
ejpam-5971	153	25	(	(	PUNCT
ejpam-5971	153	26	℘3	℘3	ADJ
ejpam-5971	153	27	−	−	ADP
ejpam-5971	153	28	℘2)n(℘2−℘)×(℘−1	℘2)n(℘2−℘)×(℘−1	NUM
ejpam-5971	153	29	)	)	PUNCT
ejpam-5971	153	30	(	(	PUNCT
ejpam-5971	153	31	℘3	℘3	ADV
ejpam-5971	153	32	−	−	ADP
ejpam-5971	153	33	℘2)n(℘−1)×(℘2−℘	℘2)n(℘−1)×(℘2−℘	PROPN
ejpam-5971	153	34	)	)	PUNCT
ejpam-5971	153	35	(	(	PUNCT
ejpam-5971	153	36	℘4	℘4	VERB
ejpam-5971	153	37	−	−	NOUN
ejpam-5971	153	38	℘2)n℘−1	℘2)n℘−1	PROPN
ejpam-5971	153	39	]	]	PUNCT
ejpam-5971	153	40	,	,	PUNCT
ejpam-5971	153	41	v.h	v.h	PROPN
ejpam-5971	153	42	.	.	PROPN
ejpam-5971	153	43	krisnawati	krisnawati	PROPN
ejpam-5971	153	44	,	,	PUNCT
ejpam-5971	153	45	n.	n.	PROPN
ejpam-5971	153	46	hidayat	hidayat	PROPN
ejpam-5971	153	47	,	,	PUNCT
ejpam-5971	153	48	a.f	a.f	PROPN
ejpam-5971	153	49	.	.	PROPN
ejpam-5971	153	50	musyarrofah	musyarrofah	PROPN
ejpam-5971	153	51	/	/	SYM
ejpam-5971	153	52	eur	eur	PROPN
ejpam-5971	153	53	.	.	PUNCT
ejpam-5971	154	1	j.	j.	PROPN
ejpam-5971	154	2	pure	pure	PROPN
ejpam-5971	154	3	appl	appl	PROPN
ejpam-5971	154	4	.	.	PROPN
ejpam-5971	154	5	math	math	PROPN
ejpam-5971	154	6	,	,	PUNCT
ejpam-5971	154	7	18	18	NUM
ejpam-5971	154	8	(	(	PUNCT
ejpam-5971	154	9	2	2	NUM
ejpam-5971	154	10	)	)	PUNCT
ejpam-5971	154	11	(	(	PUNCT
ejpam-5971	154	12	2025	2025	NUM
ejpam-5971	154	13	)	)	PUNCT
ejpam-5971	154	14	,	,	PUNCT
ejpam-5971	154	15	5971	5971	NUM
ejpam-5971	154	16	7	7	NUM
ejpam-5971	154	17	of	of	ADP
ejpam-5971	154	18	19	19	NUM
ejpam-5971	154	19	thus	thus	ADV
ejpam-5971	154	20	,	,	PUNCT
ejpam-5971	154	21	s	s	AUX
ejpam-5971	154	22	−rp−1q	−rp−1q	PROPN
ejpam-5971	154	23	becomes	become	VERB
ejpam-5971	154	24	s	s	PROPN
ejpam-5971	154	25	−rp−1q	−rp−1q	PROPN
ejpam-5971	154	26	=	=	SYM
ejpam-5971	154	27	c(−λ+	c(−λ+	PROPN
ejpam-5971	154	28	b	b	PROPN
ejpam-5971	154	29	λ	λ	PROPN
ejpam-5971	154	30	,	,	PUNCT
ejpam-5971	154	31	1	1	NUM
ejpam-5971	154	32	+	+	SYM
ejpam-5971	154	33	b	b	PROPN
ejpam-5971	154	34	λ	λ	PROPN
ejpam-5971	154	35	,	,	PUNCT
ejpam-5971	154	36	c	c	NOUN
ejpam-5971	154	37	)	)	PUNCT
ejpam-5971	154	38	(	(	PUNCT
ejpam-5971	154	39	1	1	NUM
ejpam-5971	154	40	+	+	NUM
ejpam-5971	154	41	b	b	PROPN
ejpam-5971	154	42	λ	λ	PROPN
ejpam-5971	154	43	)	)	PUNCT
ejpam-5971	154	44	nc×d	nc×d	PROPN
ejpam-5971	154	45	(	(	PUNCT
ejpam-5971	154	46	1	1	NUM
ejpam-5971	154	47	+	+	NUM
ejpam-5971	154	48	b	b	PROPN
ejpam-5971	154	49	λ	λ	NOUN
ejpam-5971	154	50	)	)	PUNCT
ejpam-5971	154	51	nd×c	nd×c	ADP
ejpam-5971	154	52	c(−λ+	c(−λ+	NOUN
ejpam-5971	154	53	a	a	DET
ejpam-5971	154	54	λ	λ	PROPN
ejpam-5971	154	55	,	,	PUNCT
ejpam-5971	154	56	1	1	NUM
ejpam-5971	154	57	+	+	CCONJ
ejpam-5971	154	58	a	a	DET
ejpam-5971	154	59	λ	λ	PROPN
ejpam-5971	154	60	,	,	PUNCT
ejpam-5971	154	61	d	d	NOUN
ejpam-5971	154	62	)	)	PUNCT
ejpam-5971	154	63			NOUN
ejpam-5971	154	64	=	=	PUNCT
ejpam-5971	155	1	[	[	PUNCT
ejpam-5971	155	2	x1	x1	NOUN
ejpam-5971	155	3	y	y	PROPN
ejpam-5971	155	4	y	y	PROPN
ejpam-5971	155	5	t	t	PROPN
ejpam-5971	155	6	x2	x2	X
ejpam-5971	155	7	]	]	PUNCT
ejpam-5971	155	8	,	,	PUNCT
ejpam-5971	155	9	where	where	SCONJ
ejpam-5971	155	10	a	a	DET
ejpam-5971	155	11	=	=	X
ejpam-5971	155	12	℘4	℘4	NOUN
ejpam-5971	155	13	−	−	PROPN
ejpam-5971	155	14	℘2	℘2	PROPN
ejpam-5971	155	15	,	,	PUNCT
ejpam-5971	155	16	b	b	NOUN
ejpam-5971	155	17	=	=	SYM
ejpam-5971	155	18	℘3	℘3	ADJ
ejpam-5971	155	19	−	−	PROPN
ejpam-5971	155	20	℘2	℘2	PROPN
ejpam-5971	155	21	,	,	PUNCT
ejpam-5971	155	22	c	c	NOUN
ejpam-5971	155	23	=	=	SYM
ejpam-5971	155	24	℘2	℘2	PROPN
ejpam-5971	155	25	−	−	PROPN
ejpam-5971	155	26	℘	℘	PROPN
ejpam-5971	155	27	,	,	PUNCT
ejpam-5971	155	28	dan	dan	PROPN
ejpam-5971	155	29	d	d	PROPN
ejpam-5971	155	30	=	=	PROPN
ejpam-5971	155	31	℘−	℘−	NOUN
ejpam-5971	155	32	1	1	NUM
ejpam-5971	155	33	.	.	PUNCT
ejpam-5971	155	34	applying	apply	VERB
ejpam-5971	155	35	lemma	lemma	PROPN
ejpam-5971	155	36	1	1	NUM
ejpam-5971	155	37	once	once	ADV
ejpam-5971	155	38	again	again	ADV
ejpam-5971	155	39	,	,	PUNCT
ejpam-5971	155	40	det(s	det(s	PROPN
ejpam-5971	155	41	−rp−1q	−rp−1q	PROPN
ejpam-5971	155	42	)	)	PUNCT
ejpam-5971	155	43	=	=	PUNCT
ejpam-5971	156	1	det(x1	det(x1	ADJ
ejpam-5971	156	2	)	)	PUNCT
ejpam-5971	156	3	·	·	PUNCT
ejpam-5971	157	1	det(x2	det(x2	NOUN
ejpam-5971	157	2	−	−	PROPN
ejpam-5971	157	3	y	y	PROPN
ejpam-5971	157	4	tx−1	tx−1	PROPN
ejpam-5971	157	5	1	1	NUM
ejpam-5971	157	6	y	y	PROPN
ejpam-5971	157	7	)	)	PUNCT
ejpam-5971	157	8	.	.	PUNCT
ejpam-5971	158	1	by	by	ADP
ejpam-5971	158	2	proposition	proposition	NOUN
ejpam-5971	158	3	1	1	NUM
ejpam-5971	158	4	,	,	PUNCT
ejpam-5971	158	5	it	it	PRON
ejpam-5971	158	6	can	can	AUX
ejpam-5971	158	7	be	be	AUX
ejpam-5971	158	8	seen	see	VERB
ejpam-5971	158	9	that	that	SCONJ
ejpam-5971	158	10	det(x1	det(x1	ADJ
ejpam-5971	158	11	)	)	PUNCT
ejpam-5971	158	12	=	=	SYM
ejpam-5971	158	13	(	(	PUNCT
ejpam-5971	158	14	−λ−	−λ−	X
ejpam-5971	158	15	1)c−1	1)c−1	NUM
ejpam-5971	158	16	f(λ	f(λ	NOUN
ejpam-5971	158	17	)	)	PUNCT
ejpam-5971	158	18	,	,	PUNCT
ejpam-5971	158	19	(	(	PUNCT
ejpam-5971	158	20	3	3	X
ejpam-5971	158	21	)	)	PUNCT
ejpam-5971	158	22	where	where	SCONJ
ejpam-5971	158	23	f(λ	f(λ	NOUN
ejpam-5971	158	24	)	)	PUNCT
ejpam-5971	158	25	=	=	SYM
ejpam-5971	158	26	−λ2+(c−1)λ+cb	−λ2+(c−1)λ+cb	PROPN
ejpam-5971	158	27	λ	λ	PROPN
ejpam-5971	158	28	.	.	PUNCT
ejpam-5971	159	1	also	also	ADV
ejpam-5971	159	2	by	by	ADP
ejpam-5971	159	3	proposition	proposition	NOUN
ejpam-5971	159	4	2	2	NUM
ejpam-5971	159	5	,	,	PUNCT
ejpam-5971	159	6	x−1	x−1	PROPN
ejpam-5971	159	7	1	1	NUM
ejpam-5971	159	8	=	=	SYM
ejpam-5971	159	9	1	1	NUM
ejpam-5971	159	10	(	(	PUNCT
ejpam-5971	159	11	−λ−	−λ−	NOUN
ejpam-5971	159	12	1)c−1	1)c−1	NUM
ejpam-5971	159	13	f(λ	f(λ	NOUN
ejpam-5971	159	14	)	)	PUNCT
ejpam-5971	159	15	c(φc−1	c(φc−1	NUM
ejpam-5971	159	16	,	,	PUNCT
ejpam-5971	159	17	ϑc−1	ϑc−1	NOUN
ejpam-5971	159	18	,	,	PUNCT
ejpam-5971	159	19	c	c	NOUN
ejpam-5971	159	20	)	)	PUNCT
ejpam-5971	159	21	,	,	PUNCT
ejpam-5971	159	22	where	where	SCONJ
ejpam-5971	159	23	φc−1	φc−1	PROPN
ejpam-5971	159	24	=	=	PUNCT
ejpam-5971	159	25	(	(	PUNCT
ejpam-5971	159	26	−λ+	−λ+	NOUN
ejpam-5971	159	27	c−	c−	X
ejpam-5971	159	28	2	2	NUM
ejpam-5971	159	29	+	+	NUM
ejpam-5971	159	30	cb−b	cb−b	NOUN
ejpam-5971	159	31	λ	λ	PROPN
ejpam-5971	159	32	)	)	PUNCT
ejpam-5971	159	33	(	(	PUNCT
ejpam-5971	159	34	−λ−	−λ−	NOUN
ejpam-5971	159	35	1)c−2	1)c−2	NUM
ejpam-5971	159	36	and	and	CCONJ
ejpam-5971	159	37	ϑc−1	ϑc−1	PROPN
ejpam-5971	159	38	=	=	SYM
ejpam-5971	159	39	(	(	PUNCT
ejpam-5971	159	40	−1−	−1−	PROPN
ejpam-5971	159	41	b	b	PROPN
ejpam-5971	159	42	λ	λ	PROPN
ejpam-5971	159	43	)	)	PUNCT
ejpam-5971	159	44	(	(	PUNCT
ejpam-5971	159	45	−λ−	−λ−	NOUN
ejpam-5971	159	46	1)c−2	1)c−2	NUM
ejpam-5971	159	47	.	.	PUNCT
ejpam-5971	160	1	let	let	VERB
ejpam-5971	160	2	g(λ	g(λ	PROPN
ejpam-5971	160	3	)	)	PUNCT
ejpam-5971	161	1	=	=	SYM
ejpam-5971	161	2	−λ+	−λ+	NOUN
ejpam-5971	161	3	c−	c−	NOUN
ejpam-5971	161	4	2	2	NUM
ejpam-5971	161	5	+	+	SYM
ejpam-5971	161	6	cb−	cb−	PROPN
ejpam-5971	161	7	b	b	NOUN
ejpam-5971	161	8	λ	λ	PROPN
ejpam-5971	161	9	,	,	PUNCT
ejpam-5971	161	10	and	and	CCONJ
ejpam-5971	161	11	h(λ	h(λ	NOUN
ejpam-5971	161	12	)	)	PUNCT
ejpam-5971	162	1	=	=	PUNCT
ejpam-5971	163	1	−1−	−1−	PROPN
ejpam-5971	163	2	b	b	PROPN
ejpam-5971	163	3	λ	λ	PROPN
ejpam-5971	163	4	.	.	PUNCT
ejpam-5971	164	1	then	then	ADV
ejpam-5971	164	2	φc−1	φc−1	PROPN
ejpam-5971	164	3	=	=	PUNCT
ejpam-5971	164	4	(	(	PUNCT
ejpam-5971	164	5	−λ−	−λ−	NOUN
ejpam-5971	164	6	1)c−2g(λ	1)c−2g(λ	NUM
ejpam-5971	164	7	)	)	PUNCT
ejpam-5971	164	8	and	and	CCONJ
ejpam-5971	164	9	ϑc−1	ϑc−1	NOUN
ejpam-5971	164	10	=	=	SYM
ejpam-5971	164	11	(	(	PUNCT
ejpam-5971	164	12	−λ−	−λ−	NOUN
ejpam-5971	164	13	1)c−2h(λ	1)c−2h(λ	NUM
ejpam-5971	164	14	)	)	PUNCT
ejpam-5971	164	15	.	.	PUNCT
ejpam-5971	165	1	thus	thus	ADV
ejpam-5971	165	2	,	,	PUNCT
ejpam-5971	165	3	x−1	x−1	PROPN
ejpam-5971	165	4	1	1	NUM
ejpam-5971	165	5	=	=	SYM
ejpam-5971	165	6	1	1	NUM
ejpam-5971	165	7	(	(	PUNCT
ejpam-5971	165	8	−λ−	−λ−	NOUN
ejpam-5971	165	9	1)f(λ	1)f(λ	NUM
ejpam-5971	165	10	)	)	PUNCT
ejpam-5971	165	11	c(g(λ	c(g(λ	PROPN
ejpam-5971	165	12	)	)	PUNCT
ejpam-5971	165	13	,	,	PUNCT
ejpam-5971	165	14	h(λ	h(λ	PROPN
ejpam-5971	165	15	)	)	PUNCT
ejpam-5971	165	16	,	,	PUNCT
ejpam-5971	165	17	c	c	NOUN
ejpam-5971	165	18	)	)	PUNCT
ejpam-5971	165	19	.	.	PUNCT
ejpam-5971	165	20	also	also	ADV
ejpam-5971	165	21	,	,	PUNCT
ejpam-5971	165	22	x2	x2	PRON
ejpam-5971	165	23	−	−	PROPN
ejpam-5971	165	24	y	y	PROPN
ejpam-5971	165	25	tx−1	tx−1	PROPN
ejpam-5971	165	26	1	1	NUM
ejpam-5971	165	27	y	y	PROPN
ejpam-5971	165	28	=	=	SYM
ejpam-5971	165	29	c	c	X
ejpam-5971	165	30	(	(	PUNCT
ejpam-5971	165	31	−λ+	−λ+	PROPN
ejpam-5971	165	32	a	a	DET
ejpam-5971	165	33	λ	λ	PROPN
ejpam-5971	165	34	−	−	PROPN
ejpam-5971	165	35	c(b+λ)2	c(b+λ)2	PROPN
ejpam-5971	165	36	λ2f(λ	λ2f(λ	PROPN
ejpam-5971	165	37	)	)	PUNCT
ejpam-5971	165	38	,	,	PUNCT
ejpam-5971	165	39	1	1	NUM
ejpam-5971	165	40	+	+	NUM
ejpam-5971	165	41	a	a	DET
ejpam-5971	165	42	λ	λ	NOUN
ejpam-5971	165	43	−	−	PROPN
ejpam-5971	165	44	c(b+λ)2	c(b+λ)2	NOUN
ejpam-5971	165	45	λ2f(λ	λ2f(λ	PROPN
ejpam-5971	165	46	)	)	PUNCT
ejpam-5971	165	47	,	,	PUNCT
ejpam-5971	165	48	d	d	NOUN
ejpam-5971	165	49	)	)	PUNCT
ejpam-5971	165	50	.	.	PUNCT
ejpam-5971	166	1	by	by	ADP
ejpam-5971	166	2	proposition	proposition	NOUN
ejpam-5971	166	3	1	1	NUM
ejpam-5971	166	4	,	,	PUNCT
ejpam-5971	166	5	the	the	DET
ejpam-5971	166	6	determinant	determinant	NOUN
ejpam-5971	166	7	of	of	ADP
ejpam-5971	166	8	x2	x2	NOUN
ejpam-5971	166	9	−	−	PROPN
ejpam-5971	166	10	y	y	PROPN
ejpam-5971	166	11	tx−1	tx−1	PROPN
ejpam-5971	166	12	1	1	NUM
ejpam-5971	166	13	y	y	PROPN
ejpam-5971	166	14	is	be	AUX
ejpam-5971	166	15	det	det	NOUN
ejpam-5971	166	16	(	(	PUNCT
ejpam-5971	166	17	x2	x2	INTJ
ejpam-5971	166	18	−	−	PROPN
ejpam-5971	166	19	y	y	PROPN
ejpam-5971	166	20	tx−1	tx−1	PROPN
ejpam-5971	166	21	1	1	NUM
ejpam-5971	166	22	y	y	PROPN
ejpam-5971	166	23	)	)	PUNCT
ejpam-5971	167	1	=	=	PUNCT
ejpam-5971	167	2	(	(	PUNCT
ejpam-5971	167	3	−λ+	−λ+	PROPN
ejpam-5971	167	4	a	a	DET
ejpam-5971	167	5	λ	λ	X
ejpam-5971	167	6	−	−	NOUN
ejpam-5971	167	7	c(b+	c(b+	NOUN
ejpam-5971	167	8	λ)2	λ)2	NOUN
ejpam-5971	167	9	λ2f(λ	λ2f(λ	PROPN
ejpam-5971	167	10	)	)	PUNCT
ejpam-5971	168	1	+	+	CCONJ
ejpam-5971	168	2	(	(	PUNCT
ejpam-5971	168	3	d−	d−	PROPN
ejpam-5971	168	4	1	1	NUM
ejpam-5971	168	5	)	)	PUNCT
ejpam-5971	168	6	(	(	PUNCT
ejpam-5971	168	7	1	1	NUM
ejpam-5971	168	8	+	+	CCONJ
ejpam-5971	168	9	a	a	DET
ejpam-5971	168	10	λ	λ	NOUN
ejpam-5971	168	11	−	−	NOUN
ejpam-5971	168	12	c(b+	c(b+	NOUN
ejpam-5971	168	13	λ)2	λ)2	NOUN
ejpam-5971	168	14	λ2f(λ	λ2f(λ	PROPN
ejpam-5971	168	15	)	)	PUNCT
ejpam-5971	168	16	)	)	PUNCT
ejpam-5971	168	17	)	)	PUNCT
ejpam-5971	168	18	(	(	PUNCT
ejpam-5971	168	19	−λ−	−λ−	NOUN
ejpam-5971	168	20	1)d−1	1)d−1	NUM
ejpam-5971	168	21	v.h	v.h	PROPN
ejpam-5971	168	22	.	.	PROPN
ejpam-5971	168	23	krisnawati	krisnawati	PROPN
ejpam-5971	168	24	,	,	PUNCT
ejpam-5971	168	25	n.	n.	PROPN
ejpam-5971	168	26	hidayat	hidayat	PROPN
ejpam-5971	168	27	,	,	PUNCT
ejpam-5971	168	28	a.f	a.f	PROPN
ejpam-5971	168	29	.	.	PROPN
ejpam-5971	168	30	musyarrofah	musyarrofah	PROPN
ejpam-5971	168	31	/	/	SYM
ejpam-5971	168	32	eur	eur	PROPN
ejpam-5971	168	33	.	.	PUNCT
ejpam-5971	169	1	j.	j.	PROPN
ejpam-5971	169	2	pure	pure	PROPN
ejpam-5971	169	3	appl	appl	PROPN
ejpam-5971	169	4	.	.	PROPN
ejpam-5971	169	5	math	math	PROPN
ejpam-5971	169	6	,	,	PUNCT
ejpam-5971	169	7	18	18	NUM
ejpam-5971	169	8	(	(	PUNCT
ejpam-5971	169	9	2	2	NUM
ejpam-5971	169	10	)	)	PUNCT
ejpam-5971	169	11	(	(	PUNCT
ejpam-5971	169	12	2025	2025	NUM
ejpam-5971	169	13	)	)	PUNCT
ejpam-5971	169	14	,	,	PUNCT
ejpam-5971	169	15	5971	5971	NUM
ejpam-5971	169	16	8	8	NUM
ejpam-5971	169	17	of	of	ADP
ejpam-5971	169	18	19	19	NUM
ejpam-5971	169	19	=	=	SYM
ejpam-5971	169	20	(	(	PUNCT
ejpam-5971	169	21	−λ3f(λ	−λ3f(λ	PROPN
ejpam-5971	169	22	)	)	PUNCT
ejpam-5971	170	1	+	+	CCONJ
ejpam-5971	170	2	(	(	PUNCT
ejpam-5971	170	3	d−	d−	PROPN
ejpam-5971	170	4	1)λ2f(λ	1)λ2f(λ	NUM
ejpam-5971	170	5	)	)	PUNCT
ejpam-5971	170	6	+	+	CCONJ
ejpam-5971	170	7	daλf(λ)−	daλf(λ)−	ADJ
ejpam-5971	170	8	dc(b+	dc(b+	PROPN
ejpam-5971	170	9	λ)2	λ)2	NOUN
ejpam-5971	170	10	λ2f(λ	λ2f(λ	PROPN
ejpam-5971	170	11	)	)	PUNCT
ejpam-5971	170	12	)	)	PUNCT
ejpam-5971	171	1	(	(	PUNCT
ejpam-5971	171	2	−λ−	−λ−	NOUN
ejpam-5971	171	3	1)d−1	1)d−1	NUM
ejpam-5971	171	4	=	=	SYM
ejpam-5971	171	5	ϕ(λ	ϕ(λ	PROPN
ejpam-5971	171	6	)	)	PUNCT
ejpam-5971	171	7	λ2f(λ	λ2f(λ	INTJ
ejpam-5971	171	8	)	)	PUNCT
ejpam-5971	171	9	(	(	PUNCT
ejpam-5971	171	10	−λ−	−λ−	NOUN
ejpam-5971	171	11	1)d−1	1)d−1	NUM
ejpam-5971	171	12	.	.	PUNCT
ejpam-5971	171	13	(	(	PUNCT
ejpam-5971	171	14	4	4	NUM
ejpam-5971	171	15	)	)	PUNCT
ejpam-5971	171	16	where	where	SCONJ
ejpam-5971	171	17	ϕ(λ	ϕ(λ	X
ejpam-5971	171	18	)	)	PUNCT
ejpam-5971	171	19	is	be	AUX
ejpam-5971	171	20	ϕ(λ	ϕ(λ	PROPN
ejpam-5971	171	21	)	)	PUNCT
ejpam-5971	172	1	=	=	NOUN
ejpam-5971	172	2	λ4	λ4	ADJ
ejpam-5971	172	3	−	−	PROPN
ejpam-5971	173	1	(	(	PUNCT
ejpam-5971	173	2	℘2	℘2	NOUN
ejpam-5971	173	3	−	−	PROPN
ejpam-5971	173	4	3	3	NUM
ejpam-5971	173	5	)	)	PUNCT
ejpam-5971	173	6	λ3	λ3	PROPN
ejpam-5971	173	7	−	−	PROPN
ejpam-5971	173	8	(	(	PUNCT
ejpam-5971	173	9	2℘5	2℘5	NUM
ejpam-5971	173	10	−	−	NUM
ejpam-5971	173	11	3℘4	3℘4	NUM
ejpam-5971	173	12	+	+	SYM
ejpam-5971	173	13	2℘2	2℘2	NUM
ejpam-5971	173	14	−	−	NUM
ejpam-5971	173	15	2	2	NUM
ejpam-5971	173	16	)	)	PUNCT
ejpam-5971	173	17	λ2	λ2	PROPN
ejpam-5971	173	18	+	+	CCONJ
ejpam-5971	173	19	℘3	℘3	ADJ
ejpam-5971	173	20	(	(	PUNCT
ejpam-5971	173	21	℘3	℘3	ADJ
ejpam-5971	173	22	−	−	PROPN
ejpam-5971	173	23	℘2	℘2	NOUN
ejpam-5971	173	24	−	−	PROPN
ejpam-5971	173	25	2℘−	2℘−	NUM
ejpam-5971	173	26	1	1	NUM
ejpam-5971	173	27	)	)	PUNCT
ejpam-5971	173	28	(	(	PUNCT
ejpam-5971	173	29	℘−	℘−	NOUN
ejpam-5971	173	30	1)2λ+	1)2λ+	NUM
ejpam-5971	173	31	℘6(℘−	℘6(℘−	NOUN
ejpam-5971	173	32	1)4	1)4	NUM
ejpam-5971	173	33	.	.	PUNCT
ejpam-5971	174	1	based	base	VERB
ejpam-5971	174	2	on	on	ADP
ejpam-5971	174	3	equation	equation	NOUN
ejpam-5971	174	4	(	(	PUNCT
ejpam-5971	174	5	2	2	NUM
ejpam-5971	174	6	)	)	PUNCT
ejpam-5971	174	7	,	,	PUNCT
ejpam-5971	174	8	(	(	PUNCT
ejpam-5971	174	9	3	3	NUM
ejpam-5971	174	10	)	)	PUNCT
ejpam-5971	174	11	,	,	PUNCT
ejpam-5971	174	12	and	and	CCONJ
ejpam-5971	174	13	(	(	PUNCT
ejpam-5971	174	14	4	4	NUM
ejpam-5971	174	15	)	)	PUNCT
ejpam-5971	174	16	,	,	PUNCT
ejpam-5971	174	17	we	we	PRON
ejpam-5971	174	18	obtain	obtain	VERB
ejpam-5971	174	19	determinant	determinant	ADJ
ejpam-5971	174	20	a(g)−	a(g)−	NOUN
ejpam-5971	174	21	λi	λi	ADP
ejpam-5971	174	22	,	,	PUNCT
ejpam-5971	174	23	is	be	AUX
ejpam-5971	174	24	det(a(g)−	det(a(g)−	PROPN
ejpam-5971	174	25	λi	λi	NOUN
ejpam-5971	174	26	)	)	PUNCT
ejpam-5971	174	27	=	=	SYM
ejpam-5971	174	28	det(p	det(p	NOUN
ejpam-5971	174	29	)	)	PUNCT
ejpam-5971	174	30	·	·	PUNCT
ejpam-5971	175	1	det(x1	det(x1	ADJ
ejpam-5971	175	2	)	)	PUNCT
ejpam-5971	175	3	·	·	PUNCT
ejpam-5971	175	4	det	det	NOUN
ejpam-5971	175	5	(	(	PUNCT
ejpam-5971	175	6	x2	x2	INTJ
ejpam-5971	175	7	−	−	PROPN
ejpam-5971	176	1	y	y	PROPN
ejpam-5971	177	1	tx−1	tx−1	PROPN
ejpam-5971	178	1	1	1	NUM
ejpam-5971	179	1	y	y	PROPN
ejpam-5971	179	2	)	)	PUNCT
ejpam-5971	179	3	=	=	SYM
ejpam-5971	179	4	(	(	PUNCT
ejpam-5971	179	5	−λ)℘	−λ)℘	X
ejpam-5971	179	6	4−℘2−2	4−℘2−2	NUM
ejpam-5971	179	7	·	·	PUNCT
ejpam-5971	179	8	(	(	PUNCT
ejpam-5971	179	9	−λ−	−λ−	NOUN
ejpam-5971	179	10	1	1	NUM
ejpam-5971	179	11	)	)	PUNCT
ejpam-5971	179	12	℘2−3	℘2−3	X
ejpam-5971	179	13	·	·	PUNCT
ejpam-5971	179	14	ϕ(λ	ϕ(λ	X
ejpam-5971	179	15	)	)	PUNCT
ejpam-5971	179	16	.	.	PUNCT
ejpam-5971	180	1	thus	thus	ADV
ejpam-5971	180	2	the	the	DET
ejpam-5971	180	3	characteristic	characteristic	ADJ
ejpam-5971	180	4	polynomial	polynomial	NOUN
ejpam-5971	180	5	of	of	ADP
ejpam-5971	180	6	a(g	a(g	PROPN
ejpam-5971	180	7	)	)	PUNCT
ejpam-5971	180	8	is	be	AUX
ejpam-5971	180	9	(	(	PUNCT
ejpam-5971	180	10	−λ)℘	−λ)℘	X
ejpam-5971	180	11	4−℘2−2	4−℘2−2	NUM
ejpam-5971	180	12	·	·	PUNCT
ejpam-5971	180	13	(	(	PUNCT
ejpam-5971	180	14	−λ−	−λ−	NOUN
ejpam-5971	180	15	1	1	NUM
ejpam-5971	180	16	)	)	PUNCT
ejpam-5971	180	17	℘2−3	℘2−3	X
ejpam-5971	180	18	·	·	PUNCT
ejpam-5971	181	1	ϕ(λ	ϕ(λ	X
ejpam-5971	181	2	)	)	PUNCT
ejpam-5971	181	3	=	=	SYM
ejpam-5971	181	4	0	0	NUM
ejpam-5971	181	5	,	,	PUNCT
ejpam-5971	181	6	hence	hence	ADV
ejpam-5971	181	7	,	,	PUNCT
ejpam-5971	181	8	0	0	NUM
ejpam-5971	181	9	and	and	CCONJ
ejpam-5971	181	10	1	1	NUM
ejpam-5971	181	11	are	be	AUX
ejpam-5971	181	12	eigenvalue	eigenvalue	NOUN
ejpam-5971	181	13	of	of	ADP
ejpam-5971	181	14	g	g	NOUN
ejpam-5971	181	15	with	with	ADP
ejpam-5971	181	16	multiplicity	multiplicity	NOUN
ejpam-5971	181	17	℘4−℘2−2	℘4−℘2−2	PROPN
ejpam-5971	181	18	and	and	CCONJ
ejpam-5971	181	19	℘2−3	℘2−3	VERB
ejpam-5971	181	20	respectively	respectively	ADV
ejpam-5971	181	21	.	.	PUNCT
ejpam-5971	182	1	the	the	DET
ejpam-5971	182	2	other	other	ADJ
ejpam-5971	182	3	eigenvalues	eigenvalue	NOUN
ejpam-5971	182	4	of	of	ADP
ejpam-5971	182	5	g	g	PROPN
ejpam-5971	182	6	are	be	AUX
ejpam-5971	182	7	solutions	solution	NOUN
ejpam-5971	182	8	to	to	ADP
ejpam-5971	182	9	the	the	DET
ejpam-5971	182	10	following	follow	VERB
ejpam-5971	182	11	polynomial	polynomial	ADJ
ejpam-5971	182	12	λ4	λ4	PROPN
ejpam-5971	182	13	−	−	PROPN
ejpam-5971	182	14	(	(	PUNCT
ejpam-5971	182	15	℘2	℘2	NOUN
ejpam-5971	182	16	−	−	PROPN
ejpam-5971	182	17	3	3	NUM
ejpam-5971	182	18	)	)	PUNCT
ejpam-5971	182	19	λ3	λ3	PROPN
ejpam-5971	182	20	−	−	PROPN
ejpam-5971	182	21	(	(	PUNCT
ejpam-5971	182	22	2℘5	2℘5	NUM
ejpam-5971	182	23	−	−	NUM
ejpam-5971	182	24	3℘4	3℘4	NUM
ejpam-5971	182	25	+	+	SYM
ejpam-5971	182	26	2℘2	2℘2	NUM
ejpam-5971	182	27	−	−	NUM
ejpam-5971	182	28	2	2	NUM
ejpam-5971	182	29	)	)	PUNCT
ejpam-5971	182	30	λ2	λ2	PROPN
ejpam-5971	182	31	+	+	CCONJ
ejpam-5971	182	32	℘3	℘3	ADJ
ejpam-5971	182	33	(	(	PUNCT
ejpam-5971	182	34	℘3	℘3	ADJ
ejpam-5971	182	35	−	−	PROPN
ejpam-5971	182	36	℘2	℘2	NOUN
ejpam-5971	182	37	−	−	PROPN
ejpam-5971	182	38	2℘−	2℘−	NUM
ejpam-5971	182	39	1	1	NUM
ejpam-5971	182	40	)	)	PUNCT
ejpam-5971	182	41	(	(	PUNCT
ejpam-5971	182	42	℘−	℘−	NOUN
ejpam-5971	182	43	1)2λ	1)2λ	PROPN
ejpam-5971	182	44	+	+	CCONJ
ejpam-5971	182	45	℘6(℘−	℘6(℘−	VERB
ejpam-5971	182	46	1)4	1)4	NOUN
ejpam-5971	182	47	=	=	SYM
ejpam-5971	182	48	0	0	X
ejpam-5971	182	49	.	.	PUNCT
ejpam-5971	183	1	theorem	theorem	NOUN
ejpam-5971	183	2	2	2	NUM
ejpam-5971	183	3	.	.	PUNCT
ejpam-5971	184	1	let	let	VERB
ejpam-5971	184	2	g	g	PRON
ejpam-5971	184	3	∼=	∼=	PROPN
ejpam-5971	184	4	γ(z℘[x]/⟨x5⟩	γ(z℘[x]/⟨x5⟩	NUM
ejpam-5971	184	5	)	)	PUNCT
ejpam-5971	184	6	.	.	PUNCT
ejpam-5971	185	1	then	then	ADV
ejpam-5971	185	2	en(g	en(g	NUM
ejpam-5971	185	3	)	)	PUNCT
ejpam-5971	185	4	≥	≥	PROPN
ejpam-5971	185	5	℘2	℘2	NOUN
ejpam-5971	185	6	−	−	PROPN
ejpam-5971	185	7	3	3	NUM
ejpam-5971	185	8	+	+	CCONJ
ejpam-5971	185	9	√	√	PROPN
ejpam-5971	185	10	4℘5	4℘5	NUM
ejpam-5971	185	11	−	−	PROPN
ejpam-5971	185	12	5℘4	5℘4	NUM
ejpam-5971	185	13	−	−	NUM
ejpam-5971	185	14	2℘2	2℘2	NUM
ejpam-5971	185	15	+	+	CCONJ
ejpam-5971	185	16	5	5	NUM
ejpam-5971	185	17	+	+	SYM
ejpam-5971	185	18	12(℘6(℘−	12(℘6(℘−	NUM
ejpam-5971	185	19	1)4)1/2	1)4)1/2	NUM
ejpam-5971	185	20	and	and	CCONJ
ejpam-5971	185	21	en(g	en(g	NUM
ejpam-5971	185	22	)	)	PUNCT
ejpam-5971	185	23	≤	≤	NUM
ejpam-5971	185	24	℘2	℘2	NOUN
ejpam-5971	185	25	−	−	PROPN
ejpam-5971	185	26	3	3	NUM
ejpam-5971	185	27	+	+	CCONJ
ejpam-5971	185	28	2	2	NUM
ejpam-5971	185	29	√	√	NUM
ejpam-5971	185	30	4℘5	4℘5	NUM
ejpam-5971	185	31	−	−	PROPN
ejpam-5971	185	32	5℘4	5℘4	NUM
ejpam-5971	185	33	−	−	NUM
ejpam-5971	185	34	2℘2	2℘2	NUM
ejpam-5971	185	35	+	+	CCONJ
ejpam-5971	185	36	5	5	X
ejpam-5971	185	37	.	.	X
ejpam-5971	185	38	proof	proof	NOUN
ejpam-5971	185	39	.	.	PUNCT
ejpam-5971	186	1	let	let	VERB
ejpam-5971	186	2	ζ1	ζ1	NOUN
ejpam-5971	186	3	,	,	PUNCT
ejpam-5971	186	4	ζ2	ζ2	NOUN
ejpam-5971	186	5	,	,	PUNCT
ejpam-5971	186	6	ζ3	ζ3	NOUN
ejpam-5971	186	7	,	,	PUNCT
ejpam-5971	186	8	ζ4	ζ4	PROPN
ejpam-5971	186	9	be	be	VERB
ejpam-5971	186	10	an	an	DET
ejpam-5971	186	11	eigenvalues	eigenvalue	NOUN
ejpam-5971	186	12	that	that	PRON
ejpam-5971	186	13	satisfy	satisfy	VERB
ejpam-5971	186	14	λ4	λ4	PROPN
ejpam-5971	186	15	−	−	PROPN
ejpam-5971	187	1	(	(	PUNCT
ejpam-5971	187	2	℘2	℘2	NOUN
ejpam-5971	187	3	−	−	PROPN
ejpam-5971	187	4	3	3	NUM
ejpam-5971	187	5	)	)	PUNCT
ejpam-5971	187	6	λ3	λ3	PROPN
ejpam-5971	187	7	−	−	PROPN
ejpam-5971	187	8	(	(	PUNCT
ejpam-5971	187	9	2℘5	2℘5	NUM
ejpam-5971	187	10	−	−	NUM
ejpam-5971	187	11	3℘4	3℘4	NUM
ejpam-5971	187	12	+	+	SYM
ejpam-5971	187	13	2℘2	2℘2	NUM
ejpam-5971	187	14	−	−	NUM
ejpam-5971	187	15	2	2	NUM
ejpam-5971	187	16	)	)	PUNCT
ejpam-5971	187	17	λ2	λ2	PROPN
ejpam-5971	187	18	+	+	CCONJ
ejpam-5971	187	19	℘3	℘3	ADJ
ejpam-5971	187	20	(	(	PUNCT
ejpam-5971	187	21	℘3	℘3	ADJ
ejpam-5971	187	22	−	−	PROPN
ejpam-5971	187	23	℘2	℘2	NOUN
ejpam-5971	187	24	−	−	PROPN
ejpam-5971	187	25	2℘−	2℘−	NUM
ejpam-5971	187	26	1	1	NUM
ejpam-5971	187	27	)	)	PUNCT
ejpam-5971	187	28	(	(	PUNCT
ejpam-5971	187	29	℘−	℘−	NOUN
ejpam-5971	187	30	1)2λ+	1)2λ+	NUM
ejpam-5971	187	31	℘6(℘−	℘6(℘−	NOUN
ejpam-5971	187	32	1)4	1)4	NOUN
ejpam-5971	187	33	=	=	SYM
ejpam-5971	187	34	0	0	NUM
ejpam-5971	187	35	.	.	PUNCT
ejpam-5971	188	1	(	(	PUNCT
ejpam-5971	188	2	5	5	X
ejpam-5971	188	3	)	)	PUNCT
ejpam-5971	188	4	it	it	PRON
ejpam-5971	188	5	is	be	AUX
ejpam-5971	188	6	obtained	obtain	VERB
ejpam-5971	188	7	that	that	SCONJ
ejpam-5971	188	8	the	the	DET
ejpam-5971	188	9	sum	sum	NOUN
ejpam-5971	188	10	and	and	CCONJ
ejpam-5971	188	11	the	the	DET
ejpam-5971	188	12	product	product	NOUN
ejpam-5971	188	13	of	of	ADP
ejpam-5971	188	14	the	the	DET
ejpam-5971	188	15	eigenvalues	eigenvalue	NOUN
ejpam-5971	188	16	from	from	ADP
ejpam-5971	188	17	the	the	DET
ejpam-5971	188	18	equation	equation	NOUN
ejpam-5971	188	19	(	(	PUNCT
ejpam-5971	188	20	5	5	X
ejpam-5971	188	21	)	)	PUNCT
ejpam-5971	188	22	are	be	AUX
ejpam-5971	188	23	v.h	v.h	PROPN
ejpam-5971	188	24	.	.	PROPN
ejpam-5971	188	25	krisnawati	krisnawati	PROPN
ejpam-5971	188	26	,	,	PUNCT
ejpam-5971	188	27	n.	n.	PROPN
ejpam-5971	188	28	hidayat	hidayat	PROPN
ejpam-5971	188	29	,	,	PUNCT
ejpam-5971	188	30	a.f	a.f	PROPN
ejpam-5971	188	31	.	.	PROPN
ejpam-5971	188	32	musyarrofah	musyarrofah	PROPN
ejpam-5971	188	33	/	/	SYM
ejpam-5971	188	34	eur	eur	PROPN
ejpam-5971	188	35	.	.	PUNCT
ejpam-5971	189	1	j.	j.	PROPN
ejpam-5971	189	2	pure	pure	PROPN
ejpam-5971	189	3	appl	appl	PROPN
ejpam-5971	189	4	.	.	PROPN
ejpam-5971	189	5	math	math	PROPN
ejpam-5971	189	6	,	,	PUNCT
ejpam-5971	189	7	18	18	NUM
ejpam-5971	189	8	(	(	PUNCT
ejpam-5971	189	9	2	2	NUM
ejpam-5971	189	10	)	)	PUNCT
ejpam-5971	189	11	(	(	PUNCT
ejpam-5971	189	12	2025	2025	NUM
ejpam-5971	189	13	)	)	PUNCT
ejpam-5971	189	14	,	,	PUNCT
ejpam-5971	189	15	5971	5971	NUM
ejpam-5971	189	16	9	9	NUM
ejpam-5971	189	17	of	of	ADP
ejpam-5971	189	18	19	19	NUM
ejpam-5971	189	19	as	as	SCONJ
ejpam-5971	189	20	follows	follow	VERB
ejpam-5971	189	21	4∑	4∑	NOUN
ejpam-5971	189	22	i=1	i=1	PROPN
ejpam-5971	189	23	ζi	ζi	PROPN
ejpam-5971	189	24	=	=	PUNCT
ejpam-5971	189	25	℘2	℘2	PROPN
ejpam-5971	189	26	−	−	PROPN
ejpam-5971	189	27	3,∑	3,∑	NUM
ejpam-5971	189	28	1≤i	1≤i	NUM
ejpam-5971	189	29	<	<	X
ejpam-5971	189	30	j≤4	j≤4	PROPN
ejpam-5971	189	31	ζiζj	ζiζj	NOUN
ejpam-5971	189	32	=	=	SYM
ejpam-5971	189	33	−(2℘5	−(2℘5	X
ejpam-5971	190	1	−	−	X
ejpam-5971	191	1	3℘4	3℘4	NUM
ejpam-5971	191	2	+	+	SYM
ejpam-5971	191	3	2℘2	2℘2	NUM
ejpam-5971	191	4	−	−	NOUN
ejpam-5971	191	5	2	2	NUM
ejpam-5971	191	6	)	)	PUNCT
ejpam-5971	191	7	=	=	NOUN
ejpam-5971	191	8	−2℘5	−2℘5	NOUN
ejpam-5971	192	1	+	+	CCONJ
ejpam-5971	192	2	3℘4	3℘4	NUM
ejpam-5971	192	3	−	−	NOUN
ejpam-5971	192	4	2℘2	2℘2	NUM
ejpam-5971	192	5	+	+	CCONJ
ejpam-5971	192	6	2	2	NUM
ejpam-5971	192	7	,	,	PUNCT
ejpam-5971	192	8	4∏	4∏	NUM
ejpam-5971	192	9	i=1	i=1	PROPN
ejpam-5971	192	10	ζi	ζi	PROPN
ejpam-5971	192	11	=	=	PUNCT
ejpam-5971	192	12	℘6(℘−	℘6(℘−	NOUN
ejpam-5971	192	13	1)4	1)4	NUM
ejpam-5971	192	14	.	.	PUNCT
ejpam-5971	193	1	next	next	ADV
ejpam-5971	193	2	,	,	PUNCT
ejpam-5971	193	3	we	we	PRON
ejpam-5971	193	4	can	can	AUX
ejpam-5971	193	5	write	write	VERB
ejpam-5971	193	6	the	the	DET
ejpam-5971	193	7	energy	energy	NOUN
ejpam-5971	193	8	of	of	ADP
ejpam-5971	193	9	g	g	NOUN
ejpam-5971	193	10	as	as	ADP
ejpam-5971	193	11	en(g	en(g	NUM
ejpam-5971	193	12	)	)	PUNCT
ejpam-5971	193	13	=	=	PUNCT
ejpam-5971	194	1	℘4−1∑	℘4−1∑	NUM
ejpam-5971	194	2	i=1	i=1	VERB
ejpam-5971	195	1	|	|	ADV
ejpam-5971	195	2	λi	λi	ADP
ejpam-5971	195	3	|=	|=	NOUN
ejpam-5971	195	4	℘2	℘2	NOUN
ejpam-5971	195	5	−	−	PROPN
ejpam-5971	195	6	3	3	NUM
ejpam-5971	195	7	+	+	NUM
ejpam-5971	195	8	4∑	4∑	NUM
ejpam-5971	195	9	i=1	i=1	PROPN
ejpam-5971	195	10	|ζi|	|ζi|	NOUN
ejpam-5971	195	11	(	(	PUNCT
ejpam-5971	195	12	6	6	NUM
ejpam-5971	195	13	)	)	PUNCT
ejpam-5971	195	14	then	then	ADV
ejpam-5971	195	15	,	,	PUNCT
ejpam-5971	195	16	using	use	VERB
ejpam-5971	195	17	the	the	DET
ejpam-5971	195	18	first	first	ADJ
ejpam-5971	195	19	inequality	inequality	NOUN
ejpam-5971	195	20	of	of	ADP
ejpam-5971	195	21	(	(	PUNCT
ejpam-5971	195	22	1	1	NUM
ejpam-5971	195	23	)	)	PUNCT
ejpam-5971	195	24	to	to	ADP
ejpam-5971	195	25	the	the	DET
ejpam-5971	195	26	set	set	NOUN
ejpam-5971	195	27	{	{	PUNCT
ejpam-5971	195	28	|ζ1|	|ζ1|	NOUN
ejpam-5971	195	29	,	,	PUNCT
ejpam-5971	195	30	|ζ2|	|ζ2|	NOUN
ejpam-5971	195	31	,	,	PUNCT
ejpam-5971	195	32	|ζ3|	|ζ3|	NOUN
ejpam-5971	195	33	,	,	PUNCT
ejpam-5971	195	34	|ζ4|	|ζ4|	ADJ
ejpam-5971	195	35	}	}	PUNCT
ejpam-5971	195	36	,	,	PUNCT
ejpam-5971	195	37	we	we	PRON
ejpam-5971	195	38	have	have	VERB
ejpam-5971	195	39	(	(	PUNCT
ejpam-5971	195	40	∑4	∑4	PROPN
ejpam-5971	195	41	i=1	i=1	PROPN
ejpam-5971	195	42	|ζi|	|ζi|	PROPN
ejpam-5971	195	43	4	4	NUM
ejpam-5971	195	44	)	)	SYM
ejpam-5971	195	45	2	2	NUM
ejpam-5971	195	46	≥	≥	NOUN
ejpam-5971	195	47	1	1	NUM
ejpam-5971	195	48	4(4−1	4(4−1	NOUN
ejpam-5971	195	49	)	)	PUNCT
ejpam-5971	195	50	2	2	NUM
ejpam-5971	196	1			PROPN
ejpam-5971	196	2	∑	∑	PUNCT
ejpam-5971	196	3	1≤i	1≤i	PROPN
ejpam-5971	196	4	<	<	X
ejpam-5971	196	5	j≤4	j≤4	PROPN
ejpam-5971	196	6	|ζi||ζj	|ζi||ζj	PROPN
ejpam-5971	196	7	|	|	ADV
ejpam-5971	196	8			PROPN
ejpam-5971	196	9	.	.	PUNCT
ejpam-5971	197	1	(	(	PUNCT
ejpam-5971	197	2	7	7	X
ejpam-5971	197	3	)	)	PUNCT
ejpam-5971	197	4	thus	thus	ADV
ejpam-5971	197	5	(	(	PUNCT
ejpam-5971	197	6	4∑	4∑	NOUN
ejpam-5971	197	7	i=1	i=1	PROPN
ejpam-5971	197	8	|ζi|	|ζi|	NOUN
ejpam-5971	197	9	)	)	PUNCT
ejpam-5971	197	10	2	2	NUM
ejpam-5971	197	11	≥	≥	NOUN
ejpam-5971	197	12	16	16	NUM
ejpam-5971	197	13	6	6	NUM
ejpam-5971	197	14			PROPN
ejpam-5971	197	15	∑	∑	PUNCT
ejpam-5971	197	16	1≤i	1≤i	PROPN
ejpam-5971	197	17	<	<	X
ejpam-5971	197	18	j≤4	j≤4	PROPN
ejpam-5971	197	19	|ζi||ζj	|ζi||ζj	PROPN
ejpam-5971	197	20	|	|	ADV
ejpam-5971	197	21			PROPN
ejpam-5971	197	22	.	.	PUNCT
ejpam-5971	198	1	(	(	PUNCT
ejpam-5971	198	2	8)	8)	NUM
ejpam-5971	198	3	it	it	PRON
ejpam-5971	198	4	can	can	AUX
ejpam-5971	198	5	be	be	AUX
ejpam-5971	198	6	seen	see	VERB
ejpam-5971	198	7	that	that	SCONJ
ejpam-5971	198	8	(	(	PUNCT
ejpam-5971	198	9	4∑	4∑	NOUN
ejpam-5971	198	10	i=1	i=1	PROPN
ejpam-5971	198	11	|ζi|	|ζi|	NOUN
ejpam-5971	198	12	)	)	PUNCT
ejpam-5971	198	13	2	2	NUM
ejpam-5971	198	14	=	=	SYM
ejpam-5971	198	15	4∑	4∑	NUM
ejpam-5971	198	16	i=1	i=1	X
ejpam-5971	198	17	|ζi|2	|ζi|2	PUNCT
ejpam-5971	198	18	+	+	NUM
ejpam-5971	198	19	2	2	NUM
ejpam-5971	198	20	∑	∑	SYM
ejpam-5971	198	21	1≤i	1≤i	NUM
ejpam-5971	198	22	<	<	X
ejpam-5971	198	23	j≤4	j≤4	PROPN
ejpam-5971	198	24	|ζi||ζj	|ζi||ζj	PROPN
ejpam-5971	198	25	|	|	CCONJ
ejpam-5971	198	26	⇐	⇐	ADJ
ejpam-5971	198	27	⇒	⇒	NOUN
ejpam-5971	198	28	∑	∑	PUNCT
ejpam-5971	198	29	1≤i	1≤i	PROPN
ejpam-5971	198	30	<	<	X
ejpam-5971	198	31	j≤4	j≤4	PROPN
ejpam-5971	198	32	|ζi||ζj	|ζi||ζj	PROPN
ejpam-5971	198	33	|	|	NOUN
ejpam-5971	198	34	=	=	NOUN
ejpam-5971	198	35	1	1	NUM
ejpam-5971	198	36	2	2	NUM
ejpam-5971	198	37			PROPN
ejpam-5971	198	38	(	(	PUNCT
ejpam-5971	198	39	4∑	4∑	NOUN
ejpam-5971	198	40	i=1	i=1	PROPN
ejpam-5971	198	41	|ζi|	|ζi|	NOUN
ejpam-5971	198	42	)	)	PUNCT
ejpam-5971	198	43	2	2	NUM
ejpam-5971	198	44	−	−	PROPN
ejpam-5971	198	45	4∑	4∑	NOUN
ejpam-5971	198	46	i=1	i=1	PROPN
ejpam-5971	198	47	ζ2i	ζ2i	VERB
ejpam-5971	198	48			PROPN
ejpam-5971	198	49	.	.	PUNCT
ejpam-5971	199	1	(	(	PUNCT
ejpam-5971	199	2	9	9	NUM
ejpam-5971	199	3	)	)	PUNCT
ejpam-5971	199	4	next	next	ADV
ejpam-5971	199	5	,	,	PUNCT
ejpam-5971	199	6	by	by	ADP
ejpam-5971	199	7	substituting	substitute	VERB
ejpam-5971	199	8	equation	equation	NOUN
ejpam-5971	199	9	(	(	PUNCT
ejpam-5971	199	10	9	9	NUM
ejpam-5971	199	11	)	)	PUNCT
ejpam-5971	199	12	into	into	ADP
ejpam-5971	199	13	equation	equation	NOUN
ejpam-5971	199	14	(	(	PUNCT
ejpam-5971	199	15	8)	8)	NUM
ejpam-5971	199	16	,	,	PUNCT
ejpam-5971	199	17	we	we	PRON
ejpam-5971	199	18	obtain	obtain	VERB
ejpam-5971	199	19	(	(	PUNCT
ejpam-5971	199	20	4∑	4∑	NOUN
ejpam-5971	199	21	i=1	i=1	PROPN
ejpam-5971	199	22	|ζi|	|ζi|	NOUN
ejpam-5971	199	23	)	)	PUNCT
ejpam-5971	199	24	2	2	NUM
ejpam-5971	199	25	≥	≥	NOUN
ejpam-5971	199	26	4	4	NUM
ejpam-5971	199	27	3	3	NUM
ejpam-5971	199	28			PROPN
ejpam-5971	199	29	(	(	PUNCT
ejpam-5971	199	30	4∑	4∑	NOUN
ejpam-5971	199	31	i=1	i=1	PROPN
ejpam-5971	199	32	|ζi|	|ζi|	NOUN
ejpam-5971	199	33	)	)	PUNCT
ejpam-5971	199	34	2	2	NUM
ejpam-5971	199	35	−	−	PROPN
ejpam-5971	199	36	4∑	4∑	NOUN
ejpam-5971	199	37	i=1	i=1	PROPN
ejpam-5971	199	38	ζ2i	ζ2i	PROPN
ejpam-5971	199	39			PROPN
ejpam-5971	199	40	⇐	⇐	ADJ
ejpam-5971	199	41	⇒	⇒	NOUN
ejpam-5971	199	42	(	(	PUNCT
ejpam-5971	199	43	4∑	4∑	NOUN
ejpam-5971	199	44	i=1	i=1	PROPN
ejpam-5971	199	45	|ζi|	|ζi|	NOUN
ejpam-5971	199	46	)	)	PUNCT
ejpam-5971	199	47	2	2	NUM
ejpam-5971	199	48	≤	≤	NUM
ejpam-5971	199	49	4	4	NUM
ejpam-5971	199	50	4∑	4∑	NUM
ejpam-5971	199	51	i=1	i=1	PROPN
ejpam-5971	199	52	ζ2i	ζ2i	PROPN
ejpam-5971	199	53	v.h	v.h	PROPN
ejpam-5971	199	54	.	.	PROPN
ejpam-5971	199	55	krisnawati	krisnawati	PROPN
ejpam-5971	199	56	,	,	PUNCT
ejpam-5971	199	57	n.	n.	PROPN
ejpam-5971	199	58	hidayat	hidayat	PROPN
ejpam-5971	199	59	,	,	PUNCT
ejpam-5971	199	60	a.f	a.f	PROPN
ejpam-5971	199	61	.	.	PROPN
ejpam-5971	199	62	musyarrofah	musyarrofah	PROPN
ejpam-5971	199	63	/	/	SYM
ejpam-5971	199	64	eur	eur	PROPN
ejpam-5971	199	65	.	.	PUNCT
ejpam-5971	200	1	j.	j.	PROPN
ejpam-5971	200	2	pure	pure	PROPN
ejpam-5971	200	3	appl	appl	PROPN
ejpam-5971	200	4	.	.	PROPN
ejpam-5971	200	5	math	math	PROPN
ejpam-5971	200	6	,	,	PUNCT
ejpam-5971	200	7	18	18	NUM
ejpam-5971	200	8	(	(	PUNCT
ejpam-5971	200	9	2	2	NUM
ejpam-5971	200	10	)	)	PUNCT
ejpam-5971	200	11	(	(	PUNCT
ejpam-5971	200	12	2025	2025	NUM
ejpam-5971	200	13	)	)	PUNCT
ejpam-5971	200	14	,	,	PUNCT
ejpam-5971	200	15	5971	5971	NUM
ejpam-5971	200	16	10	10	NUM
ejpam-5971	200	17	of	of	ADP
ejpam-5971	200	18	19	19	NUM
ejpam-5971	200	19	⇐	⇐	ADJ
ejpam-5971	200	20	⇒	⇒	NOUN
ejpam-5971	200	21	(	(	PUNCT
ejpam-5971	200	22	4∑	4∑	NOUN
ejpam-5971	200	23	i=1	i=1	PROPN
ejpam-5971	200	24	|ζi|	|ζi|	NOUN
ejpam-5971	200	25	)	)	PUNCT
ejpam-5971	200	26	2	2	NUM
ejpam-5971	200	27	≤	≤	NUM
ejpam-5971	200	28	4	4	NUM
ejpam-5971	200	29			PROPN
ejpam-5971	200	30	(	(	PUNCT
ejpam-5971	200	31	4∑	4∑	NOUN
ejpam-5971	200	32	i=1	i=1	PRON
ejpam-5971	200	33	ζi	ζi	PROPN
ejpam-5971	200	34	)	)	PUNCT
ejpam-5971	200	35	2	2	NUM
ejpam-5971	200	36	−	−	NOUN
ejpam-5971	200	37	2	2	NUM
ejpam-5971	201	1			PROPN
ejpam-5971	201	2	∑	∑	ADV
ejpam-5971	201	3	1≤i	1≤i	PROPN
ejpam-5971	201	4	<	<	X
ejpam-5971	201	5	j≤4	j≤4	NOUN
ejpam-5971	201	6	ζiζj	ζiζj	ADJ
ejpam-5971	201	7			PROPN
ejpam-5971	201	8	⇐	⇐	ADJ
ejpam-5971	201	9	⇒	⇒	NOUN
ejpam-5971	201	10	(	(	PUNCT
ejpam-5971	201	11	4∑	4∑	NOUN
ejpam-5971	201	12	i=1	i=1	PROPN
ejpam-5971	201	13	|ζi|	|ζi|	NOUN
ejpam-5971	201	14	)	)	PUNCT
ejpam-5971	201	15	2	2	NUM
ejpam-5971	201	16	≤	≤	NUM
ejpam-5971	201	17	4	4	NUM
ejpam-5971	201	18	(	(	PUNCT
ejpam-5971	201	19	(	(	PUNCT
ejpam-5971	201	20	℘2	℘2	NOUN
ejpam-5971	201	21	−	−	PROPN
ejpam-5971	201	22	3)2	3)2	NUM
ejpam-5971	201	23	−	−	NUM
ejpam-5971	201	24	2(−2℘5	2(−2℘5	PROPN
ejpam-5971	202	1	+	+	CCONJ
ejpam-5971	202	2	3℘4	3℘4	NUM
ejpam-5971	202	3	−	−	NOUN
ejpam-5971	202	4	2℘2	2℘2	NUM
ejpam-5971	202	5	+	+	CCONJ
ejpam-5971	202	6	2	2	NUM
ejpam-5971	202	7	)	)	PUNCT
ejpam-5971	202	8	)	)	PUNCT
ejpam-5971	203	1	⇐	⇐	ADJ
ejpam-5971	203	2	⇒	⇒	NOUN
ejpam-5971	203	3	4∑	4∑	NOUN
ejpam-5971	203	4	i=1	i=1	PROPN
ejpam-5971	203	5	|ζi|	|ζi|	NOUN
ejpam-5971	203	6	≤	≤	ADJ
ejpam-5971	203	7	2	2	NUM
ejpam-5971	203	8	√	√	NUM
ejpam-5971	203	9	4℘5	4℘5	NUM
ejpam-5971	203	10	−	−	PROPN
ejpam-5971	203	11	5℘4	5℘4	NUM
ejpam-5971	203	12	−	−	NUM
ejpam-5971	203	13	2℘2	2℘2	NUM
ejpam-5971	203	14	+	+	SYM
ejpam-5971	203	15	5	5	NUM
ejpam-5971	203	16	based	base	VERB
ejpam-5971	203	17	on	on	ADP
ejpam-5971	203	18	equation	equation	NOUN
ejpam-5971	203	19	(	(	PUNCT
ejpam-5971	203	20	6	6	NUM
ejpam-5971	203	21	)	)	PUNCT
ejpam-5971	203	22	,	,	PUNCT
ejpam-5971	203	23	we	we	PRON
ejpam-5971	203	24	have	have	VERB
ejpam-5971	203	25	en(g	en(g	NUM
ejpam-5971	203	26	)	)	PUNCT
ejpam-5971	203	27	≤	≤	NUM
ejpam-5971	203	28	℘2	℘2	NOUN
ejpam-5971	203	29	−	−	PROPN
ejpam-5971	203	30	3	3	NUM
ejpam-5971	203	31	+	+	CCONJ
ejpam-5971	203	32	2	2	NUM
ejpam-5971	203	33	√	√	NUM
ejpam-5971	203	34	4℘5	4℘5	NUM
ejpam-5971	203	35	−	−	PROPN
ejpam-5971	203	36	5℘4	5℘4	NUM
ejpam-5971	203	37	−	−	NUM
ejpam-5971	203	38	2℘2	2℘2	NUM
ejpam-5971	203	39	+	+	NUM
ejpam-5971	203	40	5	5	NUM
ejpam-5971	203	41	.	.	PUNCT
ejpam-5971	204	1	(	(	PUNCT
ejpam-5971	204	2	10	10	NUM
ejpam-5971	204	3	)	)	PUNCT
ejpam-5971	204	4	the	the	DET
ejpam-5971	204	5	equality	equality	NOUN
ejpam-5971	204	6	holds	hold	VERB
ejpam-5971	204	7	if	if	SCONJ
ejpam-5971	204	8	and	and	CCONJ
ejpam-5971	204	9	only	only	ADV
ejpam-5971	204	10	if	if	SCONJ
ejpam-5971	204	11	equality	equality	NOUN
ejpam-5971	204	12	holds	hold	VERB
ejpam-5971	204	13	in	in	ADP
ejpam-5971	204	14	equation	equation	NOUN
ejpam-5971	204	15	(	(	PUNCT
ejpam-5971	204	16	7	7	NUM
ejpam-5971	204	17	)	)	PUNCT
ejpam-5971	204	18	,	,	PUNCT
ejpam-5971	204	19	that	that	ADV
ejpam-5971	204	20	is	is	ADV
ejpam-5971	204	21	,	,	PUNCT
ejpam-5971	204	22	|ζ1|	|ζ1|	X
ejpam-5971	204	23	=	=	SYM
ejpam-5971	204	24	|ζ2|	|ζ2|	NOUN
ejpam-5971	204	25	=	=	SYM
ejpam-5971	204	26	|ζ3|	|ζ3|	NOUN
ejpam-5971	204	27	=	=	SYM
ejpam-5971	204	28	|ζ4|	|ζ4|	NOUN
ejpam-5971	204	29	.	.	PUNCT
ejpam-5971	205	1	next	next	ADV
ejpam-5971	205	2	,	,	PUNCT
ejpam-5971	205	3	we	we	PRON
ejpam-5971	205	4	determine	determine	VERB
ejpam-5971	205	5	the	the	DET
ejpam-5971	205	6	lower	low	ADJ
ejpam-5971	205	7	bound	bind	VERB
ejpam-5971	205	8	of	of	ADP
ejpam-5971	205	9	energy	energy	NOUN
ejpam-5971	205	10	of	of	ADP
ejpam-5971	205	11	g.	g.	PROPN
ejpam-5971	205	12	again	again	ADV
ejpam-5971	205	13	using	use	VERB
ejpam-5971	205	14	the	the	DET
ejpam-5971	205	15	inequality	inequality	NOUN
ejpam-5971	205	16	of	of	ADP
ejpam-5971	205	17	(	(	PUNCT
ejpam-5971	205	18	1	1	NUM
ejpam-5971	205	19	)	)	PUNCT
ejpam-5971	205	20	,	,	PUNCT
ejpam-5971	205	21	we	we	PRON
ejpam-5971	205	22	have	have	VERB
ejpam-5971	205	23	1	1	NUM
ejpam-5971	205	24	4(4−1	4(4−1	NUM
ejpam-5971	205	25	)	)	PUNCT
ejpam-5971	205	26	2	2	NUM
ejpam-5971	206	1			PROPN
ejpam-5971	206	2	∑	∑	PUNCT
ejpam-5971	206	3	1≤i	1≤i	PROPN
ejpam-5971	206	4	<	<	X
ejpam-5971	206	5	j≤4	j≤4	PROPN
ejpam-5971	206	6	|ζi||ζj	|ζi||ζj	PROPN
ejpam-5971	206	7	|	|	CCONJ
ejpam-5971	206	8			PROPN
ejpam-5971	206	9	≥	≥	PROPN
ejpam-5971	206	10	(	(	PUNCT
ejpam-5971	206	11	4∏	4∏	NUM
ejpam-5971	206	12	i=1	i=1	PROPN
ejpam-5971	206	13	|ζi|	|ζi|	PROPN
ejpam-5971	206	14	)	)	PUNCT
ejpam-5971	206	15	1/2	1/2	NUM
ejpam-5971	206	16	.	.	PUNCT
ejpam-5971	207	1	(	(	PUNCT
ejpam-5971	207	2	11	11	NUM
ejpam-5971	207	3	)	)	PUNCT
ejpam-5971	207	4	thus	thus	ADV
ejpam-5971	207	5	,	,	PUNCT
ejpam-5971	207	6	1	1	NUM
ejpam-5971	207	7	6	6	NUM
ejpam-5971	207	8			PROPN
ejpam-5971	207	9	∑	∑	PUNCT
ejpam-5971	207	10	1≤i	1≤i	PROPN
ejpam-5971	207	11	<	<	X
ejpam-5971	207	12	j≤4	j≤4	PROPN
ejpam-5971	207	13	|ζi||ζj	|ζi||ζj	PROPN
ejpam-5971	207	14	|	|	CCONJ
ejpam-5971	207	15			PROPN
ejpam-5971	207	16	≥	≥	PROPN
ejpam-5971	207	17	(	(	PUNCT
ejpam-5971	207	18	4∏	4∏	NUM
ejpam-5971	207	19	i=1	i=1	PROPN
ejpam-5971	207	20	|ζi|	|ζi|	PROPN
ejpam-5971	207	21	)	)	PUNCT
ejpam-5971	207	22	1/2	1/2	NUM
ejpam-5971	207	23	(	(	PUNCT
ejpam-5971	207	24	12	12	NUM
ejpam-5971	207	25	)	)	PUNCT
ejpam-5971	207	26	next	next	ADV
ejpam-5971	207	27	,	,	PUNCT
ejpam-5971	207	28	by	by	ADP
ejpam-5971	207	29	substituting	substitute	VERB
ejpam-5971	207	30	equation	equation	NOUN
ejpam-5971	207	31	(	(	PUNCT
ejpam-5971	207	32	9	9	NUM
ejpam-5971	207	33	)	)	PUNCT
ejpam-5971	207	34	into	into	ADP
ejpam-5971	207	35	equation	equation	NOUN
ejpam-5971	207	36	(	(	PUNCT
ejpam-5971	207	37	12	12	NUM
ejpam-5971	207	38	)	)	PUNCT
ejpam-5971	207	39	,	,	PUNCT
ejpam-5971	207	40	we	we	PRON
ejpam-5971	207	41	obtain	obtain	VERB
ejpam-5971	207	42	1	1	NUM
ejpam-5971	207	43	12	12	NUM
ejpam-5971	207	44			PROPN
ejpam-5971	207	45	(	(	PUNCT
ejpam-5971	207	46	4∑	4∑	NOUN
ejpam-5971	207	47	i=1	i=1	PROPN
ejpam-5971	207	48	|ζi|	|ζi|	NOUN
ejpam-5971	207	49	)	)	PUNCT
ejpam-5971	207	50	2	2	NUM
ejpam-5971	207	51	−	−	PROPN
ejpam-5971	207	52	4∑	4∑	NOUN
ejpam-5971	207	53	i=1	i=1	PROPN
ejpam-5971	207	54	ζ2i	ζ2i	VERB
ejpam-5971	208	1			PROPN
ejpam-5971	208	2	≥	≥	NUM
ejpam-5971	208	3	(	(	PUNCT
ejpam-5971	208	4	4∏	4∏	NUM
ejpam-5971	208	5	i=1	i=1	PROPN
ejpam-5971	208	6	|ζi|	|ζi|	PROPN
ejpam-5971	208	7	)	)	PUNCT
ejpam-5971	208	8	1/2	1/2	NUM
ejpam-5971	208	9	⇐	⇐	ADJ
ejpam-5971	208	10	⇒	⇒	NOUN
ejpam-5971	208	11	(	(	PUNCT
ejpam-5971	208	12	4∑	4∑	NOUN
ejpam-5971	208	13	i=1	i=1	PROPN
ejpam-5971	208	14	|ζi|	|ζi|	NOUN
ejpam-5971	208	15	)	)	PUNCT
ejpam-5971	208	16	2	2	NUM
ejpam-5971	208	17	≥	≥	NOUN
ejpam-5971	208	18	4∑	4∑	NUM
ejpam-5971	208	19	i=1	i=1	PROPN
ejpam-5971	208	20	ζ2i	ζ2i	PROPN
ejpam-5971	209	1	+	+	CCONJ
ejpam-5971	209	2	12	12	NUM
ejpam-5971	209	3	(	(	PUNCT
ejpam-5971	209	4	4∏	4∏	NUM
ejpam-5971	209	5	i=1	i=1	PROPN
ejpam-5971	209	6	|ζi|	|ζi|	PROPN
ejpam-5971	209	7	)	)	PUNCT
ejpam-5971	209	8	1/2	1/2	NUM
ejpam-5971	209	9	⇐	⇐	ADJ
ejpam-5971	209	10	⇒	⇒	NOUN
ejpam-5971	209	11	(	(	PUNCT
ejpam-5971	209	12	4∑	4∑	NOUN
ejpam-5971	209	13	i=1	i=1	PROPN
ejpam-5971	209	14	|ζi|	|ζi|	NOUN
ejpam-5971	209	15	)	)	PUNCT
ejpam-5971	209	16	2	2	NUM
ejpam-5971	209	17	≥	≥	NOUN
ejpam-5971	209	18	(	(	PUNCT
ejpam-5971	209	19	4∑	4∑	NOUN
ejpam-5971	209	20	i=1	i=1	PRON
ejpam-5971	209	21	ζi	ζi	PROPN
ejpam-5971	209	22	)	)	PUNCT
ejpam-5971	209	23	2	2	NUM
ejpam-5971	209	24	−	−	NOUN
ejpam-5971	209	25	2	2	NUM
ejpam-5971	210	1			PROPN
ejpam-5971	210	2	∑	∑	ADV
ejpam-5971	210	3	1≤i	1≤i	PROPN
ejpam-5971	210	4	<	<	X
ejpam-5971	210	5	j≤4	j≤4	NOUN
ejpam-5971	210	6	ζiζj	ζiζj	ADJ
ejpam-5971	210	7	+	+	PROPN
ejpam-5971	210	8	12	12	NUM
ejpam-5971	210	9	(	(	PUNCT
ejpam-5971	210	10	∣∣∣∣∣	∣∣∣∣∣	PROPN
ejpam-5971	210	11	4∏	4∏	NUM
ejpam-5971	210	12	i=1	i=1	X
ejpam-5971	210	13	ζi	ζi	PRON
ejpam-5971	210	14	∣∣∣∣∣	∣∣∣∣∣	ADJ
ejpam-5971	210	15	)	)	PUNCT
ejpam-5971	210	16	1/2	1/2	NUM
ejpam-5971	210	17	⇐	⇐	ADJ
ejpam-5971	210	18	⇒	⇒	NOUN
ejpam-5971	210	19	(	(	PUNCT
ejpam-5971	210	20	4∑	4∑	NOUN
ejpam-5971	210	21	i=1	i=1	PROPN
ejpam-5971	210	22	|ζi|	|ζi|	NOUN
ejpam-5971	210	23	)	)	PUNCT
ejpam-5971	210	24	2	2	NUM
ejpam-5971	210	25	≥	≥	NOUN
ejpam-5971	210	26	(	(	PUNCT
ejpam-5971	210	27	℘2	℘2	NOUN
ejpam-5971	210	28	−	−	PROPN
ejpam-5971	211	1	3)2	3)2	NUM
ejpam-5971	211	2	−	−	NUM
ejpam-5971	211	3	2(−2℘5	2(−2℘5	PROPN
ejpam-5971	212	1	+	+	CCONJ
ejpam-5971	212	2	3℘4	3℘4	NUM
ejpam-5971	212	3	−	−	NOUN
ejpam-5971	212	4	2℘2	2℘2	NUM
ejpam-5971	212	5	+	+	CCONJ
ejpam-5971	212	6	2	2	NUM
ejpam-5971	212	7	)	)	PUNCT
ejpam-5971	212	8	+	+	CCONJ
ejpam-5971	213	1	12(|℘6(℘−	12(|℘6(℘−	NUM
ejpam-5971	213	2	1)4|)1/2	1)4|)1/2	NUM
ejpam-5971	213	3	v.h	v.h	PROPN
ejpam-5971	213	4	.	.	PROPN
ejpam-5971	213	5	krisnawati	krisnawati	PROPN
ejpam-5971	213	6	,	,	PUNCT
ejpam-5971	213	7	n.	n.	PROPN
ejpam-5971	213	8	hidayat	hidayat	PROPN
ejpam-5971	213	9	,	,	PUNCT
ejpam-5971	213	10	a.f	a.f	PROPN
ejpam-5971	213	11	.	.	PROPN
ejpam-5971	213	12	musyarrofah	musyarrofah	PROPN
ejpam-5971	213	13	/	/	SYM
ejpam-5971	213	14	eur	eur	PROPN
ejpam-5971	213	15	.	.	PUNCT
ejpam-5971	214	1	j.	j.	PROPN
ejpam-5971	214	2	pure	pure	PROPN
ejpam-5971	214	3	appl	appl	PROPN
ejpam-5971	214	4	.	.	PROPN
ejpam-5971	214	5	math	math	PROPN
ejpam-5971	214	6	,	,	PUNCT
ejpam-5971	214	7	18	18	NUM
ejpam-5971	214	8	(	(	PUNCT
ejpam-5971	214	9	2	2	NUM
ejpam-5971	214	10	)	)	PUNCT
ejpam-5971	214	11	(	(	PUNCT
ejpam-5971	214	12	2025	2025	NUM
ejpam-5971	214	13	)	)	PUNCT
ejpam-5971	214	14	,	,	PUNCT
ejpam-5971	214	15	5971	5971	NUM
ejpam-5971	214	16	11	11	NUM
ejpam-5971	214	17	of	of	ADP
ejpam-5971	214	18	19	19	NUM
ejpam-5971	214	19	⇐	⇐	ADJ
ejpam-5971	214	20	⇒	⇒	NOUN
ejpam-5971	214	21	4∑	4∑	PROPN
ejpam-5971	214	22	i=1	i=1	PROPN
ejpam-5971	214	23	|ζi|	|ζi|	NOUN
ejpam-5971	214	24	≥	≥	NOUN
ejpam-5971	214	25	√	√	PROPN
ejpam-5971	214	26	4℘5	4℘5	NUM
ejpam-5971	214	27	−	−	PROPN
ejpam-5971	214	28	5℘4	5℘4	NUM
ejpam-5971	214	29	−	−	NUM
ejpam-5971	214	30	2℘2	2℘2	NUM
ejpam-5971	214	31	+	+	CCONJ
ejpam-5971	214	32	5	5	NUM
ejpam-5971	214	33	+	+	SYM
ejpam-5971	214	34	12(℘6(℘−	12(℘6(℘−	NUM
ejpam-5971	214	35	1)4)1/2	1)4)1/2	NUM
ejpam-5971	214	36	.	.	PUNCT
ejpam-5971	215	1	based	base	VERB
ejpam-5971	215	2	on	on	ADP
ejpam-5971	215	3	equation	equation	NOUN
ejpam-5971	215	4	(	(	PUNCT
ejpam-5971	215	5	6	6	NUM
ejpam-5971	215	6	)	)	PUNCT
ejpam-5971	215	7	,	,	PUNCT
ejpam-5971	215	8	we	we	PRON
ejpam-5971	215	9	get	get	VERB
ejpam-5971	215	10	en(g	en(g	NUM
ejpam-5971	215	11	)	)	PUNCT
ejpam-5971	216	1	≥	≥	PROPN
ejpam-5971	216	2	℘2	℘2	NOUN
ejpam-5971	216	3	−	−	PROPN
ejpam-5971	216	4	3	3	NUM
ejpam-5971	216	5	+	+	CCONJ
ejpam-5971	216	6	√	√	PROPN
ejpam-5971	216	7	4℘5	4℘5	NUM
ejpam-5971	216	8	−	−	PROPN
ejpam-5971	216	9	5℘4	5℘4	NUM
ejpam-5971	216	10	−	−	NUM
ejpam-5971	216	11	2℘2	2℘2	NUM
ejpam-5971	216	12	+	+	CCONJ
ejpam-5971	216	13	5	5	NUM
ejpam-5971	216	14	+	+	SYM
ejpam-5971	216	15	12(℘6(℘−	12(℘6(℘−	NUM
ejpam-5971	216	16	1)4)1/2	1)4)1/2	NUM
ejpam-5971	216	17	.	.	PUNCT
ejpam-5971	217	1	(	(	PUNCT
ejpam-5971	217	2	13	13	X
ejpam-5971	217	3	)	)	PUNCT
ejpam-5971	217	4	equality	equality	NOUN
ejpam-5971	217	5	holds	hold	VERB
ejpam-5971	217	6	if	if	SCONJ
ejpam-5971	217	7	and	and	CCONJ
ejpam-5971	217	8	only	only	ADV
ejpam-5971	217	9	if	if	SCONJ
ejpam-5971	217	10	|ζ1|	|ζ1|	NOUN
ejpam-5971	217	11	=	=	SYM
ejpam-5971	217	12	|ζ2|	|ζ2|	NOUN
ejpam-5971	217	13	=	=	SYM
ejpam-5971	217	14	|ζ3|	|ζ3|	NOUN
ejpam-5971	217	15	=	=	SYM
ejpam-5971	217	16	|ζ4|	|ζ4|	NOUN
ejpam-5971	217	17	.	.	PUNCT
ejpam-5971	218	1	therefore	therefore	ADV
ejpam-5971	218	2	,	,	PUNCT
ejpam-5971	218	3	from	from	ADP
ejpam-5971	218	4	(	(	PUNCT
ejpam-5971	218	5	13	13	NUM
ejpam-5971	218	6	)	)	PUNCT
ejpam-5971	218	7	and	and	CCONJ
ejpam-5971	218	8	(	(	PUNCT
ejpam-5971	218	9	10	10	NUM
ejpam-5971	218	10	)	)	PUNCT
ejpam-5971	218	11	,	,	PUNCT
ejpam-5971	218	12	we	we	PRON
ejpam-5971	218	13	get	get	VERB
ejpam-5971	218	14	en(g	en(g	NUM
ejpam-5971	218	15	)	)	PUNCT
ejpam-5971	218	16	≥	≥	PROPN
ejpam-5971	218	17	℘2	℘2	NOUN
ejpam-5971	218	18	−	−	PROPN
ejpam-5971	218	19	3	3	NUM
ejpam-5971	218	20	+	+	CCONJ
ejpam-5971	218	21	√	√	PROPN
ejpam-5971	218	22	4℘5	4℘5	NUM
ejpam-5971	218	23	−	−	PROPN
ejpam-5971	218	24	5℘4	5℘4	NUM
ejpam-5971	218	25	−	−	NUM
ejpam-5971	218	26	2℘2	2℘2	NUM
ejpam-5971	218	27	+	+	CCONJ
ejpam-5971	218	28	5	5	NUM
ejpam-5971	218	29	+	+	SYM
ejpam-5971	218	30	12(℘6(℘−	12(℘6(℘−	NUM
ejpam-5971	218	31	1)4)1/2	1)4)1/2	NUM
ejpam-5971	218	32	and	and	CCONJ
ejpam-5971	218	33	en(g	en(g	NUM
ejpam-5971	218	34	)	)	PUNCT
ejpam-5971	218	35	≤	≤	NUM
ejpam-5971	218	36	℘2	℘2	NOUN
ejpam-5971	218	37	−	−	PROPN
ejpam-5971	218	38	3	3	NUM
ejpam-5971	218	39	+	+	CCONJ
ejpam-5971	218	40	2	2	NUM
ejpam-5971	218	41	√	√	NUM
ejpam-5971	218	42	4℘5	4℘5	NUM
ejpam-5971	218	43	−	−	PROPN
ejpam-5971	218	44	5℘4	5℘4	NUM
ejpam-5971	218	45	−	−	NUM
ejpam-5971	218	46	2℘2	2℘2	NUM
ejpam-5971	218	47	+	+	NUM
ejpam-5971	218	48	5	5	X
ejpam-5971	218	49	.	.	X
ejpam-5971	218	50	for	for	ADP
ejpam-5971	218	51	example	example	NOUN
ejpam-5971	218	52	,	,	PUNCT
ejpam-5971	218	53	if	if	SCONJ
ejpam-5971	218	54	℘	℘	NUM
ejpam-5971	218	55	=	=	SYM
ejpam-5971	218	56	2	2	NUM
ejpam-5971	218	57	,	,	PUNCT
ejpam-5971	218	58	the	the	DET
ejpam-5971	218	59	vertex	vertex	NOUN
ejpam-5971	218	60	set	set	NOUN
ejpam-5971	218	61	of	of	ADP
ejpam-5971	218	62	γ(z2[x]/⟨x5⟩	γ(z2[x]/⟨x5⟩	PROPN
ejpam-5971	218	63	)	)	PUNCT
ejpam-5971	218	64	is	be	AUX
ejpam-5971	218	65	given	give	VERB
ejpam-5971	218	66	by	by	ADP
ejpam-5971	218	67	a	a	DET
ejpam-5971	218	68	=	=	SYM
ejpam-5971	218	69	{	{	PUNCT
ejpam-5971	218	70	x	x	NOUN
ejpam-5971	218	71	,	,	PUNCT
ejpam-5971	218	72	x2	x2	PROPN
ejpam-5971	219	1	+	+	CCONJ
ejpam-5971	219	2	x	x	X
ejpam-5971	219	3	,	,	PUNCT
ejpam-5971	219	4	x3	x3	VERB
ejpam-5971	219	5	+	+	CCONJ
ejpam-5971	219	6	x	x	X
ejpam-5971	219	7	,	,	PUNCT
ejpam-5971	219	8	x3	x3	VERB
ejpam-5971	220	1	+	+	CCONJ
ejpam-5971	220	2	x2	x2	PROPN
ejpam-5971	221	1	+	+	CCONJ
ejpam-5971	221	2	x	x	SYM
ejpam-5971	221	3	,	,	PUNCT
ejpam-5971	221	4	x4	x4	PROPN
ejpam-5971	222	1	+	+	CCONJ
ejpam-5971	222	2	x	x	SYM
ejpam-5971	222	3	,	,	PUNCT
ejpam-5971	222	4	x4	x4	PROPN
ejpam-5971	222	5	+	+	CCONJ
ejpam-5971	223	1	x2	x2	PROPN
ejpam-5971	224	1	+	+	CCONJ
ejpam-5971	224	2	x	x	SYM
ejpam-5971	224	3	,	,	PUNCT
ejpam-5971	224	4	x4	x4	PROPN
ejpam-5971	225	1	+	+	CCONJ
ejpam-5971	225	2	x3	x3	ADJ
ejpam-5971	225	3	+	+	CCONJ
ejpam-5971	225	4	x	x	SYM
ejpam-5971	225	5	,	,	PUNCT
ejpam-5971	225	6	x4	x4	PROPN
ejpam-5971	226	1	+	+	CCONJ
ejpam-5971	226	2	x3	x3	ADJ
ejpam-5971	226	3	+	+	CCONJ
ejpam-5971	226	4	x2	x2	PROPN
ejpam-5971	227	1	+	+	CCONJ
ejpam-5971	227	2	x	x	X
ejpam-5971	227	3	}	}	PUNCT
ejpam-5971	227	4	,	,	PUNCT
ejpam-5971	227	5	b	b	X
ejpam-5971	227	6	=	=	PRON
ejpam-5971	227	7	{	{	PUNCT
ejpam-5971	227	8	x2	x2	PROPN
ejpam-5971	227	9	,	,	PUNCT
ejpam-5971	227	10	x3	x3	PROPN
ejpam-5971	227	11	+	+	CCONJ
ejpam-5971	227	12	x2	x2	ADJ
ejpam-5971	227	13	,	,	PUNCT
ejpam-5971	227	14	x4	x4	PROPN
ejpam-5971	228	1	+	+	CCONJ
ejpam-5971	228	2	x2	x2	PROPN
ejpam-5971	228	3	,	,	PUNCT
ejpam-5971	228	4	x4	x4	PROPN
ejpam-5971	229	1	+	+	CCONJ
ejpam-5971	229	2	x3	x3	ADJ
ejpam-5971	229	3	+	+	CCONJ
ejpam-5971	229	4	x2	x2	ADJ
ejpam-5971	229	5	}	}	PUNCT
ejpam-5971	229	6	,	,	PUNCT
ejpam-5971	229	7	c	c	X
ejpam-5971	229	8	=	=	PRON
ejpam-5971	229	9	{	{	PUNCT
ejpam-5971	229	10	x3	x3	PROPN
ejpam-5971	229	11	,	,	PUNCT
ejpam-5971	229	12	x4	x4	PROPN
ejpam-5971	229	13	+	+	CCONJ
ejpam-5971	229	14	x3	x3	ADJ
ejpam-5971	229	15	}	}	PUNCT
ejpam-5971	229	16	,	,	PUNCT
ejpam-5971	229	17	andd	andd	PROPN
ejpam-5971	229	18	=	=	PRON
ejpam-5971	229	19	{	{	PUNCT
ejpam-5971	229	20	x4	x4	PROPN
ejpam-5971	229	21	}	}	PUNCT
ejpam-5971	229	22	.	.	PUNCT
ejpam-5971	230	1	the	the	DET
ejpam-5971	230	2	zero	zero	NUM
ejpam-5971	230	3	-	-	PUNCT
ejpam-5971	230	4	divisor	divisor	NOUN
ejpam-5971	230	5	graph	graph	NOUN
ejpam-5971	230	6	of	of	ADP
ejpam-5971	230	7	z2[x]/⟨x5⟩	z2[x]/⟨x5⟩	PROPN
ejpam-5971	230	8	is	be	AUX
ejpam-5971	230	9	presented	present	VERB
ejpam-5971	230	10	in	in	ADP
ejpam-5971	230	11	figure	figure	NOUN
ejpam-5971	230	12	1	1	NUM
ejpam-5971	230	13	.	.	PUNCT
ejpam-5971	231	1	figure	figure	NOUN
ejpam-5971	231	2	1	1	NUM
ejpam-5971	231	3	:	:	PUNCT
ejpam-5971	231	4	γ(z2[x]/⟨x5⟩	γ(z2[x]/⟨x5⟩	PROPN
ejpam-5971	231	5	)	)	PUNCT
ejpam-5971	232	1	v.h	v.h	PROPN
ejpam-5971	232	2	.	.	PROPN
ejpam-5971	232	3	krisnawati	krisnawati	PROPN
ejpam-5971	232	4	,	,	PUNCT
ejpam-5971	232	5	n.	n.	PROPN
ejpam-5971	232	6	hidayat	hidayat	PROPN
ejpam-5971	232	7	,	,	PUNCT
ejpam-5971	232	8	a.f	a.f	PROPN
ejpam-5971	232	9	.	.	PROPN
ejpam-5971	232	10	musyarrofah	musyarrofah	PROPN
ejpam-5971	232	11	/	/	SYM
ejpam-5971	232	12	eur	eur	PROPN
ejpam-5971	232	13	.	.	PUNCT
ejpam-5971	233	1	j.	j.	PROPN
ejpam-5971	233	2	pure	pure	PROPN
ejpam-5971	233	3	appl	appl	PROPN
ejpam-5971	233	4	.	.	PROPN
ejpam-5971	233	5	math	math	PROPN
ejpam-5971	233	6	,	,	PUNCT
ejpam-5971	233	7	18	18	NUM
ejpam-5971	233	8	(	(	PUNCT
ejpam-5971	233	9	2	2	NUM
ejpam-5971	233	10	)	)	PUNCT
ejpam-5971	233	11	(	(	PUNCT
ejpam-5971	233	12	2025	2025	NUM
ejpam-5971	233	13	)	)	PUNCT
ejpam-5971	233	14	,	,	PUNCT
ejpam-5971	233	15	5971	5971	NUM
ejpam-5971	233	16	12	12	NUM
ejpam-5971	233	17	of	of	ADP
ejpam-5971	233	18	19	19	NUM
ejpam-5971	233	19	the	the	DET
ejpam-5971	233	20	adjacency	adjacency	NOUN
ejpam-5971	233	21	matrix	matrix	NOUN
ejpam-5971	233	22	of	of	ADP
ejpam-5971	233	23	γ(z2[x]/⟨x5⟩	γ(z2[x]/⟨x5⟩	PROPN
ejpam-5971	233	24	)	)	PUNCT
ejpam-5971	233	25	is	be	AUX
ejpam-5971	233	26	a(γ(z2[x]/⟨x5⟩	a(γ(z2[x]/⟨x5⟩	NOUN
ejpam-5971	233	27	)	)	PUNCT
ejpam-5971	233	28	)	)	PUNCT
ejpam-5971	234	1	=	=	SYM
ejpam-5971	234	2			NOUN
ejpam-5971	234	3	0	0	NUM
ejpam-5971	234	4	0	0	NUM
ejpam-5971	234	5	0	0	NUM
ejpam-5971	234	6	0	0	NUM
ejpam-5971	234	7	0	0	NUM
ejpam-5971	234	8	0	0	NUM
ejpam-5971	234	9	0	0	NUM
ejpam-5971	234	10	0	0	NUM
ejpam-5971	234	11	0	0	NUM
ejpam-5971	234	12	0	0	NUM
ejpam-5971	234	13	0	0	NUM
ejpam-5971	234	14	0	0	NUM
ejpam-5971	234	15	0	0	NUM
ejpam-5971	234	16	0	0	NUM
ejpam-5971	234	17	1	1	NUM
ejpam-5971	234	18	0	0	NUM
ejpam-5971	234	19	0	0	NUM
ejpam-5971	234	20	0	0	NUM
ejpam-5971	234	21	0	0	NUM
ejpam-5971	234	22	0	0	NUM
ejpam-5971	234	23	0	0	NUM
ejpam-5971	234	24	0	0	NUM
ejpam-5971	234	25	0	0	NUM
ejpam-5971	234	26	0	0	NUM
ejpam-5971	234	27	0	0	NUM
ejpam-5971	234	28	0	0	NUM
ejpam-5971	234	29	0	0	NUM
ejpam-5971	234	30	0	0	NUM
ejpam-5971	234	31	0	0	NUM
ejpam-5971	234	32	1	1	NUM
ejpam-5971	234	33	0	0	NUM
ejpam-5971	234	34	0	0	NUM
ejpam-5971	234	35	0	0	NUM
ejpam-5971	234	36	0	0	NUM
ejpam-5971	234	37	0	0	NUM
ejpam-5971	234	38	0	0	NUM
ejpam-5971	234	39	0	0	NUM
ejpam-5971	234	40	0	0	NUM
ejpam-5971	234	41	0	0	NUM
ejpam-5971	234	42	0	0	NUM
ejpam-5971	234	43	0	0	NUM
ejpam-5971	234	44	0	0	NUM
ejpam-5971	234	45	0	0	NUM
ejpam-5971	234	46	0	0	NUM
ejpam-5971	234	47	1	1	NUM
ejpam-5971	234	48	0	0	NUM
ejpam-5971	234	49	0	0	NUM
ejpam-5971	234	50	0	0	NUM
ejpam-5971	234	51	0	0	NUM
ejpam-5971	234	52	0	0	NUM
ejpam-5971	234	53	0	0	NUM
ejpam-5971	234	54	0	0	NUM
ejpam-5971	234	55	0	0	NUM
ejpam-5971	234	56	0	0	NUM
ejpam-5971	234	57	0	0	NUM
ejpam-5971	234	58	0	0	NUM
ejpam-5971	234	59	0	0	NUM
ejpam-5971	234	60	0	0	NUM
ejpam-5971	234	61	0	0	NUM
ejpam-5971	234	62	1	1	NUM
ejpam-5971	234	63	0	0	NUM
ejpam-5971	234	64	0	0	NUM
ejpam-5971	234	65	0	0	NUM
ejpam-5971	234	66	0	0	NUM
ejpam-5971	234	67	0	0	NUM
ejpam-5971	234	68	0	0	NUM
ejpam-5971	234	69	0	0	NUM
ejpam-5971	234	70	0	0	NUM
ejpam-5971	234	71	0	0	NUM
ejpam-5971	234	72	0	0	NUM
ejpam-5971	234	73	0	0	NUM
ejpam-5971	234	74	0	0	NUM
ejpam-5971	234	75	0	0	NUM
ejpam-5971	234	76	0	0	NUM
ejpam-5971	234	77	1	1	NUM
ejpam-5971	234	78	0	0	NUM
ejpam-5971	234	79	0	0	NUM
ejpam-5971	234	80	0	0	NUM
ejpam-5971	234	81	0	0	NUM
ejpam-5971	234	82	0	0	NUM
ejpam-5971	234	83	0	0	NUM
ejpam-5971	234	84	0	0	NUM
ejpam-5971	234	85	0	0	NUM
ejpam-5971	234	86	0	0	NUM
ejpam-5971	234	87	0	0	NUM
ejpam-5971	234	88	0	0	NUM
ejpam-5971	234	89	0	0	NUM
ejpam-5971	234	90	0	0	NUM
ejpam-5971	234	91	0	0	NUM
ejpam-5971	234	92	1	1	NUM
ejpam-5971	234	93	0	0	NUM
ejpam-5971	234	94	0	0	NUM
ejpam-5971	234	95	0	0	NUM
ejpam-5971	234	96	0	0	NUM
ejpam-5971	234	97	0	0	NUM
ejpam-5971	234	98	0	0	NUM
ejpam-5971	234	99	0	0	NUM
ejpam-5971	234	100	0	0	NUM
ejpam-5971	234	101	0	0	NUM
ejpam-5971	234	102	0	0	NUM
ejpam-5971	234	103	0	0	NUM
ejpam-5971	234	104	0	0	NUM
ejpam-5971	234	105	0	0	NUM
ejpam-5971	234	106	0	0	NUM
ejpam-5971	234	107	1	1	NUM
ejpam-5971	234	108	0	0	NUM
ejpam-5971	234	109	0	0	NUM
ejpam-5971	234	110	0	0	NUM
ejpam-5971	234	111	0	0	NUM
ejpam-5971	234	112	0	0	NUM
ejpam-5971	234	113	0	0	NUM
ejpam-5971	234	114	0	0	NUM
ejpam-5971	234	115	0	0	NUM
ejpam-5971	234	116	0	0	NUM
ejpam-5971	234	117	0	0	NUM
ejpam-5971	234	118	0	0	NUM
ejpam-5971	234	119	0	0	NUM
ejpam-5971	234	120	0	0	NUM
ejpam-5971	234	121	0	0	NUM
ejpam-5971	234	122	1	1	NUM
ejpam-5971	234	123	0	0	NUM
ejpam-5971	234	124	0	0	NUM
ejpam-5971	234	125	0	0	NUM
ejpam-5971	234	126	0	0	NUM
ejpam-5971	234	127	0	0	NUM
ejpam-5971	234	128	0	0	NUM
ejpam-5971	234	129	0	0	NUM
ejpam-5971	234	130	0	0	NUM
ejpam-5971	234	131	0	0	NUM
ejpam-5971	234	132	0	0	NUM
ejpam-5971	234	133	0	0	NUM
ejpam-5971	234	134	0	0	NUM
ejpam-5971	234	135	1	1	NUM
ejpam-5971	234	136	1	1	NUM
ejpam-5971	234	137	1	1	NUM
ejpam-5971	234	138	0	0	NUM
ejpam-5971	234	139	0	0	NUM
ejpam-5971	234	140	0	0	NUM
ejpam-5971	234	141	0	0	NUM
ejpam-5971	234	142	0	0	NUM
ejpam-5971	234	143	0	0	NUM
ejpam-5971	234	144	0	0	NUM
ejpam-5971	234	145	0	0	NUM
ejpam-5971	234	146	0	0	NUM
ejpam-5971	234	147	0	0	NUM
ejpam-5971	234	148	0	0	NUM
ejpam-5971	234	149	0	0	NUM
ejpam-5971	234	150	1	1	NUM
ejpam-5971	234	151	1	1	NUM
ejpam-5971	234	152	1	1	NUM
ejpam-5971	234	153	0	0	NUM
ejpam-5971	234	154	0	0	NUM
ejpam-5971	234	155	0	0	NUM
ejpam-5971	234	156	0	0	NUM
ejpam-5971	234	157	0	0	NUM
ejpam-5971	234	158	0	0	NUM
ejpam-5971	234	159	0	0	NUM
ejpam-5971	234	160	0	0	NUM
ejpam-5971	234	161	0	0	NUM
ejpam-5971	234	162	0	0	NUM
ejpam-5971	234	163	0	0	NUM
ejpam-5971	234	164	0	0	NUM
ejpam-5971	234	165	1	1	NUM
ejpam-5971	234	166	1	1	NUM
ejpam-5971	234	167	1	1	NUM
ejpam-5971	234	168	0	0	NUM
ejpam-5971	234	169	0	0	NUM
ejpam-5971	234	170	0	0	NUM
ejpam-5971	234	171	0	0	NUM
ejpam-5971	234	172	0	0	NUM
ejpam-5971	234	173	0	0	NUM
ejpam-5971	234	174	0	0	NUM
ejpam-5971	234	175	0	0	NUM
ejpam-5971	234	176	0	0	NUM
ejpam-5971	234	177	0	0	NUM
ejpam-5971	234	178	0	0	NUM
ejpam-5971	234	179	0	0	NUM
ejpam-5971	234	180	1	1	NUM
ejpam-5971	234	181	1	1	NUM
ejpam-5971	234	182	1	1	NUM
ejpam-5971	234	183	0	0	NUM
ejpam-5971	234	184	0	0	NUM
ejpam-5971	234	185	0	0	NUM
ejpam-5971	234	186	0	0	NUM
ejpam-5971	234	187	0	0	NUM
ejpam-5971	234	188	0	0	NUM
ejpam-5971	234	189	0	0	NUM
ejpam-5971	234	190	0	0	NUM
ejpam-5971	234	191	1	1	NUM
ejpam-5971	234	192	1	1	NUM
ejpam-5971	234	193	1	1	NUM
ejpam-5971	234	194	1	1	NUM
ejpam-5971	234	195	0	0	NUM
ejpam-5971	234	196	1	1	NUM
ejpam-5971	234	197	1	1	NUM
ejpam-5971	234	198	0	0	NUM
ejpam-5971	234	199	0	0	NUM
ejpam-5971	234	200	0	0	NUM
ejpam-5971	234	201	0	0	NUM
ejpam-5971	234	202	0	0	NUM
ejpam-5971	234	203	0	0	NUM
ejpam-5971	234	204	0	0	NUM
ejpam-5971	234	205	0	0	NUM
ejpam-5971	234	206	1	1	NUM
ejpam-5971	234	207	1	1	NUM
ejpam-5971	234	208	1	1	NUM
ejpam-5971	234	209	1	1	NUM
ejpam-5971	234	210	1	1	NUM
ejpam-5971	234	211	0	0	NUM
ejpam-5971	234	212	1	1	NUM
ejpam-5971	234	213	1	1	NUM
ejpam-5971	234	214	1	1	NUM
ejpam-5971	234	215	1	1	NUM
ejpam-5971	234	216	1	1	NUM
ejpam-5971	234	217	1	1	NUM
ejpam-5971	234	218	1	1	NUM
ejpam-5971	234	219	1	1	NUM
ejpam-5971	234	220	1	1	NUM
ejpam-5971	234	221	1	1	NUM
ejpam-5971	234	222	1	1	NUM
ejpam-5971	234	223	1	1	NUM
ejpam-5971	234	224	1	1	NUM
ejpam-5971	234	225	1	1	NUM
ejpam-5971	234	226	1	1	NUM
ejpam-5971	234	227	0	0	NUM
ejpam-5971	234	228			NUM
ejpam-5971	234	229	=	=	SYM
ejpam-5971	234	230			NOUN
ejpam-5971	234	231	o8	o8	NOUN
ejpam-5971	234	232	o8×4	o8×4	NOUN
ejpam-5971	234	233	o8×2	o8×2	PROPN
ejpam-5971	235	1	n8×1	n8×1	ADJ
ejpam-5971	235	2	o4×8	o4×8	NOUN
ejpam-5971	235	3	o4	o4	PROPN
ejpam-5971	235	4	n4×2	n4×2	ADJ
ejpam-5971	235	5	n4×1	n4×1	NOUN
ejpam-5971	235	6	o2×8	o2×8	PROPN
ejpam-5971	235	7	n2×4	n2×4	ADV
ejpam-5971	235	8	n2	n2	ADJ
ejpam-5971	235	9	−	−	PROPN
ejpam-5971	235	10	i2	i2	PROPN
ejpam-5971	235	11	n2×1	n2×1	NOUN
ejpam-5971	235	12	n1×8	n1×8	PROPN
ejpam-5971	235	13	n1×4	n1×4	PROPN
ejpam-5971	235	14	n1×2	n1×2	NOUN
ejpam-5971	235	15	n1	n1	PROPN
ejpam-5971	235	16	−	−	PROPN
ejpam-5971	235	17	i1	i1	PROPN
ejpam-5971	235	18	.	.	PROPN
ejpam-5971	235	19	by	by	ADP
ejpam-5971	235	20	using	use	VERB
ejpam-5971	235	21	maple	maple	NOUN
ejpam-5971	235	22	software	software	NOUN
ejpam-5971	235	23	,	,	PUNCT
ejpam-5971	235	24	the	the	DET
ejpam-5971	235	25	characteristic	characteristic	ADJ
ejpam-5971	235	26	equation	equation	NOUN
ejpam-5971	235	27	of	of	ADP
ejpam-5971	235	28	the	the	DET
ejpam-5971	235	29	matrix	matrix	NOUN
ejpam-5971	235	30	is	be	AUX
ejpam-5971	235	31	obtained	obtain	VERB
ejpam-5971	235	32	as	as	ADP
ejpam-5971	235	33	:	:	PUNCT
ejpam-5971	235	34	(	(	PUNCT
ejpam-5971	235	35	−λ)10(−λ−	−λ)10(−λ−	NUM
ejpam-5971	235	36	1)(λ4	1)(λ4	NUM
ejpam-5971	235	37	−	−	PROPN
ejpam-5971	236	1	λ3	λ3	PROPN
ejpam-5971	236	2	−	−	PROPN
ejpam-5971	236	3	22λ2	22λ2	NUM
ejpam-5971	236	4	−	−	PROPN
ejpam-5971	236	5	4λ+	4λ+	NUM
ejpam-5971	236	6	64	64	NUM
ejpam-5971	236	7	)	)	PUNCT
ejpam-5971	236	8	=	=	SYM
ejpam-5971	237	1	0	0	X
ejpam-5971	237	2	.	.	PUNCT
ejpam-5971	238	1	and	and	CCONJ
ejpam-5971	238	2	its	its	PRON
ejpam-5971	238	3	approximated	approximate	VERB
ejpam-5971	238	4	the	the	DET
ejpam-5971	238	5	zeros	zero	NOUN
ejpam-5971	238	6	are	be	AUX
ejpam-5971	238	7	0,-1,-3.4746	0,-1,-3.4746	NUM
ejpam-5971	238	8	,	,	PUNCT
ejpam-5971	238	9	-2.2111	-2.2111	NOUN
ejpam-5971	238	10	,	,	PUNCT
ejpam-5971	238	11	1.6564	1.6564	NUM
ejpam-5971	238	12	,	,	PUNCT
ejpam-5971	238	13	5.0294	5.0294	NUM
ejpam-5971	238	14	.	.	PUNCT
ejpam-5971	239	1	thus	thus	ADV
ejpam-5971	239	2	,	,	PUNCT
ejpam-5971	239	3	the	the	DET
ejpam-5971	239	4	spectrum	spectrum	NOUN
ejpam-5971	239	5	of	of	ADP
ejpam-5971	239	6	γ(z2[x]/⟨x5⟩	γ(z2[x]/⟨x5⟩	PROPN
ejpam-5971	239	7	is	be	AUX
ejpam-5971	239	8	{	{	PUNCT
ejpam-5971	239	9	0[10],−1,−3.4746,−2.2111	0[10],−1,−3.4746,−2.2111	PROPN
ejpam-5971	239	10	,	,	PUNCT
ejpam-5971	239	11	1.6564	1.6564	NUM
ejpam-5971	239	12	,	,	PUNCT
ejpam-5971	239	13	5.0294	5.0294	NUM
ejpam-5971	239	14	}	}	PUNCT
ejpam-5971	239	15	.	.	PUNCT
ejpam-5971	240	1	from	from	ADP
ejpam-5971	240	2	this	this	DET
ejpam-5971	240	3	spectrum	spectrum	NOUN
ejpam-5971	240	4	,	,	PUNCT
ejpam-5971	240	5	we	we	PRON
ejpam-5971	240	6	calculate	calculate	VERB
ejpam-5971	240	7	the	the	DET
ejpam-5971	240	8	energy	energy	NOUN
ejpam-5971	240	9	of	of	ADP
ejpam-5971	240	10	γ(z2[x]/⟨x5⟩	γ(z2[x]/⟨x5⟩	PROPN
ejpam-5971	240	11	)	)	PUNCT
ejpam-5971	240	12	and	and	CCONJ
ejpam-5971	240	13	we	we	PRON
ejpam-5971	240	14	have	have	VERB
ejpam-5971	240	15	en(γ(z2[x]/⟨x5⟩	en(γ(z2[x]/⟨x5⟩	NUM
ejpam-5971	240	16	)	)	PUNCT
ejpam-5971	240	17	)	)	PUNCT
ejpam-5971	241	1	=	=	PUNCT
ejpam-5971	242	1	15∑	15∑	NUM
ejpam-5971	242	2	i=1	i=1	PRON
ejpam-5971	242	3	|λi|	|λi|	X
ejpam-5971	243	1	=	=	PUNCT
ejpam-5971	243	2	|	|	ADV
ejpam-5971	243	3	−	−	PROPN
ejpam-5971	244	1	1|+	1|+	NUM
ejpam-5971	245	1	|	|	ADV
ejpam-5971	245	2	−	−	PROPN
ejpam-5971	245	3	3.4746|+	3.4746|+	NOUN
ejpam-5971	246	1	|	|	ADV
ejpam-5971	246	2	−	−	PROPN
ejpam-5971	246	3	2.2111|+	2.2111|+	NUM
ejpam-5971	246	4	|1.6564|+	|1.6564|+	X
ejpam-5971	246	5	|5.0294|	|5.0294|	NOUN
ejpam-5971	246	6	=	=	NOUN
ejpam-5971	246	7	13.3715	13.3715	NUM
ejpam-5971	246	8	.	.	PUNCT
ejpam-5971	247	1	to	to	PART
ejpam-5971	247	2	further	far	ADV
ejpam-5971	247	3	validate	validate	VERB
ejpam-5971	247	4	these	these	DET
ejpam-5971	247	5	results	result	NOUN
ejpam-5971	247	6	,	,	PUNCT
ejpam-5971	247	7	we	we	PRON
ejpam-5971	247	8	compute	compute	VERB
ejpam-5971	247	9	the	the	DET
ejpam-5971	247	10	eigenvalues	eigenvalue	NOUN
ejpam-5971	247	11	and	and	CCONJ
ejpam-5971	247	12	energy	energy	NOUN
ejpam-5971	247	13	of	of	ADP
ejpam-5971	247	14	γ(z2[x]/⟨x5⟩	γ(z2[x]/⟨x5⟩	PROPN
ejpam-5971	247	15	)	)	PUNCT
ejpam-5971	247	16	using	use	VERB
ejpam-5971	247	17	theorem	theorem	ADJ
ejpam-5971	247	18	1	1	NUM
ejpam-5971	247	19	and	and	CCONJ
ejpam-5971	247	20	theorem	theorem	VERB
ejpam-5971	247	21	2	2	NUM
ejpam-5971	247	22	.	.	PUNCT
ejpam-5971	248	1	if	if	SCONJ
ejpam-5971	248	2	℘=	℘=	ADJ
ejpam-5971	248	3	2	2	NUM
ejpam-5971	248	4	,	,	PUNCT
ejpam-5971	248	5	the	the	DET
ejpam-5971	248	6	eigenvalues	eigenvalue	NOUN
ejpam-5971	248	7	of	of	ADP
ejpam-5971	248	8	γ(z2[x]/⟨x5⟩	γ(z2[x]/⟨x5⟩	PROPN
ejpam-5971	248	9	)	)	PUNCT
ejpam-5971	248	10	are	be	AUX
ejpam-5971	248	11	0	0	NUM
ejpam-5971	248	12	with	with	ADP
ejpam-5971	248	13	multiplicity	multiplicity	NOUN
ejpam-5971	248	14	10	10	NUM
ejpam-5971	248	15	,	,	PUNCT
ejpam-5971	248	16	and	and	CCONJ
ejpam-5971	248	17	-1	-1	ADP
ejpam-5971	248	18	with	with	ADP
ejpam-5971	248	19	multiplicity	multiplicity	NOUN
ejpam-5971	248	20	1	1	NUM
ejpam-5971	248	21	,	,	PUNCT
ejpam-5971	248	22	as	as	ADV
ejpam-5971	248	23	well	well	ADV
ejpam-5971	248	24	as	as	ADP
ejpam-5971	248	25	the	the	DET
ejpam-5971	248	26	eigenvalues	eigenvalue	NOUN
ejpam-5971	248	27	satisfying	satisfy	VERB
ejpam-5971	248	28	the	the	DET
ejpam-5971	248	29	equation	equation	NOUN
ejpam-5971	248	30	λ4	λ4	PROPN
ejpam-5971	248	31	−	−	PROPN
ejpam-5971	249	1	λ3	λ3	PROPN
ejpam-5971	249	2	−	−	PROPN
ejpam-5971	250	1	22λ2	22λ2	NUM
ejpam-5971	251	1	−	−	PROPN
ejpam-5971	251	2	4λ	4λ	PROPN
ejpam-5971	251	3	+	+	CCONJ
ejpam-5971	251	4	64	64	NUM
ejpam-5971	251	5	=	=	SYM
ejpam-5971	251	6	0	0	NUM
ejpam-5971	251	7	,	,	PUNCT
ejpam-5971	251	8	which	which	PRON
ejpam-5971	251	9	are	be	AUX
ejpam-5971	251	10	-3.4746	-3.4746	PRON
ejpam-5971	251	11	,	,	PUNCT
ejpam-5971	251	12	-2.2111	-2.2111	PROPN
ejpam-5971	251	13	,	,	PUNCT
ejpam-5971	251	14	1.6564	1.6564	NUM
ejpam-5971	251	15	,	,	PUNCT
ejpam-5971	251	16	5.0294	5.0294	NUM
ejpam-5971	251	17	.	.	PUNCT
ejpam-5971	252	1	then	then	ADV
ejpam-5971	252	2	the	the	DET
ejpam-5971	252	3	v.h	v.h	PROPN
ejpam-5971	252	4	.	.	PROPN
ejpam-5971	252	5	krisnawati	krisnawati	PROPN
ejpam-5971	252	6	,	,	PUNCT
ejpam-5971	252	7	n.	n.	PROPN
ejpam-5971	252	8	hidayat	hidayat	PROPN
ejpam-5971	252	9	,	,	PUNCT
ejpam-5971	252	10	a.f	a.f	PROPN
ejpam-5971	252	11	.	.	PROPN
ejpam-5971	252	12	musyarrofah	musyarrofah	PROPN
ejpam-5971	252	13	/	/	SYM
ejpam-5971	252	14	eur	eur	PROPN
ejpam-5971	252	15	.	.	PUNCT
ejpam-5971	253	1	j.	j.	PROPN
ejpam-5971	253	2	pure	pure	PROPN
ejpam-5971	253	3	appl	appl	PROPN
ejpam-5971	253	4	.	.	PROPN
ejpam-5971	253	5	math	math	PROPN
ejpam-5971	253	6	,	,	PUNCT
ejpam-5971	253	7	18	18	NUM
ejpam-5971	253	8	(	(	PUNCT
ejpam-5971	253	9	2	2	NUM
ejpam-5971	253	10	)	)	PUNCT
ejpam-5971	253	11	(	(	PUNCT
ejpam-5971	253	12	2025	2025	NUM
ejpam-5971	253	13	)	)	PUNCT
ejpam-5971	253	14	,	,	PUNCT
ejpam-5971	253	15	5971	5971	NUM
ejpam-5971	253	16	13	13	NUM
ejpam-5971	253	17	of	of	ADP
ejpam-5971	253	18	19	19	NUM
ejpam-5971	253	19	spectrum	spectrum	NOUN
ejpam-5971	253	20	is	be	AUX
ejpam-5971	253	21	{	{	PUNCT
ejpam-5971	253	22	0[10],−1,−3.4746,−2.2111	0[10],−1,−3.4746,−2.2111	ADJ
ejpam-5971	253	23	,	,	PUNCT
ejpam-5971	253	24	1.6564	1.6564	NUM
ejpam-5971	253	25	,	,	PUNCT
ejpam-5971	253	26	5.0294	5.0294	NUM
ejpam-5971	253	27	}	}	PUNCT
ejpam-5971	253	28	.	.	PUNCT
ejpam-5971	254	1	it	it	PRON
ejpam-5971	254	2	can	can	AUX
ejpam-5971	254	3	be	be	AUX
ejpam-5971	254	4	observed	observe	VERB
ejpam-5971	254	5	that	that	SCONJ
ejpam-5971	254	6	these	these	DET
ejpam-5971	254	7	eigenvalues	eigenvalue	NOUN
ejpam-5971	254	8	match	match	VERB
ejpam-5971	254	9	the	the	DET
ejpam-5971	254	10	results	result	NOUN
ejpam-5971	254	11	from	from	ADP
ejpam-5971	254	12	the	the	DET
ejpam-5971	254	13	maple	maple	NOUN
ejpam-5971	254	14	computation	computation	NOUN
ejpam-5971	254	15	,	,	PUNCT
ejpam-5971	254	16	confirming	confirm	VERB
ejpam-5971	254	17	that	that	SCONJ
ejpam-5971	254	18	theorem	theorem	VERB
ejpam-5971	254	19	1	1	NUM
ejpam-5971	254	20	holds	hold	NOUN
ejpam-5971	254	21	.	.	PUNCT
ejpam-5971	255	1	further	far	ADV
ejpam-5971	255	2	,	,	PUNCT
ejpam-5971	255	3	by	by	ADP
ejpam-5971	255	4	theorem	theorem	NOUN
ejpam-5971	255	5	2	2	NUM
ejpam-5971	255	6	,	,	PUNCT
ejpam-5971	255	7	the	the	DET
ejpam-5971	255	8	lower	low	ADJ
ejpam-5971	255	9	and	and	CCONJ
ejpam-5971	255	10	upper	upper	ADJ
ejpam-5971	255	11	bounds	bound	NOUN
ejpam-5971	255	12	of	of	ADP
ejpam-5971	255	13	the	the	DET
ejpam-5971	255	14	energy	energy	NOUN
ejpam-5971	255	15	for	for	ADP
ejpam-5971	255	16	γ(z2[x]/⟨x5⟩	γ(z2[x]/⟨x5⟩	PROPN
ejpam-5971	255	17	are	be	AUX
ejpam-5971	255	18	12.8743	12.8743	NUM
ejpam-5971	255	19	≤	≤	NUM
ejpam-5971	255	20	en(γ(z2[x]/⟨x5⟩	en(γ(z2[x]/⟨x5⟩	PROPN
ejpam-5971	255	21	)	)	PUNCT
ejpam-5971	255	22	)	)	PUNCT
ejpam-5971	256	1	≤	≤	NOUN
ejpam-5971	256	2	14.4164	14.4164	NUM
ejpam-5971	256	3	.	.	PUNCT
ejpam-5971	257	1	it	it	PRON
ejpam-5971	257	2	can	can	AUX
ejpam-5971	257	3	be	be	AUX
ejpam-5971	257	4	seen	see	VERB
ejpam-5971	257	5	that	that	SCONJ
ejpam-5971	257	6	the	the	DET
ejpam-5971	257	7	energy	energy	NOUN
ejpam-5971	257	8	of	of	ADP
ejpam-5971	257	9	γ(z2[x]/⟨x5⟩	γ(z2[x]/⟨x5⟩	PROPN
ejpam-5971	257	10	)	)	PUNCT
ejpam-5971	257	11	falls	fall	VERB
ejpam-5971	257	12	between	between	ADP
ejpam-5971	257	13	these	these	DET
ejpam-5971	257	14	lower	low	ADJ
ejpam-5971	257	15	and	and	CCONJ
ejpam-5971	257	16	upper	upper	ADJ
ejpam-5971	257	17	bounds	bound	NOUN
ejpam-5971	257	18	.	.	PUNCT
ejpam-5971	258	1	therefore	therefore	ADV
ejpam-5971	258	2	,	,	PUNCT
ejpam-5971	258	3	theorem	theorem	ADJ
ejpam-5971	258	4	2	2	NUM
ejpam-5971	258	5	is	be	AUX
ejpam-5971	258	6	satisfied	satisfied	ADJ
ejpam-5971	258	7	.	.	PUNCT
ejpam-5971	259	1	to	to	PART
ejpam-5971	259	2	clarify	clarify	VERB
ejpam-5971	259	3	the	the	DET
ejpam-5971	259	4	relationships	relationship	NOUN
ejpam-5971	259	5	between	between	ADP
ejpam-5971	259	6	energy	energy	NOUN
ejpam-5971	259	7	values	value	NOUN
ejpam-5971	259	8	and	and	CCONJ
ejpam-5971	259	9	the	the	DET
ejpam-5971	259	10	defined	define	VERB
ejpam-5971	259	11	bounds	bound	NOUN
ejpam-5971	259	12	,	,	PUNCT
ejpam-5971	259	13	we	we	PRON
ejpam-5971	259	14	present	present	VERB
ejpam-5971	259	15	a	a	DET
ejpam-5971	259	16	table	table	NOUN
ejpam-5971	259	17	showing	show	VERB
ejpam-5971	259	18	numerical	numerical	ADJ
ejpam-5971	259	19	results	result	NOUN
ejpam-5971	259	20	of	of	ADP
ejpam-5971	259	21	the	the	DET
ejpam-5971	259	22	lower	lower	ADV
ejpam-5971	259	23	bound	bind	VERB
ejpam-5971	259	24	,	,	PUNCT
ejpam-5971	259	25	energy	energy	NOUN
ejpam-5971	259	26	,	,	PUNCT
ejpam-5971	259	27	and	and	CCONJ
ejpam-5971	259	28	upper	upper	ADJ
ejpam-5971	259	29	bound	bind	VERB
ejpam-5971	259	30	for	for	ADP
ejpam-5971	259	31	several	several	ADJ
ejpam-5971	259	32	prime	prime	ADJ
ejpam-5971	259	33	numbers	number	NOUN
ejpam-5971	259	34	.	.	PUNCT
ejpam-5971	260	1	from	from	ADP
ejpam-5971	260	2	table	table	NOUN
ejpam-5971	260	3	1	1	NUM
ejpam-5971	260	4	,	,	PUNCT
ejpam-5971	260	5	it	it	PRON
ejpam-5971	260	6	can	can	AUX
ejpam-5971	260	7	be	be	AUX
ejpam-5971	260	8	seen	see	VERB
ejpam-5971	260	9	that	that	SCONJ
ejpam-5971	260	10	for	for	ADP
ejpam-5971	260	11	prime	prime	ADJ
ejpam-5971	260	12	numbers	number	NOUN
ejpam-5971	260	13	less	less	ADJ
ejpam-5971	260	14	than	than	ADP
ejpam-5971	260	15	100	100	NUM
ejpam-5971	260	16	,	,	PUNCT
ejpam-5971	260	17	the	the	DET
ejpam-5971	260	18	lower	low	ADJ
ejpam-5971	260	19	and	and	CCONJ
ejpam-5971	260	20	upper	upper	ADJ
ejpam-5971	260	21	bounds	bound	NOUN
ejpam-5971	260	22	are	be	AUX
ejpam-5971	260	23	quite	quite	ADV
ejpam-5971	260	24	close	close	ADJ
ejpam-5971	260	25	to	to	ADP
ejpam-5971	260	26	the	the	DET
ejpam-5971	260	27	energy	energy	NOUN
ejpam-5971	260	28	value	value	NOUN
ejpam-5971	260	29	.	.	PUNCT
ejpam-5971	261	1	this	this	PRON
ejpam-5971	261	2	indicates	indicate	VERB
ejpam-5971	261	3	that	that	SCONJ
ejpam-5971	261	4	the	the	DET
ejpam-5971	261	5	formulas	formula	NOUN
ejpam-5971	261	6	for	for	ADP
ejpam-5971	261	7	the	the	DET
ejpam-5971	261	8	lower	low	ADJ
ejpam-5971	261	9	and	and	CCONJ
ejpam-5971	261	10	upper	upper	ADJ
ejpam-5971	261	11	bounds	bound	NOUN
ejpam-5971	261	12	can	can	AUX
ejpam-5971	261	13	be	be	AUX
ejpam-5971	261	14	effectively	effectively	ADV
ejpam-5971	261	15	used	use	VERB
ejpam-5971	261	16	to	to	PART
ejpam-5971	261	17	estimate	estimate	VERB
ejpam-5971	261	18	the	the	DET
ejpam-5971	261	19	energy	energy	NOUN
ejpam-5971	261	20	of	of	ADP
ejpam-5971	261	21	the	the	DET
ejpam-5971	261	22	graph	graph	NOUN
ejpam-5971	261	23	.	.	PUNCT
ejpam-5971	262	1	this	this	PRON
ejpam-5971	262	2	suggests	suggest	VERB
ejpam-5971	262	3	that	that	SCONJ
ejpam-5971	262	4	the	the	DET
ejpam-5971	262	5	methods	method	NOUN
ejpam-5971	262	6	used	use	VERB
ejpam-5971	262	7	to	to	PART
ejpam-5971	262	8	calculate	calculate	VERB
ejpam-5971	262	9	these	these	DET
ejpam-5971	262	10	bounds	bound	NOUN
ejpam-5971	262	11	are	be	AUX
ejpam-5971	262	12	effective	effective	ADJ
ejpam-5971	262	13	in	in	ADP
ejpam-5971	262	14	describing	describe	VERB
ejpam-5971	262	15	the	the	DET
ejpam-5971	262	16	energy	energy	NOUN
ejpam-5971	262	17	of	of	ADP
ejpam-5971	262	18	the	the	DET
ejpam-5971	262	19	graph	graph	NOUN
ejpam-5971	262	20	.	.	PUNCT
ejpam-5971	262	21	table	table	NOUN
ejpam-5971	262	22	1	1	NUM
ejpam-5971	262	23	:	:	PUNCT
ejpam-5971	262	24	lower	lower	ADV
ejpam-5971	262	25	bound	bind	VERB
ejpam-5971	262	26	,	,	PUNCT
ejpam-5971	262	27	energy	energy	NOUN
ejpam-5971	262	28	,	,	PUNCT
ejpam-5971	262	29	and	and	CCONJ
ejpam-5971	262	30	upper	upper	ADJ
ejpam-5971	262	31	bound	bind	VERB
ejpam-5971	262	32	for	for	ADP
ejpam-5971	262	33	various	various	ADJ
ejpam-5971	262	34	prime	prime	ADJ
ejpam-5971	262	35	numbers	number	NOUN
ejpam-5971	262	36	℘	℘	PROPN
ejpam-5971	262	37	℘	℘	VERB
ejpam-5971	262	38	lower	lower	ADV
ejpam-5971	262	39	bound	bind	VERB
ejpam-5971	262	40	graph	graph	NOUN
ejpam-5971	262	41	energy	energy	NOUN
ejpam-5971	262	42	upper	upper	ADV
ejpam-5971	262	43	bound	bind	VERB
ejpam-5971	262	44	2	2	NUM
ejpam-5971	262	45	12.8743	12.8743	NUM
ejpam-5971	262	46	13.3715	13.3715	NUM
ejpam-5971	262	47	14.4164	14.4164	NUM
ejpam-5971	262	48	3	3	NUM
ejpam-5971	262	49	49.0116	49.0116	NUM
ejpam-5971	262	50	50.2380	50.2380	NUM
ejpam-5971	262	51	53.0744	53.0744	NUM
ejpam-5971	262	52	5	5	NUM
ejpam-5971	262	53	204.5651	204.5651	NUM
ejpam-5971	262	54	207.8708	207.8708	NUM
ejpam-5971	262	55	215.1839	215.1839	NUM
ejpam-5971	262	56	7	7	NUM
ejpam-5971	262	57	496.8947	496.8947	NUM
ejpam-5971	262	58	502.8265	502.8265	NUM
ejpam-5971	262	59	515.5956	515.5956	NUM
ejpam-5971	262	60	...	...	PUNCT
ejpam-5971	262	61	...	...	PUNCT
ejpam-5971	262	62	...	...	PUNCT
ejpam-5971	263	1	...	...	PUNCT
ejpam-5971	264	1	79	79	NUM
ejpam-5971	264	2	225576.2183	225576.2183	NUM
ejpam-5971	264	3	225836.4582	225836.4582	NUM
ejpam-5971	264	4	226360.3543	226360.3543	NUM
ejpam-5971	264	5	83	83	NUM
ejpam-5971	264	6	255190.6650	255190.6650	NUM
ejpam-5971	264	7	255471.0792	255471.0792	NUM
ejpam-5971	264	8	256035.4105	256035.4105	NUM
ejpam-5971	264	9	89	89	NUM
ejpam-5971	264	10	303779.2343	303779.2343	NUM
ejpam-5971	265	1	304090.8360	304090.8360	NUM
ejpam-5971	266	1	304717.6682	304717.6682	NUM
ejpam-5971	266	2	97	97	NUM
ejpam-5971	266	3	376613.0645	376613.0645	NUM
ejpam-5971	266	4	376967.9188	376967.9188	NUM
ejpam-5971	266	5	377681.4176	377681.4176	NOUN
ejpam-5971	266	6	4	4	X
ejpam-5971	266	7	.	.	PUNCT
ejpam-5971	267	1	topological	topological	ADJ
ejpam-5971	267	2	indices	index	NOUN
ejpam-5971	267	3	of	of	ADP
ejpam-5971	267	4	zero	zero	NUM
ejpam-5971	267	5	-	-	PUNCT
ejpam-5971	267	6	divisor	divisor	NOUN
ejpam-5971	267	7	graph	graph	NOUN
ejpam-5971	267	8	of	of	ADP
ejpam-5971	267	9	z℘[x]/⟨x5⟩	z℘[x]/⟨x5⟩	PROPN
ejpam-5971	267	10	in	in	ADP
ejpam-5971	267	11	this	this	DET
ejpam-5971	267	12	section	section	NOUN
ejpam-5971	267	13	,	,	PUNCT
ejpam-5971	267	14	we	we	PRON
ejpam-5971	267	15	determine	determine	VERB
ejpam-5971	267	16	the	the	DET
ejpam-5971	267	17	wiener	wiener	NOUN
ejpam-5971	267	18	index	index	NOUN
ejpam-5971	267	19	,	,	PUNCT
ejpam-5971	267	20	hyper	hyper	NOUN
ejpam-5971	267	21	-	-	ADJ
ejpam-5971	267	22	wiener	wiener	NOUN
ejpam-5971	267	23	index	index	NOUN
ejpam-5971	267	24	,	,	PUNCT
ejpam-5971	267	25	first	first	PROPN
ejpam-5971	267	26	zagreb	zagreb	PROPN
ejpam-5971	267	27	index	index	PROPN
ejpam-5971	267	28	,	,	PUNCT
ejpam-5971	267	29	second	second	PROPN
ejpam-5971	267	30	zagreb	zagreb	PROPN
ejpam-5971	267	31	index	index	PROPN
ejpam-5971	267	32	,	,	PUNCT
ejpam-5971	267	33	narumi	narumi	PROPN
ejpam-5971	267	34	-	-	PUNCT
ejpam-5971	267	35	katayama	katayama	PROPN
ejpam-5971	267	36	index	index	NOUN
ejpam-5971	267	37	.	.	PUNCT
ejpam-5971	268	1	v.h	v.h	PROPN
ejpam-5971	268	2	.	.	PROPN
ejpam-5971	268	3	krisnawati	krisnawati	PROPN
ejpam-5971	268	4	,	,	PUNCT
ejpam-5971	268	5	n.	n.	PROPN
ejpam-5971	268	6	hidayat	hidayat	PROPN
ejpam-5971	268	7	,	,	PUNCT
ejpam-5971	268	8	a.f	a.f	PROPN
ejpam-5971	268	9	.	.	PROPN
ejpam-5971	268	10	musyarrofah	musyarrofah	PROPN
ejpam-5971	268	11	/	/	SYM
ejpam-5971	268	12	eur	eur	PROPN
ejpam-5971	268	13	.	.	PUNCT
ejpam-5971	269	1	j.	j.	PROPN
ejpam-5971	269	2	pure	pure	PROPN
ejpam-5971	269	3	appl	appl	PROPN
ejpam-5971	269	4	.	.	PROPN
ejpam-5971	269	5	math	math	PROPN
ejpam-5971	269	6	,	,	PUNCT
ejpam-5971	269	7	18	18	NUM
ejpam-5971	269	8	(	(	PUNCT
ejpam-5971	269	9	2	2	NUM
ejpam-5971	269	10	)	)	PUNCT
ejpam-5971	269	11	(	(	PUNCT
ejpam-5971	269	12	2025	2025	NUM
ejpam-5971	269	13	)	)	PUNCT
ejpam-5971	269	14	,	,	PUNCT
ejpam-5971	269	15	5971	5971	NUM
ejpam-5971	269	16	14	14	NUM
ejpam-5971	269	17	of	of	ADP
ejpam-5971	269	18	19	19	NUM
ejpam-5971	269	19	theorem	theorem	NOUN
ejpam-5971	269	20	3	3	NUM
ejpam-5971	269	21	.	.	PUNCT
ejpam-5971	270	1	the	the	DET
ejpam-5971	270	2	wiener	wiener	NOUN
ejpam-5971	270	3	index	index	NOUN
ejpam-5971	270	4	of	of	ADP
ejpam-5971	270	5	graph	graph	NOUN
ejpam-5971	270	6	g	g	PROPN
ejpam-5971	270	7	∼=	∼=	PROPN
ejpam-5971	270	8	γ(z℘[x]/⟨x5⟩	γ(z℘[x]/⟨x5⟩	NUM
ejpam-5971	270	9	)	)	PUNCT
ejpam-5971	270	10	,	,	PUNCT
ejpam-5971	270	11	is	be	AUX
ejpam-5971	270	12	w(g	w(g	PROPN
ejpam-5971	270	13	)	)	PUNCT
ejpam-5971	270	14	=	=	SYM
ejpam-5971	270	15	1	1	NUM
ejpam-5971	270	16	2	2	NUM
ejpam-5971	270	17	(	(	PUNCT
ejpam-5971	270	18	2℘8	2℘8	NUM
ejpam-5971	270	19	−	−	NOUN
ejpam-5971	270	20	4℘5	4℘5	NUM
ejpam-5971	270	21	−	−	ADP
ejpam-5971	270	22	℘4	℘4	NOUN
ejpam-5971	270	23	+	+	CCONJ
ejpam-5971	270	24	℘2	℘2	NOUN
ejpam-5971	270	25	+	+	CCONJ
ejpam-5971	270	26	2	2	NUM
ejpam-5971	270	27	)	)	PUNCT
ejpam-5971	270	28	.	.	PUNCT
ejpam-5971	271	1	proof	proof	NOUN
ejpam-5971	271	2	.	.	PUNCT
ejpam-5971	272	1	let	let	VERB
ejpam-5971	272	2	g	g	PRON
ejpam-5971	272	3	∼=	∼=	PROPN
ejpam-5971	272	4	γ(z℘[x]/⟨x5⟩	γ(z℘[x]/⟨x5⟩	NUM
ejpam-5971	272	5	)	)	PUNCT
ejpam-5971	272	6	.	.	PUNCT
ejpam-5971	273	1	the	the	DET
ejpam-5971	273	2	distances	distance	NOUN
ejpam-5971	273	3	between	between	ADP
ejpam-5971	273	4	the	the	DET
ejpam-5971	273	5	vertices	vertex	NOUN
ejpam-5971	273	6	of	of	ADP
ejpam-5971	273	7	g	g	PROPN
ejpam-5971	273	8	have	have	AUX
ejpam-5971	273	9	been	be	AUX
ejpam-5971	273	10	determined	determine	VERB
ejpam-5971	273	11	by	by	ADP
ejpam-5971	273	12	musyarrofah	musyarrofah	PROPN
ejpam-5971	273	13	et	et	PROPN
ejpam-5971	273	14	al	al	PROPN
ejpam-5971	273	15	.	.	PUNCT
ejpam-5971	274	1	in	in	ADP
ejpam-5971	274	2	[	[	X
ejpam-5971	274	3	24	24	NUM
ejpam-5971	274	4	]	]	PUNCT
ejpam-5971	274	5	.	.	PUNCT
ejpam-5971	275	1	it	it	PRON
ejpam-5971	275	2	was	be	AUX
ejpam-5971	275	3	shown	show	VERB
ejpam-5971	275	4	that	that	SCONJ
ejpam-5971	275	5	the	the	DET
ejpam-5971	275	6	distance	distance	NOUN
ejpam-5971	275	7	between	between	ADP
ejpam-5971	275	8	adjacent	adjacent	ADJ
ejpam-5971	275	9	vertices	vertex	NOUN
ejpam-5971	275	10	in	in	ADP
ejpam-5971	275	11	g	g	PROPN
ejpam-5971	275	12	is	be	AUX
ejpam-5971	275	13	1	1	NUM
ejpam-5971	275	14	,	,	PUNCT
ejpam-5971	275	15	and	and	CCONJ
ejpam-5971	275	16	for	for	ADP
ejpam-5971	275	17	non	non	ADJ
ejpam-5971	275	18	-	-	ADJ
ejpam-5971	275	19	adjacent	adjacent	ADJ
ejpam-5971	275	20	vertices	vertex	NOUN
ejpam-5971	275	21	,	,	PUNCT
ejpam-5971	275	22	it	it	PRON
ejpam-5971	275	23	is	be	AUX
ejpam-5971	275	24	2	2	NUM
ejpam-5971	275	25	.	.	PUNCT
ejpam-5971	276	1	as	as	ADP
ejpam-5971	276	2	a	a	DET
ejpam-5971	276	3	result	result	NOUN
ejpam-5971	276	4	,	,	PUNCT
ejpam-5971	276	5	the	the	DET
ejpam-5971	276	6	distance	distance	NOUN
ejpam-5971	276	7	matrix	matrix	NOUN
ejpam-5971	276	8	for	for	ADP
ejpam-5971	276	9	g	g	NOUN
ejpam-5971	276	10	,	,	PUNCT
ejpam-5971	276	11	d(g	d(g	PROPN
ejpam-5971	276	12	)	)	PUNCT
ejpam-5971	276	13	is	be	AUX
ejpam-5971	276	14	represented	represent	VERB
ejpam-5971	276	15	as	as	SCONJ
ejpam-5971	276	16	follows	follow	VERB
ejpam-5971	276	17	:	:	PUNCT
ejpam-5971	277	1			NOUN
ejpam-5971	277	2	a	a	DET
ejpam-5971	277	3	b	b	X
ejpam-5971	277	4	c	c	NOUN
ejpam-5971	277	5	d	d	NOUN
ejpam-5971	277	6	a	a	DET
ejpam-5971	277	7	2(n℘4−℘3	2(n℘4−℘3	ADJ
ejpam-5971	277	8	−	−	PROPN
ejpam-5971	277	9	i℘4−℘3	i℘4−℘3	NOUN
ejpam-5971	277	10	)	)	PUNCT
ejpam-5971	277	11	2n(℘4−℘3)×(℘3−℘2	2n(℘4−℘3)×(℘3−℘2	NUM
ejpam-5971	277	12	)	)	PUNCT
ejpam-5971	277	13	2n(℘4−℘3)×(℘2−℘	2n(℘4−℘3)×(℘2−℘	NOUN
ejpam-5971	277	14	)	)	PUNCT
ejpam-5971	277	15	n(℘4−℘3)×(℘−1	n(℘4−℘3)×(℘−1	NOUN
ejpam-5971	277	16	)	)	PUNCT
ejpam-5971	277	17	b	b	NOUN
ejpam-5971	277	18	2n(℘3−℘2)×(℘4−℘3	2n(℘3−℘2)×(℘4−℘3	NUM
ejpam-5971	277	19	)	)	PUNCT
ejpam-5971	277	20	2(n℘3−℘2	2(n℘3−℘2	NUM
ejpam-5971	277	21	−	−	NOUN
ejpam-5971	277	22	i℘3−℘2	i℘3−℘2	NOUN
ejpam-5971	277	23	)	)	PUNCT
ejpam-5971	277	24	n(℘3−℘2)×(℘2−℘	n(℘3−℘2)×(℘2−℘	NOUN
ejpam-5971	277	25	)	)	PUNCT
ejpam-5971	277	26	n(℘3−℘2)×(℘−1	n(℘3−℘2)×(℘−1	PROPN
ejpam-5971	277	27	)	)	PUNCT
ejpam-5971	277	28	c	c	NOUN
ejpam-5971	277	29	2n(℘2−℘)×(℘4−℘3	2n(℘2−℘)×(℘4−℘3	PROPN
ejpam-5971	277	30	)	)	PUNCT
ejpam-5971	277	31	n(℘2−℘)×(℘3−℘2	n(℘2−℘)×(℘3−℘2	PROPN
ejpam-5971	277	32	)	)	PUNCT
ejpam-5971	277	33	n℘2−℘	n℘2−℘	NOUN
ejpam-5971	278	1	−	−	PROPN
ejpam-5971	278	2	i℘2−℘	i℘2−℘	PROPN
ejpam-5971	278	3	n(℘2−℘)×(℘−1	n(℘2−℘)×(℘−1	PROPN
ejpam-5971	278	4	)	)	PUNCT
ejpam-5971	278	5	d	d	NOUN
ejpam-5971	278	6	n(℘−1)×(℘4−℘3	n(℘−1)×(℘4−℘3	NOUN
ejpam-5971	278	7	)	)	PUNCT
ejpam-5971	278	8	n(℘−1)×(℘3−℘2	n(℘−1)×(℘3−℘2	ADJ
ejpam-5971	278	9	)	)	PUNCT
ejpam-5971	278	10	n(℘−1)×(℘2−℘	n(℘−1)×(℘2−℘	NOUN
ejpam-5971	278	11	)	)	PUNCT
ejpam-5971	278	12	n℘−1	n℘−1	PROPN
ejpam-5971	278	13	−	−	PROPN
ejpam-5971	278	14	i℘−1	i℘−1	PROPN
ejpam-5971	278	15	.	.	PROPN
ejpam-5971	278	16	here	here	ADV
ejpam-5971	278	17	o	o	NOUN
ejpam-5971	278	18	represents	represent	VERB
ejpam-5971	278	19	the	the	DET
ejpam-5971	278	20	zero	zero	NUM
ejpam-5971	278	21	matrix	matrix	NOUN
ejpam-5971	278	22	,	,	PUNCT
ejpam-5971	278	23	n	n	PRON
ejpam-5971	278	24	represents	represent	VERB
ejpam-5971	278	25	the	the	DET
ejpam-5971	278	26	matrix	matrix	NOUN
ejpam-5971	278	27	of	of	ADP
ejpam-5971	278	28	ones	one	NOUN
ejpam-5971	278	29	,	,	PUNCT
ejpam-5971	278	30	and	and	CCONJ
ejpam-5971	278	31	i	i	PRON
ejpam-5971	278	32	represents	represent	VERB
ejpam-5971	278	33	the	the	DET
ejpam-5971	278	34	identity	identity	NOUN
ejpam-5971	278	35	matrix	matrix	NOUN
ejpam-5971	278	36	.	.	PUNCT
ejpam-5971	279	1	thus	thus	ADV
ejpam-5971	279	2	,	,	PUNCT
ejpam-5971	279	3	the	the	DET
ejpam-5971	279	4	wiener	wiener	NOUN
ejpam-5971	279	5	index	index	NOUN
ejpam-5971	279	6	of	of	ADP
ejpam-5971	279	7	g	g	PROPN
ejpam-5971	279	8	is	be	AUX
ejpam-5971	279	9	w(g	w(g	PROPN
ejpam-5971	279	10	)	)	PUNCT
ejpam-5971	279	11	=	=	SYM
ejpam-5971	279	12	1	1	NUM
ejpam-5971	279	13	2	2	NUM
ejpam-5971	279	14	℘4−1∑	℘4−1∑	NUM
ejpam-5971	279	15	i=1	i=1	PRON
ejpam-5971	279	16	℘4−1∑	℘4−1∑	X
ejpam-5971	280	1	j=1	j=1	ADJ
ejpam-5971	280	2	dij	dij	NOUN
ejpam-5971	281	1	=	=	SYM
ejpam-5971	281	2	1	1	NUM
ejpam-5971	281	3	2	2	NUM
ejpam-5971	281	4	(	(	PUNCT
ejpam-5971	281	5	2	2	NUM
ejpam-5971	281	6	(	(	PUNCT
ejpam-5971	281	7	℘4	℘4	VERB
ejpam-5971	281	8	−	−	PROPN
ejpam-5971	281	9	℘3	℘3	NUM
ejpam-5971	281	10	)	)	PUNCT
ejpam-5971	281	11	2	2	NUM
ejpam-5971	281	12	−	−	NOUN
ejpam-5971	281	13	2(℘4	2(℘4	NUM
ejpam-5971	281	14	−	−	PROPN
ejpam-5971	281	15	℘3	℘3	NUM
ejpam-5971	281	16	)	)	PUNCT
ejpam-5971	282	1	+	+	CCONJ
ejpam-5971	282	2	4	4	NUM
ejpam-5971	282	3	(	(	PUNCT
ejpam-5971	282	4	℘4	℘4	VERB
ejpam-5971	282	5	−	−	PROPN
ejpam-5971	282	6	℘3	℘3	NUM
ejpam-5971	282	7	)	)	PUNCT
ejpam-5971	282	8	(	(	PUNCT
ejpam-5971	282	9	℘3	℘3	ADV
ejpam-5971	282	10	−	−	PROPN
ejpam-5971	282	11	℘2	℘2	NOUN
ejpam-5971	282	12	)	)	PUNCT
ejpam-5971	282	13	+	+	CCONJ
ejpam-5971	282	14	4	4	NUM
ejpam-5971	282	15	(	(	PUNCT
ejpam-5971	282	16	℘4	℘4	VERB
ejpam-5971	282	17	−	−	PROPN
ejpam-5971	282	18	℘3	℘3	NUM
ejpam-5971	282	19	)	)	PUNCT
ejpam-5971	282	20	(	(	PUNCT
ejpam-5971	282	21	℘2	℘2	NOUN
ejpam-5971	282	22	−	−	PROPN
ejpam-5971	282	23	℘	℘	PROPN
ejpam-5971	282	24	)	)	PUNCT
ejpam-5971	283	1	+	+	CCONJ
ejpam-5971	283	2	2	2	NUM
ejpam-5971	283	3	(	(	PUNCT
ejpam-5971	283	4	℘4	℘4	VERB
ejpam-5971	283	5	−	−	NOUN
ejpam-5971	283	6	℘3	℘3	NUM
ejpam-5971	283	7	)	)	PUNCT
ejpam-5971	283	8	(	(	PUNCT
ejpam-5971	283	9	℘−	℘−	NOUN
ejpam-5971	283	10	1	1	NUM
ejpam-5971	283	11	)	)	PUNCT
ejpam-5971	283	12	+	+	CCONJ
ejpam-5971	283	13	2	2	NUM
ejpam-5971	283	14	(	(	PUNCT
ejpam-5971	283	15	℘3	℘3	ADJ
ejpam-5971	283	16	−	−	PROPN
ejpam-5971	283	17	℘2	℘2	NOUN
ejpam-5971	283	18	)	)	PUNCT
ejpam-5971	283	19	2	2	NUM
ejpam-5971	283	20	−	−	PROPN
ejpam-5971	283	21	2(℘3	2(℘3	NUM
ejpam-5971	283	22	−	−	PROPN
ejpam-5971	283	23	℘2	℘2	PROPN
ejpam-5971	283	24	)	)	PUNCT
ejpam-5971	283	25	+	+	CCONJ
ejpam-5971	283	26	2	2	NUM
ejpam-5971	283	27	(	(	PUNCT
ejpam-5971	283	28	℘3	℘3	ADJ
ejpam-5971	283	29	−	−	PROPN
ejpam-5971	283	30	℘2	℘2	NOUN
ejpam-5971	283	31	)	)	PUNCT
ejpam-5971	283	32	(	(	PUNCT
ejpam-5971	283	33	℘2	℘2	NOUN
ejpam-5971	283	34	−	−	PROPN
ejpam-5971	283	35	℘	℘	PROPN
ejpam-5971	283	36	)	)	PUNCT
ejpam-5971	284	1	+	+	CCONJ
ejpam-5971	284	2	2	2	NUM
ejpam-5971	284	3	(	(	PUNCT
ejpam-5971	284	4	℘3	℘3	ADJ
ejpam-5971	284	5	−	−	PROPN
ejpam-5971	284	6	℘2	℘2	NOUN
ejpam-5971	284	7	)	)	PUNCT
ejpam-5971	284	8	(	(	PUNCT
ejpam-5971	284	9	℘−	℘−	NOUN
ejpam-5971	284	10	1	1	NUM
ejpam-5971	284	11	)	)	PUNCT
ejpam-5971	284	12	+	+	CCONJ
ejpam-5971	284	13	(	(	PUNCT
ejpam-5971	284	14	℘2	℘2	NOUN
ejpam-5971	284	15	−	−	PROPN
ejpam-5971	284	16	℘	℘	PROPN
ejpam-5971	284	17	)	)	PUNCT
ejpam-5971	284	18	2	2	NUM
ejpam-5971	284	19	−	−	PROPN
ejpam-5971	284	20	(	(	PUNCT
ejpam-5971	284	21	℘2	℘2	NOUN
ejpam-5971	284	22	−	−	PROPN
ejpam-5971	284	23	℘	℘	NOUN
ejpam-5971	284	24	)	)	PUNCT
ejpam-5971	284	25	+	+	CCONJ
ejpam-5971	284	26	2	2	NUM
ejpam-5971	284	27	(	(	PUNCT
ejpam-5971	284	28	℘2	℘2	NOUN
ejpam-5971	284	29	−	−	PROPN
ejpam-5971	284	30	℘	℘	PROPN
ejpam-5971	284	31	)	)	PUNCT
ejpam-5971	284	32	(	(	PUNCT
ejpam-5971	284	33	℘−	℘−	NOUN
ejpam-5971	284	34	1	1	NUM
ejpam-5971	284	35	)	)	PUNCT
ejpam-5971	284	36	+	+	CCONJ
ejpam-5971	284	37	(	(	PUNCT
ejpam-5971	284	38	℘−	℘−	NOUN
ejpam-5971	284	39	1)2	1)2	NUM
ejpam-5971	284	40	−	−	PROPN
ejpam-5971	285	1	(	(	PUNCT
ejpam-5971	285	2	℘−	℘−	NOUN
ejpam-5971	285	3	1	1	NUM
ejpam-5971	285	4	)	)	PUNCT
ejpam-5971	285	5	)	)	PUNCT
ejpam-5971	286	1	=	=	SYM
ejpam-5971	286	2	1	1	NUM
ejpam-5971	286	3	2	2	NUM
ejpam-5971	286	4	(	(	PUNCT
ejpam-5971	286	5	2℘8	2℘8	NUM
ejpam-5971	286	6	−	−	NOUN
ejpam-5971	286	7	4℘5	4℘5	NUM
ejpam-5971	286	8	−	−	ADP
ejpam-5971	286	9	℘4	℘4	NOUN
ejpam-5971	286	10	+	+	CCONJ
ejpam-5971	286	11	℘2	℘2	NOUN
ejpam-5971	286	12	+	+	CCONJ
ejpam-5971	286	13	2	2	NUM
ejpam-5971	286	14	)	)	PUNCT
ejpam-5971	286	15	.	.	PUNCT
ejpam-5971	287	1	theorem	theorem	ADJ
ejpam-5971	287	2	4	4	NUM
ejpam-5971	287	3	.	.	PUNCT
ejpam-5971	288	1	the	the	DET
ejpam-5971	288	2	hyper	hyper	ADJ
ejpam-5971	288	3	-	-	ADJ
ejpam-5971	288	4	wiener	wiener	NOUN
ejpam-5971	288	5	index	index	NOUN
ejpam-5971	288	6	of	of	ADP
ejpam-5971	288	7	graph	graph	NOUN
ejpam-5971	288	8	g	g	PROPN
ejpam-5971	288	9	∼=	∼=	PROPN
ejpam-5971	288	10	γ(z℘[x]/⟨x5⟩	γ(z℘[x]/⟨x5⟩	NUM
ejpam-5971	288	11	)	)	PUNCT
ejpam-5971	288	12	is	be	AUX
ejpam-5971	288	13	ww(g	ww(g	PRON
ejpam-5971	288	14	)	)	PUNCT
ejpam-5971	288	15	=	=	SYM
ejpam-5971	288	16	1	1	NUM
ejpam-5971	288	17	2	2	NUM
ejpam-5971	288	18	(	(	PUNCT
ejpam-5971	288	19	3℘8	3℘8	NUM
ejpam-5971	288	20	−	−	NUM
ejpam-5971	288	21	8℘5	8℘5	NUM
ejpam-5971	288	22	+	+	CCONJ
ejpam-5971	288	23	℘4	℘4	VERB
ejpam-5971	288	24	+	+	CCONJ
ejpam-5971	288	25	2℘2	2℘2	NUM
ejpam-5971	288	26	+	+	CCONJ
ejpam-5971	288	27	2	2	NUM
ejpam-5971	288	28	)	)	PUNCT
ejpam-5971	288	29	.	.	PUNCT
ejpam-5971	289	1	proof	proof	NOUN
ejpam-5971	289	2	.	.	PUNCT
ejpam-5971	290	1	based	base	VERB
ejpam-5971	290	2	on	on	ADP
ejpam-5971	290	3	the	the	DET
ejpam-5971	290	4	proof	proof	NOUN
ejpam-5971	290	5	of	of	ADP
ejpam-5971	290	6	the	the	DET
ejpam-5971	290	7	theorem	theorem	NOUN
ejpam-5971	290	8	3	3	NUM
ejpam-5971	290	9	,	,	PUNCT
ejpam-5971	290	10	the	the	DET
ejpam-5971	290	11	distance	distance	NOUN
ejpam-5971	290	12	matrix	matrix	NOUN
ejpam-5971	290	13	of	of	ADP
ejpam-5971	290	14	g	g	PROPN
ejpam-5971	290	15	has	have	AUX
ejpam-5971	290	16	been	be	AUX
ejpam-5971	290	17	determined	determine	VERB
ejpam-5971	290	18	,	,	PUNCT
ejpam-5971	290	19	so	so	ADV
ejpam-5971	290	20	the	the	DET
ejpam-5971	290	21	hyper	hyper	ADJ
ejpam-5971	290	22	-	-	ADJ
ejpam-5971	290	23	wiener	wiener	NOUN
ejpam-5971	290	24	index	index	NOUN
ejpam-5971	290	25	of	of	ADP
ejpam-5971	290	26	graph	graph	NOUN
ejpam-5971	290	27	g	g	PROPN
ejpam-5971	290	28	is	be	AUX
ejpam-5971	290	29	ww(g	ww(g	PUNCT
ejpam-5971	290	30	)	)	PUNCT
ejpam-5971	290	31	=	=	SYM
ejpam-5971	290	32	1	1	NUM
ejpam-5971	290	33	2	2	NUM
ejpam-5971	290	34	w(g	w(g	NUM
ejpam-5971	290	35	)	)	PUNCT
ejpam-5971	291	1	+	+	CCONJ
ejpam-5971	291	2	1	1	NUM
ejpam-5971	291	3	4	4	NUM
ejpam-5971	291	4	℘4−1∑	℘4−1∑	NUM
ejpam-5971	291	5	i=1	i=1	PRON
ejpam-5971	291	6	℘4−1∑	℘4−1∑	X
ejpam-5971	292	1	j=1	j=1	NOUN
ejpam-5971	292	2	(	(	PUNCT
ejpam-5971	292	3	dij	dij	NOUN
ejpam-5971	292	4	)	)	PUNCT
ejpam-5971	292	5	2	2	NUM
ejpam-5971	292	6	=	=	SYM
ejpam-5971	292	7	1	1	NUM
ejpam-5971	292	8	2	2	NUM
ejpam-5971	292	9	w(g	w(g	NUM
ejpam-5971	292	10	)	)	PUNCT
ejpam-5971	292	11	+	+	CCONJ
ejpam-5971	292	12	1	1	NUM
ejpam-5971	292	13	4	4	NUM
ejpam-5971	292	14	(	(	PUNCT
ejpam-5971	292	15	4	4	NUM
ejpam-5971	292	16	(	(	PUNCT
ejpam-5971	292	17	℘4	℘4	VERB
ejpam-5971	292	18	−	−	PROPN
ejpam-5971	292	19	℘3	℘3	NUM
ejpam-5971	292	20	)	)	PUNCT
ejpam-5971	292	21	2	2	NUM
ejpam-5971	292	22	−	−	NOUN
ejpam-5971	292	23	4(℘4	4(℘4	NUM
ejpam-5971	292	24	−	−	PROPN
ejpam-5971	292	25	℘3	℘3	NUM
ejpam-5971	292	26	)	)	PUNCT
ejpam-5971	293	1	+	+	CCONJ
ejpam-5971	293	2	8	8	NUM
ejpam-5971	293	3	(	(	PUNCT
ejpam-5971	293	4	℘4	℘4	VERB
ejpam-5971	293	5	−	−	PROPN
ejpam-5971	293	6	℘3	℘3	NUM
ejpam-5971	293	7	)	)	PUNCT
ejpam-5971	293	8	(	(	PUNCT
ejpam-5971	293	9	℘3	℘3	ADV
ejpam-5971	293	10	−	−	PROPN
ejpam-5971	293	11	℘2	℘2	NOUN
ejpam-5971	293	12	)	)	PUNCT
ejpam-5971	294	1	+	+	CCONJ
ejpam-5971	294	2	8	8	NUM
ejpam-5971	294	3	(	(	PUNCT
ejpam-5971	294	4	℘4	℘4	VERB
ejpam-5971	294	5	−	−	PROPN
ejpam-5971	294	6	℘3	℘3	NUM
ejpam-5971	294	7	)	)	PUNCT
ejpam-5971	294	8	(	(	PUNCT
ejpam-5971	294	9	℘2	℘2	NOUN
ejpam-5971	294	10	−	−	PROPN
ejpam-5971	294	11	℘	℘	PROPN
ejpam-5971	294	12	)	)	PUNCT
ejpam-5971	295	1	+	+	CCONJ
ejpam-5971	295	2	2	2	NUM
ejpam-5971	295	3	(	(	PUNCT
ejpam-5971	295	4	℘4	℘4	VERB
ejpam-5971	295	5	−	−	NOUN
ejpam-5971	295	6	℘3	℘3	NUM
ejpam-5971	295	7	)	)	PUNCT
ejpam-5971	295	8	(	(	PUNCT
ejpam-5971	295	9	℘−	℘−	NOUN
ejpam-5971	295	10	1	1	NUM
ejpam-5971	295	11	)	)	PUNCT
ejpam-5971	295	12	+	+	CCONJ
ejpam-5971	295	13	4	4	NUM
ejpam-5971	295	14	(	(	PUNCT
ejpam-5971	295	15	℘3	℘3	ADJ
ejpam-5971	295	16	−	−	PROPN
ejpam-5971	295	17	℘2	℘2	NOUN
ejpam-5971	295	18	)	)	PUNCT
ejpam-5971	295	19	2	2	NUM
ejpam-5971	295	20	−	−	PROPN
ejpam-5971	295	21	4(℘3	4(℘3	NOUN
ejpam-5971	295	22	−	−	PROPN
ejpam-5971	295	23	℘2	℘2	PROPN
ejpam-5971	295	24	)	)	PUNCT
ejpam-5971	295	25	+	+	CCONJ
ejpam-5971	295	26	2	2	NUM
ejpam-5971	295	27	(	(	PUNCT
ejpam-5971	295	28	℘3	℘3	ADJ
ejpam-5971	295	29	−	−	PROPN
ejpam-5971	295	30	℘2	℘2	NOUN
ejpam-5971	295	31	)	)	PUNCT
ejpam-5971	295	32	(	(	PUNCT
ejpam-5971	295	33	℘2	℘2	NOUN
ejpam-5971	295	34	−	−	PROPN
ejpam-5971	295	35	℘	℘	PROPN
ejpam-5971	295	36	)	)	PUNCT
ejpam-5971	296	1	+	+	CCONJ
ejpam-5971	296	2	2	2	NUM
ejpam-5971	296	3	(	(	PUNCT
ejpam-5971	296	4	℘3	℘3	ADJ
ejpam-5971	296	5	−	−	PROPN
ejpam-5971	296	6	℘2	℘2	NOUN
ejpam-5971	296	7	)	)	PUNCT
ejpam-5971	296	8	(	(	PUNCT
ejpam-5971	296	9	℘−	℘−	NOUN
ejpam-5971	296	10	1	1	NUM
ejpam-5971	296	11	)	)	PUNCT
ejpam-5971	296	12	v.h	v.h	PROPN
ejpam-5971	296	13	.	.	PROPN
ejpam-5971	296	14	krisnawati	krisnawati	PROPN
ejpam-5971	296	15	,	,	PUNCT
ejpam-5971	296	16	n.	n.	PROPN
ejpam-5971	296	17	hidayat	hidayat	PROPN
ejpam-5971	296	18	,	,	PUNCT
ejpam-5971	296	19	a.f	a.f	PROPN
ejpam-5971	296	20	.	.	PROPN
ejpam-5971	296	21	musyarrofah	musyarrofah	PROPN
ejpam-5971	296	22	/	/	SYM
ejpam-5971	296	23	eur	eur	PROPN
ejpam-5971	296	24	.	.	PUNCT
ejpam-5971	297	1	j.	j.	PROPN
ejpam-5971	297	2	pure	pure	PROPN
ejpam-5971	297	3	appl	appl	PROPN
ejpam-5971	297	4	.	.	PROPN
ejpam-5971	297	5	math	math	PROPN
ejpam-5971	297	6	,	,	PUNCT
ejpam-5971	297	7	18	18	NUM
ejpam-5971	297	8	(	(	PUNCT
ejpam-5971	297	9	2	2	NUM
ejpam-5971	297	10	)	)	PUNCT
ejpam-5971	297	11	(	(	PUNCT
ejpam-5971	297	12	2025	2025	NUM
ejpam-5971	297	13	)	)	PUNCT
ejpam-5971	297	14	,	,	PUNCT
ejpam-5971	297	15	5971	5971	NUM
ejpam-5971	297	16	15	15	NUM
ejpam-5971	297	17	of	of	ADP
ejpam-5971	297	18	19	19	NUM
ejpam-5971	297	19	+	+	CCONJ
ejpam-5971	297	20	(	(	PUNCT
ejpam-5971	297	21	℘2	℘2	NOUN
ejpam-5971	297	22	−	−	PROPN
ejpam-5971	297	23	℘	℘	PROPN
ejpam-5971	297	24	)	)	PUNCT
ejpam-5971	297	25	2	2	NUM
ejpam-5971	297	26	−	−	PROPN
ejpam-5971	297	27	(	(	PUNCT
ejpam-5971	297	28	℘2	℘2	NOUN
ejpam-5971	297	29	−	−	PROPN
ejpam-5971	297	30	℘	℘	NOUN
ejpam-5971	297	31	)	)	PUNCT
ejpam-5971	297	32	+	+	CCONJ
ejpam-5971	297	33	2	2	NUM
ejpam-5971	297	34	(	(	PUNCT
ejpam-5971	297	35	℘2	℘2	NOUN
ejpam-5971	297	36	−	−	PROPN
ejpam-5971	297	37	℘	℘	PROPN
ejpam-5971	297	38	)	)	PUNCT
ejpam-5971	297	39	(	(	PUNCT
ejpam-5971	297	40	℘−	℘−	NOUN
ejpam-5971	297	41	1	1	NUM
ejpam-5971	297	42	)	)	PUNCT
ejpam-5971	297	43	+	+	CCONJ
ejpam-5971	297	44	(	(	PUNCT
ejpam-5971	297	45	℘−	℘−	NOUN
ejpam-5971	297	46	1)2	1)2	NUM
ejpam-5971	297	47	−	−	PROPN
ejpam-5971	297	48	(	(	PUNCT
ejpam-5971	297	49	℘−	℘−	NOUN
ejpam-5971	297	50	1	1	NUM
ejpam-5971	297	51	)	)	PUNCT
ejpam-5971	297	52	)	)	PUNCT
ejpam-5971	298	1	=	=	SYM
ejpam-5971	298	2	1	1	NUM
ejpam-5971	298	3	2	2	NUM
ejpam-5971	298	4	(	(	PUNCT
ejpam-5971	298	5	2℘8	2℘8	NUM
ejpam-5971	298	6	−	−	NOUN
ejpam-5971	298	7	4℘5	4℘5	NUM
ejpam-5971	298	8	−	−	ADP
ejpam-5971	298	9	℘4	℘4	NOUN
ejpam-5971	298	10	+	+	CCONJ
ejpam-5971	298	11	℘2	℘2	NOUN
ejpam-5971	298	12	+	+	CCONJ
ejpam-5971	298	13	2	2	NUM
ejpam-5971	298	14	2	2	NUM
ejpam-5971	298	15	)	)	PUNCT
ejpam-5971	298	16	+	+	CCONJ
ejpam-5971	298	17	1	1	NUM
ejpam-5971	298	18	4	4	NUM
ejpam-5971	298	19	(	(	PUNCT
ejpam-5971	298	20	4℘8	4℘8	NUM
ejpam-5971	298	21	−	−	PROPN
ejpam-5971	298	22	12℘5	12℘5	NUM
ejpam-5971	299	1	+	+	CCONJ
ejpam-5971	299	2	3℘4	3℘4	NUM
ejpam-5971	299	3	+	+	SYM
ejpam-5971	299	4	3℘2	3℘2	NUM
ejpam-5971	299	5	+	+	SYM
ejpam-5971	299	6	2	2	X
ejpam-5971	299	7	)	)	PUNCT
ejpam-5971	299	8	=	=	SYM
ejpam-5971	299	9	1	1	NUM
ejpam-5971	299	10	2	2	NUM
ejpam-5971	299	11	(	(	PUNCT
ejpam-5971	299	12	3℘8	3℘8	NUM
ejpam-5971	299	13	−	−	NUM
ejpam-5971	299	14	8℘5	8℘5	NUM
ejpam-5971	299	15	+	+	CCONJ
ejpam-5971	299	16	℘4	℘4	VERB
ejpam-5971	299	17	+	+	CCONJ
ejpam-5971	299	18	2℘2	2℘2	NUM
ejpam-5971	299	19	+	+	CCONJ
ejpam-5971	299	20	2	2	NUM
ejpam-5971	299	21	)	)	PUNCT
ejpam-5971	299	22	.	.	PUNCT
ejpam-5971	300	1	theorem	theorem	NOUN
ejpam-5971	300	2	5	5	NUM
ejpam-5971	300	3	.	.	PUNCT
ejpam-5971	301	1	the	the	DET
ejpam-5971	301	2	first	first	ADJ
ejpam-5971	301	3	and	and	CCONJ
ejpam-5971	301	4	second	second	ADJ
ejpam-5971	301	5	zagreb	zagreb	PROPN
ejpam-5971	301	6	indices	index	NOUN
ejpam-5971	301	7	of	of	ADP
ejpam-5971	301	8	graph	graph	NOUN
ejpam-5971	301	9	g	g	ADP
ejpam-5971	301	10	∼=	∼=	PROPN
ejpam-5971	301	11	γ(z℘[x]/⟨x5⟩	γ(z℘[x]/⟨x5⟩	NUM
ejpam-5971	301	12	)	)	PUNCT
ejpam-5971	301	13	respectively	respectively	ADV
ejpam-5971	301	14	are	be	AUX
ejpam-5971	301	15	m1(g	m1(g	NOUN
ejpam-5971	301	16	)	)	PUNCT
ejpam-5971	301	17	=	=	SYM
ejpam-5971	302	1	℘9	℘9	NOUN
ejpam-5971	302	2	−	−	PROPN
ejpam-5971	302	3	13℘5	13℘5	NUM
ejpam-5971	303	1	+	+	CCONJ
ejpam-5971	303	2	13℘4	13℘4	NUM
ejpam-5971	303	3	+	+	CCONJ
ejpam-5971	303	4	3℘2	3℘2	NUM
ejpam-5971	303	5	−	−	ADP
ejpam-5971	303	6	4	4	NUM
ejpam-5971	303	7	.	.	X
ejpam-5971	304	1	m2(g	m2(g	X
ejpam-5971	305	1	)	)	PUNCT
ejpam-5971	305	2	=	=	SYM
ejpam-5971	305	3	1	1	NUM
ejpam-5971	305	4	2	2	NUM
ejpam-5971	305	5	(	(	PUNCT
ejpam-5971	305	6	℘−	℘−	NOUN
ejpam-5971	305	7	1)(10℘9	1)(10℘9	NUM
ejpam-5971	305	8	−	−	PROPN
ejpam-5971	305	9	13℘8	13℘8	NUM
ejpam-5971	305	10	−	−	NOUN
ejpam-5971	305	11	3℘7	3℘7	NUM
ejpam-5971	305	12	−	−	NOUN
ejpam-5971	305	13	8℘6	8℘6	NUM
ejpam-5971	305	14	−	−	PROPN
ejpam-5971	305	15	4℘5	4℘5	NUM
ejpam-5971	305	16	+	+	CCONJ
ejpam-5971	305	17	32℘4	32℘4	NUM
ejpam-5971	305	18	−	−	PROPN
ejpam-5971	305	19	8℘−	8℘−	NUM
ejpam-5971	305	20	8)	8)	NUM
ejpam-5971	305	21	.	.	PUNCT
ejpam-5971	306	1	proof	proof	NOUN
ejpam-5971	306	2	.	.	PUNCT
ejpam-5971	307	1	let	let	VERB
ejpam-5971	307	2	a	a	DET
ejpam-5971	307	3	∈	∈	PROPN
ejpam-5971	307	4	a	a	PRON
ejpam-5971	307	5	,	,	PUNCT
ejpam-5971	307	6	b	b	PROPN
ejpam-5971	307	7	∈	∈	PROPN
ejpam-5971	307	8	b	b	PROPN
ejpam-5971	307	9	,	,	PUNCT
ejpam-5971	307	10	c	c	NOUN
ejpam-5971	307	11	,	,	PUNCT
ejpam-5971	307	12	c′	c′	NOUN
ejpam-5971	307	13	∈	∈	PROPN
ejpam-5971	307	14	c	c	PROPN
ejpam-5971	307	15	for	for	ADP
ejpam-5971	307	16	c	c	PROPN
ejpam-5971	307	17	̸=	̸=	PROPN
ejpam-5971	307	18	c′	c′	NOUN
ejpam-5971	307	19	,	,	PUNCT
ejpam-5971	307	20	and	and	CCONJ
ejpam-5971	307	21	d	d	NOUN
ejpam-5971	307	22	,	,	PUNCT
ejpam-5971	307	23	d′	d′	X
ejpam-5971	307	24	∈	∈	PROPN
ejpam-5971	307	25	d	d	NOUN
ejpam-5971	307	26	for	for	ADP
ejpam-5971	307	27	d	d	PROPN
ejpam-5971	307	28	̸=	̸=	PROPN
ejpam-5971	307	29	d′	d′	NUM
ejpam-5971	307	30	,	,	PUNCT
ejpam-5971	307	31	where	where	SCONJ
ejpam-5971	307	32	a	a	DET
ejpam-5971	307	33	,	,	PUNCT
ejpam-5971	307	34	b	b	NOUN
ejpam-5971	307	35	,	,	PUNCT
ejpam-5971	307	36	c	c	NOUN
ejpam-5971	307	37	,	,	PUNCT
ejpam-5971	307	38	d	d	X
ejpam-5971	307	39	are	be	AUX
ejpam-5971	307	40	the	the	DET
ejpam-5971	307	41	partition	partition	NOUN
ejpam-5971	307	42	of	of	ADP
ejpam-5971	307	43	the	the	DET
ejpam-5971	307	44	vertex	vertex	NOUN
ejpam-5971	307	45	set	set	NOUN
ejpam-5971	307	46	of	of	ADP
ejpam-5971	307	47	g.	g.	PROPN
ejpam-5971	307	48	based	base	VERB
ejpam-5971	307	49	on	on	ADP
ejpam-5971	307	50	lemma	lemma	PROPN
ejpam-5971	307	51	2	2	NUM
ejpam-5971	307	52	,	,	PUNCT
ejpam-5971	307	53	it	it	PRON
ejpam-5971	307	54	is	be	AUX
ejpam-5971	307	55	clear	clear	ADJ
ejpam-5971	307	56	that	that	SCONJ
ejpam-5971	307	57	the	the	DET
ejpam-5971	307	58	set	set	NOUN
ejpam-5971	307	59	of	of	ADP
ejpam-5971	307	60	edges	edge	NOUN
ejpam-5971	307	61	established	establish	VERB
ejpam-5971	307	62	of	of	ADP
ejpam-5971	307	63	graph	graph	NOUN
ejpam-5971	307	64	g	g	PROPN
ejpam-5971	307	65	is	be	AUX
ejpam-5971	307	66	as	as	SCONJ
ejpam-5971	307	67	follows	follow	VERB
ejpam-5971	307	68	:	:	PUNCT
ejpam-5971	307	69	e1	e1	NOUN
ejpam-5971	307	70	=	=	SYM
ejpam-5971	307	71	{	{	PUNCT
ejpam-5971	307	72	ad	ad	NOUN
ejpam-5971	307	73	∈	∈	PROPN
ejpam-5971	307	74	e(g	e(g	PROPN
ejpam-5971	307	75	)	)	PUNCT
ejpam-5971	307	76	|	|	ADV
ejpam-5971	307	77	a	a	DET
ejpam-5971	307	78	∈	∈	PROPN
ejpam-5971	307	79	a	a	PRON
ejpam-5971	307	80	,	,	PUNCT
ejpam-5971	307	81	d	d	PROPN
ejpam-5971	307	82	∈	∈	PROPN
ejpam-5971	308	1	d	d	X
ejpam-5971	308	2	}	}	PUNCT
ejpam-5971	308	3	,	,	PUNCT
ejpam-5971	308	4	|e1|	|e1|	NOUN
ejpam-5971	308	5	=	=	PROPN
ejpam-5971	308	6	℘5	℘5	PROPN
ejpam-5971	308	7	−	−	PROPN
ejpam-5971	308	8	2℘4	2℘4	NUM
ejpam-5971	308	9	+	+	CCONJ
ejpam-5971	308	10	℘3	℘3	ADJ
ejpam-5971	308	11	,	,	PUNCT
ejpam-5971	308	12	e2	e2	PROPN
ejpam-5971	308	13	=	=	SYM
ejpam-5971	308	14	{	{	PUNCT
ejpam-5971	308	15	bc	bc	PROPN
ejpam-5971	308	16	∈	∈	PROPN
ejpam-5971	308	17	e(g	e(g	PROPN
ejpam-5971	308	18	)	)	PUNCT
ejpam-5971	309	1	|	|	ADV
ejpam-5971	309	2	b	b	X
ejpam-5971	309	3	∈	∈	PROPN
ejpam-5971	309	4	b	b	PROPN
ejpam-5971	309	5	,	,	PUNCT
ejpam-5971	309	6	c	c	PROPN
ejpam-5971	309	7	∈	∈	PROPN
ejpam-5971	309	8	c	c	X
ejpam-5971	309	9	}	}	PUNCT
ejpam-5971	309	10	,	,	PUNCT
ejpam-5971	309	11	|e2|	|e2|	ADJ
ejpam-5971	309	12	=	=	SYM
ejpam-5971	309	13	℘5	℘5	NOUN
ejpam-5971	309	14	−	−	PROPN
ejpam-5971	309	15	2℘4	2℘4	NUM
ejpam-5971	309	16	+	+	CCONJ
ejpam-5971	309	17	℘3	℘3	ADJ
ejpam-5971	309	18	,	,	PUNCT
ejpam-5971	309	19	e3	e3	PROPN
ejpam-5971	309	20	=	=	SYM
ejpam-5971	309	21	{	{	PUNCT
ejpam-5971	309	22	bd	bd	PROPN
ejpam-5971	309	23	∈	∈	PROPN
ejpam-5971	309	24	e(g	e(g	PROPN
ejpam-5971	309	25	)	)	PUNCT
ejpam-5971	310	1	|	|	ADV
ejpam-5971	310	2	b	b	X
ejpam-5971	310	3	∈	∈	PROPN
ejpam-5971	310	4	b	b	PROPN
ejpam-5971	310	5	,	,	PUNCT
ejpam-5971	310	6	d	d	PROPN
ejpam-5971	310	7	∈	∈	PROPN
ejpam-5971	310	8	d	d	X
ejpam-5971	310	9	}	}	PUNCT
ejpam-5971	310	10	,	,	PUNCT
ejpam-5971	310	11	|e3|	|e3|	NOUN
ejpam-5971	310	12	=	=	PUNCT
ejpam-5971	310	13	℘4	℘4	NOUN
ejpam-5971	310	14	−	−	PROPN
ejpam-5971	310	15	2℘3	2℘3	NUM
ejpam-5971	310	16	+	+	CCONJ
ejpam-5971	310	17	℘2	℘2	PROPN
ejpam-5971	310	18	,	,	PUNCT
ejpam-5971	310	19	e4	e4	PROPN
ejpam-5971	310	20	=	=	SYM
ejpam-5971	310	21	{	{	PUNCT
ejpam-5971	310	22	cc′	cc′	NOUN
ejpam-5971	310	23	∈	∈	PROPN
ejpam-5971	310	24	e(g	e(g	PROPN
ejpam-5971	310	25	)	)	PUNCT
ejpam-5971	311	1	|	|	ADV
ejpam-5971	311	2	c	c	X
ejpam-5971	311	3	,	,	PUNCT
ejpam-5971	311	4	c′	c′	NOUN
ejpam-5971	311	5	∈	∈	PROPN
ejpam-5971	311	6	c	c	AUX
ejpam-5971	311	7	,	,	PUNCT
ejpam-5971	311	8	c	c	PROPN
ejpam-5971	311	9	̸=	̸=	PROPN
ejpam-5971	311	10	c′	c′	PROPN
ejpam-5971	311	11	}	}	PUNCT
ejpam-5971	311	12	,	,	PUNCT
ejpam-5971	311	13	|e4|	|e4|	NOUN
ejpam-5971	311	14	=	=	NOUN
ejpam-5971	311	15	1	1	NUM
ejpam-5971	311	16	2	2	NUM
ejpam-5971	311	17	(	(	PUNCT
ejpam-5971	311	18	℘4	℘4	VERB
ejpam-5971	311	19	−	−	PROPN
ejpam-5971	311	20	2℘3	2℘3	NUM
ejpam-5971	311	21	+	+	CCONJ
ejpam-5971	311	22	℘	℘	NOUN
ejpam-5971	311	23	)	)	PUNCT
ejpam-5971	311	24	,	,	PUNCT
ejpam-5971	311	25	e5	e5	PROPN
ejpam-5971	311	26	=	=	PUNCT
ejpam-5971	311	27	{	{	PUNCT
ejpam-5971	311	28	cd	cd	PROPN
ejpam-5971	311	29	∈	∈	PROPN
ejpam-5971	311	30	e(g	e(g	PROPN
ejpam-5971	311	31	)	)	PUNCT
ejpam-5971	312	1	|	|	ADV
ejpam-5971	312	2	c	c	X
ejpam-5971	312	3	∈	∈	PROPN
ejpam-5971	312	4	c	c	X
ejpam-5971	312	5	,	,	PUNCT
ejpam-5971	312	6	d	d	PROPN
ejpam-5971	312	7	∈	∈	PROPN
ejpam-5971	312	8	d	d	X
ejpam-5971	312	9	}	}	PUNCT
ejpam-5971	312	10	,	,	PUNCT
ejpam-5971	312	11	|e5|	|e5|	X
ejpam-5971	312	12	=	=	SYM
ejpam-5971	312	13	℘3	℘3	CCONJ
ejpam-5971	312	14	−	−	PROPN
ejpam-5971	312	15	2℘2	2℘2	NUM
ejpam-5971	312	16	+	+	NUM
ejpam-5971	312	17	℘	℘	NOUN
ejpam-5971	312	18	,	,	PUNCT
ejpam-5971	312	19	e6	e6	NOUN
ejpam-5971	312	20	=	=	SYM
ejpam-5971	312	21	{	{	PUNCT
ejpam-5971	312	22	dd′	dd′	PROPN
ejpam-5971	312	23	∈	∈	PROPN
ejpam-5971	312	24	e(g	e(g	PROPN
ejpam-5971	312	25	)	)	PUNCT
ejpam-5971	313	1	|	|	ADV
ejpam-5971	313	2	d	d	X
ejpam-5971	313	3	,	,	PUNCT
ejpam-5971	313	4	d′	d′	X
ejpam-5971	313	5	∈	∈	PROPN
ejpam-5971	313	6	d	d	NOUN
ejpam-5971	313	7	,	,	PUNCT
ejpam-5971	313	8	d	d	PROPN
ejpam-5971	313	9	̸=	̸=	PROPN
ejpam-5971	313	10	d′	d′	NUM
ejpam-5971	313	11	}	}	PUNCT
ejpam-5971	313	12	,	,	PUNCT
ejpam-5971	313	13	|e6|	|e6|	ADJ
ejpam-5971	313	14	=	=	SYM
ejpam-5971	313	15	1	1	NUM
ejpam-5971	313	16	2	2	NUM
ejpam-5971	313	17	(	(	PUNCT
ejpam-5971	313	18	℘2	℘2	NOUN
ejpam-5971	313	19	−	−	NOUN
ejpam-5971	313	20	3℘+	3℘+	NUM
ejpam-5971	313	21	2	2	NUM
ejpam-5971	313	22	)	)	PUNCT
ejpam-5971	313	23	.	.	PUNCT
ejpam-5971	314	1	in	in	ADP
ejpam-5971	314	2	[	[	X
ejpam-5971	314	3	24	24	NUM
ejpam-5971	314	4	]	]	PUNCT
ejpam-5971	314	5	,	,	PUNCT
ejpam-5971	314	6	musyarrofah	musyarrofah	PROPN
ejpam-5971	314	7	et	et	PROPN
ejpam-5971	314	8	al	al	PROPN
ejpam-5971	314	9	.	.	PROPN
ejpam-5971	314	10	determined	determine	VERB
ejpam-5971	314	11	the	the	DET
ejpam-5971	314	12	degree	degree	NOUN
ejpam-5971	314	13	of	of	ADP
ejpam-5971	314	14	each	each	DET
ejpam-5971	314	15	vertex	vertex	NOUN
ejpam-5971	314	16	of	of	ADP
ejpam-5971	314	17	the	the	DET
ejpam-5971	314	18	graph	graph	NOUN
ejpam-5971	314	19	g	g	NOUN
ejpam-5971	314	20	as	as	SCONJ
ejpam-5971	314	21	follows	follow	VERB
ejpam-5971	314	22	.	.	PUNCT
ejpam-5971	315	1	deg(a	deg(a	X
ejpam-5971	315	2	)	)	PUNCT
ejpam-5971	315	3	=	=	SYM
ejpam-5971	316	1	℘−	℘−	NOUN
ejpam-5971	316	2	1	1	NUM
ejpam-5971	316	3	,	,	PUNCT
ejpam-5971	316	4	deg(b	deg(b	NUM
ejpam-5971	316	5	)	)	PUNCT
ejpam-5971	316	6	=	=	SYM
ejpam-5971	316	7	℘2	℘2	NOUN
ejpam-5971	316	8	−	−	PROPN
ejpam-5971	316	9	1	1	NUM
ejpam-5971	316	10	,	,	PUNCT
ejpam-5971	316	11	deg(c	deg(c	PROPN
ejpam-5971	316	12	)	)	PUNCT
ejpam-5971	316	13	=	=	PUNCT
ejpam-5971	317	1	℘3	℘3	ADJ
ejpam-5971	317	2	−	−	NOUN
ejpam-5971	317	3	2	2	NUM
ejpam-5971	317	4	,	,	PUNCT
ejpam-5971	317	5	deg(d	deg(d	PROPN
ejpam-5971	317	6	)	)	PUNCT
ejpam-5971	317	7	=	=	PUNCT
ejpam-5971	317	8	℘4	℘4	NOUN
ejpam-5971	317	9	−	−	NOUN
ejpam-5971	317	10	2	2	NUM
ejpam-5971	317	11	.	.	PUNCT
ejpam-5971	318	1	thus	thus	ADV
ejpam-5971	318	2	,	,	PUNCT
ejpam-5971	318	3	the	the	DET
ejpam-5971	318	4	first	first	ADJ
ejpam-5971	318	5	zagreb	zagreb	PROPN
ejpam-5971	318	6	of	of	ADP
ejpam-5971	318	7	g	g	PROPN
ejpam-5971	318	8	is	be	AUX
ejpam-5971	318	9	m1(g	m1(g	NOUN
ejpam-5971	318	10	)	)	PUNCT
ejpam-5971	318	11	=	=	SYM
ejpam-5971	318	12	∑	∑	PUNCT
ejpam-5971	318	13	vw∈e(g	vw∈e(g	NUM
ejpam-5971	318	14	)	)	PUNCT
ejpam-5971	319	1	[	[	X
ejpam-5971	319	2	deg(v	deg(v	X
ejpam-5971	319	3	)	)	PUNCT
ejpam-5971	319	4	+	+	SYM
ejpam-5971	319	5	deg(w	deg(w	NUM
ejpam-5971	319	6	)	)	PUNCT
ejpam-5971	319	7	]	]	PUNCT
ejpam-5971	320	1	=	=	PUNCT
ejpam-5971	320	2	[	[	PUNCT
ejpam-5971	320	3	(	(	PUNCT
ejpam-5971	320	4	℘−	℘−	NOUN
ejpam-5971	320	5	1	1	NUM
ejpam-5971	320	6	)	)	PUNCT
ejpam-5971	320	7	+	+	CCONJ
ejpam-5971	320	8	(	(	PUNCT
ejpam-5971	320	9	℘4	℘4	VERB
ejpam-5971	320	10	−	−	NOUN
ejpam-5971	320	11	2	2	NUM
ejpam-5971	320	12	)	)	PUNCT
ejpam-5971	320	13	]	]	PUNCT
ejpam-5971	320	14	(	(	PUNCT
ejpam-5971	320	15	℘5	℘5	VERB
ejpam-5971	320	16	−	−	PROPN
ejpam-5971	320	17	2℘4	2℘4	NUM
ejpam-5971	320	18	+	+	X
ejpam-5971	320	19	℘3	℘3	ADJ
ejpam-5971	320	20	)	)	PUNCT
ejpam-5971	320	21	+	+	CCONJ
ejpam-5971	320	22	[	[	X
ejpam-5971	320	23	(	(	PUNCT
ejpam-5971	320	24	℘2	℘2	NOUN
ejpam-5971	320	25	−	−	PROPN
ejpam-5971	320	26	1	1	NUM
ejpam-5971	320	27	)	)	PUNCT
ejpam-5971	320	28	+	+	CCONJ
ejpam-5971	320	29	(	(	PUNCT
ejpam-5971	320	30	℘3	℘3	ADV
ejpam-5971	320	31	−	−	PROPN
ejpam-5971	320	32	2	2	NUM
ejpam-5971	320	33	)	)	PUNCT
ejpam-5971	320	34	]	]	PUNCT
ejpam-5971	320	35	(	(	PUNCT
ejpam-5971	320	36	℘5	℘5	VERB
ejpam-5971	320	37	−	−	PROPN
ejpam-5971	320	38	2℘4	2℘4	NUM
ejpam-5971	320	39	+	+	X
ejpam-5971	320	40	℘3	℘3	ADJ
ejpam-5971	320	41	)	)	PUNCT
ejpam-5971	321	1	+	+	PUNCT
ejpam-5971	321	2	[	[	X
ejpam-5971	321	3	(	(	PUNCT
ejpam-5971	321	4	℘2	℘2	NOUN
ejpam-5971	321	5	−	−	PROPN
ejpam-5971	321	6	1	1	NUM
ejpam-5971	321	7	)	)	PUNCT
ejpam-5971	321	8	+	+	CCONJ
ejpam-5971	321	9	(	(	PUNCT
ejpam-5971	321	10	℘4	℘4	VERB
ejpam-5971	321	11	−	−	NOUN
ejpam-5971	321	12	2	2	NUM
ejpam-5971	321	13	)	)	PUNCT
ejpam-5971	321	14	]	]	PUNCT
ejpam-5971	322	1	(	(	PUNCT
ejpam-5971	322	2	℘4	℘4	VERB
ejpam-5971	322	3	−	−	PROPN
ejpam-5971	322	4	2℘3	2℘3	NUM
ejpam-5971	322	5	+	+	CCONJ
ejpam-5971	322	6	℘2	℘2	NOUN
ejpam-5971	322	7	)	)	PUNCT
ejpam-5971	323	1	+	+	CCONJ
ejpam-5971	324	1	[	[	X
ejpam-5971	324	2	(	(	PUNCT
ejpam-5971	324	3	℘3	℘3	ADJ
ejpam-5971	324	4	−	−	PROPN
ejpam-5971	324	5	2	2	NUM
ejpam-5971	324	6	)	)	PUNCT
ejpam-5971	325	1	+	+	CCONJ
ejpam-5971	325	2	(	(	PUNCT
ejpam-5971	325	3	℘3	℘3	ADV
ejpam-5971	325	4	−	−	PROPN
ejpam-5971	325	5	2	2	NUM
ejpam-5971	325	6	)	)	PUNCT
ejpam-5971	325	7	]	]	PUNCT
ejpam-5971	325	8	1	1	NUM
ejpam-5971	325	9	2	2	NUM
ejpam-5971	325	10	(	(	PUNCT
ejpam-5971	325	11	℘4	℘4	VERB
ejpam-5971	325	12	−	−	PROPN
ejpam-5971	325	13	2℘3	2℘3	NUM
ejpam-5971	325	14	+	+	CCONJ
ejpam-5971	325	15	℘	℘	PROPN
ejpam-5971	325	16	)	)	PUNCT
ejpam-5971	326	1	+	+	PUNCT
ejpam-5971	326	2	[	[	X
ejpam-5971	326	3	(	(	PUNCT
ejpam-5971	326	4	℘3	℘3	ADJ
ejpam-5971	326	5	−	−	PROPN
ejpam-5971	326	6	2	2	NUM
ejpam-5971	326	7	)	)	PUNCT
ejpam-5971	327	1	+	+	CCONJ
ejpam-5971	327	2	(	(	PUNCT
ejpam-5971	327	3	℘4	℘4	VERB
ejpam-5971	327	4	−	−	NOUN
ejpam-5971	327	5	2	2	NUM
ejpam-5971	327	6	)	)	PUNCT
ejpam-5971	327	7	]	]	PUNCT
ejpam-5971	328	1	(	(	PUNCT
ejpam-5971	328	2	℘3	℘3	ADV
ejpam-5971	328	3	−	−	PROPN
ejpam-5971	328	4	2℘2	2℘2	NUM
ejpam-5971	328	5	+	+	NUM
ejpam-5971	328	6	℘	℘	NOUN
ejpam-5971	328	7	)	)	PUNCT
ejpam-5971	329	1	+	+	CCONJ
ejpam-5971	330	1	[	[	X
ejpam-5971	330	2	(	(	PUNCT
ejpam-5971	330	3	℘4	℘4	VERB
ejpam-5971	330	4	−	−	NOUN
ejpam-5971	330	5	2	2	NUM
ejpam-5971	330	6	)	)	PUNCT
ejpam-5971	330	7	+	+	CCONJ
ejpam-5971	330	8	(	(	PUNCT
ejpam-5971	330	9	℘4	℘4	VERB
ejpam-5971	330	10	−	−	NOUN
ejpam-5971	330	11	2	2	NUM
ejpam-5971	330	12	)	)	PUNCT
ejpam-5971	330	13	]	]	PUNCT
ejpam-5971	330	14	1	1	NUM
ejpam-5971	330	15	2	2	NUM
ejpam-5971	330	16	(	(	PUNCT
ejpam-5971	330	17	℘2	℘2	NOUN
ejpam-5971	330	18	−	−	PROPN
ejpam-5971	330	19	3℘+	3℘+	NUM
ejpam-5971	330	20	2	2	NUM
ejpam-5971	330	21	)	)	PUNCT
ejpam-5971	330	22	=	=	SYM
ejpam-5971	330	23	℘9	℘9	NOUN
ejpam-5971	330	24	−	−	PROPN
ejpam-5971	330	25	13℘5	13℘5	NUM
ejpam-5971	330	26	+	+	CCONJ
ejpam-5971	330	27	13℘4	13℘4	NUM
ejpam-5971	330	28	+	+	CCONJ
ejpam-5971	330	29	3℘2	3℘2	NUM
ejpam-5971	330	30	−	−	NOUN
ejpam-5971	330	31	4	4	X
ejpam-5971	330	32	.	.	PUNCT
ejpam-5971	331	1	v.h	v.h	PROPN
ejpam-5971	331	2	.	.	PROPN
ejpam-5971	331	3	krisnawati	krisnawati	PROPN
ejpam-5971	331	4	,	,	PUNCT
ejpam-5971	331	5	n.	n.	PROPN
ejpam-5971	331	6	hidayat	hidayat	PROPN
ejpam-5971	331	7	,	,	PUNCT
ejpam-5971	331	8	a.f	a.f	PROPN
ejpam-5971	331	9	.	.	PROPN
ejpam-5971	331	10	musyarrofah	musyarrofah	PROPN
ejpam-5971	331	11	/	/	SYM
ejpam-5971	331	12	eur	eur	PROPN
ejpam-5971	331	13	.	.	PUNCT
ejpam-5971	332	1	j.	j.	PROPN
ejpam-5971	332	2	pure	pure	PROPN
ejpam-5971	332	3	appl	appl	PROPN
ejpam-5971	332	4	.	.	PROPN
ejpam-5971	332	5	math	math	PROPN
ejpam-5971	332	6	,	,	PUNCT
ejpam-5971	332	7	18	18	NUM
ejpam-5971	332	8	(	(	PUNCT
ejpam-5971	332	9	2	2	NUM
ejpam-5971	332	10	)	)	PUNCT
ejpam-5971	332	11	(	(	PUNCT
ejpam-5971	332	12	2025	2025	NUM
ejpam-5971	332	13	)	)	PUNCT
ejpam-5971	332	14	,	,	PUNCT
ejpam-5971	332	15	5971	5971	NUM
ejpam-5971	332	16	16	16	NUM
ejpam-5971	332	17	of	of	ADP
ejpam-5971	332	18	19	19	NUM
ejpam-5971	332	19	moreover	moreover	ADV
ejpam-5971	332	20	,	,	PUNCT
ejpam-5971	332	21	the	the	DET
ejpam-5971	332	22	second	second	ADJ
ejpam-5971	332	23	zagreb	zagreb	PROPN
ejpam-5971	332	24	index	index	NOUN
ejpam-5971	332	25	of	of	ADP
ejpam-5971	332	26	g	g	PROPN
ejpam-5971	332	27	is	be	AUX
ejpam-5971	332	28	m2(g	m2(g	NOUN
ejpam-5971	332	29	)	)	PUNCT
ejpam-5971	332	30	=	=	SYM
ejpam-5971	332	31	∑	∑	PUNCT
ejpam-5971	332	32	vw∈e(g	vw∈e(g	NUM
ejpam-5971	332	33	)	)	PUNCT
ejpam-5971	333	1	[	[	X
ejpam-5971	333	2	deg(v	deg(v	X
ejpam-5971	333	3	)	)	PUNCT
ejpam-5971	333	4	deg(v	deg(v	PROPN
ejpam-5971	333	5	)	)	PUNCT
ejpam-5971	333	6	]	]	PUNCT
ejpam-5971	334	1	=	=	SYM
ejpam-5971	334	2	(	(	PUNCT
ejpam-5971	334	3	℘−	℘−	NOUN
ejpam-5971	334	4	1	1	NUM
ejpam-5971	334	5	)	)	PUNCT
ejpam-5971	334	6	(	(	PUNCT
ejpam-5971	334	7	℘4	℘4	VERB
ejpam-5971	334	8	−	−	PROPN
ejpam-5971	334	9	2	2	NUM
ejpam-5971	334	10	)	)	PUNCT
ejpam-5971	334	11	(	(	PUNCT
ejpam-5971	334	12	℘5	℘5	VERB
ejpam-5971	334	13	−	−	PROPN
ejpam-5971	334	14	2℘4	2℘4	NUM
ejpam-5971	334	15	+	+	X
ejpam-5971	334	16	℘3	℘3	ADJ
ejpam-5971	334	17	)	)	PUNCT
ejpam-5971	335	1	+	+	CCONJ
ejpam-5971	335	2	(	(	PUNCT
ejpam-5971	335	3	℘2	℘2	NOUN
ejpam-5971	335	4	−	−	PROPN
ejpam-5971	335	5	1	1	NUM
ejpam-5971	335	6	)	)	PUNCT
ejpam-5971	335	7	(	(	PUNCT
ejpam-5971	335	8	℘3	℘3	ADV
ejpam-5971	335	9	−	−	PROPN
ejpam-5971	335	10	2	2	NUM
ejpam-5971	335	11	)	)	PUNCT
ejpam-5971	335	12	(	(	PUNCT
ejpam-5971	335	13	℘5	℘5	VERB
ejpam-5971	335	14	−	−	PROPN
ejpam-5971	335	15	2℘4	2℘4	NUM
ejpam-5971	335	16	+	+	CCONJ
ejpam-5971	335	17	℘3	℘3	ADJ
ejpam-5971	335	18	)	)	PUNCT
ejpam-5971	336	1	+	+	ADJ
ejpam-5971	336	2	(	(	PUNCT
ejpam-5971	336	3	℘2	℘2	NOUN
ejpam-5971	336	4	−	−	PROPN
ejpam-5971	336	5	1	1	NUM
ejpam-5971	336	6	)	)	PUNCT
ejpam-5971	336	7	(	(	PUNCT
ejpam-5971	336	8	℘4	℘4	VERB
ejpam-5971	336	9	−	−	NOUN
ejpam-5971	336	10	2	2	NUM
ejpam-5971	336	11	)	)	PUNCT
ejpam-5971	336	12	(	(	PUNCT
ejpam-5971	336	13	℘4	℘4	VERB
ejpam-5971	336	14	−	−	PROPN
ejpam-5971	336	15	2℘3	2℘3	NUM
ejpam-5971	336	16	+	+	CCONJ
ejpam-5971	336	17	℘2	℘2	NOUN
ejpam-5971	336	18	)	)	PUNCT
ejpam-5971	337	1	+	+	CCONJ
ejpam-5971	337	2	1	1	NUM
ejpam-5971	337	3	2	2	NUM
ejpam-5971	337	4	(	(	PUNCT
ejpam-5971	337	5	(	(	PUNCT
ejpam-5971	337	6	℘3	℘3	ADV
ejpam-5971	337	7	−	−	PROPN
ejpam-5971	337	8	2	2	NUM
ejpam-5971	337	9	)	)	PUNCT
ejpam-5971	337	10	(	(	PUNCT
ejpam-5971	337	11	℘3	℘3	ADV
ejpam-5971	337	12	−	−	PROPN
ejpam-5971	337	13	2	2	NUM
ejpam-5971	337	14	)	)	PUNCT
ejpam-5971	337	15	(	(	PUNCT
ejpam-5971	337	16	℘4	℘4	VERB
ejpam-5971	337	17	−	−	PROPN
ejpam-5971	337	18	2℘3	2℘3	NUM
ejpam-5971	337	19	+	+	CCONJ
ejpam-5971	337	20	℘	℘	PROPN
ejpam-5971	337	21	)	)	PUNCT
ejpam-5971	337	22	)	)	PUNCT
ejpam-5971	338	1	+	+	ADV
ejpam-5971	338	2	(	(	PUNCT
ejpam-5971	338	3	℘3	℘3	ADJ
ejpam-5971	338	4	−	−	PROPN
ejpam-5971	338	5	2	2	NUM
ejpam-5971	338	6	)	)	PUNCT
ejpam-5971	338	7	(	(	PUNCT
ejpam-5971	338	8	℘4	℘4	VERB
ejpam-5971	338	9	−	−	PROPN
ejpam-5971	338	10	2	2	NUM
ejpam-5971	338	11	)	)	PUNCT
ejpam-5971	338	12	(	(	PUNCT
ejpam-5971	338	13	℘3	℘3	ADV
ejpam-5971	338	14	−	−	PROPN
ejpam-5971	338	15	2℘2	2℘2	NUM
ejpam-5971	338	16	+	+	NUM
ejpam-5971	338	17	℘	℘	NOUN
ejpam-5971	338	18	)	)	PUNCT
ejpam-5971	339	1	+	+	CCONJ
ejpam-5971	339	2	1	1	NUM
ejpam-5971	339	3	2	2	NUM
ejpam-5971	339	4	(	(	PUNCT
ejpam-5971	339	5	(	(	PUNCT
ejpam-5971	339	6	℘4	℘4	VERB
ejpam-5971	339	7	−	−	NOUN
ejpam-5971	339	8	2	2	NUM
ejpam-5971	339	9	)	)	PUNCT
ejpam-5971	339	10	(	(	PUNCT
ejpam-5971	339	11	℘4	℘4	VERB
ejpam-5971	339	12	−	−	PROPN
ejpam-5971	339	13	2	2	NUM
ejpam-5971	339	14	)	)	PUNCT
ejpam-5971	339	15	(	(	PUNCT
ejpam-5971	339	16	℘2	℘2	NOUN
ejpam-5971	339	17	−	−	PROPN
ejpam-5971	339	18	3℘+	3℘+	NUM
ejpam-5971	339	19	2	2	NUM
ejpam-5971	339	20	)	)	PUNCT
ejpam-5971	339	21	)	)	PUNCT
ejpam-5971	340	1	=	=	SYM
ejpam-5971	340	2	1	1	NUM
ejpam-5971	340	3	2	2	NUM
ejpam-5971	340	4	(	(	PUNCT
ejpam-5971	340	5	℘−	℘−	NOUN
ejpam-5971	340	6	1)(10℘9	1)(10℘9	NUM
ejpam-5971	340	7	−	−	PROPN
ejpam-5971	340	8	13℘8	13℘8	NUM
ejpam-5971	340	9	−	−	NOUN
ejpam-5971	340	10	3℘7	3℘7	NUM
ejpam-5971	340	11	−	−	NOUN
ejpam-5971	340	12	8℘6	8℘6	NUM
ejpam-5971	340	13	−	−	PROPN
ejpam-5971	340	14	4℘5	4℘5	NUM
ejpam-5971	340	15	+	+	CCONJ
ejpam-5971	340	16	32℘4	32℘4	NUM
ejpam-5971	340	17	−	−	PROPN
ejpam-5971	340	18	8℘−	8℘−	NUM
ejpam-5971	340	19	8)	8)	NUM
ejpam-5971	340	20	.	.	PUNCT
ejpam-5971	340	21	theorem	theorem	NOUN
ejpam-5971	340	22	6	6	NUM
ejpam-5971	340	23	.	.	PUNCT
ejpam-5971	341	1	the	the	DET
ejpam-5971	341	2	narumi	narumi	PROPN
ejpam-5971	341	3	-	-	PUNCT
ejpam-5971	341	4	katayama	katayama	NOUN
ejpam-5971	341	5	index	index	NOUN
ejpam-5971	341	6	of	of	ADP
ejpam-5971	341	7	graph	graph	NOUN
ejpam-5971	341	8	g	g	PROPN
ejpam-5971	341	9	∼=	∼=	PROPN
ejpam-5971	341	10	γ(z℘[x]/⟨x5⟩	γ(z℘[x]/⟨x5⟩	NUM
ejpam-5971	341	11	)	)	PUNCT
ejpam-5971	341	12	is	be	AUX
ejpam-5971	341	13	nk(g	nk(g	NOUN
ejpam-5971	341	14	)	)	PUNCT
ejpam-5971	341	15	=	=	SYM
ejpam-5971	342	1	(	(	PUNCT
ejpam-5971	342	2	℘−	℘−	NOUN
ejpam-5971	342	3	1	1	NUM
ejpam-5971	342	4	)	)	PUNCT
ejpam-5971	342	5	℘4−℘3	℘4−℘3	PROPN
ejpam-5971	342	6	(	(	PUNCT
ejpam-5971	342	7	℘2	℘2	NOUN
ejpam-5971	342	8	−	−	PROPN
ejpam-5971	342	9	1	1	NUM
ejpam-5971	342	10	)	)	PUNCT
ejpam-5971	342	11	℘3−℘2	℘3−℘2	PROPN
ejpam-5971	342	12	(	(	PUNCT
ejpam-5971	342	13	℘3	℘3	ADV
ejpam-5971	342	14	−	−	PROPN
ejpam-5971	342	15	2	2	NUM
ejpam-5971	342	16	)	)	PUNCT
ejpam-5971	342	17	℘2−℘	℘2−℘	NUM
ejpam-5971	342	18	(	(	PUNCT
ejpam-5971	342	19	℘4	℘4	VERB
ejpam-5971	342	20	−	−	NOUN
ejpam-5971	342	21	2	2	NUM
ejpam-5971	342	22	)	)	PUNCT
ejpam-5971	342	23	℘−1	℘−1	NOUN
ejpam-5971	342	24	proof	proof	NOUN
ejpam-5971	342	25	.	.	PUNCT
ejpam-5971	343	1	based	base	VERB
ejpam-5971	343	2	on	on	ADP
ejpam-5971	343	3	musyarrofah	musyarrofah	PROPN
ejpam-5971	343	4	et	et	PROPN
ejpam-5971	343	5	al	al	PROPN
ejpam-5971	343	6	.	.	PUNCT
ejpam-5971	344	1	[	[	X
ejpam-5971	344	2	24	24	NUM
ejpam-5971	344	3	]	]	PUNCT
ejpam-5971	344	4	,	,	PUNCT
ejpam-5971	344	5	the	the	DET
ejpam-5971	344	6	degrees	degree	NOUN
ejpam-5971	344	7	of	of	ADP
ejpam-5971	344	8	the	the	DET
ejpam-5971	344	9	vertices	vertex	NOUN
ejpam-5971	344	10	in	in	ADP
ejpam-5971	344	11	graph	graph	NOUN
ejpam-5971	344	12	g	g	PROPN
ejpam-5971	344	13	as	as	SCONJ
ejpam-5971	344	14	follows	follow	VERB
ejpam-5971	344	15	:	:	PUNCT
ejpam-5971	344	16	deg(a	deg(a	PROPN
ejpam-5971	344	17	)	)	PUNCT
ejpam-5971	344	18	=	=	SYM
ejpam-5971	344	19	℘−	℘−	NOUN
ejpam-5971	344	20	1	1	NUM
ejpam-5971	344	21	,	,	PUNCT
ejpam-5971	344	22	deg(b	deg(b	NUM
ejpam-5971	344	23	)	)	PUNCT
ejpam-5971	344	24	=	=	SYM
ejpam-5971	344	25	℘2	℘2	NOUN
ejpam-5971	344	26	−	−	PROPN
ejpam-5971	344	27	1	1	NUM
ejpam-5971	344	28	,	,	PUNCT
ejpam-5971	344	29	deg(c	deg(c	PROPN
ejpam-5971	344	30	)	)	PUNCT
ejpam-5971	344	31	=	=	PUNCT
ejpam-5971	345	1	℘3	℘3	ADJ
ejpam-5971	345	2	−	−	NOUN
ejpam-5971	345	3	2	2	NUM
ejpam-5971	345	4	,	,	PUNCT
ejpam-5971	345	5	deg(d	deg(d	PROPN
ejpam-5971	345	6	)	)	PUNCT
ejpam-5971	345	7	=	=	PUNCT
ejpam-5971	345	8	℘4	℘4	NOUN
ejpam-5971	345	9	−	−	NOUN
ejpam-5971	345	10	2	2	NUM
ejpam-5971	345	11	.	.	PUNCT
ejpam-5971	346	1	thus	thus	ADV
ejpam-5971	346	2	,	,	PUNCT
ejpam-5971	346	3	the	the	DET
ejpam-5971	346	4	narumi	narumi	PROPN
ejpam-5971	346	5	-	-	PUNCT
ejpam-5971	346	6	katayama	katayama	NOUN
ejpam-5971	346	7	index	index	NOUN
ejpam-5971	346	8	of	of	ADP
ejpam-5971	346	9	graph	graph	NOUN
ejpam-5971	346	10	g	g	PROPN
ejpam-5971	346	11	is	be	AUX
ejpam-5971	346	12	nk(g	nk(g	NOUN
ejpam-5971	346	13	)	)	PUNCT
ejpam-5971	347	1	=	=	SYM
ejpam-5971	347	2	∏	∏	PROPN
ejpam-5971	347	3	v∈v	v∈v	NOUN
ejpam-5971	347	4	(	(	PUNCT
ejpam-5971	347	5	g	g	NOUN
ejpam-5971	347	6	)	)	PUNCT
ejpam-5971	347	7	deg(v	deg(v	PROPN
ejpam-5971	347	8	)	)	PUNCT
ejpam-5971	347	9	=	=	SYM
ejpam-5971	347	10	(	(	PUNCT
ejpam-5971	347	11	℘−	℘−	NOUN
ejpam-5971	347	12	1)(℘−	1)(℘−	NUM
ejpam-5971	347	13	1	1	NUM
ejpam-5971	347	14	)	)	PUNCT
ejpam-5971	347	15	·	·	PUNCT
ejpam-5971	347	16	·	·	PUNCT
ejpam-5971	347	17	·	·	PUNCT
ejpam-5971	347	18	(	(	PUNCT
ejpam-5971	347	19	℘−	℘−	NOUN
ejpam-5971	347	20	1)︸	1)︸	NUM
ejpam-5971	347	21	︷︷	︷︷	PROPN
ejpam-5971	347	22	︸	︸	NOUN
ejpam-5971	347	23	℘4−℘3	℘4−℘3	PROPN
ejpam-5971	347	24	-times	-time	NOUN
ejpam-5971	347	25	×	×	NOUN
ejpam-5971	347	26	(	(	PUNCT
ejpam-5971	347	27	℘2	℘2	PROPN
ejpam-5971	347	28	−	−	PROPN
ejpam-5971	347	29	1)(℘2	1)(℘2	NUM
ejpam-5971	347	30	−	−	NOUN
ejpam-5971	347	31	1	1	NUM
ejpam-5971	347	32	)	)	PUNCT
ejpam-5971	347	33	·	·	PUNCT
ejpam-5971	347	34	·	·	PUNCT
ejpam-5971	347	35	·	·	PUNCT
ejpam-5971	347	36	(	(	PUNCT
ejpam-5971	347	37	℘2	℘2	PROPN
ejpam-5971	347	38	−	−	PROPN
ejpam-5971	347	39	1)︸	1)︸	PRON
ejpam-5971	347	40	︷︷	︷︷	PROPN
ejpam-5971	347	41	︸	︸	PRON
ejpam-5971	347	42	℘3−℘2	℘3−℘2	NUM
ejpam-5971	347	43	-times	-time	NOUN
ejpam-5971	347	44	×	×	NOUN
ejpam-5971	347	45	(	(	PUNCT
ejpam-5971	347	46	℘3	℘3	ADJ
ejpam-5971	347	47	−	−	PROPN
ejpam-5971	347	48	2)(℘3	2)(℘3	NUM
ejpam-5971	347	49	−	−	PROPN
ejpam-5971	347	50	2	2	NUM
ejpam-5971	347	51	)	)	PUNCT
ejpam-5971	347	52	·	·	PUNCT
ejpam-5971	347	53	·	·	PUNCT
ejpam-5971	347	54	·	·	PUNCT
ejpam-5971	347	55	(	(	PUNCT
ejpam-5971	347	56	℘3	℘3	ADV
ejpam-5971	347	57	−	−	PROPN
ejpam-5971	347	58	2)︸	2)︸	NUM
ejpam-5971	347	59	︷︷	︷︷	PROPN
ejpam-5971	347	60	︸	︸	ADP
ejpam-5971	347	61	℘2−℘-times	℘2−℘-times	PROPN
ejpam-5971	347	62	×	×	NOUN
ejpam-5971	347	63	(	(	PUNCT
ejpam-5971	347	64	℘4	℘4	VERB
ejpam-5971	347	65	−	−	NOUN
ejpam-5971	347	66	2)(℘4	2)(℘4	NUM
ejpam-5971	347	67	−	−	NOUN
ejpam-5971	347	68	2	2	NUM
ejpam-5971	347	69	)	)	PUNCT
ejpam-5971	347	70	·	·	PUNCT
ejpam-5971	347	71	·	·	PUNCT
ejpam-5971	347	72	·	·	PUNCT
ejpam-5971	347	73	(	(	PUNCT
ejpam-5971	347	74	℘4	℘4	VERB
ejpam-5971	347	75	−	−	PROPN
ejpam-5971	347	76	2)︸	2)︸	NOUN
ejpam-5971	347	77	︷︷	︷︷	NOUN
ejpam-5971	347	78	︸	︸	ADP
ejpam-5971	347	79	℘−1	℘−1	PROPN
ejpam-5971	347	80	-	-	PUNCT
ejpam-5971	347	81	times	time	NOUN
ejpam-5971	347	82	=	=	SYM
ejpam-5971	347	83	(	(	PUNCT
ejpam-5971	347	84	℘−	℘−	NOUN
ejpam-5971	347	85	1	1	NUM
ejpam-5971	347	86	)	)	PUNCT
ejpam-5971	347	87	℘4−℘3	℘4−℘3	PROPN
ejpam-5971	347	88	(	(	PUNCT
ejpam-5971	347	89	℘2	℘2	NOUN
ejpam-5971	347	90	−	−	PROPN
ejpam-5971	347	91	1	1	NUM
ejpam-5971	347	92	)	)	PUNCT
ejpam-5971	347	93	℘3−℘2	℘3−℘2	PROPN
ejpam-5971	347	94	(	(	PUNCT
ejpam-5971	347	95	℘3	℘3	ADV
ejpam-5971	347	96	−	−	PROPN
ejpam-5971	347	97	2	2	NUM
ejpam-5971	347	98	)	)	PUNCT
ejpam-5971	347	99	℘2−℘	℘2−℘	NUM
ejpam-5971	347	100	(	(	PUNCT
ejpam-5971	347	101	℘4	℘4	VERB
ejpam-5971	347	102	−	−	NOUN
ejpam-5971	347	103	2	2	NUM
ejpam-5971	347	104	)	)	PUNCT
ejpam-5971	347	105	℘−1	℘−1	PROPN
ejpam-5971	347	106	.	.	PUNCT
ejpam-5971	348	1	after	after	ADP
ejpam-5971	348	2	deriving	derive	VERB
ejpam-5971	348	3	the	the	DET
ejpam-5971	348	4	formulas	formula	NOUN
ejpam-5971	348	5	for	for	ADP
ejpam-5971	348	6	each	each	DET
ejpam-5971	348	7	topological	topological	ADJ
ejpam-5971	348	8	index	index	NOUN
ejpam-5971	348	9	,	,	PUNCT
ejpam-5971	348	10	numerical	numerical	ADJ
ejpam-5971	348	11	simulations	simulation	NOUN
ejpam-5971	348	12	(	(	PUNCT
ejpam-5971	348	13	except	except	SCONJ
ejpam-5971	348	14	narumi	narumi	PROPN
ejpam-5971	348	15	-	-	PUNCT
ejpam-5971	348	16	katayama	katayama	NOUN
ejpam-5971	348	17	index	index	NOUN
ejpam-5971	348	18	)	)	PUNCT
ejpam-5971	348	19	are	be	AUX
ejpam-5971	348	20	performed	perform	VERB
ejpam-5971	348	21	for	for	ADP
ejpam-5971	348	22	several	several	ADJ
ejpam-5971	348	23	prime	prime	ADJ
ejpam-5971	348	24	numbers	number	NOUN
ejpam-5971	348	25	℘	℘	PROPN
ejpam-5971	348	26	on	on	ADP
ejpam-5971	348	27	the	the	DET
ejpam-5971	348	28	graph	graph	NOUN
ejpam-5971	348	29	g	g	ADP
ejpam-5971	348	30	∼=	∼=	PROPN
ejpam-5971	348	31	z℘[x]/⟨x5⟩	z℘[x]/⟨x5⟩	NOUN
ejpam-5971	348	32	using	use	VERB
ejpam-5971	348	33	a	a	DET
ejpam-5971	348	34	computer	computer	NOUN
ejpam-5971	348	35	software	software	NOUN
ejpam-5971	348	36	matlab	matlab	PROPN
ejpam-5971	348	37	.	.	PUNCT
ejpam-5971	349	1	we	we	PRON
ejpam-5971	349	2	exclude	exclude	VERB
ejpam-5971	349	3	the	the	DET
ejpam-5971	349	4	computed	computed	ADJ
ejpam-5971	349	5	value	value	NOUN
ejpam-5971	349	6	of	of	ADP
ejpam-5971	349	7	the	the	DET
ejpam-5971	349	8	narumi	narumi	PROPN
ejpam-5971	349	9	-	-	PUNCT
ejpam-5971	349	10	katayama	katayama	NOUN
ejpam-5971	349	11	index	index	NOUN
ejpam-5971	349	12	,	,	PUNCT
ejpam-5971	349	13	since	since	SCONJ
ejpam-5971	349	14	the	the	DET
ejpam-5971	349	15	value	value	NOUN
ejpam-5971	349	16	is	be	AUX
ejpam-5971	349	17	close	close	ADJ
ejpam-5971	349	18	to	to	ADP
ejpam-5971	349	19	infinity	infinity	NOUN
ejpam-5971	349	20	.	.	PUNCT
ejpam-5971	350	1	the	the	DET
ejpam-5971	350	2	results	result	NOUN
ejpam-5971	350	3	of	of	ADP
ejpam-5971	350	4	these	these	DET
ejpam-5971	350	5	simulations	simulation	NOUN
ejpam-5971	350	6	are	be	AUX
ejpam-5971	350	7	presented	present	VERB
ejpam-5971	350	8	in	in	ADP
ejpam-5971	350	9	table	table	NOUN
ejpam-5971	350	10	2	2	NUM
ejpam-5971	350	11	and	and	CCONJ
ejpam-5971	350	12	figure	figure	NOUN
ejpam-5971	350	13	2	2	NUM
ejpam-5971	350	14	,	,	PUNCT
ejpam-5971	350	15	which	which	PRON
ejpam-5971	350	16	display	display	VERB
ejpam-5971	350	17	the	the	DET
ejpam-5971	350	18	values	value	NOUN
ejpam-5971	350	19	of	of	ADP
ejpam-5971	350	20	the	the	DET
ejpam-5971	350	21	indices	index	NOUN
ejpam-5971	350	22	w(g	w(g	PROPN
ejpam-5971	350	23	)	)	PUNCT
ejpam-5971	350	24	,	,	PUNCT
ejpam-5971	350	25	ww(g	ww(g	NUM
ejpam-5971	350	26	)	)	PUNCT
ejpam-5971	350	27	,	,	PUNCT
ejpam-5971	350	28	m1(g	m1(g	NOUN
ejpam-5971	350	29	)	)	PUNCT
ejpam-5971	350	30	,	,	PUNCT
ejpam-5971	350	31	and	and	CCONJ
ejpam-5971	350	32	m2(g	m2(g	NOUN
ejpam-5971	350	33	)	)	PUNCT
ejpam-5971	350	34	for	for	ADP
ejpam-5971	350	35	various	various	ADJ
ejpam-5971	350	36	prime	prime	ADJ
ejpam-5971	350	37	numbers	number	NOUN
ejpam-5971	350	38	℘.	℘.	PROPN
ejpam-5971	350	39	v.h	v.h	PROPN
ejpam-5971	350	40	.	.	PROPN
ejpam-5971	350	41	krisnawati	krisnawati	PROPN
ejpam-5971	350	42	,	,	PUNCT
ejpam-5971	350	43	n.	n.	PROPN
ejpam-5971	350	44	hidayat	hidayat	PROPN
ejpam-5971	350	45	,	,	PUNCT
ejpam-5971	350	46	a.f	a.f	PROPN
ejpam-5971	350	47	.	.	PROPN
ejpam-5971	350	48	musyarrofah	musyarrofah	PROPN
ejpam-5971	350	49	/	/	SYM
ejpam-5971	350	50	eur	eur	PROPN
ejpam-5971	350	51	.	.	PUNCT
ejpam-5971	351	1	j.	j.	PROPN
ejpam-5971	351	2	pure	pure	PROPN
ejpam-5971	351	3	appl	appl	PROPN
ejpam-5971	351	4	.	.	PROPN
ejpam-5971	351	5	math	math	PROPN
ejpam-5971	351	6	,	,	PUNCT
ejpam-5971	351	7	18	18	NUM
ejpam-5971	351	8	(	(	PUNCT
ejpam-5971	351	9	2	2	NUM
ejpam-5971	351	10	)	)	PUNCT
ejpam-5971	351	11	(	(	PUNCT
ejpam-5971	351	12	2025	2025	NUM
ejpam-5971	351	13	)	)	PUNCT
ejpam-5971	351	14	,	,	PUNCT
ejpam-5971	351	15	5971	5971	NUM
ejpam-5971	351	16	17	17	NUM
ejpam-5971	351	17	of	of	ADP
ejpam-5971	351	18	19	19	NUM
ejpam-5971	351	19	table	table	NOUN
ejpam-5971	351	20	2	2	NUM
ejpam-5971	351	21	:	:	PUNCT
ejpam-5971	351	22	computed	compute	VERB
ejpam-5971	351	23	values	value	NOUN
ejpam-5971	351	24	of	of	ADP
ejpam-5971	351	25	topological	topological	ADJ
ejpam-5971	351	26	indices	index	NOUN
ejpam-5971	351	27	for	for	ADP
ejpam-5971	351	28	various	various	ADJ
ejpam-5971	351	29	prime	prime	ADJ
ejpam-5971	351	30	numbers	number	NOUN
ejpam-5971	351	31	℘	℘	PROPN
ejpam-5971	351	32	w(g	w(g	NOUN
ejpam-5971	351	33	)	)	PUNCT
ejpam-5971	351	34	ww(g	ww(g	NUM
ejpam-5971	351	35	)	)	PUNCT
ejpam-5971	351	36	m1(g	m1(g	NOUN
ejpam-5971	351	37	)	)	PUNCT
ejpam-5971	351	38	m2(g	m2(g	NOUN
ejpam-5971	351	39	)	)	PUNCT
ejpam-5971	351	40	2	2	NUM
ejpam-5971	351	41	1.87×	1.87×	NUM
ejpam-5971	351	42	102	102	NUM
ejpam-5971	351	43	2.69×	2.69×	NUM
ejpam-5971	351	44	102	102	NUM
ejpam-5971	352	1	3.12×	3.12×	NUM
ejpam-5971	352	2	102	102	NUM
ejpam-5971	352	3	6.28×	6.28×	NUM
ejpam-5971	352	4	102	102	NUM
ejpam-5971	352	5	3	3	NUM
ejpam-5971	352	6	6.04×	6.04×	NUM
ejpam-5971	352	7	103	103	NUM
ejpam-5971	352	8	8.92×	8.92×	NUM
ejpam-5971	352	9	103	103	NUM
ejpam-5971	352	10	1.76×	1.76×	NUM
ejpam-5971	352	11	104	104	NUM
ejpam-5971	352	12	1.0073×	1.0073×	NUM
ejpam-5971	352	13	105	105	NUM
ejpam-5971	352	14	5	5	NUM
ejpam-5971	352	15	3.8408×	3.8408×	NUM
ejpam-5971	352	16	105	105	NUM
ejpam-5971	352	17	5.7378×	5.7378×	NUM
ejpam-5971	352	18	105	105	NUM
ejpam-5971	352	19	1.9207×	1.9207×	NUM
ejpam-5971	352	20	106	106	NUM
ejpam-5971	352	21	2.8202×	2.8202×	NUM
ejpam-5971	352	22	107	107	NUM
ejpam-5971	352	23	7	7	NUM
ejpam-5971	352	24	5.73×	5.73×	NUM
ejpam-5971	352	25	106	106	NUM
ejpam-5971	352	26	8.5812×	8.5812×	NUM
ejpam-5971	352	27	106	106	NUM
ejpam-5971	352	28	4.0166×	4.0166×	NOUN
ejpam-5971	352	29	107	107	NUM
ejpam-5971	352	30	9.7557×	9.7557×	NUM
ejpam-5971	352	31	108	108	NUM
ejpam-5971	352	32	11	11	NUM
ejpam-5971	352	33	2.1403×	2.1403×	NOUN
ejpam-5971	352	34	108	108	NUM
ejpam-5971	352	35	3.209×	3.209×	NUM
ejpam-5971	352	36	108	108	NUM
ejpam-5971	352	37	2.356×	2.356×	NUM
ejpam-5971	352	38	109	109	NUM
ejpam-5971	352	39	1.036×	1.036×	PROPN
ejpam-5971	352	40	1011	1011	NUM
ejpam-5971	352	41	13	13	NUM
ejpam-5971	352	42	8.1497×	8.1497×	NUM
ejpam-5971	352	43	108	108	NUM
ejpam-5971	352	44	1.2221×	1.2221×	NUM
ejpam-5971	352	45	109	109	NUM
ejpam-5971	352	46	1.06×	1.06×	NUM
ejpam-5971	352	47	1010	1010	NUM
ejpam-5971	352	48	5.7128×	5.7128×	NUM
ejpam-5971	352	49	1011	1011	NUM
ejpam-5971	352	50	17	17	NUM
ejpam-5971	352	51	6.9729×	6.9729×	ADV
ejpam-5971	352	52	109	109	NUM
ejpam-5971	352	53	1.0458×	1.0458×	NUM
ejpam-5971	352	54	1010	1010	NUM
ejpam-5971	352	55	1.1857×	1.1857×	NUM
ejpam-5971	352	56	1011	1011	NUM
ejpam-5971	352	57	8.7501×	8.7501×	NUM
ejpam-5971	352	58	1012	1012	NUM
ejpam-5971	352	59	19	19	NUM
ejpam-5971	352	60	1.6979×	1.6979×	NUM
ejpam-5971	352	61	1010	1010	NUM
ejpam-5971	352	62	2.5466×	2.5466×	NOUN
ejpam-5971	352	63	1010	1010	NUM
ejpam-5971	352	64	3.2266×	3.2266×	NUM
ejpam-5971	352	65	1011	1011	NUM
ejpam-5971	352	66	2.7027×	2.7027×	NUM
ejpam-5971	352	67	1013	1013	NUM
ejpam-5971	352	68	23	23	NUM
ejpam-5971	352	69	7.8298×	7.8298×	NUM
ejpam-5971	352	70	1010	1010	NUM
ejpam-5971	352	71	1.1744×	1.1744×	NUM
ejpam-5971	352	72	1011	1011	NUM
ejpam-5971	352	73	1.8011×	1.8011×	NUM
ejpam-5971	352	74	1012	1012	NUM
ejpam-5971	352	75	1.868×	1.868×	NUM
ejpam-5971	352	76	1014	1014	NUM
ejpam-5971	352	77	29	29	NUM
ejpam-5971	352	78	5.0021×	5.0021×	NUM
ejpam-5971	352	79	1011	1011	NUM
ejpam-5971	352	80	7.5029×	7.5029×	NUM
ejpam-5971	352	81	1011	1011	NUM
ejpam-5971	352	82	1.4507×	1.4507×	NUM
ejpam-5971	352	83	1013	1013	NUM
ejpam-5971	352	84	1.9392×	1.9392×	NUM
ejpam-5971	352	85	1015	1015	NUM
ejpam-5971	352	86	31	31	NUM
ejpam-5971	352	87	8.5283×	8.5283×	NUM
ejpam-5971	352	88	1011	1011	NUM
ejpam-5971	352	89	1.2792×	1.2792×	NUM
ejpam-5971	352	90	1012	1012	NUM
ejpam-5971	352	91	2.6439×	2.6439×	NUM
ejpam-5971	352	92	1013	1013	NUM
ejpam-5971	352	93	3.7983×	3.7983×	NUM
ejpam-5971	352	94	1015	1015	NUM
ejpam-5971	352	95	37	37	NUM
ejpam-5971	352	96	3.5123×	3.5123×	NUM
ejpam-5971	352	97	1012	1012	NUM
ejpam-5971	352	98	5.2684×	5.2684×	NUM
ejpam-5971	352	99	1012	1012	NUM
ejpam-5971	352	100	1.2996×	1.2996×	NUM
ejpam-5971	352	101	1014	1014	NUM
ejpam-5971	352	102	2.2566×	2.2566×	NUM
ejpam-5971	352	103	1016	1016	NUM
ejpam-5971	352	104	10	10	NUM
ejpam-5971	352	105	20	20	NUM
ejpam-5971	352	106	30	30	NUM
ejpam-5971	352	107	0	0	NUM
ejpam-5971	352	108	2	2	NUM
ejpam-5971	352	109	4	4	NUM
ejpam-5971	352	110	10	10	NUM
ejpam-5971	352	111	12	12	NUM
ejpam-5971	352	112	(	(	PUNCT
ejpam-5971	352	113	a	a	NOUN
ejpam-5971	352	114	)	)	PUNCT
ejpam-5971	352	115	10	10	NUM
ejpam-5971	352	116	20	20	NUM
ejpam-5971	352	117	30	30	NUM
ejpam-5971	352	118	0	0	NUM
ejpam-5971	352	119	2	2	NUM
ejpam-5971	352	120	4	4	NUM
ejpam-5971	352	121	6	6	NUM
ejpam-5971	352	122	10	10	NUM
ejpam-5971	352	123	12	12	NUM
ejpam-5971	352	124	(	(	PUNCT
ejpam-5971	352	125	b	b	NOUN
ejpam-5971	352	126	)	)	PUNCT
ejpam-5971	352	127	10	10	NUM
ejpam-5971	352	128	20	20	NUM
ejpam-5971	352	129	30	30	NUM
ejpam-5971	352	130	0	0	NUM
ejpam-5971	352	131	5	5	NUM
ejpam-5971	352	132	10	10	NUM
ejpam-5971	352	133	15	15	NUM
ejpam-5971	352	134	10	10	NUM
ejpam-5971	352	135	13	13	NUM
ejpam-5971	352	136	(	(	PUNCT
ejpam-5971	352	137	c	c	NOUN
ejpam-5971	352	138	)	)	PUNCT
ejpam-5971	352	139	10	10	NUM
ejpam-5971	352	140	20	20	NUM
ejpam-5971	352	141	30	30	NUM
ejpam-5971	352	142	0	0	NUM
ejpam-5971	352	143	1	1	NUM
ejpam-5971	352	144	2	2	NUM
ejpam-5971	352	145	10	10	NUM
ejpam-5971	352	146	16	16	NUM
ejpam-5971	352	147	(	(	PUNCT
ejpam-5971	352	148	d	d	NOUN
ejpam-5971	352	149	)	)	PUNCT
ejpam-5971	352	150	figure	figure	NOUN
ejpam-5971	352	151	2	2	NUM
ejpam-5971	352	152	:	:	PUNCT
ejpam-5971	352	153	numerical	numerical	PROPN
ejpam-5971	352	154	simulation	simulation	NOUN
ejpam-5971	352	155	of	of	ADP
ejpam-5971	352	156	(	(	PUNCT
ejpam-5971	352	157	a	a	DET
ejpam-5971	352	158	)	)	PUNCT
ejpam-5971	352	159	wiener	wiener	NOUN
ejpam-5971	352	160	index	index	NOUN
ejpam-5971	352	161	(	(	PUNCT
ejpam-5971	352	162	b	b	NOUN
ejpam-5971	352	163	)	)	PUNCT
ejpam-5971	352	164	hyper	hyper	ADJ
ejpam-5971	352	165	-	-	ADJ
ejpam-5971	352	166	wiener	wiener	NOUN
ejpam-5971	352	167	index	index	NOUN
ejpam-5971	352	168	(	(	PUNCT
ejpam-5971	352	169	c	c	NOUN
ejpam-5971	352	170	)	)	PUNCT
ejpam-5971	352	171	first	first	PROPN
ejpam-5971	352	172	zagreb	zagreb	PROPN
ejpam-5971	352	173	index	index	NOUN
ejpam-5971	352	174	(	(	PUNCT
ejpam-5971	352	175	d	d	NOUN
ejpam-5971	352	176	)	)	PUNCT
ejpam-5971	352	177	second	second	ADJ
ejpam-5971	352	178	zagreb	zagreb	PROPN
ejpam-5971	352	179	index	index	NOUN
ejpam-5971	352	180	based	base	VERB
ejpam-5971	352	181	on	on	ADP
ejpam-5971	352	182	table	table	NOUN
ejpam-5971	352	183	2	2	NUM
ejpam-5971	352	184	and	and	CCONJ
ejpam-5971	352	185	figure	figure	NOUN
ejpam-5971	352	186	2	2	NUM
ejpam-5971	352	187	,	,	PUNCT
ejpam-5971	352	188	it	it	PRON
ejpam-5971	352	189	is	be	AUX
ejpam-5971	352	190	observed	observe	VERB
ejpam-5971	352	191	that	that	SCONJ
ejpam-5971	352	192	for	for	SCONJ
ejpam-5971	352	193	all	all	DET
ejpam-5971	352	194	indices	index	NOUN
ejpam-5971	352	195	exhibit	exhibit	VERB
ejpam-5971	352	196	the	the	DET
ejpam-5971	352	197	same	same	ADJ
ejpam-5971	352	198	graphs	graph	NOUN
ejpam-5971	352	199	and	and	CCONJ
ejpam-5971	352	200	a	a	DET
ejpam-5971	352	201	significant	significant	ADJ
ejpam-5971	352	202	increase	increase	NOUN
ejpam-5971	352	203	as	as	ADP
ejpam-5971	352	204	℘	℘	NOUN
ejpam-5971	352	205	increases	increase	NOUN
ejpam-5971	352	206	.	.	PUNCT
ejpam-5971	353	1	in	in	ADP
ejpam-5971	353	2	particular	particular	ADJ
ejpam-5971	353	3	,	,	PUNCT
ejpam-5971	353	4	the	the	DET
ejpam-5971	353	5	second	second	ADJ
ejpam-5971	353	6	zagreb	zagreb	PROPN
ejpam-5971	353	7	index	index	NOUN
ejpam-5971	353	8	shows	show	VERB
ejpam-5971	353	9	the	the	DET
ejpam-5971	353	10	most	most	ADV
ejpam-5971	353	11	rapid	rapid	ADJ
ejpam-5971	353	12	growth	growth	NOUN
ejpam-5971	353	13	compared	compare	VERB
ejpam-5971	353	14	to	to	ADP
ejpam-5971	353	15	the	the	DET
ejpam-5971	353	16	other	other	ADJ
ejpam-5971	353	17	indices	index	NOUN
ejpam-5971	353	18	.	.	PUNCT
ejpam-5971	354	1	this	this	DET
ejpam-5971	354	2	rise	rise	NOUN
ejpam-5971	354	3	is	be	AUX
ejpam-5971	354	4	followed	follow	VERB
ejpam-5971	354	5	by	by	ADP
ejpam-5971	354	6	the	the	DET
ejpam-5971	354	7	first	first	PROPN
ejpam-5971	354	8	zagreb	zagreb	PROPN
ejpam-5971	354	9	index	index	PROPN
ejpam-5971	354	10	,	,	PUNCT
ejpam-5971	354	11	the	the	DET
ejpam-5971	354	12	hyper	hyper	ADJ
ejpam-5971	354	13	-	-	ADJ
ejpam-5971	354	14	wiener	wiener	NOUN
ejpam-5971	354	15	index	index	NOUN
ejpam-5971	354	16	,	,	PUNCT
ejpam-5971	354	17	and	and	CCONJ
ejpam-5971	354	18	the	the	DET
ejpam-5971	354	19	wiener	wiener	NOUN
ejpam-5971	354	20	index	index	NOUN
ejpam-5971	354	21	.	.	PUNCT
ejpam-5971	355	1	the	the	DET
ejpam-5971	355	2	observed	observed	ADJ
ejpam-5971	355	3	ordering	ordering	NOUN
ejpam-5971	355	4	indicates	indicate	VERB
ejpam-5971	355	5	that	that	SCONJ
ejpam-5971	355	6	degree	degree	NOUN
ejpam-5971	355	7	-	-	PUNCT
ejpam-5971	355	8	based	base	VERB
ejpam-5971	355	9	indices	index	NOUN
ejpam-5971	355	10	tend	tend	VERB
ejpam-5971	355	11	to	to	PART
ejpam-5971	355	12	grow	grow	VERB
ejpam-5971	355	13	faster	fast	ADV
ejpam-5971	355	14	than	than	ADP
ejpam-5971	355	15	distance	distance	NOUN
ejpam-5971	355	16	-	-	PUNCT
ejpam-5971	355	17	based	base	VERB
ejpam-5971	355	18	indices	index	NOUN
ejpam-5971	355	19	in	in	ADP
ejpam-5971	355	20	this	this	DET
ejpam-5971	355	21	graph	graph	NOUN
ejpam-5971	355	22	structure	structure	NOUN
ejpam-5971	355	23	.	.	PUNCT
ejpam-5971	356	1	this	this	DET
ejpam-5971	356	2	behavior	behavior	NOUN
ejpam-5971	356	3	suggests	suggest	VERB
ejpam-5971	356	4	that	that	SCONJ
ejpam-5971	356	5	as	as	SCONJ
ejpam-5971	356	6	the	the	DET
ejpam-5971	356	7	graph	graph	NOUN
ejpam-5971	356	8	expands	expand	VERB
ejpam-5971	356	9	,	,	PUNCT
ejpam-5971	356	10	the	the	DET
ejpam-5971	356	11	contribution	contribution	NOUN
ejpam-5971	356	12	of	of	ADP
ejpam-5971	356	13	higherdegree	higherdegree	NOUN
ejpam-5971	356	14	vertices	vertex	NOUN
ejpam-5971	356	15	becomes	become	VERB
ejpam-5971	356	16	more	more	ADV
ejpam-5971	356	17	dominant	dominant	ADJ
ejpam-5971	356	18	.	.	PUNCT
ejpam-5971	357	1	such	such	ADJ
ejpam-5971	357	2	insights	insight	NOUN
ejpam-5971	357	3	are	be	AUX
ejpam-5971	357	4	valuable	valuable	ADJ
ejpam-5971	357	5	for	for	ADP
ejpam-5971	357	6	understanding	understand	VERB
ejpam-5971	357	7	molecular	molecular	ADJ
ejpam-5971	357	8	stability	stability	NOUN
ejpam-5971	357	9	in	in	ADP
ejpam-5971	357	10	chemical	chemical	NOUN
ejpam-5971	357	11	graph	graph	NOUN
ejpam-5971	357	12	theory	theory	NOUN
ejpam-5971	357	13	,	,	PUNCT
ejpam-5971	357	14	where	where	SCONJ
ejpam-5971	357	15	these	these	DET
ejpam-5971	357	16	indices	index	NOUN
ejpam-5971	357	17	play	play	VERB
ejpam-5971	357	18	a	a	DET
ejpam-5971	357	19	crucial	crucial	ADJ
ejpam-5971	357	20	role	role	NOUN
ejpam-5971	357	21	in	in	ADP
ejpam-5971	357	22	modeling	model	VERB
ejpam-5971	357	23	molecular	molecular	ADJ
ejpam-5971	357	24	properties	property	NOUN
ejpam-5971	357	25	.	.	PUNCT
ejpam-5971	358	1	v.h	v.h	PROPN
ejpam-5971	358	2	.	.	PROPN
ejpam-5971	358	3	krisnawati	krisnawati	PROPN
ejpam-5971	358	4	,	,	PUNCT
ejpam-5971	358	5	n.	n.	PROPN
ejpam-5971	358	6	hidayat	hidayat	PROPN
ejpam-5971	358	7	,	,	PUNCT
ejpam-5971	358	8	a.f	a.f	PROPN
ejpam-5971	358	9	.	.	PROPN
ejpam-5971	358	10	musyarrofah	musyarrofah	PROPN
ejpam-5971	358	11	/	/	SYM
ejpam-5971	358	12	eur	eur	PROPN
ejpam-5971	358	13	.	.	PUNCT
ejpam-5971	359	1	j.	j.	PROPN
ejpam-5971	359	2	pure	pure	PROPN
ejpam-5971	359	3	appl	appl	PROPN
ejpam-5971	359	4	.	.	PROPN
ejpam-5971	359	5	math	math	PROPN
ejpam-5971	359	6	,	,	PUNCT
ejpam-5971	359	7	18	18	NUM
ejpam-5971	359	8	(	(	PUNCT
ejpam-5971	359	9	2	2	NUM
ejpam-5971	359	10	)	)	PUNCT
ejpam-5971	359	11	(	(	PUNCT
ejpam-5971	359	12	2025	2025	NUM
ejpam-5971	359	13	)	)	PUNCT
ejpam-5971	359	14	,	,	PUNCT
ejpam-5971	359	15	5971	5971	NUM
ejpam-5971	359	16	18	18	NUM
ejpam-5971	359	17	of	of	ADP
ejpam-5971	359	18	19	19	NUM
ejpam-5971	359	19	5	5	NUM
ejpam-5971	359	20	.	.	PUNCT
ejpam-5971	360	1	conclusion	conclusion	NOUN
ejpam-5971	360	2	from	from	ADP
ejpam-5971	360	3	the	the	DET
ejpam-5971	360	4	results	result	NOUN
ejpam-5971	360	5	presented	present	VERB
ejpam-5971	360	6	earlier	early	ADV
ejpam-5971	360	7	,	,	PUNCT
ejpam-5971	360	8	we	we	PRON
ejpam-5971	360	9	obtain	obtain	VERB
ejpam-5971	360	10	the	the	DET
ejpam-5971	360	11	upper	upper	ADJ
ejpam-5971	360	12	and	and	CCONJ
ejpam-5971	360	13	lower	low	ADJ
ejpam-5971	360	14	bounds	bound	NOUN
ejpam-5971	360	15	of	of	ADP
ejpam-5971	360	16	the	the	DET
ejpam-5971	360	17	energy	energy	NOUN
ejpam-5971	360	18	of	of	ADP
ejpam-5971	360	19	the	the	DET
ejpam-5971	360	20	zero	zero	NUM
ejpam-5971	360	21	-	-	PUNCT
ejpam-5971	360	22	divisor	divisor	NOUN
ejpam-5971	360	23	graph	graph	NOUN
ejpam-5971	360	24	of	of	ADP
ejpam-5971	360	25	z℘[x]/⟨x5⟩	z℘[x]/⟨x5⟩	PROPN
ejpam-5971	360	26	for	for	ADP
ejpam-5971	360	27	prime	prime	ADJ
ejpam-5971	360	28	number	number	NOUN
ejpam-5971	360	29	℘.	℘.	PROPN
ejpam-5971	360	30	we	we	PRON
ejpam-5971	360	31	conclude	conclude	VERB
ejpam-5971	360	32	that	that	SCONJ
ejpam-5971	360	33	the	the	DET
ejpam-5971	360	34	obtained	obtain	VERB
ejpam-5971	360	35	energy	energy	NOUN
ejpam-5971	360	36	bounds	bound	NOUN
ejpam-5971	360	37	are	be	AUX
ejpam-5971	360	38	sharp	sharp	ADJ
ejpam-5971	360	39	and	and	CCONJ
ejpam-5971	360	40	close	close	ADJ
ejpam-5971	360	41	to	to	ADP
ejpam-5971	360	42	the	the	DET
ejpam-5971	360	43	actual	actual	ADJ
ejpam-5971	360	44	energy	energy	NOUN
ejpam-5971	360	45	.	.	PUNCT
ejpam-5971	361	1	this	this	DET
ejpam-5971	361	2	result	result	NOUN
ejpam-5971	361	3	shows	show	VERB
ejpam-5971	361	4	that	that	SCONJ
ejpam-5971	361	5	the	the	DET
ejpam-5971	361	6	methods	method	NOUN
ejpam-5971	361	7	used	use	VERB
ejpam-5971	361	8	are	be	AUX
ejpam-5971	361	9	effective	effective	ADJ
ejpam-5971	361	10	for	for	ADP
ejpam-5971	361	11	estimating	estimate	VERB
ejpam-5971	361	12	the	the	DET
ejpam-5971	361	13	graph	graph	NOUN
ejpam-5971	361	14	’s	’s	PART
ejpam-5971	361	15	energy	energy	NOUN
ejpam-5971	361	16	accurately	accurately	ADV
ejpam-5971	361	17	.	.	PUNCT
ejpam-5971	362	1	we	we	PRON
ejpam-5971	362	2	also	also	ADV
ejpam-5971	362	3	acquire	acquire	VERB
ejpam-5971	362	4	the	the	DET
ejpam-5971	362	5	topological	topological	ADJ
ejpam-5971	362	6	indices	index	NOUN
ejpam-5971	362	7	of	of	ADP
ejpam-5971	362	8	γ(z℘[x]/⟨x5⟩	γ(z℘[x]/⟨x5⟩	PROPN
ejpam-5971	362	9	)	)	PUNCT
ejpam-5971	362	10	based	base	VERB
ejpam-5971	362	11	on	on	ADP
ejpam-5971	362	12	distance	distance	NOUN
ejpam-5971	362	13	and	and	CCONJ
ejpam-5971	362	14	degree	degree	NOUN
ejpam-5971	362	15	,	,	PUNCT
ejpam-5971	362	16	such	such	ADJ
ejpam-5971	362	17	as	as	ADP
ejpam-5971	362	18	wiener	wiener	NOUN
ejpam-5971	362	19	index	index	NOUN
ejpam-5971	362	20	,	,	PUNCT
ejpam-5971	362	21	hyper	hyper	NOUN
ejpam-5971	362	22	-	-	ADJ
ejpam-5971	362	23	wiener	wiener	NOUN
ejpam-5971	362	24	index	index	NOUN
ejpam-5971	362	25	,	,	PUNCT
ejpam-5971	362	26	first	first	PROPN
ejpam-5971	362	27	zagreb	zagreb	PROPN
ejpam-5971	362	28	index	index	PROPN
ejpam-5971	362	29	,	,	PUNCT
ejpam-5971	362	30	second	second	PROPN
ejpam-5971	362	31	zagreb	zagreb	PROPN
ejpam-5971	362	32	index	index	NOUN
ejpam-5971	362	33	,	,	PUNCT
ejpam-5971	362	34	and	and	CCONJ
ejpam-5971	362	35	narumi	narumi	PROPN
ejpam-5971	362	36	-	-	PUNCT
ejpam-5971	362	37	katayama	katayama	NOUN
ejpam-5971	362	38	index	index	NOUN
ejpam-5971	362	39	.	.	PUNCT
ejpam-5971	363	1	additionally	additionally	ADV
ejpam-5971	363	2	,	,	PUNCT
ejpam-5971	363	3	numerical	numerical	ADJ
ejpam-5971	363	4	simulations	simulation	NOUN
ejpam-5971	363	5	of	of	ADP
ejpam-5971	363	6	topological	topological	ADJ
ejpam-5971	363	7	indices	index	NOUN
ejpam-5971	363	8	(	(	PUNCT
ejpam-5971	363	9	excluding	exclude	VERB
ejpam-5971	363	10	the	the	DET
ejpam-5971	363	11	narumikatayama	narumikatayama	PROPN
ejpam-5971	363	12	index	index	NOUN
ejpam-5971	363	13	)	)	PUNCT
ejpam-5971	363	14	show	show	VERB
ejpam-5971	363	15	that	that	SCONJ
ejpam-5971	363	16	the	the	DET
ejpam-5971	363	17	second	second	ADJ
ejpam-5971	363	18	zagreb	zagreb	PROPN
ejpam-5971	363	19	index	index	NOUN
ejpam-5971	363	20	grows	grow	VERB
ejpam-5971	363	21	the	the	DET
ejpam-5971	363	22	fastest	fast	ADJ
ejpam-5971	363	23	,	,	PUNCT
ejpam-5971	363	24	followed	follow	VERB
ejpam-5971	363	25	by	by	ADP
ejpam-5971	363	26	the	the	DET
ejpam-5971	363	27	first	first	PROPN
ejpam-5971	363	28	zagreb	zagreb	PROPN
ejpam-5971	363	29	index	index	PROPN
ejpam-5971	363	30	,	,	PUNCT
ejpam-5971	363	31	while	while	SCONJ
ejpam-5971	363	32	the	the	DET
ejpam-5971	363	33	hyper	hyper	NOUN
ejpam-5971	363	34	-	-	NOUN
ejpam-5971	363	35	wiener	wiener	NOUN
ejpam-5971	363	36	and	and	CCONJ
ejpam-5971	363	37	wiener	wiener	NOUN
ejpam-5971	363	38	indices	index	NOUN
ejpam-5971	363	39	grow	grow	VERB
ejpam-5971	363	40	much	much	ADV
ejpam-5971	363	41	slower	slow	ADJ
ejpam-5971	363	42	.	.	PUNCT
ejpam-5971	364	1	for	for	ADP
ejpam-5971	364	2	further	further	ADJ
ejpam-5971	364	3	research	research	NOUN
ejpam-5971	364	4	,	,	PUNCT
ejpam-5971	364	5	the	the	DET
ejpam-5971	364	6	distance	distance	NOUN
ejpam-5971	364	7	and	and	CCONJ
ejpam-5971	364	8	laplacian	laplacian	ADJ
ejpam-5971	364	9	energy	energy	NOUN
ejpam-5971	364	10	of	of	ADP
ejpam-5971	364	11	γ(z℘[x]/⟨x5⟩	γ(z℘[x]/⟨x5⟩	NUM
ejpam-5971	364	12	)	)	PUNCT
ejpam-5971	364	13	can	can	AUX
ejpam-5971	364	14	be	be	AUX
ejpam-5971	364	15	explored	explore	VERB
ejpam-5971	364	16	,	,	PUNCT
ejpam-5971	364	17	along	along	ADP
ejpam-5971	364	18	with	with	ADP
ejpam-5971	364	19	an	an	DET
ejpam-5971	364	20	investigation	investigation	NOUN
ejpam-5971	364	21	of	of	ADP
ejpam-5971	364	22	other	other	ADJ
ejpam-5971	364	23	graph	graph	NOUN
ejpam-5971	364	24	topological	topological	ADJ
ejpam-5971	364	25	indices	index	NOUN
ejpam-5971	364	26	.	.	PUNCT
ejpam-5971	365	1	references	reference	NOUN
ejpam-5971	365	2	[	[	X
ejpam-5971	365	3	1	1	X
ejpam-5971	365	4	]	]	PUNCT
ejpam-5971	365	5	i	i	PROPN
ejpam-5971	365	6	beck	beck	PROPN
ejpam-5971	365	7	.	.	PUNCT
ejpam-5971	366	1	coloring	coloring	NOUN
ejpam-5971	366	2	of	of	ADP
ejpam-5971	366	3	commutative	commutative	ADJ
ejpam-5971	366	4	rings	ring	NOUN
ejpam-5971	366	5	.	.	PUNCT
ejpam-5971	367	1	journal	journal	PROPN
ejpam-5971	367	2	of	of	ADP
ejpam-5971	367	3	algebra	algebra	PROPN
ejpam-5971	367	4	,	,	PUNCT
ejpam-5971	367	5	116(1):208–226	116(1):208–226	NUM
ejpam-5971	367	6	,	,	PUNCT
ejpam-5971	367	7	1988	1988	NUM
ejpam-5971	367	8	.	.	PUNCT
ejpam-5971	368	1	[	[	X
ejpam-5971	368	2	2	2	NUM
ejpam-5971	368	3	]	]	X
ejpam-5971	368	4	d	d	X
ejpam-5971	368	5	f	f	PROPN
ejpam-5971	368	6	anderson	anderson	PROPN
ejpam-5971	368	7	and	and	CCONJ
ejpam-5971	368	8	p	p	PROPN
ejpam-5971	368	9	s	s	PROPN
ejpam-5971	368	10	livingston	livingston	PROPN
ejpam-5971	368	11	.	.	PUNCT
ejpam-5971	369	1	the	the	DET
ejpam-5971	369	2	zero	zero	NUM
ejpam-5971	369	3	-	-	PUNCT
ejpam-5971	369	4	divisor	divisor	NOUN
ejpam-5971	369	5	graph	graph	NOUN
ejpam-5971	369	6	of	of	ADP
ejpam-5971	369	7	a	a	DET
ejpam-5971	369	8	commutative	commutative	ADJ
ejpam-5971	369	9	ring	ring	NOUN
ejpam-5971	369	10	.	.	PUNCT
ejpam-5971	370	1	journal	journal	PROPN
ejpam-5971	370	2	of	of	ADP
ejpam-5971	370	3	algebra	algebra	PROPN
ejpam-5971	370	4	,	,	PUNCT
ejpam-5971	370	5	217(2):434–447	217(2):434–447	PROPN
ejpam-5971	370	6	,	,	PUNCT
ejpam-5971	370	7	1999	1999	NUM
ejpam-5971	370	8	.	.	PUNCT
ejpam-5971	371	1	[	[	X
ejpam-5971	371	2	3	3	X
ejpam-5971	371	3	]	]	X
ejpam-5971	371	4	k	k	PROPN
ejpam-5971	371	5	elahi	elahi	PROPN
ejpam-5971	371	6	,	,	PUNCT
ejpam-5971	371	7	a	a	DET
ejpam-5971	371	8	ahmad	ahmad	PROPN
ejpam-5971	371	9	,	,	PUNCT
ejpam-5971	371	10	and	and	CCONJ
ejpam-5971	371	11	r	r	NOUN
ejpam-5971	371	12	hasni	hasni	NOUN
ejpam-5971	371	13	.	.	PUNCT
ejpam-5971	372	1	construction	construction	NOUN
ejpam-5971	372	2	algorithm	algorithm	NOUN
ejpam-5971	372	3	for	for	ADP
ejpam-5971	372	4	zero	zero	NUM
ejpam-5971	372	5	divisor	divisor	NOUN
ejpam-5971	372	6	graphs	graph	NOUN
ejpam-5971	372	7	of	of	ADP
ejpam-5971	372	8	finite	finite	PROPN
ejpam-5971	372	9	commutative	commutative	ADJ
ejpam-5971	372	10	rings	ring	NOUN
ejpam-5971	372	11	and	and	CCONJ
ejpam-5971	372	12	their	their	PRON
ejpam-5971	372	13	vertex	vertex	NOUN
ejpam-5971	372	14	-	-	PUNCT
ejpam-5971	372	15	based	base	VERB
ejpam-5971	372	16	eccentric	eccentric	ADJ
ejpam-5971	372	17	topological	topological	ADJ
ejpam-5971	372	18	indices	index	NOUN
ejpam-5971	372	19	.	.	PUNCT
ejpam-5971	373	1	mathematics	mathematic	NOUN
ejpam-5971	373	2	,	,	PUNCT
ejpam-5971	373	3	6(12):301	6(12):301	PROPN
ejpam-5971	373	4	,	,	PUNCT
ejpam-5971	373	5	2018	2018	NUM
ejpam-5971	373	6	.	.	PUNCT
ejpam-5971	374	1	[	[	X
ejpam-5971	374	2	4	4	X
ejpam-5971	374	3	]	]	PUNCT
ejpam-5971	374	4	n	n	X
ejpam-5971	374	5	ali	ali	X
ejpam-5971	374	6	,	,	PUNCT
ejpam-5971	374	7	h	h	PROPN
ejpam-5971	374	8	m	m	VERB
ejpam-5971	374	9	a	a	DET
ejpam-5971	374	10	siddiqui	siddiqui	NOUN
ejpam-5971	374	11	,	,	PUNCT
ejpam-5971	374	12	m	m	PROPN
ejpam-5971	374	13	b	b	NOUN
ejpam-5971	374	14	riaz	riaz	PROPN
ejpam-5971	374	15	,	,	PUNCT
ejpam-5971	374	16	m	m	VERB
ejpam-5971	374	17	i	i	PRON
ejpam-5971	374	18	qureshi	qureshi	VERB
ejpam-5971	374	19	,	,	PUNCT
ejpam-5971	374	20	and	and	CCONJ
ejpam-5971	374	21	a	a	DET
ejpam-5971	374	22	akgül	akgül	PROPN
ejpam-5971	374	23	.	.	PUNCT
ejpam-5971	375	1	a	a	DET
ejpam-5971	375	2	graph	graph	NOUN
ejpam-5971	375	3	-	-	PUNCT
ejpam-5971	375	4	theoretic	theoretic	ADJ
ejpam-5971	375	5	approach	approach	NOUN
ejpam-5971	375	6	to	to	PART
ejpam-5971	375	7	ring	ring	VERB
ejpam-5971	375	8	analysis	analysis	NOUN
ejpam-5971	375	9	:	:	PUNCT
ejpam-5971	375	10	dominant	dominant	ADJ
ejpam-5971	375	11	metric	metric	ADJ
ejpam-5971	375	12	dimensions	dimension	NOUN
ejpam-5971	375	13	in	in	ADP
ejpam-5971	375	14	zero	zero	NUM
ejpam-5971	375	15	-	-	PUNCT
ejpam-5971	375	16	divisor	divisor	NOUN
ejpam-5971	375	17	graphs	graph	NOUN
ejpam-5971	375	18	.	.	PUNCT
ejpam-5971	376	1	heliyon	heliyon	NOUN
ejpam-5971	376	2	,	,	PUNCT
ejpam-5971	376	3	10(10	10(10	NUM
ejpam-5971	376	4	)	)	PUNCT
ejpam-5971	376	5	,	,	PUNCT
ejpam-5971	376	6	2024	2024	NUM
ejpam-5971	376	7	.	.	PUNCT
ejpam-5971	377	1	[	[	X
ejpam-5971	377	2	5	5	NUM
ejpam-5971	377	3	]	]	PUNCT
ejpam-5971	377	4	n	n	PRON
ejpam-5971	377	5	annamalai	annamalai	PROPN
ejpam-5971	377	6	and	and	CCONJ
ejpam-5971	377	7	c	c	PROPN
ejpam-5971	377	8	durairajan	durairajan	PROPN
ejpam-5971	377	9	.	.	PUNCT
ejpam-5971	378	1	codes	code	NOUN
ejpam-5971	378	2	from	from	ADP
ejpam-5971	378	3	the	the	DET
ejpam-5971	378	4	incidence	incidence	ADJ
ejpam-5971	378	5	matrices	matrix	NOUN
ejpam-5971	378	6	of	of	ADP
ejpam-5971	378	7	a	a	DET
ejpam-5971	378	8	zero	zero	NUM
ejpam-5971	378	9	-	-	PUNCT
ejpam-5971	378	10	divisor	divisor	NOUN
ejpam-5971	378	11	graphs	graph	NOUN
ejpam-5971	378	12	.	.	PUNCT
ejpam-5971	379	1	journal	journal	NOUN
ejpam-5971	379	2	of	of	ADP
ejpam-5971	379	3	discrete	discrete	ADJ
ejpam-5971	379	4	mathematical	mathematical	ADJ
ejpam-5971	379	5	sciences	science	NOUN
ejpam-5971	379	6	and	and	CCONJ
ejpam-5971	379	7	cryptography	cryptography	NOUN
ejpam-5971	379	8	,	,	PUNCT
ejpam-5971	379	9	pages	page	NOUN
ejpam-5971	379	10	1–9	1–9	NUM
ejpam-5971	379	11	,	,	PUNCT
ejpam-5971	379	12	2022	2022	NUM
ejpam-5971	379	13	.	.	PUNCT
ejpam-5971	380	1	[	[	X
ejpam-5971	380	2	6	6	NUM
ejpam-5971	380	3	]	]	X
ejpam-5971	380	4	r	r	NOUN
ejpam-5971	380	5	raja	raja	PROPN
ejpam-5971	380	6	,	,	PUNCT
ejpam-5971	380	7	s	s	PART
ejpam-5971	380	8	pirzada	pirzada	NOUN
ejpam-5971	380	9	,	,	PUNCT
ejpam-5971	380	10	and	and	CCONJ
ejpam-5971	380	11	s	s	PROPN
ejpam-5971	380	12	redmond	redmond	NOUN
ejpam-5971	380	13	.	.	PUNCT
ejpam-5971	381	1	on	on	ADP
ejpam-5971	381	2	locating	locate	VERB
ejpam-5971	381	3	numbers	number	NOUN
ejpam-5971	381	4	and	and	CCONJ
ejpam-5971	381	5	codes	code	NOUN
ejpam-5971	381	6	of	of	ADP
ejpam-5971	381	7	zero	zero	NUM
ejpam-5971	381	8	divisor	divisor	NOUN
ejpam-5971	381	9	graphs	graph	NOUN
ejpam-5971	381	10	associated	associate	VERB
ejpam-5971	381	11	with	with	ADP
ejpam-5971	381	12	commutative	commutative	ADJ
ejpam-5971	381	13	rings	ring	NOUN
ejpam-5971	381	14	.	.	PUNCT
ejpam-5971	382	1	journal	journal	PROPN
ejpam-5971	382	2	of	of	ADP
ejpam-5971	382	3	algebra	algebra	PROPN
ejpam-5971	382	4	and	and	CCONJ
ejpam-5971	382	5	its	its	PRON
ejpam-5971	382	6	applications	application	NOUN
ejpam-5971	382	7	,	,	PUNCT
ejpam-5971	382	8	15(01):1650014	15(01):1650014	NUM
ejpam-5971	382	9	,	,	PUNCT
ejpam-5971	382	10	2016	2016	NUM
ejpam-5971	382	11	.	.	PUNCT
ejpam-5971	383	1	[	[	X
ejpam-5971	383	2	7	7	X
ejpam-5971	383	3	]	]	X
ejpam-5971	383	4	d	d	X
ejpam-5971	383	5	f	f	PROPN
ejpam-5971	383	6	anderson	anderson	PROPN
ejpam-5971	383	7	,	,	PUNCT
ejpam-5971	383	8	t	t	PROPN
ejpam-5971	383	9	asir	asir	PROPN
ejpam-5971	383	10	,	,	PUNCT
ejpam-5971	383	11	a	a	DET
ejpam-5971	383	12	badawi	badawi	NOUN
ejpam-5971	383	13	,	,	PUNCT
ejpam-5971	383	14	and	and	CCONJ
ejpam-5971	383	15	t	t	PROPN
ejpam-5971	383	16	t	t	PROPN
ejpam-5971	383	17	chelvam	chelvam	VERB
ejpam-5971	383	18	.	.	PUNCT
ejpam-5971	384	1	distances	distance	NOUN
ejpam-5971	384	2	in	in	ADP
ejpam-5971	384	3	zero	zero	NUM
ejpam-5971	384	4	-	-	PUNCT
ejpam-5971	384	5	divisor	divisor	NOUN
ejpam-5971	384	6	graphs	graph	NOUN
ejpam-5971	384	7	:	:	PUNCT
ejpam-5971	384	8	graphs	graph	NOUN
ejpam-5971	384	9	from	from	ADP
ejpam-5971	384	10	rings	ring	NOUN
ejpam-5971	384	11	.	.	PUNCT
ejpam-5971	385	1	springer	springer	PROPN
ejpam-5971	385	2	,	,	PUNCT
ejpam-5971	385	3	cham	cham	NOUN
ejpam-5971	385	4	,	,	PUNCT
ejpam-5971	385	5	2021	2021	NUM
ejpam-5971	385	6	.	.	PUNCT
ejpam-5971	386	1	[	[	X
ejpam-5971	386	2	8	8	NUM
ejpam-5971	386	3	]	]	X
ejpam-5971	386	4	d	d	X
ejpam-5971	386	5	f	f	PROPN
ejpam-5971	386	6	anderson	anderson	PROPN
ejpam-5971	386	7	,	,	PUNCT
ejpam-5971	386	8	t	t	PROPN
ejpam-5971	386	9	asir	asir	PROPN
ejpam-5971	386	10	,	,	PUNCT
ejpam-5971	386	11	a	a	DET
ejpam-5971	386	12	badawi	badawi	NOUN
ejpam-5971	386	13	,	,	PUNCT
ejpam-5971	386	14	and	and	CCONJ
ejpam-5971	386	15	t	t	PROPN
ejpam-5971	386	16	t	t	PROPN
ejpam-5971	386	17	chelvam	chelvam	VERB
ejpam-5971	386	18	.	.	PUNCT
ejpam-5971	387	1	properties	property	NOUN
ejpam-5971	387	2	of	of	ADP
ejpam-5971	387	3	zero	zero	NUM
ejpam-5971	387	4	-	-	PUNCT
ejpam-5971	387	5	divisor	divisor	NOUN
ejpam-5971	387	6	graphs	graph	NOUN
ejpam-5971	387	7	:	:	PUNCT
ejpam-5971	387	8	graphs	graph	NOUN
ejpam-5971	387	9	from	from	ADP
ejpam-5971	387	10	rings	ring	NOUN
ejpam-5971	387	11	.	.	PUNCT
ejpam-5971	388	1	springer	springer	PROPN
ejpam-5971	388	2	,	,	PUNCT
ejpam-5971	388	3	cham	cham	NOUN
ejpam-5971	388	4	,	,	PUNCT
ejpam-5971	388	5	2021	2021	NUM
ejpam-5971	388	6	.	.	PUNCT
ejpam-5971	389	1	[	[	X
ejpam-5971	389	2	9	9	NUM
ejpam-5971	389	3	]	]	SYM
ejpam-5971	389	4	s	s	PROPN
ejpam-5971	389	5	e	e	PROPN
ejpam-5971	389	6	anderson	anderson	PROPN
ejpam-5971	389	7	,	,	PUNCT
ejpam-5971	389	8	m	m	PROPN
ejpam-5971	389	9	c	c	PROPN
ejpam-5971	389	10	axtell	axtell	PROPN
ejpam-5971	389	11	,	,	PUNCT
ejpam-5971	389	12	b	b	PROPN
ejpam-5971	389	13	k	k	PROPN
ejpam-5971	389	14	kroschel	kroschel	PROPN
ejpam-5971	389	15	,	,	PUNCT
ejpam-5971	389	16	and	and	CCONJ
ejpam-5971	389	17	j	j	PROPN
ejpam-5971	389	18	a	a	DET
ejpam-5971	389	19	stickles	stickle	NOUN
ejpam-5971	389	20	jr	jr	PROPN
ejpam-5971	389	21	.	.	PROPN
ejpam-5971	389	22	on	on	ADP
ejpam-5971	389	23	domination	domination	NOUN
ejpam-5971	389	24	numbers	number	NOUN
ejpam-5971	389	25	of	of	ADP
ejpam-5971	389	26	zero	zero	NUM
ejpam-5971	389	27	-	-	PUNCT
ejpam-5971	389	28	divisor	divisor	NOUN
ejpam-5971	389	29	graphs	graph	NOUN
ejpam-5971	389	30	of	of	ADP
ejpam-5971	389	31	commutative	commutative	ADJ
ejpam-5971	389	32	rings	ring	NOUN
ejpam-5971	389	33	.	.	PUNCT
ejpam-5971	390	1	electronic	electronic	ADJ
ejpam-5971	390	2	journal	journal	NOUN
ejpam-5971	390	3	of	of	ADP
ejpam-5971	390	4	graph	graph	NOUN
ejpam-5971	390	5	theory	theory	NOUN
ejpam-5971	390	6	and	and	CCONJ
ejpam-5971	390	7	applications	application	NOUN
ejpam-5971	390	8	,	,	PUNCT
ejpam-5971	390	9	12(2	12(2	NUM
ejpam-5971	390	10	)	)	PUNCT
ejpam-5971	390	11	,	,	PUNCT
ejpam-5971	390	12	2024	2024	NUM
ejpam-5971	390	13	.	.	PUNCT
ejpam-5971	391	1	[	[	X
ejpam-5971	391	2	10	10	NUM
ejpam-5971	391	3	]	]	X
ejpam-5971	391	4	m	m	PROPN
ejpam-5971	391	5	axtell	axtell	PROPN
ejpam-5971	391	6	,	,	PUNCT
ejpam-5971	391	7	j	j	PROPN
ejpam-5971	391	8	coykendall	coykendall	NOUN
ejpam-5971	391	9	,	,	PUNCT
ejpam-5971	391	10	and	and	CCONJ
ejpam-5971	391	11	j	j	PROPN
ejpam-5971	391	12	stickles	stickle	NOUN
ejpam-5971	391	13	.	.	PUNCT
ejpam-5971	392	1	zero	zero	NUM
ejpam-5971	392	2	-	-	PUNCT
ejpam-5971	392	3	divisor	divisor	NOUN
ejpam-5971	392	4	graphs	graph	NOUN
ejpam-5971	392	5	of	of	ADP
ejpam-5971	392	6	polynomials	polynomial	NOUN
ejpam-5971	392	7	and	and	CCONJ
ejpam-5971	392	8	power	power	NOUN
ejpam-5971	392	9	series	series	PROPN
ejpam-5971	392	10	over	over	ADP
ejpam-5971	392	11	commutative	commutative	ADJ
ejpam-5971	392	12	rings	ring	NOUN
ejpam-5971	392	13	.	.	PUNCT
ejpam-5971	393	1	communications	communication	NOUN
ejpam-5971	393	2	in	in	ADP
ejpam-5971	393	3	algebra	algebra	NOUN
ejpam-5971	393	4	,	,	PUNCT
ejpam-5971	393	5	33(6):2043–2050	33(6):2043–2050	NUM
ejpam-5971	393	6	,	,	PUNCT
ejpam-5971	393	7	2005	2005	NUM
ejpam-5971	393	8	.	.	PUNCT
ejpam-5971	394	1	[	[	X
ejpam-5971	394	2	11	11	NUM
ejpam-5971	394	3	]	]	PUNCT
ejpam-5971	394	4	t	t	PROPN
ejpam-5971	394	5	g	g	PROPN
ejpam-5971	394	6	lucas	lucas	PROPN
ejpam-5971	394	7	.	.	PUNCT
ejpam-5971	395	1	the	the	DET
ejpam-5971	395	2	diameter	diameter	NOUN
ejpam-5971	395	3	of	of	ADP
ejpam-5971	395	4	a	a	DET
ejpam-5971	395	5	zero	zero	NUM
ejpam-5971	395	6	divisor	divisor	NOUN
ejpam-5971	395	7	graph	graph	NOUN
ejpam-5971	395	8	.	.	PUNCT
ejpam-5971	395	9	journal	journal	NOUN
ejpam-5971	395	10	of	of	ADP
ejpam-5971	395	11	algebra	algebra	PROPN
ejpam-5971	395	12	,	,	PUNCT
ejpam-5971	395	13	301(1):174–193	301(1):174–193	NUM
ejpam-5971	395	14	,	,	PUNCT
ejpam-5971	395	15	2006	2006	NUM
ejpam-5971	395	16	.	.	PUNCT
ejpam-5971	396	1	v.h	v.h	PROPN
ejpam-5971	396	2	.	.	PROPN
ejpam-5971	396	3	krisnawati	krisnawati	PROPN
ejpam-5971	396	4	,	,	PUNCT
ejpam-5971	396	5	n.	n.	PROPN
ejpam-5971	396	6	hidayat	hidayat	PROPN
ejpam-5971	396	7	,	,	PUNCT
ejpam-5971	396	8	a.f	a.f	PROPN
ejpam-5971	396	9	.	.	PROPN
ejpam-5971	396	10	musyarrofah	musyarrofah	PROPN
ejpam-5971	396	11	/	/	SYM
ejpam-5971	396	12	eur	eur	PROPN
ejpam-5971	396	13	.	.	PUNCT
ejpam-5971	397	1	j.	j.	PROPN
ejpam-5971	397	2	pure	pure	PROPN
ejpam-5971	397	3	appl	appl	PROPN
ejpam-5971	397	4	.	.	PROPN
ejpam-5971	397	5	math	math	PROPN
ejpam-5971	397	6	,	,	PUNCT
ejpam-5971	397	7	18	18	NUM
ejpam-5971	397	8	(	(	PUNCT
ejpam-5971	397	9	2	2	NUM
ejpam-5971	397	10	)	)	PUNCT
ejpam-5971	397	11	(	(	PUNCT
ejpam-5971	397	12	2025	2025	NUM
ejpam-5971	397	13	)	)	PUNCT
ejpam-5971	397	14	,	,	PUNCT
ejpam-5971	397	15	5971	5971	NUM
ejpam-5971	397	16	19	19	NUM
ejpam-5971	397	17	of	of	ADP
ejpam-5971	397	18	19	19	NUM
ejpam-5971	398	1	[	[	X
ejpam-5971	398	2	12	12	NUM
ejpam-5971	398	3	]	]	X
ejpam-5971	398	4	m	m	PROPN
ejpam-5971	398	5	j	j	PROPN
ejpam-5971	398	6	park	park	NOUN
ejpam-5971	398	7	,	,	PUNCT
ejpam-5971	398	8	e	e	PROPN
ejpam-5971	398	9	s	s	PROPN
ejpam-5971	398	10	kim	kim	PROPN
ejpam-5971	398	11	,	,	PUNCT
ejpam-5971	398	12	and	and	CCONJ
ejpam-5971	398	13	j	j	PROPN
ejpam-5971	398	14	w	w	PROPN
ejpam-5971	398	15	lim	lim	PROPN
ejpam-5971	398	16	.	.	PUNCT
ejpam-5971	399	1	the	the	DET
ejpam-5971	399	2	zero	zero	NUM
ejpam-5971	399	3	-	-	PUNCT
ejpam-5971	399	4	divisor	divisor	NOUN
ejpam-5971	399	5	graph	graph	NOUN
ejpam-5971	399	6	of	of	ADP
ejpam-5971	399	7	zn[x	zn[x	NOUN
ejpam-5971	399	8	]	]	PUNCT
ejpam-5971	399	9	.	.	PUNCT
ejpam-5971	400	1	kyungpook	kyungpook	PROPN
ejpam-5971	400	2	mathematical	mathematical	PROPN
ejpam-5971	400	3	journal	journal	PROPN
ejpam-5971	400	4	,	,	PUNCT
ejpam-5971	400	5	60(4):723–729	60(4):723–729	PROPN
ejpam-5971	400	6	,	,	PUNCT
ejpam-5971	400	7	2020	2020	NUM
ejpam-5971	400	8	.	.	PUNCT
ejpam-5971	401	1	[	[	X
ejpam-5971	401	2	13	13	NUM
ejpam-5971	401	3	]	]	X
ejpam-5971	401	4	i	i	PROPN
ejpam-5971	401	5	gutman	gutman	PROPN
ejpam-5971	401	6	.	.	PUNCT
ejpam-5971	402	1	the	the	DET
ejpam-5971	402	2	energy	energy	NOUN
ejpam-5971	402	3	of	of	ADP
ejpam-5971	402	4	a	a	DET
ejpam-5971	402	5	graph	graph	NOUN
ejpam-5971	402	6	.	.	PUNCT
ejpam-5971	403	1	berichte	berichte	NOUN
ejpam-5971	403	2	der	der	ADJ
ejpam-5971	403	3	mathematisch	mathematisch	PROPN
ejpam-5971	403	4	-	-	PUNCT
ejpam-5971	403	5	statistischen	statistischen	NOUN
ejpam-5971	403	6	sektion	sektion	NOUN
ejpam-5971	404	1	i	i	PRON
ejpam-5971	404	2	m	m	VERB
ejpam-5971	404	3	forschungszentrum	forschungszentrum	PROPN
ejpam-5971	404	4	graz	graz	PROPN
ejpam-5971	404	5	,	,	PUNCT
ejpam-5971	404	6	103:1–22	103:1–22	NUM
ejpam-5971	404	7	,	,	PUNCT
ejpam-5971	404	8	1978	1978	NUM
ejpam-5971	404	9	.	.	PUNCT
ejpam-5971	405	1	[	[	X
ejpam-5971	405	2	14	14	NUM
ejpam-5971	405	3	]	]	X
ejpam-5971	405	4	x	x	PROPN
ejpam-5971	405	5	li	li	PROPN
ejpam-5971	405	6	y	y	PROPN
ejpam-5971	405	7	shi	shi	PROPN
ejpam-5971	405	8	and	and	CCONJ
ejpam-5971	405	9	i	i	PROPN
ejpam-5971	405	10	gutman	gutman	PROPN
ejpam-5971	405	11	.	.	PUNCT
ejpam-5971	406	1	graph	graph	NOUN
ejpam-5971	406	2	energy	energy	NOUN
ejpam-5971	406	3	.	.	PUNCT
ejpam-5971	407	1	springer	springer	NOUN
ejpam-5971	407	2	,	,	PUNCT
ejpam-5971	407	3	new	new	PROPN
ejpam-5971	407	4	york	york	PROPN
ejpam-5971	407	5	,	,	PUNCT
ejpam-5971	407	6	2012	2012	NUM
ejpam-5971	407	7	.	.	PUNCT
ejpam-5971	408	1	[	[	X
ejpam-5971	408	2	15	15	NUM
ejpam-5971	408	3	]	]	X
ejpam-5971	408	4	h	h	NOUN
ejpam-5971	408	5	wiener	wiener	NOUN
ejpam-5971	408	6	.	.	PUNCT
ejpam-5971	409	1	structural	structural	ADJ
ejpam-5971	409	2	determination	determination	NOUN
ejpam-5971	409	3	of	of	ADP
ejpam-5971	409	4	paraffin	paraffin	NOUN
ejpam-5971	409	5	boiling	boiling	NOUN
ejpam-5971	409	6	points	point	NOUN
ejpam-5971	409	7	.	.	PUNCT
ejpam-5971	410	1	journal	journal	NOUN
ejpam-5971	410	2	of	of	ADP
ejpam-5971	410	3	the	the	DET
ejpam-5971	410	4	american	american	PROPN
ejpam-5971	410	5	chemical	chemical	PROPN
ejpam-5971	410	6	society	society	PROPN
ejpam-5971	410	7	,	,	PUNCT
ejpam-5971	410	8	69:17–20	69:17–20	NUM
ejpam-5971	410	9	,	,	PUNCT
ejpam-5971	410	10	1947	1947	NUM
ejpam-5971	410	11	.	.	PUNCT
ejpam-5971	411	1	[	[	X
ejpam-5971	411	2	16	16	NUM
ejpam-5971	411	3	]	]	X
ejpam-5971	411	4	m	m	VERB
ejpam-5971	411	5	randić.	randić.	NOUN
ejpam-5971	411	6	novel	novel	ADJ
ejpam-5971	411	7	molecular	molecular	ADJ
ejpam-5971	411	8	descriptor	descriptor	NOUN
ejpam-5971	411	9	for	for	ADP
ejpam-5971	411	10	structure	structure	NOUN
ejpam-5971	411	11	–	–	PUNCT
ejpam-5971	411	12	property	property	NOUN
ejpam-5971	411	13	studies	study	NOUN
ejpam-5971	411	14	.	.	PUNCT
ejpam-5971	412	1	chemical	chemical	PROPN
ejpam-5971	412	2	physics	physics	PROPN
ejpam-5971	412	3	letters	letter	NOUN
ejpam-5971	412	4	,	,	PUNCT
ejpam-5971	412	5	211(4–5):478–483	211(4–5):478–483	NUM
ejpam-5971	412	6	,	,	PUNCT
ejpam-5971	412	7	1993	1993	NUM
ejpam-5971	412	8	.	.	PUNCT
ejpam-5971	413	1	[	[	X
ejpam-5971	413	2	17	17	NUM
ejpam-5971	413	3	]	]	X
ejpam-5971	413	4	i	i	PRON
ejpam-5971	413	5	gutman	gutman	NOUN
ejpam-5971	413	6	and	and	CCONJ
ejpam-5971	413	7	n	n	CCONJ
ejpam-5971	413	8	trinajstić.	trinajstić.	PROPN
ejpam-5971	413	9	graph	graph	NOUN
ejpam-5971	413	10	theory	theory	NOUN
ejpam-5971	413	11	and	and	CCONJ
ejpam-5971	413	12	molecular	molecular	ADJ
ejpam-5971	413	13	orbitals	orbital	NOUN
ejpam-5971	413	14	.	.	PUNCT
ejpam-5971	414	1	total	total	ADJ
ejpam-5971	414	2	ψ	ψ	ADJ
ejpam-5971	414	3	-	-	NOUN
ejpam-5971	414	4	electron	electron	NOUN
ejpam-5971	414	5	energy	energy	NOUN
ejpam-5971	414	6	of	of	ADP
ejpam-5971	414	7	alternant	alternant	ADJ
ejpam-5971	414	8	hydrocarbons	hydrocarbon	NOUN
ejpam-5971	414	9	.	.	PUNCT
ejpam-5971	415	1	chemical	chemical	PROPN
ejpam-5971	415	2	physics	physics	PROPN
ejpam-5971	415	3	letters	letter	NOUN
ejpam-5971	415	4	,	,	PUNCT
ejpam-5971	415	5	17(4):535–538	17(4):535–538	NUM
ejpam-5971	415	6	,	,	PUNCT
ejpam-5971	415	7	1972	1972	NUM
ejpam-5971	415	8	.	.	PUNCT
ejpam-5971	416	1	[	[	X
ejpam-5971	416	2	18	18	NUM
ejpam-5971	416	3	]	]	X
ejpam-5971	416	4	h	h	NOUN
ejpam-5971	416	5	narumi	narumi	PROPN
ejpam-5971	416	6	and	and	CCONJ
ejpam-5971	416	7	m	m	PROPN
ejpam-5971	416	8	katayama	katayama	NOUN
ejpam-5971	416	9	.	.	PUNCT
ejpam-5971	417	1	simple	simple	ADJ
ejpam-5971	417	2	topological	topological	ADJ
ejpam-5971	417	3	index	index	NOUN
ejpam-5971	417	4	:	:	PUNCT
ejpam-5971	417	5	a	a	DET
ejpam-5971	417	6	newly	newly	ADV
ejpam-5971	417	7	devised	devise	VERB
ejpam-5971	417	8	index	index	NOUN
ejpam-5971	417	9	characterizing	characterize	VERB
ejpam-5971	417	10	the	the	DET
ejpam-5971	417	11	topological	topological	ADJ
ejpam-5971	417	12	nature	nature	NOUN
ejpam-5971	417	13	of	of	ADP
ejpam-5971	417	14	structural	structural	ADJ
ejpam-5971	417	15	isomers	isomer	NOUN
ejpam-5971	417	16	of	of	ADP
ejpam-5971	417	17	saturated	saturated	ADJ
ejpam-5971	417	18	hydrocarbons	hydrocarbon	NOUN
ejpam-5971	417	19	.	.	PUNCT
ejpam-5971	418	1	memoirs	memoir	NOUN
ejpam-5971	418	2	of	of	ADP
ejpam-5971	418	3	the	the	DET
ejpam-5971	418	4	faculty	faculty	NOUN
ejpam-5971	418	5	of	of	ADP
ejpam-5971	418	6	engineering	engineering	PROPN
ejpam-5971	418	7	,	,	PUNCT
ejpam-5971	418	8	hokkaido	hokkaido	PROPN
ejpam-5971	418	9	university	university	PROPN
ejpam-5971	418	10	,	,	PUNCT
ejpam-5971	418	11	16(3):209–214	16(3):209–214	NUM
ejpam-5971	418	12	,	,	PUNCT
ejpam-5971	418	13	1984	1984	NUM
ejpam-5971	418	14	.	.	PUNCT
ejpam-5971	419	1	[	[	X
ejpam-5971	419	2	19	19	NUM
ejpam-5971	419	3	]	]	SYM
ejpam-5971	419	4	m	m	VERB
ejpam-5971	419	5	r	r	NOUN
ejpam-5971	419	6	ahmadi	ahmadi	NOUN
ejpam-5971	419	7	and	and	CCONJ
ejpam-5971	419	8	r	r	NOUN
ejpam-5971	419	9	jahani	jahani	X
ejpam-5971	419	10	-	-	PUNCT
ejpam-5971	419	11	nezhad	nezhad	VERB
ejpam-5971	419	12	.	.	PUNCT
ejpam-5971	420	1	energy	energy	NOUN
ejpam-5971	420	2	and	and	CCONJ
ejpam-5971	420	3	wiener	wiener	NOUN
ejpam-5971	420	4	index	index	NOUN
ejpam-5971	420	5	of	of	ADP
ejpam-5971	420	6	zero	zero	NUM
ejpam-5971	420	7	-	-	PUNCT
ejpam-5971	420	8	divisor	divisor	NOUN
ejpam-5971	420	9	graphs	graph	NOUN
ejpam-5971	420	10	.	.	PUNCT
ejpam-5971	421	1	iranian	iranian	ADJ
ejpam-5971	421	2	journal	journal	PROPN
ejpam-5971	421	3	of	of	ADP
ejpam-5971	421	4	mathematical	mathematical	ADJ
ejpam-5971	421	5	chemistry	chemistry	NOUN
ejpam-5971	421	6	,	,	PUNCT
ejpam-5971	421	7	2(1):45–51	2(1):45–51	NUM
ejpam-5971	421	8	,	,	PUNCT
ejpam-5971	421	9	2011	2011	NUM
ejpam-5971	421	10	.	.	PUNCT
ejpam-5971	422	1	[	[	X
ejpam-5971	422	2	20	20	NUM
ejpam-5971	422	3	]	]	X
ejpam-5971	422	4	c	c	PROPN
ejpam-5971	422	5	johnson	johnson	PROPN
ejpam-5971	422	6	and	and	CCONJ
ejpam-5971	422	7	r	r	NOUN
ejpam-5971	422	8	sankar	sankar	NOUN
ejpam-5971	422	9	.	.	PUNCT
ejpam-5971	423	1	graph	graph	NOUN
ejpam-5971	423	2	energy	energy	NOUN
ejpam-5971	423	3	and	and	CCONJ
ejpam-5971	423	4	topological	topological	ADJ
ejpam-5971	423	5	descriptors	descriptor	NOUN
ejpam-5971	423	6	of	of	ADP
ejpam-5971	423	7	zero	zero	NUM
ejpam-5971	423	8	divisor	divisor	NOUN
ejpam-5971	423	9	graph	graph	NOUN
ejpam-5971	423	10	associated	associate	VERB
ejpam-5971	423	11	with	with	ADP
ejpam-5971	423	12	commutative	commutative	ADJ
ejpam-5971	423	13	ring	ring	NOUN
ejpam-5971	423	14	.	.	PUNCT
ejpam-5971	424	1	journal	journal	PROPN
ejpam-5971	424	2	of	of	ADP
ejpam-5971	424	3	applied	apply	VERB
ejpam-5971	424	4	mathematics	mathematic	NOUN
ejpam-5971	424	5	and	and	CCONJ
ejpam-5971	424	6	computation	computation	NOUN
ejpam-5971	424	7	,	,	PUNCT
ejpam-5971	424	8	69(3):2641–2656	69(3):2641–2656	NUM
ejpam-5971	424	9	,	,	PUNCT
ejpam-5971	424	10	2023	2023	NUM
ejpam-5971	424	11	.	.	PUNCT
ejpam-5971	425	1	[	[	X
ejpam-5971	425	2	21	21	NUM
ejpam-5971	425	3	]	]	X
ejpam-5971	425	4	b	b	NOUN
ejpam-5971	425	5	a	a	DET
ejpam-5971	425	6	rather	rather	NOUN
ejpam-5971	425	7	.	.	PUNCT
ejpam-5971	426	1	a	a	DET
ejpam-5971	426	2	note	note	NOUN
ejpam-5971	426	3	on	on	ADP
ejpam-5971	426	4	eigenvalues	eigenvalue	NOUN
ejpam-5971	426	5	of	of	ADP
ejpam-5971	426	6	zero	zero	NUM
ejpam-5971	426	7	divisor	divisor	NOUN
ejpam-5971	426	8	graphs	graph	NOUN
ejpam-5971	426	9	associated	associate	VERB
ejpam-5971	426	10	with	with	ADP
ejpam-5971	426	11	commutative	commutative	ADJ
ejpam-5971	426	12	rings	ring	NOUN
ejpam-5971	426	13	.	.	PUNCT
ejpam-5971	427	1	arxiv	arxiv	PROPN
ejpam-5971	427	2	preprint	preprint	PROPN
ejpam-5971	427	3	,	,	PUNCT
ejpam-5971	427	4	2024	2024	NUM
ejpam-5971	427	5	.	.	PUNCT
ejpam-5971	428	1	[	[	X
ejpam-5971	428	2	22	22	NUM
ejpam-5971	428	3	]	]	X
ejpam-5971	428	4	c	c	PROPN
ejpam-5971	428	5	j	j	PROPN
ejpam-5971	428	6	rayer	rayer	PROPN
ejpam-5971	428	7	and	and	CCONJ
ejpam-5971	428	8	r	r	NOUN
ejpam-5971	428	9	s	s	NOUN
ejpam-5971	428	10	jeyaraj	jeyaraj	NOUN
ejpam-5971	428	11	.	.	PUNCT
ejpam-5971	429	1	applications	application	NOUN
ejpam-5971	429	2	on	on	ADP
ejpam-5971	429	3	topological	topological	ADJ
ejpam-5971	429	4	indices	index	NOUN
ejpam-5971	429	5	of	of	ADP
ejpam-5971	429	6	zero	zero	NUM
ejpam-5971	429	7	-	-	PUNCT
ejpam-5971	429	8	divisor	divisor	NOUN
ejpam-5971	429	9	graph	graph	NOUN
ejpam-5971	429	10	associated	associate	VERB
ejpam-5971	429	11	with	with	ADP
ejpam-5971	429	12	commutative	commutative	ADJ
ejpam-5971	429	13	rings	ring	NOUN
ejpam-5971	429	14	.	.	PUNCT
ejpam-5971	430	1	symmetry	symmetry	PROPN
ejpam-5971	430	2	,	,	PUNCT
ejpam-5971	430	3	15(2):335	15(2):335	NUM
ejpam-5971	430	4	,	,	PUNCT
ejpam-5971	430	5	2023	2023	NUM
ejpam-5971	430	6	.	.	PUNCT
ejpam-5971	431	1	[	[	X
ejpam-5971	431	2	23	23	NUM
ejpam-5971	431	3	]	]	X
ejpam-5971	431	4	c	c	PROPN
ejpam-5971	431	5	j	j	PROPN
ejpam-5971	431	6	rayer	rayer	PROPN
ejpam-5971	431	7	and	and	CCONJ
ejpam-5971	431	8	r	r	NOUN
ejpam-5971	431	9	s	s	NOUN
ejpam-5971	431	10	jeyaraj	jeyaraj	VERB
ejpam-5971	431	11	.	.	PUNCT
ejpam-5971	432	1	computation	computation	NOUN
ejpam-5971	432	2	of	of	ADP
ejpam-5971	432	3	some	some	DET
ejpam-5971	432	4	graph	graph	NOUN
ejpam-5971	432	5	energies	energy	NOUN
ejpam-5971	432	6	of	of	ADP
ejpam-5971	432	7	the	the	DET
ejpam-5971	432	8	zero	zero	NUM
ejpam-5971	432	9	-	-	PUNCT
ejpam-5971	432	10	divisor	divisor	NOUN
ejpam-5971	432	11	graph	graph	NOUN
ejpam-5971	432	12	associated	associate	VERB
ejpam-5971	432	13	with	with	ADP
ejpam-5971	432	14	the	the	DET
ejpam-5971	432	15	commutative	commutative	ADJ
ejpam-5971	432	16	ring	ring	NOUN
ejpam-5971	432	17	z℘2	z℘2	PROPN
ejpam-5971	433	1	[	[	X
ejpam-5971	433	2	x]/⟨x2⟩.	x]/⟨x2⟩.	NUM
ejpam-5971	433	3	iranian	iranian	ADJ
ejpam-5971	433	4	journal	journal	PROPN
ejpam-5971	433	5	of	of	ADP
ejpam-5971	433	6	mathematical	mathematical	ADJ
ejpam-5971	433	7	chemistry	chemistry	NOUN
ejpam-5971	433	8	,	,	PUNCT
ejpam-5971	433	9	15(2):79–90	15(2):79–90	NUM
ejpam-5971	433	10	,	,	PUNCT
ejpam-5971	433	11	2024	2024	NUM
ejpam-5971	433	12	.	.	PUNCT
ejpam-5971	434	1	[	[	X
ejpam-5971	434	2	24	24	NUM
ejpam-5971	434	3	]	]	PUNCT
ejpam-5971	434	4	a	a	DET
ejpam-5971	434	5	f	f	PROPN
ejpam-5971	434	6	musyarrofah	musyarrofah	ADV
ejpam-5971	434	7	,	,	PUNCT
ejpam-5971	434	8	v	v	ADP
ejpam-5971	434	9	h	h	NOUN
ejpam-5971	434	10	krisnawati	krisnawati	NOUN
ejpam-5971	434	11	,	,	PUNCT
ejpam-5971	434	12	and	and	CCONJ
ejpam-5971	434	13	n	n	DET
ejpam-5971	434	14	hidayat	hidayat	PROPN
ejpam-5971	434	15	.	.	PUNCT
ejpam-5971	435	1	zero	zero	NUM
ejpam-5971	435	2	divisor	divisor	NOUN
ejpam-5971	435	3	graph	graph	NOUN
ejpam-5971	435	4	of	of	ADP
ejpam-5971	435	5	quotient	quotient	NOUN
ejpam-5971	435	6	ring	ring	NOUN
ejpam-5971	435	7	.	.	PUNCT
ejpam-5971	436	1	cauchy	cauchy	PROPN
ejpam-5971	436	2	:	:	PUNCT
ejpam-5971	436	3	jurnal	jurnal	ADJ
ejpam-5971	436	4	matematika	matematika	PROPN
ejpam-5971	436	5	murni	murni	PROPN
ejpam-5971	436	6	dan	dan	PROPN
ejpam-5971	436	7	aplikasi	aplikasi	PROPN
ejpam-5971	436	8	,	,	PUNCT
ejpam-5971	436	9	9(2):260–269	9(2):260–269	NUM
ejpam-5971	436	10	,	,	PUNCT
ejpam-5971	436	11	2024	2024	NUM
ejpam-5971	436	12	.	.	PUNCT
ejpam-5971	437	1	[	[	X
ejpam-5971	437	2	25	25	NUM
ejpam-5971	437	3	]	]	X
ejpam-5971	437	4	g	g	PROPN
ejpam-5971	437	5	chartrand	chartrand	NOUN
ejpam-5971	437	6	,	,	PUNCT
ejpam-5971	437	7	l	l	PROPN
ejpam-5971	437	8	lesniak	lesniak	PROPN
ejpam-5971	437	9	,	,	PUNCT
ejpam-5971	437	10	and	and	CCONJ
ejpam-5971	437	11	p	p	PROPN
ejpam-5971	437	12	zhang	zhang	PROPN
ejpam-5971	437	13	.	.	PUNCT
ejpam-5971	437	14	graphs	graph	NOUN
ejpam-5971	437	15	and	and	CCONJ
ejpam-5971	437	16	digraphs	digraph	NOUN
ejpam-5971	437	17	.	.	PUNCT
ejpam-5971	438	1	crc	crc	PROPN
ejpam-5971	438	2	press	press	PROPN
ejpam-5971	438	3	,	,	PUNCT
ejpam-5971	438	4	new	new	PROPN
ejpam-5971	438	5	york	york	PROPN
ejpam-5971	438	6	,	,	PUNCT
ejpam-5971	438	7	sixth	sixth	ADJ
ejpam-5971	438	8	edition	edition	NOUN
ejpam-5971	438	9	,	,	PUNCT
ejpam-5971	438	10	2016	2016	NUM
ejpam-5971	438	11	.	.	PUNCT
ejpam-5971	439	1	[	[	X
ejpam-5971	439	2	26	26	NUM
ejpam-5971	439	3	]	]	X
ejpam-5971	439	4	f	f	PROPN
ejpam-5971	439	5	zhang	zhang	PROPN
ejpam-5971	439	6	.	.	PUNCT
ejpam-5971	440	1	the	the	DET
ejpam-5971	440	2	schur	schur	PROPN
ejpam-5971	440	3	complement	complement	PROPN
ejpam-5971	440	4	and	and	CCONJ
ejpam-5971	440	5	its	its	PRON
ejpam-5971	440	6	applications	application	NOUN
ejpam-5971	440	7	.	.	PUNCT
ejpam-5971	441	1	springer	springer	NOUN
ejpam-5971	441	2	,	,	PUNCT
ejpam-5971	441	3	new	new	PROPN
ejpam-5971	441	4	york	york	PROPN
ejpam-5971	441	5	,	,	PUNCT
ejpam-5971	441	6	2006	2006	NUM
ejpam-5971	441	7	.	.	PUNCT
ejpam-5971	442	1	[	[	X
ejpam-5971	442	2	27	27	NUM
ejpam-5971	442	3	]	]	X
ejpam-5971	442	4	p	p	X
ejpam-5971	442	5	m	m	PROPN
ejpam-5971	442	6	magi	magi	NOUN
ejpam-5971	442	7	,	,	PUNCT
ejpam-5971	442	8	s	s	PART
ejpam-5971	442	9	m	m	NOUN
ejpam-5971	442	10	jose	jose	NOUN
ejpam-5971	442	11	,	,	PUNCT
ejpam-5971	442	12	and	and	CCONJ
ejpam-5971	442	13	a	a	DET
ejpam-5971	442	14	kishore	kishore	NOUN
ejpam-5971	442	15	.	.	PUNCT
ejpam-5971	443	1	adjacency	adjacency	PROPN
ejpam-5971	443	2	matrix	matrix	NOUN
ejpam-5971	443	3	and	and	CCONJ
ejpam-5971	443	4	eigenvalues	eigenvalue	NOUN
ejpam-5971	443	5	of	of	ADP
ejpam-5971	443	6	the	the	DET
ejpam-5971	443	7	zero	zero	NUM
ejpam-5971	443	8	divisor	divisor	NOUN
ejpam-5971	443	9	graph	graph	NOUN
ejpam-5971	443	10	γ(zn	γ(zn	PROPN
ejpam-5971	443	11	)	)	PUNCT
ejpam-5971	443	12	.	.	PUNCT
ejpam-5971	444	1	journal	journal	PROPN
ejpam-5971	444	2	of	of	ADP
ejpam-5971	444	3	mathematics	mathematics	PROPN
ejpam-5971	444	4	and	and	CCONJ
ejpam-5971	444	5	computer	computer	NOUN
ejpam-5971	444	6	science	science	NOUN
ejpam-5971	444	7	,	,	PUNCT
ejpam-5971	444	8	10(4):1285–1297	10(4):1285–1297	NUM
ejpam-5971	444	9	,	,	PUNCT
ejpam-5971	444	10	2020	2020	NUM
ejpam-5971	444	11	.	.	PUNCT
ejpam-5971	445	1	[	[	X
ejpam-5971	445	2	28	28	NUM
ejpam-5971	445	3	]	]	X
ejpam-5971	445	4	p	p	X
ejpam-5971	445	5	biler	biler	NOUN
ejpam-5971	445	6	and	and	CCONJ
ejpam-5971	445	7	a	a	DET
ejpam-5971	445	8	witkowski	witkowski	NOUN
ejpam-5971	445	9	.	.	PUNCT
ejpam-5971	446	1	problems	problem	NOUN
ejpam-5971	446	2	in	in	ADP
ejpam-5971	446	3	mathematical	mathematical	ADJ
ejpam-5971	446	4	analysis	analysis	NOUN
ejpam-5971	446	5	.	.	PUNCT
ejpam-5971	447	1	crc	crc	PROPN
ejpam-5971	447	2	press	press	PROPN
ejpam-5971	447	3	,	,	PUNCT
ejpam-5971	447	4	florida	florida	PROPN
ejpam-5971	447	5	,	,	PUNCT
ejpam-5971	447	6	2017	2017	NUM
ejpam-5971	447	7	.	.	PUNCT