id	sid	tid	token	lemma	pos
ejpam-3587	1	1	european	european	PROPN
ejpam-3587	1	2	journal	journal	PROPN
ejpam-3587	1	3	of	of	ADP
ejpam-3587	1	4	pure	pure	ADJ
ejpam-3587	1	5	and	and	CCONJ
ejpam-3587	1	6	applied	apply	VERB
ejpam-3587	1	7	mathematics	mathematic	NOUN
ejpam-3587	1	8	vol	vol	NOUN
ejpam-3587	1	9	.	.	PROPN
ejpam-3587	2	1	13	13	NUM
ejpam-3587	2	2	,	,	PUNCT
ejpam-3587	2	3	no	no	INTJ
ejpam-3587	2	4	.	.	NOUN
ejpam-3587	2	5	1	1	NUM
ejpam-3587	2	6	,	,	PUNCT
ejpam-3587	2	7	2020	2020	NUM
ejpam-3587	2	8	,	,	PUNCT
ejpam-3587	2	9	84	84	NUM
ejpam-3587	2	10	-	-	SYM
ejpam-3587	2	11	95	95	NUM
ejpam-3587	2	12	issn	issn	PROPN
ejpam-3587	2	13	1307	1307	NUM
ejpam-3587	2	14	-	-	SYM
ejpam-3587	2	15	5543	5543	NUM
ejpam-3587	2	16	–	–	PUNCT
ejpam-3587	2	17	www.ejpam.com	www.ejpam.com	X
ejpam-3587	2	18	published	publish	VERB
ejpam-3587	2	19	by	by	ADP
ejpam-3587	2	20	new	new	PROPN
ejpam-3587	2	21	york	york	PROPN
ejpam-3587	2	22	business	business	PROPN
ejpam-3587	2	23	global	global	PROPN
ejpam-3587	2	24	a	a	DET
ejpam-3587	2	25	systematic	systematic	ADJ
ejpam-3587	2	26	approach	approach	NOUN
ejpam-3587	2	27	to	to	ADP
ejpam-3587	2	28	group	group	NOUN
ejpam-3587	2	29	properties	property	NOUN
ejpam-3587	2	30	using	use	VERB
ejpam-3587	2	31	its	its	PRON
ejpam-3587	2	32	geometric	geometric	ADJ
ejpam-3587	2	33	structure	structure	NOUN
ejpam-3587	2	34	muhammed	muhamme	VERB
ejpam-3587	2	35	bello1,2,∗	bello1,2,∗	PROPN
ejpam-3587	2	36	,	,	PUNCT
ejpam-3587	2	37	nor	nor	CCONJ
ejpam-3587	2	38	muhainiah	muhainiah	PROPN
ejpam-3587	2	39	mohd	mohd	PROPN
ejpam-3587	2	40	ali2	ali2	PROPN
ejpam-3587	2	41	,	,	PUNCT
ejpam-3587	2	42	nurfarah	nurfarah	PROPN
ejpam-3587	2	43	zulkifli2	zulkifli2	PROPN
ejpam-3587	2	44	1	1	NUM
ejpam-3587	2	45	department	department	NOUN
ejpam-3587	2	46	of	of	ADP
ejpam-3587	2	47	mathematics	mathematic	NOUN
ejpam-3587	2	48	and	and	CCONJ
ejpam-3587	2	49	computer	computer	NOUN
ejpam-3587	2	50	science	science	NOUN
ejpam-3587	2	51	,	,	PUNCT
ejpam-3587	2	52	federal	federal	ADJ
ejpam-3587	2	53	university	university	PROPN
ejpam-3587	2	54	of	of	ADP
ejpam-3587	2	55	kashere	kashere	PROPN
ejpam-3587	2	56	,	,	PUNCT
ejpam-3587	2	57	p.m.b	p.m.b	VERB
ejpam-3587	2	58	0182	0182	NUM
ejpam-3587	2	59	gombe	gombe	ADJ
ejpam-3587	2	60	,	,	PUNCT
ejpam-3587	2	61	gombe	gombe	ADJ
ejpam-3587	2	62	state	state	NOUN
ejpam-3587	2	63	nigeria	nigeria	PROPN
ejpam-3587	2	64	,	,	PUNCT
ejpam-3587	2	65	2	2	NUM
ejpam-3587	2	66	department	department	NOUN
ejpam-3587	2	67	of	of	ADP
ejpam-3587	2	68	mathematical	mathematical	ADJ
ejpam-3587	2	69	sciences	science	NOUN
ejpam-3587	2	70	,	,	PUNCT
ejpam-3587	2	71	faculty	faculty	NOUN
ejpam-3587	2	72	of	of	ADP
ejpam-3587	2	73	science	science	PROPN
ejpam-3587	2	74	universiti	universiti	PROPN
ejpam-3587	2	75	teknologi	teknologi	PROPN
ejpam-3587	2	76	malaysia	malaysia	PROPN
ejpam-3587	2	77	81310	81310	NUM
ejpam-3587	2	78	utm	utm	PROPN
ejpam-3587	2	79	johor	johor	PROPN
ejpam-3587	2	80	bahru	bahru	PROPN
ejpam-3587	2	81	,	,	PUNCT
ejpam-3587	2	82	johor	johor	PROPN
ejpam-3587	2	83	abstract	abstract	PROPN
ejpam-3587	2	84	.	.	PUNCT
ejpam-3587	3	1	the	the	DET
ejpam-3587	3	2	algebraic	algebraic	ADJ
ejpam-3587	3	3	properties	property	NOUN
ejpam-3587	3	4	of	of	ADP
ejpam-3587	3	5	a	a	DET
ejpam-3587	3	6	group	group	NOUN
ejpam-3587	3	7	can	can	AUX
ejpam-3587	3	8	be	be	AUX
ejpam-3587	3	9	explored	explore	VERB
ejpam-3587	3	10	through	through	ADP
ejpam-3587	3	11	the	the	DET
ejpam-3587	3	12	relationship	relationship	NOUN
ejpam-3587	3	13	among	among	ADP
ejpam-3587	3	14	its	its	PRON
ejpam-3587	3	15	elements	element	NOUN
ejpam-3587	3	16	.	.	PUNCT
ejpam-3587	4	1	in	in	ADP
ejpam-3587	4	2	this	this	DET
ejpam-3587	4	3	paper	paper	NOUN
ejpam-3587	4	4	,	,	PUNCT
ejpam-3587	4	5	we	we	PRON
ejpam-3587	4	6	define	define	VERB
ejpam-3587	4	7	the	the	DET
ejpam-3587	4	8	graph	graph	NOUN
ejpam-3587	4	9	that	that	PRON
ejpam-3587	4	10	establishes	establish	VERB
ejpam-3587	4	11	a	a	DET
ejpam-3587	4	12	systematic	systematic	ADJ
ejpam-3587	4	13	relationship	relationship	NOUN
ejpam-3587	4	14	among	among	ADP
ejpam-3587	4	15	the	the	DET
ejpam-3587	4	16	group	group	NOUN
ejpam-3587	4	17	elements	element	NOUN
ejpam-3587	4	18	.	.	PUNCT
ejpam-3587	5	1	let	let	VERB
ejpam-3587	5	2	g	g	PRON
ejpam-3587	5	3	be	be	AUX
ejpam-3587	5	4	a	a	DET
ejpam-3587	5	5	finite	finite	ADJ
ejpam-3587	5	6	group	group	NOUN
ejpam-3587	5	7	,	,	PUNCT
ejpam-3587	5	8	the	the	DET
ejpam-3587	5	9	order	order	NOUN
ejpam-3587	5	10	product	product	NOUN
ejpam-3587	5	11	prime	prime	ADJ
ejpam-3587	5	12	graph	graph	NOUN
ejpam-3587	5	13	of	of	ADP
ejpam-3587	5	14	a	a	DET
ejpam-3587	5	15	group	group	NOUN
ejpam-3587	5	16	g	g	NOUN
ejpam-3587	5	17	,	,	PUNCT
ejpam-3587	5	18	is	be	AUX
ejpam-3587	5	19	a	a	DET
ejpam-3587	5	20	graph	graph	NOUN
ejpam-3587	5	21	having	have	VERB
ejpam-3587	5	22	the	the	DET
ejpam-3587	5	23	elements	element	NOUN
ejpam-3587	5	24	of	of	ADP
ejpam-3587	5	25	g	g	PROPN
ejpam-3587	5	26	as	as	ADP
ejpam-3587	5	27	its	its	PRON
ejpam-3587	5	28	vertices	vertex	NOUN
ejpam-3587	5	29	and	and	CCONJ
ejpam-3587	5	30	two	two	NUM
ejpam-3587	5	31	vertices	vertex	NOUN
ejpam-3587	5	32	are	be	AUX
ejpam-3587	5	33	adjacent	adjacent	ADJ
ejpam-3587	5	34	if	if	SCONJ
ejpam-3587	5	35	and	and	CCONJ
ejpam-3587	5	36	only	only	ADV
ejpam-3587	5	37	if	if	SCONJ
ejpam-3587	5	38	the	the	DET
ejpam-3587	5	39	product	product	NOUN
ejpam-3587	5	40	of	of	ADP
ejpam-3587	5	41	their	their	PRON
ejpam-3587	5	42	order	order	NOUN
ejpam-3587	5	43	is	be	AUX
ejpam-3587	5	44	a	a	DET
ejpam-3587	5	45	prime	prime	ADJ
ejpam-3587	5	46	power	power	NOUN
ejpam-3587	5	47	.	.	PUNCT
ejpam-3587	6	1	we	we	PRON
ejpam-3587	6	2	give	give	VERB
ejpam-3587	6	3	the	the	DET
ejpam-3587	6	4	general	general	ADJ
ejpam-3587	6	5	presentation	presentation	NOUN
ejpam-3587	6	6	for	for	ADP
ejpam-3587	6	7	the	the	DET
ejpam-3587	6	8	graph	graph	NOUN
ejpam-3587	6	9	on	on	ADP
ejpam-3587	6	10	dihedral	dihedral	ADJ
ejpam-3587	6	11	groups	group	NOUN
ejpam-3587	6	12	and	and	CCONJ
ejpam-3587	6	13	cyclic	cyclic	ADJ
ejpam-3587	6	14	groups	group	NOUN
ejpam-3587	6	15	and	and	CCONJ
ejpam-3587	6	16	classify	classify	VERB
ejpam-3587	6	17	finite	finite	ADJ
ejpam-3587	6	18	dihedral	dihedral	ADJ
ejpam-3587	6	19	groups	group	NOUN
ejpam-3587	6	20	and	and	CCONJ
ejpam-3587	6	21	cyclic	cyclic	ADJ
ejpam-3587	6	22	groups	group	NOUN
ejpam-3587	6	23	in	in	ADP
ejpam-3587	6	24	terms	term	NOUN
ejpam-3587	6	25	of	of	ADP
ejpam-3587	6	26	the	the	DET
ejpam-3587	6	27	order	order	NOUN
ejpam-3587	6	28	product	product	NOUN
ejpam-3587	6	29	prime	prime	ADJ
ejpam-3587	6	30	graph	graph	NOUN
ejpam-3587	6	31	as	as	ADP
ejpam-3587	6	32	one	one	NUM
ejpam-3587	6	33	of	of	ADP
ejpam-3587	6	34	connected	connected	ADJ
ejpam-3587	6	35	,	,	PUNCT
ejpam-3587	6	36	complete	complete	ADJ
ejpam-3587	6	37	,	,	PUNCT
ejpam-3587	6	38	regular	regular	ADJ
ejpam-3587	6	39	and	and	CCONJ
ejpam-3587	6	40	planar	planar	ADJ
ejpam-3587	6	41	.	.	PUNCT
ejpam-3587	7	1	we	we	PRON
ejpam-3587	7	2	also	also	ADV
ejpam-3587	7	3	obtained	obtain	VERB
ejpam-3587	7	4	some	some	DET
ejpam-3587	7	5	invariants	invariant	NOUN
ejpam-3587	7	6	of	of	ADP
ejpam-3587	7	7	the	the	DET
ejpam-3587	7	8	graph	graph	NOUN
ejpam-3587	7	9	such	such	ADJ
ejpam-3587	7	10	as	as	ADP
ejpam-3587	7	11	its	its	PRON
ejpam-3587	7	12	diameter	diameter	NOUN
ejpam-3587	7	13	,	,	PUNCT
ejpam-3587	7	14	girth	girth	ADV
ejpam-3587	7	15	,	,	PUNCT
ejpam-3587	7	16	independent	independent	ADJ
ejpam-3587	7	17	number	number	NOUN
ejpam-3587	7	18	and	and	CCONJ
ejpam-3587	7	19	the	the	DET
ejpam-3587	7	20	clique	clique	ADJ
ejpam-3587	7	21	number	number	NOUN
ejpam-3587	7	22	.	.	PUNCT
ejpam-3587	8	1	furthermore	furthermore	ADV
ejpam-3587	8	2	,	,	PUNCT
ejpam-3587	8	3	we	we	PRON
ejpam-3587	8	4	used	use	VERB
ejpam-3587	8	5	the	the	DET
ejpam-3587	8	6	vertex	vertex	NOUN
ejpam-3587	8	7	-	-	PUNCT
ejpam-3587	8	8	cut	cut	NOUN
ejpam-3587	8	9	of	of	ADP
ejpam-3587	8	10	the	the	DET
ejpam-3587	8	11	graph	graph	NOUN
ejpam-3587	8	12	in	in	ADP
ejpam-3587	8	13	determining	determine	VERB
ejpam-3587	8	14	the	the	DET
ejpam-3587	8	15	nilpotency	nilpotency	NOUN
ejpam-3587	8	16	status	status	NOUN
ejpam-3587	8	17	of	of	ADP
ejpam-3587	8	18	dihedral	dihedral	ADJ
ejpam-3587	8	19	group	group	NOUN
ejpam-3587	8	20	.	.	PUNCT
ejpam-3587	9	1	the	the	DET
ejpam-3587	9	2	graph	graph	NOUN
ejpam-3587	9	3	on	on	ADP
ejpam-3587	9	4	dihedral	dihedral	ADJ
ejpam-3587	9	5	group	group	NOUN
ejpam-3587	9	6	is	be	AUX
ejpam-3587	9	7	proven	prove	VERB
ejpam-3587	9	8	to	to	PART
ejpam-3587	9	9	be	be	AUX
ejpam-3587	9	10	regular	regular	ADJ
ejpam-3587	9	11	and	and	CCONJ
ejpam-3587	9	12	complete	complete	ADJ
ejpam-3587	9	13	only	only	ADV
ejpam-3587	9	14	if	if	SCONJ
ejpam-3587	9	15	the	the	DET
ejpam-3587	9	16	degree	degree	NOUN
ejpam-3587	9	17	of	of	ADP
ejpam-3587	9	18	the	the	DET
ejpam-3587	9	19	corresponding	corresponding	ADJ
ejpam-3587	9	20	group	group	NOUN
ejpam-3587	9	21	is	be	AUX
ejpam-3587	9	22	even	even	ADV
ejpam-3587	9	23	prime	prime	ADJ
ejpam-3587	9	24	power	power	NOUN
ejpam-3587	9	25	and	and	CCONJ
ejpam-3587	9	26	connected	connect	VERB
ejpam-3587	9	27	for	for	ADP
ejpam-3587	9	28	all	all	DET
ejpam-3587	9	29	prime	prime	ADJ
ejpam-3587	9	30	power	power	NOUN
ejpam-3587	9	31	degree	degree	NOUN
ejpam-3587	9	32	.	.	PUNCT
ejpam-3587	10	1	it	it	PRON
ejpam-3587	10	2	is	be	AUX
ejpam-3587	10	3	also	also	ADV
ejpam-3587	10	4	proven	prove	VERB
ejpam-3587	10	5	on	on	ADP
ejpam-3587	10	6	cyclic	cyclic	ADJ
ejpam-3587	10	7	group	group	NOUN
ejpam-3587	10	8	to	to	PART
ejpam-3587	10	9	be	be	AUX
ejpam-3587	10	10	both	both	ADV
ejpam-3587	10	11	regular	regular	ADJ
ejpam-3587	10	12	,	,	PUNCT
ejpam-3587	10	13	complete	complete	ADJ
ejpam-3587	10	14	and	and	CCONJ
ejpam-3587	10	15	connected	connect	VERB
ejpam-3587	10	16	if	if	SCONJ
ejpam-3587	10	17	the	the	DET
ejpam-3587	10	18	group	group	NOUN
ejpam-3587	10	19	has	have	VERB
ejpam-3587	10	20	prime	prime	ADJ
ejpam-3587	10	21	power	power	NOUN
ejpam-3587	10	22	order	order	NOUN
ejpam-3587	10	23	.	.	PUNCT
ejpam-3587	11	1	additionally	additionally	ADV
ejpam-3587	11	2	,	,	PUNCT
ejpam-3587	11	3	the	the	DET
ejpam-3587	11	4	result	result	NOUN
ejpam-3587	11	5	turn	turn	VERB
ejpam-3587	11	6	out	out	ADP
ejpam-3587	11	7	to	to	PART
ejpam-3587	11	8	show	show	VERB
ejpam-3587	11	9	that	that	SCONJ
ejpam-3587	11	10	any	any	DET
ejpam-3587	11	11	dihedral	dihedral	ADJ
ejpam-3587	11	12	group	group	NOUN
ejpam-3587	11	13	whose	whose	DET
ejpam-3587	11	14	order	order	NOUN
ejpam-3587	11	15	product	product	NOUN
ejpam-3587	11	16	prime	prime	ADJ
ejpam-3587	11	17	graph	graph	NOUN
ejpam-3587	11	18	’s	’s	PART
ejpam-3587	11	19	vertex	vertex	NOUN
ejpam-3587	11	20	-	-	PUNCT
ejpam-3587	11	21	cut	cut	NOUN
ejpam-3587	11	22	is	be	AUX
ejpam-3587	11	23	greater	great	ADJ
ejpam-3587	11	24	than	than	ADP
ejpam-3587	11	25	one	one	NUM
ejpam-3587	11	26	is	be	AUX
ejpam-3587	11	27	nilpotent	nilpotent	ADJ
ejpam-3587	11	28	.	.	PUNCT
ejpam-3587	12	1	we	we	PRON
ejpam-3587	12	2	also	also	ADV
ejpam-3587	12	3	show	show	VERB
ejpam-3587	12	4	that	that	SCONJ
ejpam-3587	12	5	the	the	DET
ejpam-3587	12	6	order	order	NOUN
ejpam-3587	12	7	product	product	NOUN
ejpam-3587	12	8	prime	prime	ADJ
ejpam-3587	12	9	graph	graph	NOUN
ejpam-3587	12	10	is	be	AUX
ejpam-3587	12	11	planar	planar	ADJ
ejpam-3587	12	12	only	only	ADV
ejpam-3587	12	13	when	when	SCONJ
ejpam-3587	12	14	the	the	DET
ejpam-3587	12	15	degree	degree	NOUN
ejpam-3587	12	16	of	of	ADP
ejpam-3587	12	17	the	the	DET
ejpam-3587	12	18	group	group	NOUN
ejpam-3587	12	19	is	be	AUX
ejpam-3587	12	20	three	three	NUM
ejpam-3587	12	21	for	for	ADP
ejpam-3587	12	22	dihedral	dihedral	ADJ
ejpam-3587	12	23	group	group	NOUN
ejpam-3587	12	24	and	and	CCONJ
ejpam-3587	12	25	less	less	ADJ
ejpam-3587	12	26	than	than	ADP
ejpam-3587	12	27	five	five	NUM
ejpam-3587	12	28	for	for	ADP
ejpam-3587	12	29	cyclic	cyclic	ADJ
ejpam-3587	12	30	group	group	NOUN
ejpam-3587	12	31	.	.	PUNCT
ejpam-3587	13	1	our	our	PRON
ejpam-3587	13	2	final	final	ADJ
ejpam-3587	13	3	result	result	NOUN
ejpam-3587	13	4	shows	show	VERB
ejpam-3587	13	5	that	that	SCONJ
ejpam-3587	13	6	the	the	DET
ejpam-3587	13	7	order	order	NOUN
ejpam-3587	13	8	product	product	NOUN
ejpam-3587	13	9	prime	prime	ADJ
ejpam-3587	13	10	graphs	graph	NOUN
ejpam-3587	13	11	of	of	ADP
ejpam-3587	13	12	any	any	DET
ejpam-3587	13	13	two	two	NUM
ejpam-3587	13	14	isomorphic	isomorphic	ADJ
ejpam-3587	13	15	groups	group	NOUN
ejpam-3587	13	16	are	be	AUX
ejpam-3587	13	17	isomophic	isomophic	ADJ
ejpam-3587	13	18	.	.	PUNCT
ejpam-3587	14	1	2020	2020	NUM
ejpam-3587	14	2	mathematics	mathematic	NOUN
ejpam-3587	14	3	subject	subject	NOUN
ejpam-3587	14	4	classifications	classification	NOUN
ejpam-3587	14	5	:	:	PUNCT
ejpam-3587	14	6	05c25	05c25	NUM
ejpam-3587	14	7	,	,	PUNCT
ejpam-3587	14	8	20f65	20f65	NUM
ejpam-3587	14	9	key	key	ADJ
ejpam-3587	14	10	words	word	NOUN
ejpam-3587	14	11	and	and	CCONJ
ejpam-3587	14	12	phrases	phrase	NOUN
ejpam-3587	14	13	:	:	PUNCT
ejpam-3587	14	14	order	order	NOUN
ejpam-3587	14	15	product	product	NOUN
ejpam-3587	14	16	prime	prime	ADJ
ejpam-3587	14	17	graph	graph	NOUN
ejpam-3587	14	18	,	,	PUNCT
ejpam-3587	14	19	vertex	vertex	NOUN
ejpam-3587	14	20	adjacency	adjacency	NOUN
ejpam-3587	14	21	,	,	PUNCT
ejpam-3587	14	22	graph	graph	NOUN
ejpam-3587	14	23	invariant	invariant	ADJ
ejpam-3587	14	24	,	,	PUNCT
ejpam-3587	14	25	nilpotency	nilpotency	NOUN
ejpam-3587	14	26	of	of	ADP
ejpam-3587	14	27	a	a	DET
ejpam-3587	14	28	group	group	NOUN
ejpam-3587	14	29	1	1	NUM
ejpam-3587	14	30	.	.	PUNCT
ejpam-3587	15	1	introduction	introduction	NOUN
ejpam-3587	15	2	various	various	ADJ
ejpam-3587	15	3	techniques	technique	NOUN
ejpam-3587	15	4	have	have	AUX
ejpam-3587	15	5	been	be	AUX
ejpam-3587	15	6	used	use	VERB
ejpam-3587	15	7	by	by	ADP
ejpam-3587	15	8	researchers	researcher	NOUN
ejpam-3587	15	9	in	in	ADP
ejpam-3587	15	10	investigating	investigate	VERB
ejpam-3587	15	11	the	the	DET
ejpam-3587	15	12	properties	property	NOUN
ejpam-3587	15	13	of	of	ADP
ejpam-3587	15	14	a	a	DET
ejpam-3587	15	15	group	group	NOUN
ejpam-3587	15	16	as	as	ADV
ejpam-3587	15	17	well	well	ADV
ejpam-3587	15	18	as	as	ADP
ejpam-3587	15	19	classifying	classify	VERB
ejpam-3587	15	20	it	it	PRON
ejpam-3587	15	21	according	accord	VERB
ejpam-3587	15	22	to	to	ADP
ejpam-3587	15	23	its	its	PRON
ejpam-3587	15	24	properties	property	NOUN
ejpam-3587	15	25	,	,	PUNCT
ejpam-3587	15	26	which	which	PRON
ejpam-3587	15	27	happen	happen	VERB
ejpam-3587	15	28	to	to	PART
ejpam-3587	15	29	be	be	AUX
ejpam-3587	15	30	one	one	NUM
ejpam-3587	15	31	of	of	ADP
ejpam-3587	15	32	the	the	DET
ejpam-3587	15	33	∗corresponding	∗corresponde	VERB
ejpam-3587	15	34	author	author	NOUN
ejpam-3587	15	35	.	.	PUNCT
ejpam-3587	16	1	doi	doi	NOUN
ejpam-3587	16	2	:	:	PUNCT
ejpam-3587	16	3	https://doi.org/10.29020/nybg.ejpam.v13i1.3587	https://doi.org/10.29020/nybg.ejpam.v13i1.3587	ADJ
ejpam-3587	16	4	email	email	NOUN
ejpam-3587	16	5	addresses	address	NOUN
ejpam-3587	16	6	:	:	PUNCT
ejpam-3587	16	7	bello.m@graduate.utm.my	bello.m@graduate.utm.my	PROPN
ejpam-3587	16	8	(	(	PUNCT
ejpam-3587	16	9	m.	m.	PROPN
ejpam-3587	16	10	bello	bello	PROPN
ejpam-3587	16	11	)	)	PUNCT
ejpam-3587	16	12	,	,	PUNCT
ejpam-3587	16	13	normuhainiah@utm.my	normuhainiah@utm.my	PRON
ejpam-3587	16	14	(	(	PUNCT
ejpam-3587	16	15	n.	n.	PROPN
ejpam-3587	16	16	m.	m.	PROPN
ejpam-3587	16	17	m.	m.	PROPN
ejpam-3587	16	18	ali	ali	PROPN
ejpam-3587	16	19	)	)	PUNCT
ejpam-3587	16	20	,	,	PUNCT
ejpam-3587	16	21	nurfarah3@graduate.utm.my	nurfarah3@graduate.utm.my	PROPN
ejpam-3587	16	22	(	(	PUNCT
ejpam-3587	16	23	n.	n.	PROPN
ejpam-3587	16	24	zulkifli	zulkifli	PROPN
ejpam-3587	16	25	)	)	PUNCT
ejpam-3587	16	26	http://www.ejpam.com	http://www.ejpam.com	X
ejpam-3587	17	1	84	84	NUM
ejpam-3587	18	1	c	c	X
ejpam-3587	18	2	©	©	NOUN
ejpam-3587	18	3	2020	2020	NUM
ejpam-3587	18	4	ejpam	ejpam	VERB
ejpam-3587	18	5	all	all	DET
ejpam-3587	18	6	rights	right	NOUN
ejpam-3587	18	7	reserved	reserve	VERB
ejpam-3587	18	8	.	.	PUNCT
ejpam-3587	19	1	m.	m.	PROPN
ejpam-3587	19	2	bello	bello	PROPN
ejpam-3587	19	3	,	,	PUNCT
ejpam-3587	19	4	n.	n.	PROPN
ejpam-3587	19	5	m.	m.	NOUN
ejpam-3587	19	6	mohd	mohd	PROPN
ejpam-3587	19	7	ali	ali	PROPN
ejpam-3587	19	8	,	,	PUNCT
ejpam-3587	19	9	n.	n.	PROPN
ejpam-3587	19	10	zulkifli	zulkifli	PROPN
ejpam-3587	19	11	/	/	SYM
ejpam-3587	19	12	eur	eur	PROPN
ejpam-3587	19	13	.	.	PUNCT
ejpam-3587	20	1	j.	j.	PROPN
ejpam-3587	20	2	pure	pure	PROPN
ejpam-3587	20	3	appl	appl	PROPN
ejpam-3587	20	4	.	.	PROPN
ejpam-3587	20	5	math	math	PROPN
ejpam-3587	20	6	,	,	PUNCT
ejpam-3587	20	7	13	13	NUM
ejpam-3587	20	8	(	(	PUNCT
ejpam-3587	20	9	1	1	NUM
ejpam-3587	20	10	)	)	PUNCT
ejpam-3587	20	11	(	(	PUNCT
ejpam-3587	20	12	2020	2020	NUM
ejpam-3587	20	13	)	)	PUNCT
ejpam-3587	20	14	,	,	PUNCT
ejpam-3587	20	15	84	84	NUM
ejpam-3587	20	16	-	-	SYM
ejpam-3587	20	17	95	95	NUM
ejpam-3587	20	18	85	85	NUM
ejpam-3587	20	19	great	great	ADJ
ejpam-3587	20	20	achievements	achievement	NOUN
ejpam-3587	20	21	of	of	ADP
ejpam-3587	20	22	modern	modern	ADJ
ejpam-3587	20	23	mathematics	mathematic	NOUN
ejpam-3587	20	24	.	.	PUNCT
ejpam-3587	21	1	one	one	NUM
ejpam-3587	21	2	of	of	ADP
ejpam-3587	21	3	the	the	DET
ejpam-3587	21	4	techniques	technique	NOUN
ejpam-3587	21	5	found	find	VERB
ejpam-3587	21	6	to	to	PART
ejpam-3587	21	7	be	be	AUX
ejpam-3587	21	8	useful	useful	ADJ
ejpam-3587	21	9	is	be	AUX
ejpam-3587	21	10	by	by	ADP
ejpam-3587	21	11	defining	define	VERB
ejpam-3587	21	12	graph	graph	NOUN
ejpam-3587	21	13	to	to	ADP
ejpam-3587	21	14	the	the	DET
ejpam-3587	21	15	groups	group	NOUN
ejpam-3587	21	16	and	and	CCONJ
ejpam-3587	21	17	investigate	investigate	VERB
ejpam-3587	21	18	its	its	PRON
ejpam-3587	21	19	properties	property	NOUN
ejpam-3587	21	20	using	use	VERB
ejpam-3587	21	21	the	the	DET
ejpam-3587	21	22	corresponding	corresponding	ADJ
ejpam-3587	21	23	geometric	geometric	ADJ
ejpam-3587	21	24	structure	structure	NOUN
ejpam-3587	21	25	.	.	PUNCT
ejpam-3587	22	1	according	accord	VERB
ejpam-3587	22	2	to	to	ADP
ejpam-3587	22	3	selva	selva	PROPN
ejpam-3587	22	4	and	and	CCONJ
ejpam-3587	22	5	subajini	subajini	NOUN
ejpam-3587	22	6	[	[	X
ejpam-3587	22	7	8	8	NUM
ejpam-3587	22	8	]	]	PUNCT
ejpam-3587	22	9	in	in	ADP
ejpam-3587	22	10	order	order	NOUN
ejpam-3587	22	11	to	to	PART
ejpam-3587	22	12	get	get	VERB
ejpam-3587	22	13	a	a	DET
ejpam-3587	22	14	better	well	ADJ
ejpam-3587	22	15	understanding	understanding	NOUN
ejpam-3587	22	16	of	of	ADP
ejpam-3587	22	17	a	a	DET
ejpam-3587	22	18	given	give	VERB
ejpam-3587	22	19	algebraic	algebraic	ADJ
ejpam-3587	22	20	structure	structure	NOUN
ejpam-3587	22	21	a	a	PRON
ejpam-3587	22	22	,	,	PUNCT
ejpam-3587	22	23	one	one	PRON
ejpam-3587	22	24	can	can	AUX
ejpam-3587	22	25	associate	associate	VERB
ejpam-3587	22	26	to	to	ADP
ejpam-3587	22	27	it	it	PRON
ejpam-3587	22	28	a	a	DET
ejpam-3587	22	29	graph	graph	NOUN
ejpam-3587	22	30	γ	γ	PRON
ejpam-3587	22	31	and	and	CCONJ
ejpam-3587	22	32	study	study	VERB
ejpam-3587	22	33	the	the	DET
ejpam-3587	22	34	interplay	interplay	NOUN
ejpam-3587	22	35	of	of	ADP
ejpam-3587	22	36	the	the	DET
ejpam-3587	22	37	algebraic	algebraic	ADJ
ejpam-3587	22	38	properties	property	NOUN
ejpam-3587	22	39	of	of	ADP
ejpam-3587	22	40	a	a	PRON
ejpam-3587	22	41	and	and	CCONJ
ejpam-3587	22	42	the	the	DET
ejpam-3587	22	43	combinatorial	combinatorial	ADJ
ejpam-3587	22	44	properties	property	NOUN
ejpam-3587	22	45	of	of	ADP
ejpam-3587	22	46	γ	γ	PROPN
ejpam-3587	22	47	.	.	PUNCT
ejpam-3587	23	1	this	this	DET
ejpam-3587	23	2	study	study	NOUN
ejpam-3587	23	3	gained	gain	VERB
ejpam-3587	23	4	the	the	DET
ejpam-3587	23	5	attention	attention	NOUN
ejpam-3587	23	6	of	of	ADP
ejpam-3587	23	7	many	many	ADJ
ejpam-3587	23	8	researchers	researcher	NOUN
ejpam-3587	23	9	,	,	PUNCT
ejpam-3587	23	10	for	for	ADP
ejpam-3587	23	11	instance	instance	NOUN
ejpam-3587	23	12	,	,	PUNCT
ejpam-3587	23	13	cayley	cayley	ADJ
ejpam-3587	23	14	graph	graph	NOUN
ejpam-3587	23	15	was	be	AUX
ejpam-3587	23	16	defined	define	VERB
ejpam-3587	23	17	by	by	ADP
ejpam-3587	23	18	arthur	arthur	NOUN
ejpam-3587	23	19	in	in	ADP
ejpam-3587	23	20	[	[	X
ejpam-3587	23	21	2	2	NUM
ejpam-3587	23	22	]	]	PUNCT
ejpam-3587	23	23	and	and	CCONJ
ejpam-3587	23	24	this	this	DET
ejpam-3587	23	25	graph	graph	NOUN
ejpam-3587	23	26	has	have	AUX
ejpam-3587	23	27	been	be	AUX
ejpam-3587	23	28	used	use	VERB
ejpam-3587	23	29	by	by	ADP
ejpam-3587	23	30	kelarev	kelarev	PROPN
ejpam-3587	23	31	et	et	PROPN
ejpam-3587	23	32	al	al	PROPN
ejpam-3587	23	33	.	.	PUNCT
ejpam-3587	24	1	in	in	ADP
ejpam-3587	24	2	[	[	X
ejpam-3587	24	3	7	7	NUM
ejpam-3587	24	4	]	]	PUNCT
ejpam-3587	24	5	to	to	PART
ejpam-3587	24	6	classify	classify	VERB
ejpam-3587	24	7	data	datum	NOUN
ejpam-3587	24	8	which	which	PRON
ejpam-3587	24	9	can	can	AUX
ejpam-3587	24	10	be	be	AUX
ejpam-3587	24	11	recorded	record	VERB
ejpam-3587	24	12	as	as	ADP
ejpam-3587	24	13	set	set	NOUN
ejpam-3587	24	14	of	of	ADP
ejpam-3587	24	15	strings	string	NOUN
ejpam-3587	24	16	or	or	CCONJ
ejpam-3587	24	17	sequences	sequence	NOUN
ejpam-3587	24	18	of	of	ADP
ejpam-3587	24	19	letters	letter	NOUN
ejpam-3587	24	20	over	over	ADP
ejpam-3587	24	21	a	a	DET
ejpam-3587	24	22	finite	finite	ADJ
ejpam-3587	24	23	alphabet	alphabet	NOUN
ejpam-3587	24	24	.	.	PUNCT
ejpam-3587	25	1	ganesan	ganesan	PROPN
ejpam-3587	26	1	[	[	X
ejpam-3587	26	2	4	4	NUM
ejpam-3587	26	3	]	]	PUNCT
ejpam-3587	26	4	used	use	VERB
ejpam-3587	26	5	this	this	DET
ejpam-3587	26	6	graph	graph	NOUN
ejpam-3587	26	7	to	to	PART
ejpam-3587	26	8	obtain	obtain	VERB
ejpam-3587	26	9	the	the	DET
ejpam-3587	26	10	structural	structural	ADJ
ejpam-3587	26	11	description	description	NOUN
ejpam-3587	26	12	of	of	ADP
ejpam-3587	26	13	the	the	DET
ejpam-3587	26	14	automorphism	automorphism	NOUN
ejpam-3587	26	15	group	group	NOUN
ejpam-3587	26	16	of	of	ADP
ejpam-3587	26	17	the	the	DET
ejpam-3587	26	18	modified	modify	VERB
ejpam-3587	26	19	bubble	bubble	NOUN
ejpam-3587	26	20	-	-	PUNCT
ejpam-3587	26	21	sort	sort	NOUN
ejpam-3587	26	22	graph	graph	NOUN
ejpam-3587	26	23	.	.	PUNCT
ejpam-3587	27	1	several	several	ADJ
ejpam-3587	27	2	researches	research	NOUN
ejpam-3587	27	3	has	have	AUX
ejpam-3587	27	4	also	also	ADV
ejpam-3587	27	5	been	be	AUX
ejpam-3587	27	6	conducted	conduct	VERB
ejpam-3587	27	7	on	on	ADP
ejpam-3587	27	8	the	the	DET
ejpam-3587	27	9	commuting	commuting	NOUN
ejpam-3587	27	10	graph	graph	NOUN
ejpam-3587	27	11	and	and	CCONJ
ejpam-3587	27	12	non	non	ADJ
ejpam-3587	27	13	-	-	ADJ
ejpam-3587	27	14	commuting	commuting	ADJ
ejpam-3587	27	15	graph	graph	NOUN
ejpam-3587	27	16	,	,	PUNCT
ejpam-3587	27	17	for	for	ADP
ejpam-3587	27	18	instance	instance	NOUN
ejpam-3587	27	19	,	,	PUNCT
ejpam-3587	27	20	sharafdini	sharafdini	ADJ
ejpam-3587	27	21	and	and	CCONJ
ejpam-3587	27	22	darbandi	darbandi	NOUN
ejpam-3587	27	23	[	[	X
ejpam-3587	27	24	10	10	NUM
ejpam-3587	27	25	]	]	PUNCT
ejpam-3587	27	26	computed	compute	VERB
ejpam-3587	27	27	the	the	DET
ejpam-3587	27	28	energy	energy	NOUN
ejpam-3587	27	29	of	of	ADP
ejpam-3587	27	30	commuting	commuting	NOUN
ejpam-3587	27	31	graph	graph	NOUN
ejpam-3587	27	32	for	for	ADP
ejpam-3587	27	33	groups	group	NOUN
ejpam-3587	27	34	whose	whose	DET
ejpam-3587	27	35	centralizers	centralizer	NOUN
ejpam-3587	27	36	are	be	AUX
ejpam-3587	27	37	abelian	abelian	ADJ
ejpam-3587	27	38	,	,	PUNCT
ejpam-3587	27	39	and	and	CCONJ
ejpam-3587	27	40	in	in	ADP
ejpam-3587	27	41	[	[	X
ejpam-3587	27	42	11	11	NUM
ejpam-3587	27	43	]	]	PUNCT
ejpam-3587	27	44	vahidi	vahidi	NOUN
ejpam-3587	27	45	and	and	CCONJ
ejpam-3587	27	46	talebi	talebi	PROPN
ejpam-3587	27	47	obtained	obtain	VERB
ejpam-3587	27	48	some	some	DET
ejpam-3587	27	49	invariants	invariant	NOUN
ejpam-3587	27	50	of	of	ADP
ejpam-3587	27	51	non	non	ADJ
ejpam-3587	27	52	-	-	ADJ
ejpam-3587	27	53	commuting	commuting	ADJ
ejpam-3587	27	54	graphs	graph	NOUN
ejpam-3587	27	55	on	on	ADP
ejpam-3587	27	56	dihedral	dihedral	ADJ
ejpam-3587	27	57	groups	group	NOUN
ejpam-3587	27	58	and	and	CCONJ
ejpam-3587	27	59	generalized	generalized	ADJ
ejpam-3587	27	60	quaternion	quaternion	NOUN
ejpam-3587	27	61	groups	group	NOUN
ejpam-3587	27	62	,	,	PUNCT
ejpam-3587	27	63	which	which	PRON
ejpam-3587	27	64	include	include	VERB
ejpam-3587	27	65	its	its	PRON
ejpam-3587	27	66	independent	independent	ADJ
ejpam-3587	27	67	number	number	NOUN
ejpam-3587	27	68	,	,	PUNCT
ejpam-3587	27	69	clique	clique	ADJ
ejpam-3587	27	70	number	number	NOUN
ejpam-3587	27	71	and	and	CCONJ
ejpam-3587	27	72	minimum	minimum	ADJ
ejpam-3587	27	73	size	size	NOUN
ejpam-3587	27	74	of	of	ADP
ejpam-3587	27	75	the	the	DET
ejpam-3587	27	76	vertex	vertex	NOUN
ejpam-3587	27	77	cover	cover	NOUN
ejpam-3587	27	78	of	of	ADP
ejpam-3587	27	79	the	the	DET
ejpam-3587	27	80	graph	graph	NOUN
ejpam-3587	27	81	,	,	PUNCT
ejpam-3587	27	82	in	in	ADP
ejpam-3587	27	83	their	their	PRON
ejpam-3587	27	84	paper	paper	NOUN
ejpam-3587	27	85	,	,	PUNCT
ejpam-3587	27	86	they	they	PRON
ejpam-3587	27	87	did	do	AUX
ejpam-3587	27	88	not	not	PART
ejpam-3587	27	89	find	find	VERB
ejpam-3587	27	90	the	the	DET
ejpam-3587	27	91	chromatic	chromatic	ADJ
ejpam-3587	27	92	number	number	NOUN
ejpam-3587	27	93	of	of	ADP
ejpam-3587	27	94	this	this	DET
ejpam-3587	27	95	graph	graph	NOUN
ejpam-3587	27	96	,	,	PUNCT
ejpam-3587	27	97	which	which	PRON
ejpam-3587	27	98	has	have	AUX
ejpam-3587	27	99	been	be	AUX
ejpam-3587	27	100	obtained	obtain	VERB
ejpam-3587	27	101	a	a	DET
ejpam-3587	27	102	year	year	NOUN
ejpam-3587	27	103	later	later	ADV
ejpam-3587	27	104	by	by	ADP
ejpam-3587	27	105	tamizh	tamizh	PROPN
ejpam-3587	27	106	et	et	PROPN
ejpam-3587	27	107	al	al	PROPN
ejpam-3587	27	108	.	.	PUNCT
ejpam-3587	28	1	[	[	X
ejpam-3587	28	2	9	9	NUM
ejpam-3587	28	3	]	]	PUNCT
ejpam-3587	28	4	.	.	PUNCT
ejpam-3587	29	1	akbari	akbari	PROPN
ejpam-3587	29	2	and	and	CCONJ
ejpam-3587	29	3	reza	reza	PROPN
ejpam-3587	30	1	[	[	X
ejpam-3587	30	2	3	3	X
ejpam-3587	30	3	]	]	PUNCT
ejpam-3587	30	4	used	use	VERB
ejpam-3587	30	5	the	the	DET
ejpam-3587	30	6	non	non	ADJ
ejpam-3587	30	7	-	-	ADJ
ejpam-3587	30	8	commuting	commuting	ADJ
ejpam-3587	30	9	graph	graph	NOUN
ejpam-3587	30	10	to	to	PART
ejpam-3587	30	11	determined	determined	VERB
ejpam-3587	30	12	up	up	ADP
ejpam-3587	30	13	to	to	ADP
ejpam-3587	30	14	isomophism	isomophism	NOUN
ejpam-3587	30	15	the	the	DET
ejpam-3587	30	16	structure	structure	NOUN
ejpam-3587	30	17	of	of	ADP
ejpam-3587	30	18	finite	finite	ADJ
ejpam-3587	30	19	non	non	ADJ
ejpam-3587	30	20	-	-	ADJ
ejpam-3587	30	21	abelian	abelian	ADJ
ejpam-3587	30	22	groups	group	NOUN
ejpam-3587	30	23	in	in	ADP
ejpam-3587	30	24	which	which	PRON
ejpam-3587	30	25	the	the	DET
ejpam-3587	30	26	vertex	vertex	NOUN
ejpam-3587	30	27	of	of	ADP
ejpam-3587	30	28	the	the	DET
ejpam-3587	30	29	graph	graph	NOUN
ejpam-3587	30	30	can	can	AUX
ejpam-3587	30	31	be	be	AUX
ejpam-3587	30	32	partitioned	partition	VERB
ejpam-3587	30	33	into	into	ADP
ejpam-3587	30	34	two	two	NUM
ejpam-3587	30	35	sets	set	NOUN
ejpam-3587	30	36	such	such	ADJ
ejpam-3587	30	37	that	that	SCONJ
ejpam-3587	30	38	the	the	DET
ejpam-3587	30	39	induced	induced	ADJ
ejpam-3587	30	40	subgraph	subgraph	NOUN
ejpam-3587	30	41	on	on	ADP
ejpam-3587	30	42	one	one	NUM
ejpam-3587	30	43	of	of	ADP
ejpam-3587	30	44	them	they	PRON
ejpam-3587	30	45	is	be	AUX
ejpam-3587	30	46	a	a	DET
ejpam-3587	30	47	complete	complete	ADJ
ejpam-3587	30	48	graph	graph	NOUN
ejpam-3587	30	49	and	and	CCONJ
ejpam-3587	30	50	the	the	DET
ejpam-3587	30	51	induced	induced	ADJ
ejpam-3587	30	52	subgraph	subgraph	NOUN
ejpam-3587	30	53	on	on	ADP
ejpam-3587	30	54	the	the	DET
ejpam-3587	30	55	other	other	ADJ
ejpam-3587	30	56	is	be	AUX
ejpam-3587	30	57	an	an	DET
ejpam-3587	30	58	independent	independent	ADJ
ejpam-3587	30	59	set	set	NOUN
ejpam-3587	30	60	.	.	PUNCT
ejpam-3587	31	1	ghobani	ghobani	PROPN
ejpam-3587	31	2	and	and	CCONJ
ejpam-3587	31	3	alkhansari	alkhansari	ADJ
ejpam-3587	32	1	[	[	X
ejpam-3587	32	2	5	5	NUM
ejpam-3587	32	3	]	]	PUNCT
ejpam-3587	32	4	used	use	VERB
ejpam-3587	32	5	the	the	DET
ejpam-3587	32	6	geometric	geometric	ADJ
ejpam-3587	32	7	properties	property	NOUN
ejpam-3587	32	8	of	of	ADP
ejpam-3587	32	9	a	a	DET
ejpam-3587	32	10	group	group	NOUN
ejpam-3587	32	11	to	to	PART
ejpam-3587	32	12	prove	prove	VERB
ejpam-3587	32	13	that	that	SCONJ
ejpam-3587	32	14	for	for	ADP
ejpam-3587	32	15	a	a	DET
ejpam-3587	32	16	group	group	NOUN
ejpam-3587	32	17	g	g	NOUN
ejpam-3587	32	18	,	,	PUNCT
ejpam-3587	32	19	g	g	NOUN
ejpam-3587	32	20	/	/	SYM
ejpam-3587	32	21	z(g	z(g	NOUN
ejpam-3587	32	22	)	)	PUNCT
ejpam-3587	32	23	∼=	∼=	PROPN
ejpam-3587	32	24	zn	zn	NOUN
ejpam-3587	32	25	×	×	NOUN
ejpam-3587	32	26	zn	zn	X
ejpam-3587	32	27	if	if	SCONJ
ejpam-3587	32	28	and	and	CCONJ
ejpam-3587	32	29	only	only	ADV
ejpam-3587	32	30	if	if	SCONJ
ejpam-3587	32	31	the	the	DET
ejpam-3587	32	32	non	non	ADJ
ejpam-3587	32	33	-	-	ADJ
ejpam-3587	32	34	commuting	commuting	ADJ
ejpam-3587	32	35	graph	graph	NOUN
ejpam-3587	32	36	γ(g	γ(g	PROPN
ejpam-3587	32	37	)	)	PUNCT
ejpam-3587	32	38	is	be	AUX
ejpam-3587	32	39	a	a	DET
ejpam-3587	32	40	regular	regular	ADJ
ejpam-3587	32	41	(	(	PUNCT
ejpam-3587	32	42	p+	p+	NOUN
ejpam-3587	32	43	1)-partite	1)-partite	NUM
ejpam-3587	32	44	graph	graph	NOUN
ejpam-3587	32	45	and	and	CCONJ
ejpam-3587	32	46	consider	consider	VERB
ejpam-3587	32	47	the	the	DET
ejpam-3587	32	48	isomorphism	isomorphism	NOUN
ejpam-3587	32	49	of	of	ADP
ejpam-3587	32	50	the	the	DET
ejpam-3587	32	51	non	non	ADJ
ejpam-3587	32	52	-	-	ADJ
ejpam-3587	32	53	commuting	commuting	ADJ
ejpam-3587	32	54	graph	graph	NOUN
ejpam-3587	32	55	with	with	ADP
ejpam-3587	32	56	some	some	DET
ejpam-3587	32	57	special	special	ADJ
ejpam-3587	32	58	graphs	graph	NOUN
ejpam-3587	32	59	.	.	PUNCT
ejpam-3587	33	1	the	the	DET
ejpam-3587	33	2	generalization	generalization	NOUN
ejpam-3587	33	3	of	of	ADP
ejpam-3587	33	4	non	non	ADJ
ejpam-3587	33	5	-	-	ADJ
ejpam-3587	33	6	commuting	commuting	ADJ
ejpam-3587	33	7	graph	graph	NOUN
ejpam-3587	33	8	of	of	ADP
ejpam-3587	33	9	a	a	DET
ejpam-3587	33	10	group	group	NOUN
ejpam-3587	33	11	was	be	AUX
ejpam-3587	33	12	given	give	VERB
ejpam-3587	33	13	by	by	ADP
ejpam-3587	33	14	kakeri	kakeri	PROPN
ejpam-3587	33	15	et	et	PROPN
ejpam-3587	33	16	al	al	PROPN
ejpam-3587	33	17	.	.	PUNCT
ejpam-3587	34	1	in	in	ADP
ejpam-3587	34	2	[	[	X
ejpam-3587	34	3	6	6	NUM
ejpam-3587	34	4	]	]	PUNCT
ejpam-3587	34	5	,	,	PUNCT
ejpam-3587	34	6	where	where	SCONJ
ejpam-3587	34	7	they	they	PRON
ejpam-3587	34	8	investigated	investigate	VERB
ejpam-3587	34	9	the	the	DET
ejpam-3587	34	10	connectivity	connectivity	NOUN
ejpam-3587	34	11	,	,	PUNCT
ejpam-3587	34	12	regularity	regularity	NOUN
ejpam-3587	34	13	and	and	CCONJ
ejpam-3587	34	14	planarity	planarity	NOUN
ejpam-3587	34	15	of	of	ADP
ejpam-3587	34	16	the	the	DET
ejpam-3587	34	17	graph	graph	NOUN
ejpam-3587	34	18	and	and	CCONJ
ejpam-3587	34	19	concurrently	concurrently	ADV
ejpam-3587	34	20	,	,	PUNCT
ejpam-3587	34	21	give	give	VERB
ejpam-3587	34	22	the	the	DET
ejpam-3587	34	23	numerical	numerical	ADJ
ejpam-3587	34	24	invariants	invariant	NOUN
ejpam-3587	34	25	of	of	ADP
ejpam-3587	34	26	the	the	DET
ejpam-3587	34	27	graph	graph	NOUN
ejpam-3587	34	28	which	which	PRON
ejpam-3587	34	29	happen	happen	VERB
ejpam-3587	34	30	to	to	PART
ejpam-3587	34	31	be	be	AUX
ejpam-3587	34	32	the	the	DET
ejpam-3587	34	33	improvement	improvement	NOUN
ejpam-3587	34	34	of	of	ADP
ejpam-3587	34	35	the	the	DET
ejpam-3587	34	36	result	result	NOUN
ejpam-3587	34	37	given	give	VERB
ejpam-3587	34	38	for	for	ADP
ejpam-3587	34	39	non	non	ADJ
ejpam-3587	34	40	-	-	ADJ
ejpam-3587	34	41	commuting	commuting	ADJ
ejpam-3587	34	42	graphs	graph	NOUN
ejpam-3587	34	43	.	.	PUNCT
ejpam-3587	35	1	abd	abd	PROPN
ejpam-3587	35	2	rani	rani	PROPN
ejpam-3587	35	3	et	et	PROPN
ejpam-3587	35	4	al	al	PROPN
ejpam-3587	35	5	.	.	PUNCT
ejpam-3587	36	1	[	[	X
ejpam-3587	36	2	1	1	X
ejpam-3587	36	3	]	]	PUNCT
ejpam-3587	36	4	defined	define	VERB
ejpam-3587	36	5	the	the	DET
ejpam-3587	36	6	relative	relative	ADJ
ejpam-3587	36	7	coprime	coprime	NOUN
ejpam-3587	36	8	graph	graph	NOUN
ejpam-3587	36	9	of	of	ADP
ejpam-3587	36	10	a	a	DET
ejpam-3587	36	11	group	group	NOUN
ejpam-3587	36	12	with	with	ADP
ejpam-3587	36	13	respect	respect	NOUN
ejpam-3587	36	14	to	to	ADP
ejpam-3587	36	15	its	its	PRON
ejpam-3587	36	16	subgroups	subgroup	NOUN
ejpam-3587	36	17	and	and	CCONJ
ejpam-3587	36	18	dertermined	dertermine	VERB
ejpam-3587	36	19	some	some	DET
ejpam-3587	36	20	invariants	invariant	NOUN
ejpam-3587	36	21	of	of	ADP
ejpam-3587	36	22	the	the	DET
ejpam-3587	36	23	graph	graph	NOUN
ejpam-3587	36	24	which	which	PRON
ejpam-3587	36	25	include	include	VERB
ejpam-3587	36	26	the	the	DET
ejpam-3587	36	27	domination	domination	NOUN
ejpam-3587	36	28	number	number	NOUN
ejpam-3587	36	29	,	,	PUNCT
ejpam-3587	36	30	independence	independence	NOUN
ejpam-3587	36	31	number	number	NOUN
ejpam-3587	36	32	and	and	CCONJ
ejpam-3587	36	33	give	give	VERB
ejpam-3587	36	34	the	the	DET
ejpam-3587	36	35	situation	situation	NOUN
ejpam-3587	36	36	when	when	SCONJ
ejpam-3587	36	37	the	the	DET
ejpam-3587	36	38	graph	graph	NOUN
ejpam-3587	36	39	is	be	AUX
ejpam-3587	36	40	regular	regular	ADJ
ejpam-3587	36	41	.	.	PUNCT
ejpam-3587	37	1	in	in	ADP
ejpam-3587	37	2	this	this	DET
ejpam-3587	37	3	paper	paper	NOUN
ejpam-3587	37	4	,	,	PUNCT
ejpam-3587	37	5	we	we	PRON
ejpam-3587	37	6	defined	define	VERB
ejpam-3587	37	7	order	order	NOUN
ejpam-3587	37	8	product	product	NOUN
ejpam-3587	37	9	prime	prime	ADJ
ejpam-3587	37	10	graph	graph	NOUN
ejpam-3587	37	11	of	of	ADP
ejpam-3587	37	12	finite	finite	ADJ
ejpam-3587	37	13	groups	group	NOUN
ejpam-3587	37	14	,	,	PUNCT
ejpam-3587	37	15	classify	classify	VERB
ejpam-3587	37	16	groups	group	NOUN
ejpam-3587	37	17	in	in	ADP
ejpam-3587	37	18	terms	term	NOUN
ejpam-3587	37	19	of	of	ADP
ejpam-3587	37	20	the	the	DET
ejpam-3587	37	21	properties	property	NOUN
ejpam-3587	37	22	of	of	ADP
ejpam-3587	37	23	the	the	DET
ejpam-3587	37	24	graph	graph	NOUN
ejpam-3587	37	25	as	as	ADP
ejpam-3587	37	26	one	one	NUM
ejpam-3587	37	27	of	of	ADP
ejpam-3587	37	28	connected	connected	ADJ
ejpam-3587	37	29	,	,	PUNCT
ejpam-3587	37	30	complete	complete	ADJ
ejpam-3587	37	31	,	,	PUNCT
ejpam-3587	37	32	regular	regular	ADJ
ejpam-3587	37	33	,	,	PUNCT
ejpam-3587	37	34	planar	planar	ADJ
ejpam-3587	37	35	and	and	CCONJ
ejpam-3587	37	36	obtained	obtain	VERB
ejpam-3587	37	37	some	some	PRON
ejpam-3587	37	38	of	of	ADP
ejpam-3587	37	39	its	its	PRON
ejpam-3587	37	40	invariants	invariant	NOUN
ejpam-3587	37	41	such	such	ADJ
ejpam-3587	37	42	as	as	ADP
ejpam-3587	37	43	independent	independent	ADJ
ejpam-3587	37	44	number	number	NOUN
ejpam-3587	37	45	,	,	PUNCT
ejpam-3587	37	46	clique	clique	ADJ
ejpam-3587	37	47	number	number	NOUN
ejpam-3587	37	48	,	,	PUNCT
ejpam-3587	37	49	girth	girth	NOUN
ejpam-3587	37	50	and	and	CCONJ
ejpam-3587	37	51	diameter	diameter	NOUN
ejpam-3587	37	52	.	.	PUNCT
ejpam-3587	38	1	moreover	moreover	ADV
ejpam-3587	38	2	,	,	PUNCT
ejpam-3587	38	3	we	we	PRON
ejpam-3587	38	4	investigate	investigate	VERB
ejpam-3587	38	5	the	the	DET
ejpam-3587	38	6	nilpotency	nilpotency	NOUN
ejpam-3587	38	7	status	status	NOUN
ejpam-3587	38	8	of	of	ADP
ejpam-3587	38	9	dihedral	dihedral	ADJ
ejpam-3587	38	10	group	group	NOUN
ejpam-3587	38	11	using	use	VERB
ejpam-3587	38	12	the	the	DET
ejpam-3587	38	13	connectivity	connectivity	NOUN
ejpam-3587	38	14	for	for	ADP
ejpam-3587	38	15	the	the	DET
ejpam-3587	38	16	order	order	NOUN
ejpam-3587	38	17	product	product	NOUN
ejpam-3587	38	18	prime	prime	ADJ
ejpam-3587	38	19	graphs	graph	NOUN
ejpam-3587	38	20	on	on	ADP
ejpam-3587	38	21	the	the	DET
ejpam-3587	38	22	dihedral	dihedral	ADJ
ejpam-3587	38	23	group	group	NOUN
ejpam-3587	38	24	.	.	PUNCT
ejpam-3587	39	1	2	2	X
ejpam-3587	39	2	.	.	NUM
ejpam-3587	39	3	notations	notation	NOUN
ejpam-3587	39	4	and	and	CCONJ
ejpam-3587	39	5	preliminaries	preliminary	NOUN
ejpam-3587	39	6	in	in	ADP
ejpam-3587	39	7	this	this	DET
ejpam-3587	39	8	section	section	NOUN
ejpam-3587	39	9	,	,	PUNCT
ejpam-3587	39	10	we	we	PRON
ejpam-3587	39	11	give	give	VERB
ejpam-3587	39	12	some	some	DET
ejpam-3587	39	13	basic	basic	ADJ
ejpam-3587	39	14	concepts	concept	NOUN
ejpam-3587	39	15	,	,	PUNCT
ejpam-3587	39	16	notations	notation	NOUN
ejpam-3587	39	17	and	and	CCONJ
ejpam-3587	39	18	preliminaries	preliminary	NOUN
ejpam-3587	39	19	useful	useful	ADJ
ejpam-3587	39	20	to	to	ADP
ejpam-3587	39	21	this	this	DET
ejpam-3587	39	22	paper	paper	NOUN
ejpam-3587	39	23	.	.	PUNCT
ejpam-3587	40	1	all	all	DET
ejpam-3587	40	2	groups	group	NOUN
ejpam-3587	40	3	considered	consider	VERB
ejpam-3587	40	4	in	in	ADP
ejpam-3587	40	5	this	this	DET
ejpam-3587	40	6	paper	paper	NOUN
ejpam-3587	40	7	are	be	AUX
ejpam-3587	40	8	finite	finite	ADJ
ejpam-3587	40	9	and	and	CCONJ
ejpam-3587	40	10	the	the	DET
ejpam-3587	40	11	investigation	investigation	NOUN
ejpam-3587	40	12	covered	cover	VERB
ejpam-3587	40	13	all	all	DET
ejpam-3587	40	14	dihedral	dihedral	ADJ
ejpam-3587	40	15	groups	group	NOUN
ejpam-3587	41	1	dn	dn	NOUN
ejpam-3587	41	2	=	=	PUNCT
ejpam-3587	41	3	{	{	PUNCT
ejpam-3587	41	4	a	a	X
ejpam-3587	41	5	,	,	PUNCT
ejpam-3587	41	6	b|an	b|an	PUNCT
ejpam-3587	41	7	=	=	SYM
ejpam-3587	41	8	b2	b2	NOUN
ejpam-3587	41	9	=	=	SYM
ejpam-3587	41	10	(	(	PUNCT
ejpam-3587	41	11	ab)2	ab)2	PROPN
ejpam-3587	41	12	=	=	SYM
ejpam-3587	41	13	e	e	NOUN
ejpam-3587	41	14	}	}	PUNCT
ejpam-3587	41	15	and	and	CCONJ
ejpam-3587	41	16	cyclic	cyclic	ADJ
ejpam-3587	41	17	groups	group	NOUN
ejpam-3587	41	18	zn	zn	X
ejpam-3587	42	1	=	=	NOUN
ejpam-3587	42	2	<	<	X
ejpam-3587	42	3	g	g	X
ejpam-3587	42	4	>	>	X
ejpam-3587	42	5	3	3	NUM
ejpam-3587	42	6	g	g	NOUN
ejpam-3587	42	7	∈	∈	PROPN
ejpam-3587	42	8	zn	zn	X
ejpam-3587	42	9	.	.	PUNCT
ejpam-3587	43	1	we	we	PRON
ejpam-3587	43	2	denoted	denote	VERB
ejpam-3587	43	3	the	the	DET
ejpam-3587	43	4	identity	identity	NOUN
ejpam-3587	43	5	of	of	ADP
ejpam-3587	43	6	a	a	DET
ejpam-3587	43	7	group	group	NOUN
ejpam-3587	43	8	g	g	NOUN
ejpam-3587	43	9	by	by	ADP
ejpam-3587	43	10	e.	e.	PROPN
ejpam-3587	43	11	m.	m.	PROPN
ejpam-3587	43	12	bello	bello	PROPN
ejpam-3587	43	13	,	,	PUNCT
ejpam-3587	43	14	n.	n.	PROPN
ejpam-3587	43	15	m.	m.	NOUN
ejpam-3587	43	16	mohd	mohd	PROPN
ejpam-3587	43	17	ali	ali	PROPN
ejpam-3587	43	18	,	,	PUNCT
ejpam-3587	43	19	n.	n.	PROPN
ejpam-3587	43	20	zulkifli	zulkifli	PROPN
ejpam-3587	43	21	/	/	SYM
ejpam-3587	43	22	eur	eur	PROPN
ejpam-3587	43	23	.	.	PUNCT
ejpam-3587	44	1	j.	j.	PROPN
ejpam-3587	44	2	pure	pure	PROPN
ejpam-3587	44	3	appl	appl	PROPN
ejpam-3587	44	4	.	.	PROPN
ejpam-3587	44	5	math	math	PROPN
ejpam-3587	44	6	,	,	PUNCT
ejpam-3587	44	7	13	13	NUM
ejpam-3587	44	8	(	(	PUNCT
ejpam-3587	44	9	1	1	NUM
ejpam-3587	44	10	)	)	PUNCT
ejpam-3587	44	11	(	(	PUNCT
ejpam-3587	44	12	2020	2020	NUM
ejpam-3587	44	13	)	)	PUNCT
ejpam-3587	44	14	,	,	PUNCT
ejpam-3587	44	15	84	84	NUM
ejpam-3587	44	16	-	-	SYM
ejpam-3587	44	17	95	95	NUM
ejpam-3587	44	18	86	86	NUM
ejpam-3587	44	19	on	on	ADP
ejpam-3587	44	20	the	the	DET
ejpam-3587	44	21	other	other	ADJ
ejpam-3587	44	22	hand	hand	NOUN
ejpam-3587	45	1	,	,	PUNCT
ejpam-3587	45	2	we	we	PRON
ejpam-3587	45	3	consider	consider	VERB
ejpam-3587	45	4	simple	simple	ADJ
ejpam-3587	45	5	undirected	undirected	ADJ
ejpam-3587	45	6	graphs	graph	NOUN
ejpam-3587	45	7	without	without	ADP
ejpam-3587	45	8	loop	loop	NOUN
ejpam-3587	45	9	or	or	CCONJ
ejpam-3587	45	10	multiple	multiple	ADJ
ejpam-3587	45	11	edges	edge	NOUN
ejpam-3587	45	12	.	.	PUNCT
ejpam-3587	46	1	the	the	DET
ejpam-3587	46	2	sets	set	NOUN
ejpam-3587	46	3	of	of	ADP
ejpam-3587	46	4	vertices	vertex	NOUN
ejpam-3587	46	5	and	and	CCONJ
ejpam-3587	46	6	edges	edge	NOUN
ejpam-3587	46	7	of	of	ADP
ejpam-3587	46	8	a	a	DET
ejpam-3587	46	9	graph	graph	NOUN
ejpam-3587	46	10	γ	γ	NOUN
ejpam-3587	46	11	are	be	AUX
ejpam-3587	46	12	denoted	denote	VERB
ejpam-3587	46	13	by	by	ADP
ejpam-3587	46	14	v	v	NOUN
ejpam-3587	46	15	(	(	PUNCT
ejpam-3587	46	16	γ	γ	NOUN
ejpam-3587	46	17	)	)	PUNCT
ejpam-3587	46	18	and	and	CCONJ
ejpam-3587	46	19	e(γ	e(γ	NOUN
ejpam-3587	46	20	)	)	PUNCT
ejpam-3587	46	21	respectively	respectively	ADV
ejpam-3587	46	22	.	.	PUNCT
ejpam-3587	47	1	we	we	PRON
ejpam-3587	47	2	denote	denote	VERB
ejpam-3587	47	3	the	the	DET
ejpam-3587	47	4	adjacency	adjacency	NOUN
ejpam-3587	47	5	of	of	ADP
ejpam-3587	47	6	vertices	vertex	NOUN
ejpam-3587	47	7	x	x	X
ejpam-3587	47	8	,	,	PUNCT
ejpam-3587	47	9	y	y	PROPN
ejpam-3587	47	10	by	by	ADP
ejpam-3587	47	11	x	x	PUNCT
ejpam-3587	47	12	∼	∼	NOUN
ejpam-3587	47	13	y	y	NOUN
ejpam-3587	47	14	,	,	PUNCT
ejpam-3587	47	15	number	number	NOUN
ejpam-3587	47	16	of	of	ADP
ejpam-3587	47	17	vertices	vertex	NOUN
ejpam-3587	47	18	of	of	ADP
ejpam-3587	47	19	the	the	DET
ejpam-3587	47	20	graph	graph	NOUN
ejpam-3587	47	21	γ	γ	X
ejpam-3587	47	22	by	by	ADP
ejpam-3587	47	23	|v	|v	PROPN
ejpam-3587	47	24	(	(	PUNCT
ejpam-3587	47	25	γ)|	γ)|	NOUN
ejpam-3587	47	26	,	,	PUNCT
ejpam-3587	47	27	the	the	DET
ejpam-3587	47	28	degree	degree	NOUN
ejpam-3587	47	29	of	of	ADP
ejpam-3587	47	30	the	the	DET
ejpam-3587	47	31	vertex	vertex	NOUN
ejpam-3587	47	32	v	v	NOUN
ejpam-3587	47	33	by	by	ADP
ejpam-3587	47	34	deg(v	deg(v	NOUN
ejpam-3587	47	35	)	)	PUNCT
ejpam-3587	47	36	.	.	PUNCT
ejpam-3587	48	1	a	a	DET
ejpam-3587	48	2	graph	graph	NOUN
ejpam-3587	48	3	γ	γ	X
ejpam-3587	48	4	is	be	AUX
ejpam-3587	48	5	regular	regular	ADJ
ejpam-3587	48	6	if	if	SCONJ
ejpam-3587	48	7	all	all	DET
ejpam-3587	48	8	the	the	DET
ejpam-3587	48	9	vertices	vertex	NOUN
ejpam-3587	48	10	of	of	ADP
ejpam-3587	48	11	the	the	DET
ejpam-3587	48	12	graph	graph	NOUN
ejpam-3587	48	13	have	have	VERB
ejpam-3587	48	14	the	the	DET
ejpam-3587	48	15	same	same	ADJ
ejpam-3587	48	16	degree	degree	NOUN
ejpam-3587	48	17	,	,	PUNCT
ejpam-3587	48	18	that	that	PRON
ejpam-3587	48	19	is	be	AUX
ejpam-3587	48	20	if	if	SCONJ
ejpam-3587	48	21	for	for	ADP
ejpam-3587	48	22	all	all	DET
ejpam-3587	48	23	vertices	vertex	NOUN
ejpam-3587	48	24	v1	v1	NOUN
ejpam-3587	48	25	,	,	PUNCT
ejpam-3587	48	26	v2	v2	PROPN
ejpam-3587	48	27	,	,	PUNCT
ejpam-3587	48	28	...	...	PUNCT
ejpam-3587	48	29	,	,	PUNCT
ejpam-3587	48	30	vn	vn	PROPN
ejpam-3587	48	31	of	of	ADP
ejpam-3587	48	32	γ	γ	PROPN
ejpam-3587	48	33	,	,	PUNCT
ejpam-3587	48	34	deg(v1	deg(v1	NOUN
ejpam-3587	48	35	)	)	PUNCT
ejpam-3587	48	36	=	=	SYM
ejpam-3587	48	37	deg(v2	deg(v2	NOUN
ejpam-3587	48	38	)	)	PUNCT
ejpam-3587	48	39	=	=	PUNCT
ejpam-3587	48	40	...	...	PUNCT
ejpam-3587	49	1	=	=	PUNCT
ejpam-3587	49	2	deg(vn	deg(vn	X
ejpam-3587	49	3	)	)	PUNCT
ejpam-3587	49	4	and	and	CCONJ
ejpam-3587	49	5	a	a	DET
ejpam-3587	49	6	graph	graph	NOUN
ejpam-3587	49	7	γ	γ	X
ejpam-3587	49	8	is	be	AUX
ejpam-3587	49	9	r	r	NOUN
ejpam-3587	49	10	-	-	ADJ
ejpam-3587	49	11	regular	regular	ADJ
ejpam-3587	49	12	if	if	SCONJ
ejpam-3587	49	13	deg(vi	deg(vi	NOUN
ejpam-3587	49	14	)	)	PUNCT
ejpam-3587	49	15	=	=	SYM
ejpam-3587	49	16	r	r	X
ejpam-3587	49	17	,	,	PUNCT
ejpam-3587	49	18	i	i	PRON
ejpam-3587	49	19	∈	∈	PROPN
ejpam-3587	49	20	n.	n.	VERB
ejpam-3587	49	21	a	a	DET
ejpam-3587	49	22	graph	graph	NOUN
ejpam-3587	49	23	γ	γ	X
ejpam-3587	49	24	is	be	AUX
ejpam-3587	49	25	connected	connect	VERB
ejpam-3587	49	26	if	if	SCONJ
ejpam-3587	49	27	there	there	PRON
ejpam-3587	49	28	is	be	VERB
ejpam-3587	49	29	a	a	DET
ejpam-3587	49	30	path	path	NOUN
ejpam-3587	49	31	between	between	ADP
ejpam-3587	49	32	every	every	DET
ejpam-3587	49	33	pair	pair	NOUN
ejpam-3587	49	34	of	of	ADP
ejpam-3587	49	35	its	its	PRON
ejpam-3587	49	36	vertices	vertex	NOUN
ejpam-3587	49	37	,	,	PUNCT
ejpam-3587	49	38	and	and	CCONJ
ejpam-3587	49	39	a	a	DET
ejpam-3587	49	40	graph	graph	NOUN
ejpam-3587	49	41	is	be	AUX
ejpam-3587	49	42	complete	complete	ADJ
ejpam-3587	49	43	if	if	SCONJ
ejpam-3587	49	44	there	there	PRON
ejpam-3587	49	45	is	be	VERB
ejpam-3587	49	46	an	an	DET
ejpam-3587	49	47	edge	edge	NOUN
ejpam-3587	49	48	between	between	ADP
ejpam-3587	49	49	every	every	DET
ejpam-3587	49	50	pair	pair	NOUN
ejpam-3587	49	51	of	of	ADP
ejpam-3587	49	52	its	its	PRON
ejpam-3587	49	53	vertices	vertex	NOUN
ejpam-3587	49	54	.	.	PUNCT
ejpam-3587	50	1	a	a	DET
ejpam-3587	50	2	graph	graph	NOUN
ejpam-3587	50	3	is	be	AUX
ejpam-3587	50	4	planar	planar	ADJ
ejpam-3587	50	5	if	if	SCONJ
ejpam-3587	50	6	it	it	PRON
ejpam-3587	50	7	can	can	AUX
ejpam-3587	50	8	be	be	AUX
ejpam-3587	50	9	drawn	draw	VERB
ejpam-3587	50	10	in	in	ADP
ejpam-3587	50	11	a	a	DET
ejpam-3587	50	12	plane	plane	NOUN
ejpam-3587	50	13	without	without	ADP
ejpam-3587	50	14	edge	edge	NOUN
ejpam-3587	50	15	crossing	crossing	NOUN
ejpam-3587	50	16	.	.	PUNCT
ejpam-3587	51	1	a	a	DET
ejpam-3587	51	2	clique	clique	NOUN
ejpam-3587	51	3	is	be	AUX
ejpam-3587	51	4	a	a	DET
ejpam-3587	51	5	subset	subset	ADJ
ejpam-3587	51	6	u	u	NOUN
ejpam-3587	51	7	of	of	ADP
ejpam-3587	51	8	vertices	vertex	NOUN
ejpam-3587	51	9	of	of	ADP
ejpam-3587	51	10	γ	γ	NOUN
ejpam-3587	51	11	such	such	ADJ
ejpam-3587	51	12	that	that	SCONJ
ejpam-3587	51	13	the	the	DET
ejpam-3587	51	14	induced	induced	ADJ
ejpam-3587	51	15	subgraph	subgraph	NOUN
ejpam-3587	51	16	of	of	ADP
ejpam-3587	51	17	u	u	NOUN
ejpam-3587	51	18	is	be	AUX
ejpam-3587	51	19	a	a	DET
ejpam-3587	51	20	complete	complete	ADJ
ejpam-3587	51	21	graph	graph	NOUN
ejpam-3587	51	22	,	,	PUNCT
ejpam-3587	51	23	the	the	DET
ejpam-3587	51	24	size	size	NOUN
ejpam-3587	51	25	of	of	ADP
ejpam-3587	51	26	the	the	DET
ejpam-3587	51	27	maximum	maximum	ADJ
ejpam-3587	51	28	such	such	ADJ
ejpam-3587	51	29	clique	clique	NOUN
ejpam-3587	51	30	is	be	AUX
ejpam-3587	51	31	refered	refer	VERB
ejpam-3587	51	32	to	to	ADP
ejpam-3587	51	33	as	as	ADP
ejpam-3587	51	34	the	the	DET
ejpam-3587	51	35	clique	clique	ADJ
ejpam-3587	51	36	number	number	NOUN
ejpam-3587	51	37	of	of	ADP
ejpam-3587	51	38	γ	γ	PROPN
ejpam-3587	51	39	and	and	CCONJ
ejpam-3587	51	40	denoted	denote	VERB
ejpam-3587	51	41	by	by	ADP
ejpam-3587	51	42	ω(γ	ω(γ	NOUN
ejpam-3587	51	43	)	)	PUNCT
ejpam-3587	51	44	.	.	PUNCT
ejpam-3587	52	1	an	an	DET
ejpam-3587	52	2	independent	independent	ADJ
ejpam-3587	52	3	set	set	NOUN
ejpam-3587	52	4	of	of	ADP
ejpam-3587	52	5	vertices	vertex	NOUN
ejpam-3587	52	6	of	of	ADP
ejpam-3587	52	7	a	a	DET
ejpam-3587	52	8	graph	graph	NOUN
ejpam-3587	52	9	is	be	AUX
ejpam-3587	52	10	the	the	DET
ejpam-3587	52	11	set	set	NOUN
ejpam-3587	52	12	of	of	ADP
ejpam-3587	52	13	vertices	vertex	NOUN
ejpam-3587	52	14	such	such	ADJ
ejpam-3587	52	15	that	that	SCONJ
ejpam-3587	52	16	no	no	DET
ejpam-3587	52	17	two	two	NUM
ejpam-3587	52	18	vertices	vertex	NOUN
ejpam-3587	52	19	are	be	AUX
ejpam-3587	52	20	adjacent	adjacent	ADJ
ejpam-3587	52	21	,	,	PUNCT
ejpam-3587	52	22	and	and	CCONJ
ejpam-3587	52	23	the	the	DET
ejpam-3587	52	24	independent	independent	ADJ
ejpam-3587	52	25	number	number	NOUN
ejpam-3587	52	26	of	of	ADP
ejpam-3587	52	27	a	a	DET
ejpam-3587	52	28	graph	graph	NOUN
ejpam-3587	52	29	γ	γ	NOUN
ejpam-3587	52	30	,	,	PUNCT
ejpam-3587	52	31	is	be	AUX
ejpam-3587	52	32	the	the	DET
ejpam-3587	52	33	cardinality	cardinality	NOUN
ejpam-3587	52	34	of	of	ADP
ejpam-3587	52	35	the	the	DET
ejpam-3587	52	36	largest	large	ADJ
ejpam-3587	52	37	independent	independent	ADJ
ejpam-3587	52	38	set	set	NOUN
ejpam-3587	52	39	,	,	PUNCT
ejpam-3587	52	40	which	which	PRON
ejpam-3587	52	41	is	be	AUX
ejpam-3587	52	42	denoted	denote	VERB
ejpam-3587	52	43	by	by	ADP
ejpam-3587	52	44	α(γ	α(γ	NOUN
ejpam-3587	52	45	)	)	PUNCT
ejpam-3587	52	46	.	.	PUNCT
ejpam-3587	53	1	the	the	DET
ejpam-3587	53	2	girth	girth	NOUN
ejpam-3587	53	3	of	of	ADP
ejpam-3587	53	4	a	a	DET
ejpam-3587	53	5	graph	graph	NOUN
ejpam-3587	53	6	γ	γ	NOUN
ejpam-3587	53	7	,	,	PUNCT
ejpam-3587	53	8	is	be	AUX
ejpam-3587	53	9	the	the	DET
ejpam-3587	53	10	length	length	NOUN
ejpam-3587	53	11	of	of	ADP
ejpam-3587	53	12	the	the	DET
ejpam-3587	53	13	shortest	short	ADJ
ejpam-3587	53	14	cycle	cycle	NOUN
ejpam-3587	53	15	contained	contain	VERB
ejpam-3587	53	16	in	in	ADP
ejpam-3587	53	17	the	the	DET
ejpam-3587	53	18	graph	graph	NOUN
ejpam-3587	53	19	,	,	PUNCT
ejpam-3587	53	20	which	which	PRON
ejpam-3587	53	21	is	be	AUX
ejpam-3587	53	22	∞	∞	PROPN
ejpam-3587	53	23	if	if	SCONJ
ejpam-3587	53	24	γ	γ	PROPN
ejpam-3587	53	25	has	have	VERB
ejpam-3587	53	26	no	no	DET
ejpam-3587	53	27	cycle	cycle	NOUN
ejpam-3587	53	28	.	.	PUNCT
ejpam-3587	54	1	the	the	DET
ejpam-3587	54	2	diameter	diameter	NOUN
ejpam-3587	54	3	of	of	ADP
ejpam-3587	54	4	a	a	DET
ejpam-3587	54	5	graph	graph	NOUN
ejpam-3587	54	6	is	be	AUX
ejpam-3587	54	7	the	the	DET
ejpam-3587	54	8	maximum	maximum	ADJ
ejpam-3587	54	9	distance	distance	NOUN
ejpam-3587	54	10	between	between	ADP
ejpam-3587	54	11	the	the	DET
ejpam-3587	54	12	pair	pair	NOUN
ejpam-3587	54	13	of	of	ADP
ejpam-3587	54	14	its	its	PRON
ejpam-3587	54	15	vertices	vertex	NOUN
ejpam-3587	54	16	,	,	PUNCT
ejpam-3587	54	17	which	which	PRON
ejpam-3587	54	18	is∞	is∞	VERB
ejpam-3587	54	19	if	if	SCONJ
ejpam-3587	54	20	the	the	DET
ejpam-3587	54	21	graph	graph	NOUN
ejpam-3587	54	22	is	be	AUX
ejpam-3587	54	23	disconnected	disconnect	VERB
ejpam-3587	54	24	.	.	PUNCT
ejpam-3587	55	1	throughout	throughout	ADP
ejpam-3587	55	2	this	this	DET
ejpam-3587	55	3	paper	paper	NOUN
ejpam-3587	55	4	p	p	NOUN
ejpam-3587	55	5	denotes	denote	VERB
ejpam-3587	55	6	prime	prime	ADJ
ejpam-3587	55	7	number	number	NOUN
ejpam-3587	55	8	,	,	PUNCT
ejpam-3587	55	9	and	and	CCONJ
ejpam-3587	55	10	α	α	PRON
ejpam-3587	55	11	∈	∈	PROPN
ejpam-3587	55	12	n.	n.	NOUN
ejpam-3587	55	13	3	3	NUM
ejpam-3587	55	14	.	.	NOUN
ejpam-3587	55	15	results	result	NOUN
ejpam-3587	55	16	and	and	CCONJ
ejpam-3587	55	17	discussions	discussion	NOUN
ejpam-3587	55	18	in	in	ADP
ejpam-3587	55	19	this	this	DET
ejpam-3587	55	20	section	section	NOUN
ejpam-3587	55	21	,	,	PUNCT
ejpam-3587	55	22	we	we	PRON
ejpam-3587	55	23	give	give	VERB
ejpam-3587	55	24	the	the	DET
ejpam-3587	55	25	formal	formal	ADJ
ejpam-3587	55	26	definition	definition	NOUN
ejpam-3587	55	27	of	of	ADP
ejpam-3587	55	28	the	the	DET
ejpam-3587	55	29	order	order	NOUN
ejpam-3587	55	30	product	product	NOUN
ejpam-3587	55	31	prime	prime	ADJ
ejpam-3587	55	32	graph	graph	NOUN
ejpam-3587	55	33	and	and	CCONJ
ejpam-3587	55	34	the	the	DET
ejpam-3587	55	35	general	general	ADJ
ejpam-3587	55	36	presentation	presentation	NOUN
ejpam-3587	55	37	for	for	ADP
ejpam-3587	55	38	its	its	PRON
ejpam-3587	55	39	connectivity	connectivity	NOUN
ejpam-3587	55	40	,	,	PUNCT
ejpam-3587	55	41	completeness	completeness	NOUN
ejpam-3587	55	42	,	,	PUNCT
ejpam-3587	55	43	regularity	regularity	NOUN
ejpam-3587	55	44	and	and	CCONJ
ejpam-3587	55	45	planarity	planarity	NOUN
ejpam-3587	55	46	on	on	ADP
ejpam-3587	55	47	dihedral	dihedral	ADJ
ejpam-3587	55	48	group	group	NOUN
ejpam-3587	55	49	and	and	CCONJ
ejpam-3587	55	50	cyclic	cyclic	ADJ
ejpam-3587	55	51	group	group	NOUN
ejpam-3587	55	52	,	,	PUNCT
ejpam-3587	55	53	which	which	PRON
ejpam-3587	55	54	help	help	VERB
ejpam-3587	55	55	in	in	ADP
ejpam-3587	55	56	obtaining	obtain	VERB
ejpam-3587	55	57	its	its	PRON
ejpam-3587	55	58	diameter	diameter	NOUN
ejpam-3587	55	59	,	,	PUNCT
ejpam-3587	55	60	girth	girth	ADV
ejpam-3587	55	61	,	,	PUNCT
ejpam-3587	55	62	independent	independent	ADJ
ejpam-3587	55	63	number	number	NOUN
ejpam-3587	55	64	,	,	PUNCT
ejpam-3587	55	65	and	and	CCONJ
ejpam-3587	55	66	the	the	DET
ejpam-3587	55	67	clique	clique	ADJ
ejpam-3587	55	68	number	number	NOUN
ejpam-3587	55	69	.	.	PUNCT
ejpam-3587	56	1	we	we	PRON
ejpam-3587	56	2	also	also	ADV
ejpam-3587	56	3	use	use	VERB
ejpam-3587	56	4	the	the	DET
ejpam-3587	56	5	graph	graph	NOUN
ejpam-3587	56	6	properties	property	NOUN
ejpam-3587	56	7	to	to	PART
ejpam-3587	56	8	obtain	obtain	VERB
ejpam-3587	56	9	the	the	DET
ejpam-3587	56	10	corresponding	corresponding	ADJ
ejpam-3587	56	11	group	group	NOUN
ejpam-3587	56	12	properties	property	NOUN
ejpam-3587	56	13	.	.	PUNCT
ejpam-3587	57	1	the	the	DET
ejpam-3587	57	2	formal	formal	ADJ
ejpam-3587	57	3	definition	definition	NOUN
ejpam-3587	57	4	of	of	ADP
ejpam-3587	57	5	the	the	DET
ejpam-3587	57	6	order	order	NOUN
ejpam-3587	57	7	product	product	NOUN
ejpam-3587	57	8	prime	prime	ADJ
ejpam-3587	57	9	graph	graph	NOUN
ejpam-3587	57	10	is	be	AUX
ejpam-3587	57	11	given	give	VERB
ejpam-3587	57	12	in	in	ADP
ejpam-3587	57	13	definition	definition	NOUN
ejpam-3587	57	14	1	1	NUM
ejpam-3587	57	15	below	below	ADV
ejpam-3587	57	16	,	,	PUNCT
ejpam-3587	57	17	followed	follow	VERB
ejpam-3587	57	18	by	by	ADP
ejpam-3587	57	19	an	an	DET
ejpam-3587	57	20	example	example	NOUN
ejpam-3587	57	21	which	which	PRON
ejpam-3587	57	22	demonstrate	demonstrate	VERB
ejpam-3587	57	23	the	the	DET
ejpam-3587	57	24	definition	definition	NOUN
ejpam-3587	57	25	.	.	PUNCT
ejpam-3587	58	1	definition	definition	NOUN
ejpam-3587	58	2	1	1	NUM
ejpam-3587	58	3	.	.	PUNCT
ejpam-3587	59	1	let	let	VERB
ejpam-3587	59	2	g	g	PRON
ejpam-3587	59	3	be	be	AUX
ejpam-3587	59	4	a	a	DET
ejpam-3587	59	5	finite	finite	ADJ
ejpam-3587	59	6	group	group	NOUN
ejpam-3587	59	7	,	,	PUNCT
ejpam-3587	59	8	the	the	DET
ejpam-3587	59	9	order	order	NOUN
ejpam-3587	59	10	product	product	NOUN
ejpam-3587	59	11	prime	prime	ADJ
ejpam-3587	59	12	graph	graph	NOUN
ejpam-3587	59	13	of	of	ADP
ejpam-3587	59	14	g	g	NOUN
ejpam-3587	59	15	,	,	PUNCT
ejpam-3587	59	16	γopp(g	γopp(g	NOUN
ejpam-3587	59	17	)	)	PUNCT
ejpam-3587	59	18	is	be	AUX
ejpam-3587	59	19	a	a	DET
ejpam-3587	59	20	graph	graph	NOUN
ejpam-3587	59	21	whose	whose	DET
ejpam-3587	59	22	vertices	vertex	NOUN
ejpam-3587	59	23	are	be	AUX
ejpam-3587	59	24	the	the	DET
ejpam-3587	59	25	elements	element	NOUN
ejpam-3587	59	26	of	of	ADP
ejpam-3587	59	27	g	g	PROPN
ejpam-3587	59	28	and	and	CCONJ
ejpam-3587	59	29	two	two	NUM
ejpam-3587	59	30	vertices	vertex	NOUN
ejpam-3587	59	31	x	x	X
ejpam-3587	59	32	,	,	PUNCT
ejpam-3587	59	33	y	y	PROPN
ejpam-3587	59	34	are	be	AUX
ejpam-3587	59	35	adjacent	adjacent	ADJ
ejpam-3587	59	36	if	if	SCONJ
ejpam-3587	59	37	and	and	CCONJ
ejpam-3587	59	38	only	only	ADV
ejpam-3587	59	39	if	if	SCONJ
ejpam-3587	59	40	|x||y|	|x||y|	PROPN
ejpam-3587	59	41	=	=	NOUN
ejpam-3587	59	42	pα	pα	PROPN
ejpam-3587	59	43	,	,	PUNCT
ejpam-3587	59	44	α	α	PROPN
ejpam-3587	59	45	∈	∈	PROPN
ejpam-3587	59	46	n	n	CCONJ
ejpam-3587	59	47	,	,	PUNCT
ejpam-3587	59	48	for	for	ADP
ejpam-3587	59	49	some	some	DET
ejpam-3587	59	50	prime	prime	NOUN
ejpam-3587	59	51	p	p	PROPN
ejpam-3587	59	52	.	.	PUNCT
ejpam-3587	60	1	example	example	NOUN
ejpam-3587	61	1	1	1	NUM
ejpam-3587	61	2	.	.	X
ejpam-3587	61	3	consider	consider	VERB
ejpam-3587	61	4	the	the	DET
ejpam-3587	61	5	dihedral	dihedral	ADJ
ejpam-3587	61	6	group	group	NOUN
ejpam-3587	61	7	of	of	ADP
ejpam-3587	61	8	degree	degree	NOUN
ejpam-3587	61	9	three	three	NUM
ejpam-3587	61	10	which	which	PRON
ejpam-3587	61	11	is	be	AUX
ejpam-3587	61	12	d3	d3	PROPN
ejpam-3587	61	13	=	=	SYM
ejpam-3587	61	14	{	{	PUNCT
ejpam-3587	61	15	e	e	NOUN
ejpam-3587	61	16	,	,	PUNCT
ejpam-3587	61	17	a	a	PRON
ejpam-3587	61	18	,	,	PUNCT
ejpam-3587	61	19	a2	a2	PROPN
ejpam-3587	61	20	,	,	PUNCT
ejpam-3587	61	21	b	b	PROPN
ejpam-3587	61	22	,	,	PUNCT
ejpam-3587	61	23	ab	ab	PROPN
ejpam-3587	61	24	,	,	PUNCT
ejpam-3587	61	25	a2b	a2b	NOUN
ejpam-3587	61	26	}	}	PUNCT
ejpam-3587	61	27	.	.	PUNCT
ejpam-3587	62	1	|e|	|e|	PRON
ejpam-3587	62	2	=	=	SYM
ejpam-3587	62	3	1	1	NUM
ejpam-3587	62	4	,	,	PUNCT
ejpam-3587	62	5	|a|	|a|	NOUN
ejpam-3587	62	6	=	=	PUNCT
ejpam-3587	62	7	|a2|	|a2|	NOUN
ejpam-3587	62	8	=	=	SYM
ejpam-3587	62	9	3	3	NUM
ejpam-3587	62	10	,	,	PUNCT
ejpam-3587	62	11	|b|	|b|	PROPN
ejpam-3587	62	12	=	=	PUNCT
ejpam-3587	62	13	|ab|	|ab|	PROPN
ejpam-3587	62	14	=	=	SYM
ejpam-3587	62	15	|a2b|	|a2b|	NOUN
ejpam-3587	62	16	=	=	SYM
ejpam-3587	62	17	2	2	NUM
ejpam-3587	62	18	,	,	PUNCT
ejpam-3587	62	19	then	then	ADV
ejpam-3587	62	20	,	,	PUNCT
ejpam-3587	62	21	there	there	PRON
ejpam-3587	62	22	are	be	VERB
ejpam-3587	62	23	two	two	NUM
ejpam-3587	62	24	cliques	clique	NOUN
ejpam-3587	62	25	which	which	PRON
ejpam-3587	62	26	are	be	AUX
ejpam-3587	62	27	the	the	DET
ejpam-3587	62	28	rotations	rotation	NOUN
ejpam-3587	62	29	{	{	PUNCT
ejpam-3587	62	30	a	a	DET
ejpam-3587	62	31	,	,	PUNCT
ejpam-3587	62	32	a2	a2	PROPN
ejpam-3587	62	33	}	}	PUNCT
ejpam-3587	62	34	and	and	CCONJ
ejpam-3587	62	35	the	the	DET
ejpam-3587	62	36	reflections	reflection	NOUN
ejpam-3587	62	37	{	{	PUNCT
ejpam-3587	62	38	b	b	NOUN
ejpam-3587	62	39	,	,	PUNCT
ejpam-3587	62	40	ab	ab	PROPN
ejpam-3587	62	41	,	,	PUNCT
ejpam-3587	62	42	a2b	a2b	PROPN
ejpam-3587	62	43	}	}	PUNCT
ejpam-3587	62	44	,	,	PUNCT
ejpam-3587	62	45	all	all	PRON
ejpam-3587	62	46	adjacent	adjacent	ADJ
ejpam-3587	62	47	to	to	ADP
ejpam-3587	62	48	e.	e.	PROPN
ejpam-3587	62	49	therefore	therefore	ADV
ejpam-3587	62	50	γopp(d3	γopp(d3	PROPN
ejpam-3587	62	51	)	)	PUNCT
ejpam-3587	63	1	=	=	SYM
ejpam-3587	63	2	k1	k1	NOUN
ejpam-3587	63	3	+	+	CCONJ
ejpam-3587	63	4	(	(	PUNCT
ejpam-3587	63	5	k2	k2	ADJ
ejpam-3587	63	6	∪k3	∪k3	NOUN
ejpam-3587	63	7	)	)	PUNCT
ejpam-3587	63	8	and	and	CCONJ
ejpam-3587	63	9	is	be	AUX
ejpam-3587	63	10	given	give	VERB
ejpam-3587	63	11	in	in	ADP
ejpam-3587	63	12	figure	figure	NOUN
ejpam-3587	63	13	1	1	NUM
ejpam-3587	63	14	m.	m.	NOUN
ejpam-3587	63	15	bello	bello	PROPN
ejpam-3587	63	16	,	,	PUNCT
ejpam-3587	63	17	n.	n.	PROPN
ejpam-3587	63	18	m.	m.	NOUN
ejpam-3587	63	19	mohd	mohd	PROPN
ejpam-3587	63	20	ali	ali	PROPN
ejpam-3587	63	21	,	,	PUNCT
ejpam-3587	63	22	n.	n.	PROPN
ejpam-3587	63	23	zulkifli	zulkifli	PROPN
ejpam-3587	63	24	/	/	SYM
ejpam-3587	63	25	eur	eur	PROPN
ejpam-3587	63	26	.	.	PUNCT
ejpam-3587	64	1	j.	j.	PROPN
ejpam-3587	64	2	pure	pure	PROPN
ejpam-3587	64	3	appl	appl	PROPN
ejpam-3587	64	4	.	.	PROPN
ejpam-3587	64	5	math	math	PROPN
ejpam-3587	64	6	,	,	PUNCT
ejpam-3587	64	7	13	13	NUM
ejpam-3587	64	8	(	(	PUNCT
ejpam-3587	64	9	1	1	NUM
ejpam-3587	64	10	)	)	PUNCT
ejpam-3587	64	11	(	(	PUNCT
ejpam-3587	64	12	2020	2020	NUM
ejpam-3587	64	13	)	)	PUNCT
ejpam-3587	64	14	,	,	PUNCT
ejpam-3587	64	15	84	84	NUM
ejpam-3587	64	16	-	-	SYM
ejpam-3587	64	17	95	95	NUM
ejpam-3587	64	18	87	87	NUM
ejpam-3587	64	19	figure	figure	NOUN
ejpam-3587	64	20	1	1	NUM
ejpam-3587	64	21	:	:	PUNCT
ejpam-3587	64	22	order	order	NOUN
ejpam-3587	64	23	product	product	NOUN
ejpam-3587	64	24	prime	prime	ADJ
ejpam-3587	64	25	graph	graph	NOUN
ejpam-3587	64	26	of	of	ADP
ejpam-3587	64	27	d3	d3	PROPN
ejpam-3587	64	28	the	the	DET
ejpam-3587	64	29	general	general	ADJ
ejpam-3587	64	30	presentation	presentation	NOUN
ejpam-3587	64	31	for	for	ADP
ejpam-3587	64	32	the	the	DET
ejpam-3587	64	33	order	order	NOUN
ejpam-3587	64	34	product	product	NOUN
ejpam-3587	64	35	prime	prime	ADJ
ejpam-3587	64	36	graph	graph	NOUN
ejpam-3587	64	37	on	on	ADP
ejpam-3587	64	38	dihedral	dihedral	ADJ
ejpam-3587	64	39	group	group	NOUN
ejpam-3587	64	40	and	and	CCONJ
ejpam-3587	64	41	cyclic	cyclic	ADJ
ejpam-3587	64	42	group	group	NOUN
ejpam-3587	64	43	are	be	AUX
ejpam-3587	64	44	given	give	VERB
ejpam-3587	64	45	in	in	ADP
ejpam-3587	64	46	theorem	theorem	ADJ
ejpam-3587	64	47	1	1	NUM
ejpam-3587	64	48	to	to	PART
ejpam-3587	64	49	theorem	theorem	VERB
ejpam-3587	64	50	3	3	NUM
ejpam-3587	64	51	.	.	PUNCT
ejpam-3587	64	52	theorem	theorem	NOUN
ejpam-3587	64	53	1	1	NUM
ejpam-3587	64	54	.	.	PUNCT
ejpam-3587	65	1	let	let	VERB
ejpam-3587	65	2	g	g	NOUN
ejpam-3587	65	3	be	be	AUX
ejpam-3587	65	4	the	the	DET
ejpam-3587	65	5	dihedral	dihedral	ADJ
ejpam-3587	65	6	group	group	NOUN
ejpam-3587	65	7	,	,	PUNCT
ejpam-3587	65	8	dn	dn	PROPN
ejpam-3587	65	9	,	,	PUNCT
ejpam-3587	65	10	where	where	SCONJ
ejpam-3587	65	11	n	n	PROPN
ejpam-3587	65	12	=	=	SYM
ejpam-3587	65	13	pα	pα	PROPN
ejpam-3587	65	14	,	,	PUNCT
ejpam-3587	65	15	α	α	PROPN
ejpam-3587	65	16	∈	∈	PROPN
ejpam-3587	65	17	n	n	CCONJ
ejpam-3587	65	18	,	,	PUNCT
ejpam-3587	65	19	then	then	ADV
ejpam-3587	65	20	γopp(g	γopp(g	PROPN
ejpam-3587	65	21	)	)	PUNCT
ejpam-3587	66	1	=	=	PRON
ejpam-3587	66	2	{	{	PUNCT
ejpam-3587	66	3	k2n	k2n	NOUN
ejpam-3587	66	4	if	if	SCONJ
ejpam-3587	66	5	p	p	NOUN
ejpam-3587	66	6	=	=	NOUN
ejpam-3587	66	7	2	2	NUM
ejpam-3587	66	8	,	,	PUNCT
ejpam-3587	66	9	k1	k1	NOUN
ejpam-3587	66	10	+	+	CCONJ
ejpam-3587	66	11	(	(	PUNCT
ejpam-3587	66	12	kn−1	kn−1	PROPN
ejpam-3587	66	13	∪kn	∪kn	PROPN
ejpam-3587	66	14	)	)	PUNCT
ejpam-3587	67	1	if	if	SCONJ
ejpam-3587	67	2	p	p	PROPN
ejpam-3587	67	3	6=	6=	NUM
ejpam-3587	67	4	2	2	NUM
ejpam-3587	67	5	.	.	X
ejpam-3587	68	1	proof	proof	NOUN
ejpam-3587	68	2	:	:	PUNCT
ejpam-3587	68	3	if	if	SCONJ
ejpam-3587	68	4	p	p	NOUN
ejpam-3587	68	5	=	=	NOUN
ejpam-3587	68	6	2	2	NUM
ejpam-3587	68	7	,	,	PUNCT
ejpam-3587	68	8	then	then	ADV
ejpam-3587	68	9	|g|	|g|	PROPN
ejpam-3587	68	10	=	=	SYM
ejpam-3587	68	11	2α+1	2α+1	PROPN
ejpam-3587	68	12	,	,	PUNCT
ejpam-3587	68	13	pick	pick	VERB
ejpam-3587	68	14	arbitrary	arbitrary	ADJ
ejpam-3587	68	15	xi	xi	PROPN
ejpam-3587	68	16	,	,	PUNCT
ejpam-3587	68	17	yj	yj	PROPN
ejpam-3587	68	18	∈	∈	PROPN
ejpam-3587	68	19	g	g	PROPN
ejpam-3587	68	20	,	,	PUNCT
ejpam-3587	68	21	i	i	PROPN
ejpam-3587	68	22	6=	6=	PROPN
ejpam-3587	68	23	j	j	PROPN
ejpam-3587	68	24	,	,	PUNCT
ejpam-3587	68	25	then	then	ADV
ejpam-3587	68	26	|x|	|x|	PROPN
ejpam-3587	68	27	/	/	SYM
ejpam-3587	68	28	2α+1	2α+1	PROPN
ejpam-3587	68	29	,	,	PUNCT
ejpam-3587	68	30	|y|	|y|	PROPN
ejpam-3587	68	31	/	/	SYM
ejpam-3587	68	32	2α+1	2α+1	PROPN
ejpam-3587	68	33	,	,	PUNCT
ejpam-3587	68	34	that	that	PRON
ejpam-3587	68	35	is	is	ADV
ejpam-3587	68	36	|x||y|	|x||y|	PROPN
ejpam-3587	68	37	=	=	PROPN
ejpam-3587	68	38	2	2	NUM
ejpam-3587	68	39	t	t	NOUN
ejpam-3587	68	40	,	,	PUNCT
ejpam-3587	68	41	1	1	NUM
ejpam-3587	68	42	≤	≤	NUM
ejpam-3587	68	43	t	t	NOUN
ejpam-3587	68	44	≤	≤	NUM
ejpam-3587	69	1	α	α	NOUN
ejpam-3587	69	2	.	.	PUNCT
ejpam-3587	70	1	since	since	SCONJ
ejpam-3587	70	2	any	any	DET
ejpam-3587	70	3	element	element	NOUN
ejpam-3587	70	4	of	of	ADP
ejpam-3587	70	5	g	g	PROPN
ejpam-3587	70	6	is	be	AUX
ejpam-3587	70	7	of	of	ADP
ejpam-3587	70	8	order	order	NOUN
ejpam-3587	70	9	2	2	NUM
ejpam-3587	70	10	t	t	NOUN
ejpam-3587	70	11	,	,	PUNCT
ejpam-3587	70	12	it	it	PRON
ejpam-3587	70	13	follows	follow	VERB
ejpam-3587	70	14	that	that	SCONJ
ejpam-3587	70	15	all	all	DET
ejpam-3587	70	16	the	the	DET
ejpam-3587	70	17	elements	element	NOUN
ejpam-3587	70	18	of	of	ADP
ejpam-3587	70	19	g	g	NOUN
ejpam-3587	70	20	form	form	VERB
ejpam-3587	70	21	single	single	ADJ
ejpam-3587	70	22	clique	clique	NOUN
ejpam-3587	70	23	.	.	PUNCT
ejpam-3587	71	1	therefore	therefore	ADV
ejpam-3587	71	2	γopp(g	γopp(g	NOUN
ejpam-3587	71	3	)	)	PUNCT
ejpam-3587	71	4	=	=	PUNCT
ejpam-3587	72	1	k2α+1	k2α+1	NOUN
ejpam-3587	72	2	=	=	SYM
ejpam-3587	72	3	k2n	k2n	NOUN
ejpam-3587	72	4	.	.	PUNCT
ejpam-3587	73	1	if	if	SCONJ
ejpam-3587	73	2	p	p	PROPN
ejpam-3587	73	3	6=	6=	NUM
ejpam-3587	73	4	2	2	NUM
ejpam-3587	73	5	,	,	PUNCT
ejpam-3587	73	6	then	then	ADV
ejpam-3587	73	7	|g|	|g|	PROPN
ejpam-3587	73	8	=	=	SYM
ejpam-3587	73	9	2pα	2pα	PROPN
ejpam-3587	73	10	.	.	PUNCT
ejpam-3587	74	1	let	let	VERB
ejpam-3587	74	2	a	a	PRON
ejpam-3587	74	3	and	and	CCONJ
ejpam-3587	74	4	b	b	NOUN
ejpam-3587	74	5	are	be	AUX
ejpam-3587	74	6	the	the	DET
ejpam-3587	74	7	sets	set	NOUN
ejpam-3587	74	8	of	of	ADP
ejpam-3587	74	9	non	non	ADJ
ejpam-3587	74	10	-	-	ADJ
ejpam-3587	74	11	trivial	trivial	ADJ
ejpam-3587	74	12	rotations	rotation	NOUN
ejpam-3587	74	13	and	and	CCONJ
ejpam-3587	74	14	the	the	DET
ejpam-3587	74	15	reflections	reflection	NOUN
ejpam-3587	74	16	of	of	ADP
ejpam-3587	74	17	g	g	NOUN
ejpam-3587	74	18	respectively	respectively	ADV
ejpam-3587	74	19	.	.	PUNCT
ejpam-3587	75	1	pick	pick	VERB
ejpam-3587	75	2	x	x	PUNCT
ejpam-3587	75	3	∈	∈	PROPN
ejpam-3587	75	4	a	a	X
ejpam-3587	75	5	,	,	PUNCT
ejpam-3587	75	6	y	y	PROPN
ejpam-3587	75	7	∈	∈	PROPN
ejpam-3587	75	8	b	b	PROPN
ejpam-3587	75	9	,	,	PUNCT
ejpam-3587	75	10	then	then	ADV
ejpam-3587	75	11	xpt	xpt	PROPN
ejpam-3587	75	12	=	=	PUNCT
ejpam-3587	75	13	e	e	X
ejpam-3587	75	14	=	=	PUNCT
ejpam-3587	75	15	y2	y2	PROPN
ejpam-3587	75	16	.	.	PUNCT
ejpam-3587	76	1	now	now	ADV
ejpam-3587	76	2	by	by	ADP
ejpam-3587	76	3	the	the	DET
ejpam-3587	76	4	vertex	vertex	NOUN
ejpam-3587	76	5	adjacency	adjacency	NOUN
ejpam-3587	76	6	,	,	PUNCT
ejpam-3587	76	7	a	a	PRON
ejpam-3587	76	8	and	and	CCONJ
ejpam-3587	76	9	b	b	NOUN
ejpam-3587	76	10	are	be	AUX
ejpam-3587	76	11	distinct	distinct	ADJ
ejpam-3587	76	12	cliques	clique	NOUN
ejpam-3587	76	13	in	in	ADP
ejpam-3587	76	14	γopp(g	γopp(g	NOUN
ejpam-3587	76	15	)	)	PUNCT
ejpam-3587	76	16	and	and	CCONJ
ejpam-3587	77	1	|(a)|	|(a)|	PROPN
ejpam-3587	77	2	=	=	SYM
ejpam-3587	77	3	pα	pα	NOUN
ejpam-3587	77	4	−	−	PROPN
ejpam-3587	77	5	1	1	NUM
ejpam-3587	77	6	,	,	PUNCT
ejpam-3587	77	7	|(b)|	|(b)|	PROPN
ejpam-3587	77	8	=	=	SYM
ejpam-3587	77	9	pα	pα	PROPN
ejpam-3587	77	10	,	,	PUNCT
ejpam-3587	77	11	then	then	ADV
ejpam-3587	77	12	γopp(a	γopp(a	NOUN
ejpam-3587	77	13	)	)	PUNCT
ejpam-3587	77	14	=	=	SYM
ejpam-3587	78	1	kpα−1	kpα−1	PROPN
ejpam-3587	78	2	,	,	PUNCT
ejpam-3587	78	3	γopp(b	γopp(b	NOUN
ejpam-3587	78	4	)	)	PUNCT
ejpam-3587	78	5	=	=	SYM
ejpam-3587	78	6	kpα	kpα	NOUN
ejpam-3587	78	7	are	be	AUX
ejpam-3587	78	8	subgraphs	subgraph	NOUN
ejpam-3587	78	9	of	of	ADP
ejpam-3587	78	10	γopp(g	γopp(g	NOUN
ejpam-3587	78	11	)	)	PUNCT
ejpam-3587	78	12	.	.	PUNCT
ejpam-3587	79	1	so	so	ADV
ejpam-3587	79	2	by	by	ADP
ejpam-3587	79	3	the	the	DET
ejpam-3587	79	4	vertex	vertex	NOUN
ejpam-3587	79	5	adjacency	adjacency	NOUN
ejpam-3587	79	6	,	,	PUNCT
ejpam-3587	79	7	a	a	DET
ejpam-3587	79	8	∼	∼	NOUN
ejpam-3587	79	9	e	e	NOUN
ejpam-3587	79	10	∼	∼	NOUN
ejpam-3587	79	11	b	b	NOUN
ejpam-3587	79	12	,	,	PUNCT
ejpam-3587	79	13	therefore	therefore	ADV
ejpam-3587	79	14	γopp(g	γopp(g	NOUN
ejpam-3587	79	15	)	)	PUNCT
ejpam-3587	79	16	=	=	SYM
ejpam-3587	79	17	γopp(e	γopp(e	NOUN
ejpam-3587	79	18	)	)	PUNCT
ejpam-3587	80	1	+	+	CCONJ
ejpam-3587	80	2	(	(	PUNCT
ejpam-3587	80	3	γopp(a	γopp(a	NOUN
ejpam-3587	80	4	)	)	PUNCT
ejpam-3587	80	5	∪	∪	ADP
ejpam-3587	80	6	γopp(b	γopp(b	NOUN
ejpam-3587	80	7	)	)	PUNCT
ejpam-3587	80	8	)	)	PUNCT
ejpam-3587	81	1	=	=	SYM
ejpam-3587	81	2	k1	k1	NOUN
ejpam-3587	81	3	+	+	CCONJ
ejpam-3587	81	4	(	(	PUNCT
ejpam-3587	81	5	kpα−1	kpα−1	PROPN
ejpam-3587	81	6	∪kpα	∪kpα	ADJ
ejpam-3587	81	7	)	)	PUNCT
ejpam-3587	81	8	=	=	SYM
ejpam-3587	81	9	k1	k1	NOUN
ejpam-3587	81	10	+	+	CCONJ
ejpam-3587	81	11	(	(	PUNCT
ejpam-3587	81	12	kn−1	kn−1	PROPN
ejpam-3587	81	13	∪kn	∪kn	PROPN
ejpam-3587	81	14	)	)	PUNCT
ejpam-3587	81	15	�	�	PROPN
ejpam-3587	81	16	theorem	theorem	VERB
ejpam-3587	81	17	2	2	NUM
ejpam-3587	81	18	.	.	PUNCT
ejpam-3587	82	1	let	let	VERB
ejpam-3587	82	2	g	g	PRON
ejpam-3587	82	3	be	be	AUX
ejpam-3587	82	4	a	a	DET
ejpam-3587	82	5	dihedral	dihedral	ADJ
ejpam-3587	82	6	group	group	NOUN
ejpam-3587	82	7	,	,	PUNCT
ejpam-3587	82	8	dn	dn	PROPN
ejpam-3587	82	9	,	,	PUNCT
ejpam-3587	82	10	where	where	SCONJ
ejpam-3587	82	11	n	n	NOUN
ejpam-3587	82	12	=	=	SYM
ejpam-3587	82	13	∏d	∏d	ADP
ejpam-3587	82	14	i=1	i=1	PROPN
ejpam-3587	83	1	p	p	X
ejpam-3587	83	2	αi	αi	ADV
ejpam-3587	83	3	i	i	PRON
ejpam-3587	83	4	,	,	PUNCT
ejpam-3587	83	5	then	then	ADV
ejpam-3587	83	6	γopp(g	γopp(g	PROPN
ejpam-3587	83	7	)	)	PUNCT
ejpam-3587	83	8	=	=	PUNCT
ejpam-3587	83	9			NOUN
ejpam-3587	83	10	k1	k1	NOUN
ejpam-3587	83	11	+	+	CCONJ
ejpam-3587	84	1	[	[	X
ejpam-3587	84	2	⋃d	⋃d	X
ejpam-3587	84	3	i=2k(p	i=2k(p	PROPN
ejpam-3587	84	4	αi	αi	VERB
ejpam-3587	84	5	i	i	PRON
ejpam-3587	84	6	−1	−1	NOUN
ejpam-3587	84	7	)	)	PUNCT
ejpam-3587	85	1	⋃	⋃	PUNCT
ejpam-3587	85	2	kn+p	kn+p	PROPN
ejpam-3587	85	3	α1	α1	PROPN
ejpam-3587	85	4	1	1	NUM
ejpam-3587	85	5	−1	−1	NOUN
ejpam-3587	85	6	)	)	PUNCT
ejpam-3587	85	7	]	]	PUNCT
ejpam-3587	85	8	⋃	⋃	PUNCT
ejpam-3587	85	9	kn+d−(1	kn+d−(1	NOUN
ejpam-3587	85	10	+	+	X
ejpam-3587	85	11	∑d	∑d	X
ejpam-3587	85	12	i=1	i=1	X
ejpam-3587	86	1	p	p	X
ejpam-3587	86	2	αi	αi	VERB
ejpam-3587	86	3	i	i	INTJ
ejpam-3587	86	4	)	)	PUNCT
ejpam-3587	86	5	where	where	SCONJ
ejpam-3587	86	6	p1	p1	NOUN
ejpam-3587	86	7	=	=	SYM
ejpam-3587	86	8	2	2	NUM
ejpam-3587	86	9	,	,	PUNCT
ejpam-3587	86	10	k1	k1	NOUN
ejpam-3587	86	11	+	+	CCONJ
ejpam-3587	87	1	[	[	X
ejpam-3587	87	2	⋃d	⋃d	X
ejpam-3587	87	3	i=1k(p	i=1k(p	PROPN
ejpam-3587	87	4	αi	αi	VERB
ejpam-3587	87	5	i	i	PRON
ejpam-3587	87	6	−1	−1	NOUN
ejpam-3587	87	7	)	)	PUNCT
ejpam-3587	88	1	∪kn	∪kn	NOUN
ejpam-3587	88	2	]	]	X
ejpam-3587	88	3	⋃	⋃	NOUN
ejpam-3587	88	4	kn+d−(1	kn+d−(1	NOUN
ejpam-3587	88	5	+	+	X
ejpam-3587	88	6	∑d	∑d	X
ejpam-3587	89	1	i=1	i=1	X
ejpam-3587	89	2	p	p	X
ejpam-3587	89	3	αi	αi	VERB
ejpam-3587	89	4	i	i	INTJ
ejpam-3587	89	5	)	)	PUNCT
ejpam-3587	90	1	if	if	SCONJ
ejpam-3587	90	2	n	n	PRON
ejpam-3587	90	3	is	be	AUX
ejpam-3587	90	4	odd	odd	ADJ
ejpam-3587	90	5	,	,	PUNCT
ejpam-3587	90	6	where	where	SCONJ
ejpam-3587	90	7	d	d	NOUN
ejpam-3587	90	8	is	be	AUX
ejpam-3587	90	9	the	the	DET
ejpam-3587	90	10	number	number	NOUN
ejpam-3587	90	11	of	of	ADP
ejpam-3587	90	12	prime	prime	ADJ
ejpam-3587	90	13	divisors	divisor	NOUN
ejpam-3587	90	14	of	of	ADP
ejpam-3587	90	15	n	n	PRON
ejpam-3587	90	16	and	and	CCONJ
ejpam-3587	90	17	α	α	DET
ejpam-3587	90	18	∈	∈	PROPN
ejpam-3587	90	19	n.	n.	NOUN
ejpam-3587	90	20	proof	proof	NOUN
ejpam-3587	90	21	let	let	VERB
ejpam-3587	90	22	r	r	NOUN
ejpam-3587	90	23	and	and	CCONJ
ejpam-3587	90	24	r′	r′	PROPN
ejpam-3587	90	25	be	be	AUX
ejpam-3587	90	26	the	the	DET
ejpam-3587	90	27	sets	set	NOUN
ejpam-3587	90	28	of	of	ADP
ejpam-3587	90	29	non	non	ADJ
ejpam-3587	90	30	-	-	ADJ
ejpam-3587	90	31	trivial	trivial	ADJ
ejpam-3587	90	32	rotations	rotation	NOUN
ejpam-3587	90	33	and	and	CCONJ
ejpam-3587	90	34	the	the	DET
ejpam-3587	90	35	reflections	reflection	NOUN
ejpam-3587	90	36	ofg	ofg	PROPN
ejpam-3587	90	37	respectively	respectively	ADV
ejpam-3587	90	38	,	,	PUNCT
ejpam-3587	90	39	since	since	SCONJ
ejpam-3587	90	40	n	n	NOUN
ejpam-3587	90	41	=	=	SYM
ejpam-3587	90	42	∏d	∏d	ADP
ejpam-3587	90	43	i=1	i=1	PROPN
ejpam-3587	91	1	p	p	X
ejpam-3587	91	2	αi	αi	ADV
ejpam-3587	91	3	i	i	PRON
ejpam-3587	91	4	,	,	PUNCT
ejpam-3587	91	5	then	then	ADV
ejpam-3587	91	6	each	each	DET
ejpam-3587	91	7	element	element	NOUN
ejpam-3587	91	8	of	of	ADP
ejpam-3587	91	9	order	order	NOUN
ejpam-3587	91	10	pαi	pαi	NOUN
ejpam-3587	91	11	,	,	PUNCT
ejpam-3587	91	12	where	where	SCONJ
ejpam-3587	91	13	α	α	PROPN
ejpam-3587	91	14	is	be	AUX
ejpam-3587	91	15	the	the	DET
ejpam-3587	91	16	greatest	great	ADJ
ejpam-3587	91	17	prime	prime	ADJ
ejpam-3587	91	18	power	power	NOUN
ejpam-3587	91	19	,	,	PUNCT
ejpam-3587	91	20	generates	generate	VERB
ejpam-3587	91	21	cyclic	cyclic	ADJ
ejpam-3587	91	22	subgroup	subgroup	NOUN
ejpam-3587	91	23	of	of	ADP
ejpam-3587	91	24	order	order	NOUN
ejpam-3587	91	25	pαi	pαi	VERB
ejpam-3587	91	26	−	−	PROPN
ejpam-3587	92	1	1	1	X
ejpam-3587	92	2	.	.	X
ejpam-3587	92	3	recall	recall	VERB
ejpam-3587	92	4	that	that	SCONJ
ejpam-3587	92	5	we	we	PRON
ejpam-3587	92	6	have	have	VERB
ejpam-3587	92	7	d	d	X
ejpam-3587	92	8	distinct	distinct	ADJ
ejpam-3587	92	9	primes	prime	NOUN
ejpam-3587	92	10	,	,	PUNCT
ejpam-3587	92	11	so	so	SCONJ
ejpam-3587	92	12	there	there	PRON
ejpam-3587	92	13	exist	exist	VERB
ejpam-3587	92	14	total	total	NOUN
ejpam-3587	92	15	of	of	ADP
ejpam-3587	92	16	d	d	X
ejpam-3587	92	17	complete	complete	ADJ
ejpam-3587	92	18	non	non	ADJ
ejpam-3587	92	19	-	-	ADJ
ejpam-3587	92	20	trivial	trivial	ADJ
ejpam-3587	92	21	cliques	clique	NOUN
ejpam-3587	92	22	whose	whose	DET
ejpam-3587	92	23	each	each	DET
ejpam-3587	92	24	vertex	vertex	NOUN
ejpam-3587	92	25	is	be	AUX
ejpam-3587	92	26	adjacent	adjacent	ADJ
ejpam-3587	92	27	to	to	PART
ejpam-3587	92	28	e.	e.	PROPN
ejpam-3587	92	29	let	let	VERB
ejpam-3587	92	30	i	i	PRON
ejpam-3587	92	31	be	be	AUX
ejpam-3587	92	32	the	the	DET
ejpam-3587	92	33	set	set	NOUN
ejpam-3587	92	34	of	of	ADP
ejpam-3587	92	35	the	the	DET
ejpam-3587	92	36	isolated	isolate	VERB
ejpam-3587	92	37	vertices	vertex	NOUN
ejpam-3587	92	38	of	of	ADP
ejpam-3587	92	39	γopp(g	γopp(g	NOUN
ejpam-3587	92	40	)	)	PUNCT
ejpam-3587	92	41	,	,	PUNCT
ejpam-3587	92	42	then	then	ADV
ejpam-3587	92	43	i	i	PRON
ejpam-3587	92	44	⊂	⊂	X
ejpam-3587	92	45	r	r	NOUN
ejpam-3587	92	46	and	and	CCONJ
ejpam-3587	92	47	|i|	|i|	PROPN
ejpam-3587	92	48	=	=	SYM
ejpam-3587	92	49	|r|	|r|	NOUN
ejpam-3587	92	50	−	−	PROPN
ejpam-3587	93	1	(	(	PUNCT
ejpam-3587	93	2	d∑	d∑	PROPN
ejpam-3587	93	3	i=1	i=1	PROPN
ejpam-3587	93	4	(	(	PUNCT
ejpam-3587	93	5	pαii	pαii	NOUN
ejpam-3587	93	6	−	−	PROPN
ejpam-3587	93	7	1	1	NUM
ejpam-3587	93	8	)	)	PUNCT
ejpam-3587	93	9	)	)	PUNCT
ejpam-3587	93	10	m.	m.	NOUN
ejpam-3587	93	11	bello	bello	PROPN
ejpam-3587	93	12	,	,	PUNCT
ejpam-3587	93	13	n.	n.	PROPN
ejpam-3587	93	14	m.	m.	NOUN
ejpam-3587	93	15	mohd	mohd	PROPN
ejpam-3587	93	16	ali	ali	PROPN
ejpam-3587	93	17	,	,	PUNCT
ejpam-3587	93	18	n.	n.	PROPN
ejpam-3587	93	19	zulkifli	zulkifli	PROPN
ejpam-3587	93	20	/	/	SYM
ejpam-3587	93	21	eur	eur	PROPN
ejpam-3587	93	22	.	.	PUNCT
ejpam-3587	94	1	j.	j.	PROPN
ejpam-3587	94	2	pure	pure	PROPN
ejpam-3587	94	3	appl	appl	PROPN
ejpam-3587	94	4	.	.	PROPN
ejpam-3587	94	5	math	math	PROPN
ejpam-3587	94	6	,	,	PUNCT
ejpam-3587	94	7	13	13	NUM
ejpam-3587	94	8	(	(	PUNCT
ejpam-3587	94	9	1	1	NUM
ejpam-3587	94	10	)	)	PUNCT
ejpam-3587	94	11	(	(	PUNCT
ejpam-3587	94	12	2020	2020	NUM
ejpam-3587	94	13	)	)	PUNCT
ejpam-3587	94	14	,	,	PUNCT
ejpam-3587	94	15	84	84	NUM
ejpam-3587	94	16	-	-	SYM
ejpam-3587	94	17	95	95	NUM
ejpam-3587	94	18	88	88	NUM
ejpam-3587	94	19	=	=	SYM
ejpam-3587	94	20	(	(	PUNCT
ejpam-3587	94	21	n−	n−	NOUN
ejpam-3587	94	22	1)−	1)−	NUM
ejpam-3587	94	23	pα1	pα1	NOUN
ejpam-3587	94	24	1	1	NUM
ejpam-3587	94	25	−	−	PROPN
ejpam-3587	94	26	p	p	NOUN
ejpam-3587	94	27	α2	α2	PROPN
ejpam-3587	94	28	2	2	NUM
ejpam-3587	94	29	−	−	NOUN
ejpam-3587	94	30	...	...	PUNCT
ejpam-3587	94	31	−	−	PROPN
ejpam-3587	95	1	p	p	X
ejpam-3587	95	2	αi	αi	VERB
ejpam-3587	95	3	i	i	PRON
ejpam-3587	96	1	+	+	PUNCT
ejpam-3587	96	2	d	d	NOUN
ejpam-3587	96	3	=	=	SYM
ejpam-3587	96	4	n+	n+	NUM
ejpam-3587	96	5	d−	d−	PROPN
ejpam-3587	96	6	(	(	PUNCT
ejpam-3587	96	7	1	1	NUM
ejpam-3587	96	8	+	+	NUM
ejpam-3587	96	9	d∑	d∑	PROPN
ejpam-3587	96	10	i=1	i=1	PROPN
ejpam-3587	96	11	pαii	pαii	NOUN
ejpam-3587	96	12	)	)	PUNCT
ejpam-3587	96	13	.	.	PUNCT
ejpam-3587	97	1	if	if	SCONJ
ejpam-3587	97	2	p1	p1	PROPN
ejpam-3587	97	3	=	=	SYM
ejpam-3587	97	4	2	2	NUM
ejpam-3587	97	5	,	,	PUNCT
ejpam-3587	97	6	then	then	ADV
ejpam-3587	97	7	there	there	PRON
ejpam-3587	97	8	exist	exist	VERB
ejpam-3587	97	9	an	an	DET
ejpam-3587	97	10	element	element	NOUN
ejpam-3587	97	11	a	a	DET
ejpam-3587	97	12	∈	∈	PROPN
ejpam-3587	97	13	r	r	NOUN
ejpam-3587	97	14	3	3	NUM
ejpam-3587	97	15	a2	a2	PROPN
ejpam-3587	97	16	α1	α1	PROPN
ejpam-3587	97	17	=	=	SYM
ejpam-3587	97	18	e	e	NOUN
ejpam-3587	97	19	,	,	PUNCT
ejpam-3587	97	20	let	let	VERB
ejpam-3587	97	21	x	x	PRON
ejpam-3587	97	22	be	be	AUX
ejpam-3587	97	23	the	the	DET
ejpam-3587	97	24	set	set	NOUN
ejpam-3587	97	25	of	of	ADP
ejpam-3587	97	26	these	these	PRON
ejpam-3587	97	27	a′s	a′s	ADJ
ejpam-3587	97	28	,	,	PUNCT
ejpam-3587	97	29	then	then	ADV
ejpam-3587	97	30	{	{	PUNCT
ejpam-3587	97	31	x	x	NOUN
ejpam-3587	97	32	,	,	PUNCT
ejpam-3587	97	33	r′	r′	NUM
ejpam-3587	97	34	}	}	PUNCT
ejpam-3587	97	35	is	be	AUX
ejpam-3587	97	36	a	a	DET
ejpam-3587	97	37	clique	clique	NOUN
ejpam-3587	97	38	of	of	ADP
ejpam-3587	97	39	size	size	NOUN
ejpam-3587	97	40	n+	n+	ADP
ejpam-3587	97	41	2α1	2α1	NOUN
ejpam-3587	97	42	−	−	NOUN
ejpam-3587	97	43	1	1	X
ejpam-3587	97	44	.	.	PUNCT
ejpam-3587	98	1	we	we	PRON
ejpam-3587	98	2	can	can	AUX
ejpam-3587	98	3	now	now	ADV
ejpam-3587	98	4	see	see	VERB
ejpam-3587	98	5	that	that	DET
ejpam-3587	98	6	γopp(g	γopp(g	NOUN
ejpam-3587	98	7	)	)	PUNCT
ejpam-3587	98	8	is	be	AUX
ejpam-3587	98	9	the	the	DET
ejpam-3587	98	10	union	union	NOUN
ejpam-3587	98	11	of	of	ADP
ejpam-3587	98	12	the	the	DET
ejpam-3587	98	13	non	non	ADJ
ejpam-3587	98	14	-	-	ADJ
ejpam-3587	98	15	trivial	trivial	ADJ
ejpam-3587	98	16	complete	complete	ADJ
ejpam-3587	98	17	cliques	clique	NOUN
ejpam-3587	98	18	and	and	CCONJ
ejpam-3587	98	19	set	set	VERB
ejpam-3587	98	20	i	i	PRON
ejpam-3587	98	21	,	,	PUNCT
ejpam-3587	98	22	that	that	ADV
ejpam-3587	98	23	is	is	ADV
ejpam-3587	98	24	,	,	PUNCT
ejpam-3587	98	25	γopp(g	γopp(g	NOUN
ejpam-3587	98	26	)	)	PUNCT
ejpam-3587	98	27	=	=	SYM
ejpam-3587	98	28	k1	k1	NOUN
ejpam-3587	99	1	+	+	CCONJ
ejpam-3587	99	2	[	[	PUNCT
ejpam-3587	99	3	d−1⋃	d−1⋃	NOUN
ejpam-3587	99	4	i=1	i=1	PROPN
ejpam-3587	99	5	k(p	k(p	PROPN
ejpam-3587	99	6	αi	αi	VERB
ejpam-3587	99	7	i	i	PRON
ejpam-3587	99	8	−1	−1	NOUN
ejpam-3587	99	9	)	)	PUNCT
ejpam-3587	99	10	⋃	⋃	SCONJ
ejpam-3587	99	11	kn+2α1−1	kn+2α1−1	NOUN
ejpam-3587	99	12	)	)	PUNCT
ejpam-3587	99	13	]	]	PUNCT
ejpam-3587	99	14	⋃	⋃	PUNCT
ejpam-3587	99	15	i	i	NOUN
ejpam-3587	99	16	=	=	SYM
ejpam-3587	99	17	k1	k1	NOUN
ejpam-3587	99	18	+	+	CCONJ
ejpam-3587	99	19	[	[	PUNCT
ejpam-3587	99	20	d−1⋃	d−1⋃	NOUN
ejpam-3587	99	21	i=1	i=1	PROPN
ejpam-3587	99	22	k(p	k(p	PROPN
ejpam-3587	99	23	αi	αi	VERB
ejpam-3587	99	24	i	i	PRON
ejpam-3587	99	25	−1	−1	NOUN
ejpam-3587	99	26	)	)	PUNCT
ejpam-3587	99	27	⋃	⋃	SCONJ
ejpam-3587	99	28	kn+2α1−1	kn+2α1−1	NOUN
ejpam-3587	99	29	)	)	PUNCT
ejpam-3587	99	30	]	]	PUNCT
ejpam-3587	99	31	⋃	⋃	PUNCT
ejpam-3587	99	32	kn+d−(1	kn+d−(1	NOUN
ejpam-3587	99	33	+	+	X
ejpam-3587	99	34	∑d	∑d	X
ejpam-3587	100	1	i=1	i=1	X
ejpam-3587	100	2	p	p	X
ejpam-3587	100	3	αi	αi	VERB
ejpam-3587	100	4	i	i	INTJ
ejpam-3587	100	5	)	)	PUNCT
ejpam-3587	101	1	if	if	SCONJ
ejpam-3587	101	2	n	n	PRON
ejpam-3587	101	3	is	be	AUX
ejpam-3587	101	4	odd	odd	ADJ
ejpam-3587	101	5	,	,	PUNCT
ejpam-3587	101	6	then	then	ADV
ejpam-3587	101	7	z(g	z(g	NOUN
ejpam-3587	101	8	)	)	PUNCT
ejpam-3587	101	9	is	be	AUX
ejpam-3587	101	10	trivial	trivial	ADJ
ejpam-3587	101	11	and	and	CCONJ
ejpam-3587	101	12	therefore	therefore	ADV
ejpam-3587	101	13	each	each	DET
ejpam-3587	101	14	prime	prime	NOUN
ejpam-3587	101	15	generate	generate	VERB
ejpam-3587	101	16	distinct	distinct	ADJ
ejpam-3587	101	17	clique	clique	NOUN
ejpam-3587	101	18	.	.	PUNCT
ejpam-3587	102	1	so	so	ADV
ejpam-3587	102	2	γopp(g	γopp(g	NOUN
ejpam-3587	102	3	)	)	PUNCT
ejpam-3587	102	4	=	=	SYM
ejpam-3587	102	5	k1	k1	NOUN
ejpam-3587	102	6	+	+	CCONJ
ejpam-3587	102	7	[	[	PUNCT
ejpam-3587	102	8	d⋃	d⋃	VERB
ejpam-3587	102	9	i=1	i=1	X
ejpam-3587	102	10	k(p	k(p	PROPN
ejpam-3587	102	11	αi	αi	VERB
ejpam-3587	102	12	i	i	PRON
ejpam-3587	102	13	−1	−1	NOUN
ejpam-3587	102	14	)	)	PUNCT
ejpam-3587	102	15	∪kn	∪kn	NOUN
ejpam-3587	103	1	]	]	X
ejpam-3587	103	2	⋃	⋃	PUNCT
ejpam-3587	103	3	i	i	NOUN
ejpam-3587	103	4	=	=	SYM
ejpam-3587	103	5	k1	k1	PROPN
ejpam-3587	103	6	+	+	CCONJ
ejpam-3587	103	7	[	[	PUNCT
ejpam-3587	103	8	d⋃	d⋃	VERB
ejpam-3587	103	9	i=1	i=1	X
ejpam-3587	104	1	k(p	k(p	PROPN
ejpam-3587	104	2	αi	αi	VERB
ejpam-3587	104	3	i	i	PRON
ejpam-3587	104	4	−1	−1	NOUN
ejpam-3587	104	5	)	)	PUNCT
ejpam-3587	104	6	∪kn	∪kn	NOUN
ejpam-3587	104	7	]	]	X
ejpam-3587	104	8	⋃	⋃	NOUN
ejpam-3587	104	9	kn+d−(1	kn+d−(1	NOUN
ejpam-3587	104	10	+	+	X
ejpam-3587	104	11	∑d	∑d	X
ejpam-3587	104	12	i=1	i=1	X
ejpam-3587	105	1	p	p	X
ejpam-3587	105	2	αi	αi	ADV
ejpam-3587	105	3	i	i	PRON
ejpam-3587	105	4	)	)	PUNCT
ejpam-3587	105	5	�	�	PROPN
ejpam-3587	105	6	theorem	theorem	VERB
ejpam-3587	105	7	3	3	X
ejpam-3587	105	8	.	.	PUNCT
ejpam-3587	106	1	let	let	VERB
ejpam-3587	106	2	g	g	PRON
ejpam-3587	106	3	be	be	AUX
ejpam-3587	106	4	a	a	DET
ejpam-3587	106	5	cyclic	cyclic	ADJ
ejpam-3587	106	6	group	group	NOUN
ejpam-3587	106	7	,	,	PUNCT
ejpam-3587	106	8	zn	zn	PROPN
ejpam-3587	106	9	,	,	PUNCT
ejpam-3587	106	10	then	then	ADV
ejpam-3587	106	11	γopp(g	γopp(g	PROPN
ejpam-3587	106	12	)	)	PUNCT
ejpam-3587	106	13	=	=	PUNCT
ejpam-3587	107	1			PROPN
ejpam-3587	107	2	kpα	kpα	NOUN
ejpam-3587	107	3	if	if	SCONJ
ejpam-3587	107	4	n	n	PROPN
ejpam-3587	107	5	=	=	SYM
ejpam-3587	107	6	pα	pα	PROPN
ejpam-3587	107	7	,	,	PUNCT
ejpam-3587	107	8	k1	k1	PROPN
ejpam-3587	107	9	+	+	CCONJ
ejpam-3587	107	10	⋃d	⋃d	PROPN
ejpam-3587	107	11	i=1k(p	i=1k(p	PROPN
ejpam-3587	107	12	αi	αi	VERB
ejpam-3587	107	13	i	i	PRON
ejpam-3587	107	14	−1	−1	NOUN
ejpam-3587	107	15	)	)	PUNCT
ejpam-3587	107	16	⋃	⋃	ADP
ejpam-3587	107	17	kn+d−(1	kn+d−(1	NOUN
ejpam-3587	107	18	+	+	CCONJ
ejpam-3587	107	19	∑d	∑d	X
ejpam-3587	108	1	i=1	i=1	X
ejpam-3587	108	2	p	p	X
ejpam-3587	108	3	αi	αi	VERB
ejpam-3587	108	4	i	i	INTJ
ejpam-3587	108	5	)	)	PUNCT
ejpam-3587	109	1	if	if	SCONJ
ejpam-3587	109	2	n	n	ADV
ejpam-3587	109	3	=	=	SYM
ejpam-3587	109	4	∏d	∏d	ADP
ejpam-3587	109	5	i=1	i=1	PROPN
ejpam-3587	110	1	p	p	X
ejpam-3587	110	2	αi	αi	ADV
ejpam-3587	110	3	i	i	PRON
ejpam-3587	110	4	,	,	PUNCT
ejpam-3587	110	5	where	where	SCONJ
ejpam-3587	110	6	d	d	NOUN
ejpam-3587	110	7	is	be	AUX
ejpam-3587	110	8	the	the	DET
ejpam-3587	110	9	number	number	NOUN
ejpam-3587	110	10	of	of	ADP
ejpam-3587	110	11	prime	prime	ADJ
ejpam-3587	110	12	divisors	divisor	NOUN
ejpam-3587	110	13	of	of	ADP
ejpam-3587	110	14	n	n	PRON
ejpam-3587	110	15	and	and	CCONJ
ejpam-3587	110	16	α	α	PRON
ejpam-3587	110	17	∈	∈	PROPN
ejpam-3587	110	18	n.	n.	NOUN
ejpam-3587	110	19	proof	proof	NOUN
ejpam-3587	110	20	:	:	PUNCT
ejpam-3587	110	21	if	if	SCONJ
ejpam-3587	110	22	n	n	PRON
ejpam-3587	110	23	=	=	SYM
ejpam-3587	110	24	pα	pα	PROPN
ejpam-3587	110	25	,	,	PUNCT
ejpam-3587	110	26	then	then	ADV
ejpam-3587	110	27	g	g	PROPN
ejpam-3587	110	28	is	be	AUX
ejpam-3587	110	29	a	a	DET
ejpam-3587	110	30	p	p	NOUN
ejpam-3587	110	31	-	-	PUNCT
ejpam-3587	110	32	group	group	NOUN
ejpam-3587	110	33	,	,	PUNCT
ejpam-3587	110	34	and	and	CCONJ
ejpam-3587	110	35	so	so	ADV
ejpam-3587	110	36	for	for	SCONJ
ejpam-3587	110	37	each	each	DET
ejpam-3587	110	38	x	x	SYM
ejpam-3587	110	39	∈	∈	PROPN
ejpam-3587	110	40	g	g	PROPN
ejpam-3587	110	41	,	,	PUNCT
ejpam-3587	110	42	|x|	|x|	PROPN
ejpam-3587	110	43	=	=	SYM
ejpam-3587	110	44	pt	pt	PROPN
ejpam-3587	110	45	,	,	PUNCT
ejpam-3587	110	46	1	1	NUM
ejpam-3587	110	47	≤	≤	NUM
ejpam-3587	110	48	t	t	NOUN
ejpam-3587	110	49	≤	≤	NUM
ejpam-3587	110	50	α	α	NOUN
ejpam-3587	110	51	,	,	PUNCT
ejpam-3587	110	52	hence	hence	ADV
ejpam-3587	110	53	all	all	DET
ejpam-3587	110	54	the	the	DET
ejpam-3587	110	55	elements	element	NOUN
ejpam-3587	110	56	of	of	ADP
ejpam-3587	110	57	g	g	PROPN
ejpam-3587	110	58	form	form	VERB
ejpam-3587	110	59	a	a	DET
ejpam-3587	110	60	single	single	ADJ
ejpam-3587	110	61	clique	clique	NOUN
ejpam-3587	110	62	in	in	ADP
ejpam-3587	110	63	γopp(g	γopp(g	PROPN
ejpam-3587	110	64	)	)	PUNCT
ejpam-3587	110	65	and	and	CCONJ
ejpam-3587	110	66	|g|	|g|	PROPN
ejpam-3587	110	67	=	=	SYM
ejpam-3587	110	68	pα	pα	PROPN
ejpam-3587	110	69	,	,	PUNCT
ejpam-3587	110	70	therefore	therefore	ADV
ejpam-3587	110	71	γopp(g	γopp(g	NOUN
ejpam-3587	110	72	)	)	PUNCT
ejpam-3587	110	73	=	=	SYM
ejpam-3587	110	74	kpα	kpα	PROPN
ejpam-3587	110	75	suppose	suppose	VERB
ejpam-3587	110	76	n	n	ADJ
ejpam-3587	110	77	=	=	SYM
ejpam-3587	110	78	∏d	∏d	ADP
ejpam-3587	110	79	i=1	i=1	PROPN
ejpam-3587	111	1	p	p	X
ejpam-3587	111	2	αi	αi	ADV
ejpam-3587	111	3	i	i	PRON
ejpam-3587	111	4	,	,	PUNCT
ejpam-3587	111	5	observe	observe	VERB
ejpam-3587	111	6	that	that	SCONJ
ejpam-3587	111	7	for	for	ADP
ejpam-3587	111	8	all	all	DET
ejpam-3587	111	9	n	n	CCONJ
ejpam-3587	111	10	,	,	PUNCT
ejpam-3587	111	11	zn	zn	PROPN
ejpam-3587	111	12	∼=	∼=	NOUN
ejpam-3587	111	13	r	r	NOUN
ejpam-3587	111	14	,	,	PUNCT
ejpam-3587	111	15	where	where	SCONJ
ejpam-3587	111	16	r	r	NOUN
ejpam-3587	111	17	is	be	AUX
ejpam-3587	111	18	the	the	DET
ejpam-3587	111	19	set	set	NOUN
ejpam-3587	111	20	of	of	ADP
ejpam-3587	111	21	rotations	rotation	NOUN
ejpam-3587	111	22	of	of	ADP
ejpam-3587	111	23	dihedral	dihedral	ADJ
ejpam-3587	111	24	groups	group	NOUN
ejpam-3587	111	25	.	.	PUNCT
ejpam-3587	112	1	so	so	ADV
ejpam-3587	112	2	by	by	ADP
ejpam-3587	112	3	theorem	theorem	NOUN
ejpam-3587	112	4	2	2	NUM
ejpam-3587	112	5	,	,	PUNCT
ejpam-3587	112	6	γopp(g	γopp(g	NOUN
ejpam-3587	112	7	)	)	PUNCT
ejpam-3587	112	8	∼=	∼=	PROPN
ejpam-3587	112	9	γopp(r	γopp(r	NOUN
ejpam-3587	112	10	)	)	PUNCT
ejpam-3587	112	11	=	=	SYM
ejpam-3587	112	12	k1	k1	NOUN
ejpam-3587	112	13	+	+	CCONJ
ejpam-3587	112	14	d⋃	d⋃	VERB
ejpam-3587	112	15	i=1	i=1	X
ejpam-3587	113	1	k(p	k(p	PROPN
ejpam-3587	113	2	αi	αi	VERB
ejpam-3587	113	3	i	i	PRON
ejpam-3587	113	4	−1	−1	NOUN
ejpam-3587	113	5	)	)	PUNCT
ejpam-3587	113	6	⋃	⋃	ADP
ejpam-3587	113	7	kn+d−(1	kn+d−(1	NOUN
ejpam-3587	113	8	+	+	CCONJ
ejpam-3587	113	9	∑d	∑d	X
ejpam-3587	113	10	i=1	i=1	X
ejpam-3587	114	1	p	p	X
ejpam-3587	114	2	αi	αi	ADV
ejpam-3587	114	3	i	i	INTJ
ejpam-3587	114	4	)	)	PUNCT
ejpam-3587	114	5	�	�	PROPN
ejpam-3587	114	6	the	the	DET
ejpam-3587	114	7	connectivity	connectivity	NOUN
ejpam-3587	114	8	,	,	PUNCT
ejpam-3587	114	9	regularity	regularity	NOUN
ejpam-3587	114	10	and	and	CCONJ
ejpam-3587	114	11	completeness	completeness	NOUN
ejpam-3587	114	12	of	of	ADP
ejpam-3587	114	13	the	the	DET
ejpam-3587	114	14	order	order	NOUN
ejpam-3587	114	15	product	product	NOUN
ejpam-3587	114	16	prime	prime	ADJ
ejpam-3587	114	17	graph	graph	NOUN
ejpam-3587	114	18	on	on	ADP
ejpam-3587	114	19	dihedral	dihedral	ADJ
ejpam-3587	114	20	group	group	NOUN
ejpam-3587	114	21	and	and	CCONJ
ejpam-3587	114	22	cyclic	cyclic	ADJ
ejpam-3587	114	23	group	group	NOUN
ejpam-3587	114	24	is	be	AUX
ejpam-3587	114	25	given	give	VERB
ejpam-3587	114	26	in	in	ADP
ejpam-3587	114	27	theorem	theorem	ADJ
ejpam-3587	114	28	4	4	NUM
ejpam-3587	114	29	and	and	CCONJ
ejpam-3587	114	30	theorem	theorem	VERB
ejpam-3587	114	31	5	5	NUM
ejpam-3587	114	32	below	below	ADV
ejpam-3587	114	33	;	;	PUNCT
ejpam-3587	114	34	m.	m.	PROPN
ejpam-3587	114	35	bello	bello	PROPN
ejpam-3587	114	36	,	,	PUNCT
ejpam-3587	114	37	n.	n.	PROPN
ejpam-3587	114	38	m.	m.	NOUN
ejpam-3587	114	39	mohd	mohd	PROPN
ejpam-3587	114	40	ali	ali	PROPN
ejpam-3587	114	41	,	,	PUNCT
ejpam-3587	114	42	n.	n.	PROPN
ejpam-3587	114	43	zulkifli	zulkifli	PROPN
ejpam-3587	114	44	/	/	SYM
ejpam-3587	114	45	eur	eur	PROPN
ejpam-3587	114	46	.	.	PUNCT
ejpam-3587	115	1	j.	j.	PROPN
ejpam-3587	115	2	pure	pure	PROPN
ejpam-3587	115	3	appl	appl	PROPN
ejpam-3587	115	4	.	.	PROPN
ejpam-3587	115	5	math	math	PROPN
ejpam-3587	115	6	,	,	PUNCT
ejpam-3587	115	7	13	13	NUM
ejpam-3587	115	8	(	(	PUNCT
ejpam-3587	115	9	1	1	NUM
ejpam-3587	115	10	)	)	PUNCT
ejpam-3587	115	11	(	(	PUNCT
ejpam-3587	115	12	2020	2020	NUM
ejpam-3587	115	13	)	)	PUNCT
ejpam-3587	115	14	,	,	PUNCT
ejpam-3587	115	15	84	84	NUM
ejpam-3587	115	16	-	-	SYM
ejpam-3587	115	17	95	95	NUM
ejpam-3587	115	18	89	89	NUM
ejpam-3587	115	19	theorem	theorem	NOUN
ejpam-3587	115	20	4	4	NUM
ejpam-3587	115	21	.	.	PUNCT
ejpam-3587	116	1	let	let	VERB
ejpam-3587	116	2	g	g	PRON
ejpam-3587	116	3	be	be	AUX
ejpam-3587	116	4	a	a	DET
ejpam-3587	116	5	dihedral	dihedral	ADJ
ejpam-3587	116	6	group	group	NOUN
ejpam-3587	116	7	,	,	PUNCT
ejpam-3587	116	8	dn	dn	PROPN
ejpam-3587	116	9	,	,	PUNCT
ejpam-3587	116	10	then	then	ADV
ejpam-3587	116	11	γopp(g	γopp(g	NOUN
ejpam-3587	116	12	)	)	PUNCT
ejpam-3587	116	13	is	be	AUX
ejpam-3587	116	14	regular	regular	ADJ
ejpam-3587	116	15	and	and	CCONJ
ejpam-3587	116	16	complete	complete	ADJ
ejpam-3587	116	17	only	only	ADV
ejpam-3587	116	18	if	if	SCONJ
ejpam-3587	116	19	n	n	NOUN
ejpam-3587	116	20	=	=	SYM
ejpam-3587	116	21	2α	2α	NOUN
ejpam-3587	116	22	and	and	CCONJ
ejpam-3587	116	23	connected	connect	VERB
ejpam-3587	116	24	only	only	ADV
ejpam-3587	116	25	if	if	SCONJ
ejpam-3587	116	26	n	n	PROPN
ejpam-3587	116	27	=	=	SYM
ejpam-3587	116	28	pα	pα	NOUN
ejpam-3587	116	29	,	,	PUNCT
ejpam-3587	116	30	∀	∀	NOUN
ejpam-3587	117	1	p.	p.	NOUN
ejpam-3587	117	2	proof	proof	NOUN
ejpam-3587	117	3	:	:	PUNCT
ejpam-3587	117	4	we	we	PRON
ejpam-3587	117	5	prove	prove	VERB
ejpam-3587	117	6	the	the	DET
ejpam-3587	117	7	theorem	theorem	NOUN
ejpam-3587	117	8	by	by	ADP
ejpam-3587	117	9	considering	consider	VERB
ejpam-3587	117	10	the	the	DET
ejpam-3587	117	11	degree	degree	NOUN
ejpam-3587	117	12	of	of	ADP
ejpam-3587	117	13	the	the	DET
ejpam-3587	117	14	group	group	NOUN
ejpam-3587	117	15	in	in	ADP
ejpam-3587	117	16	two	two	NUM
ejpam-3587	117	17	cases	case	NOUN
ejpam-3587	117	18	below	below	ADV
ejpam-3587	117	19	.	.	PUNCT
ejpam-3587	118	1	case	case	NOUN
ejpam-3587	118	2	1	1	NUM
ejpam-3587	118	3	:	:	PUNCT
ejpam-3587	118	4	if	if	SCONJ
ejpam-3587	118	5	n	n	NOUN
ejpam-3587	118	6	=	=	SYM
ejpam-3587	118	7	2α	2α	NOUN
ejpam-3587	118	8	,	,	PUNCT
ejpam-3587	118	9	then	then	ADV
ejpam-3587	118	10	|g|	|g|	PROPN
ejpam-3587	118	11	=	=	SYM
ejpam-3587	118	12	2α+1	2α+1	PROPN
ejpam-3587	118	13	and	and	CCONJ
ejpam-3587	118	14	so	so	ADV
ejpam-3587	118	15	all	all	DET
ejpam-3587	118	16	the	the	DET
ejpam-3587	118	17	elements	element	NOUN
ejpam-3587	118	18	of	of	ADP
ejpam-3587	118	19	g	g	PROPN
ejpam-3587	118	20	are	be	AUX
ejpam-3587	118	21	powers	power	NOUN
ejpam-3587	118	22	of	of	ADP
ejpam-3587	118	23	2	2	NUM
ejpam-3587	118	24	,	,	PUNCT
ejpam-3587	118	25	they	they	PRON
ejpam-3587	118	26	therefore	therefore	ADV
ejpam-3587	118	27	form	form	VERB
ejpam-3587	118	28	single	single	ADJ
ejpam-3587	118	29	clique	clique	NOUN
ejpam-3587	118	30	in	in	ADP
ejpam-3587	118	31	γopp(g	γopp(g	PROPN
ejpam-3587	118	32	)	)	PUNCT
ejpam-3587	118	33	.	.	PUNCT
ejpam-3587	119	1	therefore	therefore	ADV
ejpam-3587	119	2	γopp(g	γopp(g	X
ejpam-3587	119	3	)	)	PUNCT
ejpam-3587	119	4	is	be	AUX
ejpam-3587	119	5	complete	complete	ADJ
ejpam-3587	119	6	since	since	SCONJ
ejpam-3587	119	7	for	for	ADP
ejpam-3587	119	8	each	each	DET
ejpam-3587	119	9	pair	pair	NOUN
ejpam-3587	119	10	(	(	PUNCT
ejpam-3587	119	11	xi	xi	PROPN
ejpam-3587	119	12	,	,	PUNCT
ejpam-3587	119	13	xj	xj	PROPN
ejpam-3587	119	14	)	)	PUNCT
ejpam-3587	119	15	∈	∈	PROPN
ejpam-3587	119	16	g	g	PROPN
ejpam-3587	119	17	,	,	PUNCT
ejpam-3587	119	18	xi	xi	ADP
ejpam-3587	119	19	∼	∼	NOUN
ejpam-3587	119	20	xj	xj	PROPN
ejpam-3587	119	21	,	,	PUNCT
ejpam-3587	119	22	i	i	PROPN
ejpam-3587	119	23	6=	6=	PROPN
ejpam-3587	119	24	j	j	PROPN
ejpam-3587	119	25	,	,	PUNCT
ejpam-3587	119	26	hence	hence	ADV
ejpam-3587	119	27	the	the	DET
ejpam-3587	119	28	graph	graph	NOUN
ejpam-3587	119	29	is	be	AUX
ejpam-3587	119	30	also	also	ADV
ejpam-3587	119	31	connected	connect	VERB
ejpam-3587	119	32	and	and	CCONJ
ejpam-3587	119	33	regular	regular	ADJ
ejpam-3587	119	34	by	by	ADP
ejpam-3587	119	35	the	the	DET
ejpam-3587	119	36	vertex	vertex	NOUN
ejpam-3587	119	37	adjacency	adjacency	NOUN
ejpam-3587	119	38	.	.	PUNCT
ejpam-3587	120	1	if	if	SCONJ
ejpam-3587	120	2	n	n	NUM
ejpam-3587	120	3	=	=	SYM
ejpam-3587	120	4	pα	pα	PROPN
ejpam-3587	120	5	,	,	PUNCT
ejpam-3587	120	6	p	p	X
ejpam-3587	120	7	6=	6=	PROPN
ejpam-3587	120	8	2	2	NUM
ejpam-3587	120	9	,	,	PUNCT
ejpam-3587	120	10	then	then	ADV
ejpam-3587	120	11	|g|	|g|	PROPN
ejpam-3587	120	12	=	=	SYM
ejpam-3587	120	13	2pα	2pα	NOUN
ejpam-3587	121	1	so	so	ADV
ejpam-3587	121	2	we	we	PRON
ejpam-3587	121	3	only	only	ADV
ejpam-3587	121	4	have	have	VERB
ejpam-3587	121	5	the	the	DET
ejpam-3587	121	6	elements	element	NOUN
ejpam-3587	121	7	of	of	ADP
ejpam-3587	121	8	order	order	NOUN
ejpam-3587	121	9	2	2	NUM
ejpam-3587	121	10	and	and	CCONJ
ejpam-3587	121	11	pα	pα	INTJ
ejpam-3587	121	12	but	but	CCONJ
ejpam-3587	121	13	not	not	PART
ejpam-3587	121	14	2pα	2pα	NOUN
ejpam-3587	121	15	since	since	SCONJ
ejpam-3587	121	16	g	g	PROPN
ejpam-3587	121	17	is	be	AUX
ejpam-3587	121	18	not	not	PART
ejpam-3587	121	19	cyclic	cyclic	ADJ
ejpam-3587	121	20	.	.	PUNCT
ejpam-3587	122	1	let	let	VERB
ejpam-3587	122	2	r	r	NOUN
ejpam-3587	122	3	and	and	CCONJ
ejpam-3587	122	4	r	r	NOUN
ejpam-3587	122	5	′	′	NUM
ejpam-3587	122	6	be	be	AUX
ejpam-3587	122	7	the	the	DET
ejpam-3587	122	8	sets	set	NOUN
ejpam-3587	122	9	of	of	ADP
ejpam-3587	122	10	non	non	ADJ
ejpam-3587	122	11	-	-	ADJ
ejpam-3587	122	12	trivial	trivial	ADJ
ejpam-3587	122	13	rotations	rotation	NOUN
ejpam-3587	122	14	and	and	CCONJ
ejpam-3587	122	15	the	the	DET
ejpam-3587	122	16	reflections	reflection	NOUN
ejpam-3587	122	17	of	of	ADP
ejpam-3587	122	18	g	g	NOUN
ejpam-3587	122	19	respectively	respectively	ADV
ejpam-3587	122	20	,	,	PUNCT
ejpam-3587	122	21	then	then	ADV
ejpam-3587	122	22	r	r	NOUN
ejpam-3587	122	23	and	and	CCONJ
ejpam-3587	122	24	r	r	NOUN
ejpam-3587	122	25	′	′	NOUN
ejpam-3587	122	26	are	be	AUX
ejpam-3587	122	27	distinct	distinct	ADJ
ejpam-3587	122	28	cliques	clique	NOUN
ejpam-3587	122	29	and	and	CCONJ
ejpam-3587	122	30	|r|	|r|	NOUN
ejpam-3587	122	31	=	=	SYM
ejpam-3587	122	32	n	n	CCONJ
ejpam-3587	122	33	−	−	NUM
ejpam-3587	122	34	1	1	NUM
ejpam-3587	122	35	while	while	SCONJ
ejpam-3587	122	36	|r′	|r′	VERB
ejpam-3587	122	37	|	|	ADV
ejpam-3587	122	38	=	=	SYM
ejpam-3587	122	39	n	n	CCONJ
ejpam-3587	122	40	,	,	PUNCT
ejpam-3587	122	41	hence	hence	ADV
ejpam-3587	122	42	deg(xi	deg(xi	VERB
ejpam-3587	122	43	)	)	PUNCT
ejpam-3587	122	44	<	<	X
ejpam-3587	122	45	deg(yi	deg(yi	X
ejpam-3587	122	46	)	)	PUNCT
ejpam-3587	122	47	∀	∀	X
ejpam-3587	122	48	xi	xi	ADP
ejpam-3587	122	49	∈	∈	PROPN
ejpam-3587	122	50	r	r	NOUN
ejpam-3587	122	51	,	,	PUNCT
ejpam-3587	122	52	yi	yi	NOUN
ejpam-3587	122	53	∈	∈	PROPN
ejpam-3587	122	54	r	r	NOUN
ejpam-3587	123	1	′	′	NOUN
ejpam-3587	123	2	since	since	SCONJ
ejpam-3587	123	3	n−	n−	NOUN
ejpam-3587	123	4	1	1	NUM
ejpam-3587	123	5	<	<	X
ejpam-3587	123	6	n	n	CCONJ
ejpam-3587	123	7	,	,	PUNCT
ejpam-3587	123	8	therefore	therefore	ADV
ejpam-3587	123	9	γopp(g	γopp(g	NOUN
ejpam-3587	123	10	)	)	PUNCT
ejpam-3587	123	11	is	be	AUX
ejpam-3587	123	12	not	not	PART
ejpam-3587	123	13	regular	regular	ADJ
ejpam-3587	123	14	and	and	CCONJ
ejpam-3587	123	15	also	also	ADV
ejpam-3587	123	16	not	not	PART
ejpam-3587	123	17	complete	complete	ADJ
ejpam-3587	123	18	since	since	SCONJ
ejpam-3587	123	19	xi	xi	PROPN
ejpam-3587	123	20	�	�	PROPN
ejpam-3587	123	21	yi	yi	PROPN
ejpam-3587	123	22	∀i	∀i	NOUN
ejpam-3587	123	23	.	.	PUNCT
ejpam-3587	124	1	but	but	CCONJ
ejpam-3587	124	2	xi	xi	ADP
ejpam-3587	124	3	∼	∼	NOUN
ejpam-3587	124	4	e	e	NOUN
ejpam-3587	124	5	∼	∼	NOUN
ejpam-3587	124	6	yi	yi	NOUN
ejpam-3587	124	7	,	,	PUNCT
ejpam-3587	124	8	that	that	PRON
ejpam-3587	124	9	is	be	AUX
ejpam-3587	124	10	each	each	DET
ejpam-3587	124	11	element	element	NOUN
ejpam-3587	124	12	of	of	ADP
ejpam-3587	124	13	r	r	NOUN
ejpam-3587	124	14	is	be	AUX
ejpam-3587	124	15	reachable	reachable	ADJ
ejpam-3587	124	16	from	from	ADP
ejpam-3587	124	17	any	any	DET
ejpam-3587	124	18	element	element	NOUN
ejpam-3587	124	19	of	of	ADP
ejpam-3587	124	20	r′	r′	PROPN
ejpam-3587	124	21	through	through	ADP
ejpam-3587	124	22	e	e	NOUN
ejpam-3587	124	23	,	,	PUNCT
ejpam-3587	124	24	therefore	therefore	ADV
ejpam-3587	124	25	γopp(g	γopp(g	NOUN
ejpam-3587	124	26	)	)	PUNCT
ejpam-3587	124	27	is	be	AUX
ejpam-3587	124	28	connected	connect	VERB
ejpam-3587	124	29	.	.	PUNCT
ejpam-3587	125	1	case	case	NOUN
ejpam-3587	125	2	2	2	NUM
ejpam-3587	125	3	:	:	PUNCT
ejpam-3587	125	4	suppose	suppose	VERB
ejpam-3587	125	5	n	n	X
ejpam-3587	125	6	=	=	SYM
ejpam-3587	125	7	∏d	∏d	ADP
ejpam-3587	125	8	i=1	i=1	PROPN
ejpam-3587	126	1	p	p	X
ejpam-3587	126	2	αi	αi	ADV
ejpam-3587	126	3	i	i	PRON
ejpam-3587	126	4	,	,	PUNCT
ejpam-3587	126	5	then	then	ADV
ejpam-3587	126	6	we	we	PRON
ejpam-3587	126	7	have	have	VERB
ejpam-3587	126	8	total	total	ADJ
ejpam-3587	126	9	number	number	NOUN
ejpam-3587	126	10	of	of	ADP
ejpam-3587	126	11	d	d	PRON
ejpam-3587	126	12	distinct	distinct	ADJ
ejpam-3587	126	13	primes	prime	NOUN
ejpam-3587	126	14	and	and	CCONJ
ejpam-3587	126	15	each	each	DET
ejpam-3587	126	16	prime	prime	NOUN
ejpam-3587	126	17	generate	generate	VERB
ejpam-3587	126	18	a	a	DET
ejpam-3587	126	19	subgroup	subgroup	NOUN
ejpam-3587	126	20	which	which	PRON
ejpam-3587	126	21	is	be	AUX
ejpam-3587	126	22	non	non	ADJ
ejpam-3587	126	23	-	-	ADJ
ejpam-3587	126	24	trivial	trivial	ADJ
ejpam-3587	126	25	complete	complete	ADJ
ejpam-3587	126	26	clique	clique	NOUN
ejpam-3587	126	27	of	of	ADP
ejpam-3587	126	28	order	order	NOUN
ejpam-3587	126	29	pαii	pαii	NOUN
ejpam-3587	126	30	.	.	PUNCT
ejpam-3587	127	1	also	also	ADV
ejpam-3587	127	2	there	there	PRON
ejpam-3587	127	3	exist	exist	VERB
ejpam-3587	127	4	some	some	DET
ejpam-3587	127	5	elements	element	NOUN
ejpam-3587	127	6	of	of	ADP
ejpam-3587	127	7	order	order	NOUN
ejpam-3587	127	8	∏d	∏d	ADP
ejpam-3587	127	9	i=1	i=1	PROPN
ejpam-3587	128	1	p	p	X
ejpam-3587	128	2	αi	αi	ADP
ejpam-3587	128	3	i	i	PRON
ejpam-3587	128	4	which	which	PRON
ejpam-3587	128	5	are	be	AUX
ejpam-3587	128	6	the	the	DET
ejpam-3587	128	7	isolated	isolate	VERB
ejpam-3587	128	8	vertices	vertex	NOUN
ejpam-3587	128	9	of	of	ADP
ejpam-3587	128	10	the	the	DET
ejpam-3587	128	11	graph	graph	NOUN
ejpam-3587	128	12	by	by	ADP
ejpam-3587	128	13	definition	definition	NOUN
ejpam-3587	128	14	.	.	PUNCT
ejpam-3587	129	1	let	let	VERB
ejpam-3587	129	2	gi	gi	INTJ
ejpam-3587	129	3	,	,	PUNCT
ejpam-3587	129	4	gj	gj	PROPN
ejpam-3587	129	5	∈	∈	PROPN
ejpam-3587	129	6	g	g	PROPN
ejpam-3587	129	7	3	3	NUM
ejpam-3587	129	8	g	g	PROPN
ejpam-3587	129	9	p	p	NOUN
ejpam-3587	130	1	αi	αi	VERB
ejpam-3587	130	2	i	i	INTJ
ejpam-3587	131	1	i	i	PRON
ejpam-3587	131	2	=	=	PUNCT
ejpam-3587	131	3	e	e	X
ejpam-3587	131	4	=	=	SYM
ejpam-3587	131	5	g	g	NOUN
ejpam-3587	131	6	∏d	∏d	ADP
ejpam-3587	131	7	i=1	i=1	PROPN
ejpam-3587	132	1	p	p	X
ejpam-3587	132	2	αi	αi	ADV
ejpam-3587	132	3	i	i	PRON
ejpam-3587	133	1	i	i	PRON
ejpam-3587	133	2	,	,	PUNCT
ejpam-3587	133	3	then	then	ADV
ejpam-3587	133	4	gi	gi	PROPN
ejpam-3587	133	5	�	�	PROPN
ejpam-3587	133	6	gj	gj	PROPN
ejpam-3587	133	7	,	,	PUNCT
ejpam-3587	133	8	therefore	therefore	ADV
ejpam-3587	133	9	γopp(g	γopp(g	NOUN
ejpam-3587	133	10	)	)	PUNCT
ejpam-3587	133	11	is	be	AUX
ejpam-3587	133	12	not	not	PART
ejpam-3587	133	13	complete	complete	ADJ
ejpam-3587	133	14	and	and	CCONJ
ejpam-3587	133	15	hence	hence	ADV
ejpam-3587	133	16	not	not	PART
ejpam-3587	133	17	regular	regular	ADJ
ejpam-3587	133	18	.	.	PUNCT
ejpam-3587	134	1	the	the	DET
ejpam-3587	134	2	fact	fact	NOUN
ejpam-3587	134	3	that	that	SCONJ
ejpam-3587	134	4	gi	gi	NOUN
ejpam-3587	134	5	are	be	AUX
ejpam-3587	134	6	isolated	isolate	VERB
ejpam-3587	134	7	vertices	vertex	NOUN
ejpam-3587	134	8	shows	show	VERB
ejpam-3587	134	9	that	that	SCONJ
ejpam-3587	134	10	the	the	DET
ejpam-3587	134	11	graph	graph	NOUN
ejpam-3587	134	12	is	be	AUX
ejpam-3587	134	13	not	not	PART
ejpam-3587	134	14	connected	connect	VERB
ejpam-3587	134	15	.	.	PUNCT
ejpam-3587	135	1	�	�	PROPN
ejpam-3587	135	2	theorem	theorem	VERB
ejpam-3587	135	3	5	5	NUM
ejpam-3587	135	4	.	.	PUNCT
ejpam-3587	136	1	let	let	VERB
ejpam-3587	136	2	g	g	PRON
ejpam-3587	136	3	be	be	AUX
ejpam-3587	136	4	a	a	DET
ejpam-3587	136	5	cyclic	cyclic	ADJ
ejpam-3587	136	6	group	group	NOUN
ejpam-3587	136	7	,	,	PUNCT
ejpam-3587	136	8	zn	zn	PROPN
ejpam-3587	136	9	,	,	PUNCT
ejpam-3587	136	10	then	then	ADV
ejpam-3587	136	11	γopp(g	γopp(g	NOUN
ejpam-3587	136	12	)	)	PUNCT
ejpam-3587	136	13	is	be	AUX
ejpam-3587	136	14	regular	regular	ADJ
ejpam-3587	136	15	,	,	PUNCT
ejpam-3587	136	16	complete	complete	ADJ
ejpam-3587	136	17	and	and	CCONJ
ejpam-3587	136	18	connected	connect	VERB
ejpam-3587	137	1	only	only	ADV
ejpam-3587	137	2	if	if	SCONJ
ejpam-3587	137	3	n	n	PROPN
ejpam-3587	137	4	=	=	SYM
ejpam-3587	137	5	pα	pα	NOUN
ejpam-3587	137	6	.	.	PUNCT
ejpam-3587	137	7	proof	proof	NOUN
ejpam-3587	137	8	:	:	PUNCT
ejpam-3587	137	9	suppose	suppose	VERB
ejpam-3587	137	10	n	n	PROPN
ejpam-3587	137	11	=	=	SYM
ejpam-3587	137	12	pα	pα	PROPN
ejpam-3587	137	13	,	,	PUNCT
ejpam-3587	137	14	then	then	ADV
ejpam-3587	137	15	by	by	ADP
ejpam-3587	137	16	theorem	theorem	NOUN
ejpam-3587	137	17	3	3	NUM
ejpam-3587	137	18	,	,	PUNCT
ejpam-3587	137	19	γopp(g	γopp(g	NOUN
ejpam-3587	137	20	)	)	PUNCT
ejpam-3587	137	21	is	be	AUX
ejpam-3587	137	22	complete	complete	ADJ
ejpam-3587	137	23	and	and	CCONJ
ejpam-3587	137	24	hence	hence	ADV
ejpam-3587	137	25	regular	regular	ADJ
ejpam-3587	137	26	and	and	CCONJ
ejpam-3587	137	27	connected	connected	ADJ
ejpam-3587	137	28	.	.	PUNCT
ejpam-3587	138	1	on	on	ADP
ejpam-3587	138	2	the	the	DET
ejpam-3587	138	3	other	other	ADJ
ejpam-3587	138	4	hand	hand	NOUN
ejpam-3587	138	5	,	,	PUNCT
ejpam-3587	138	6	if	if	SCONJ
ejpam-3587	138	7	n	n	AUX
ejpam-3587	138	8	=	=	SYM
ejpam-3587	138	9	∏d	∏d	ADP
ejpam-3587	138	10	i=1	i=1	PROPN
ejpam-3587	138	11	p	p	X
ejpam-3587	138	12	αi	αi	ADV
ejpam-3587	138	13	i	i	PRON
ejpam-3587	138	14	,	,	PUNCT
ejpam-3587	138	15	then	then	ADV
ejpam-3587	138	16	there	there	PRON
ejpam-3587	138	17	exist	exist	VERB
ejpam-3587	138	18	x	x	PUNCT
ejpam-3587	138	19	∈	∈	PROPN
ejpam-3587	138	20	g	g	PROPN
ejpam-3587	138	21	3	3	NUM
ejpam-3587	138	22	x	x	SYM
ejpam-3587	138	23	∏d	∏d	ADP
ejpam-3587	138	24	i=1	i=1	PROPN
ejpam-3587	139	1	p	p	X
ejpam-3587	139	2	αi	αi	ADV
ejpam-3587	139	3	i	i	INTJ
ejpam-3587	140	1	i	i	NOUN
ejpam-3587	140	2	=	=	SYM
ejpam-3587	140	3	e	e	NOUN
ejpam-3587	140	4	,	,	PUNCT
ejpam-3587	140	5	x	x	X
ejpam-3587	140	6	is	be	AUX
ejpam-3587	140	7	therefore	therefore	ADV
ejpam-3587	140	8	an	an	DET
ejpam-3587	140	9	isolated	isolated	ADJ
ejpam-3587	140	10	vertex	vertex	NOUN
ejpam-3587	140	11	,	,	PUNCT
ejpam-3587	140	12	hence	hence	ADV
ejpam-3587	140	13	γopp(g	γopp(g	NOUN
ejpam-3587	140	14	)	)	PUNCT
ejpam-3587	140	15	is	be	AUX
ejpam-3587	140	16	not	not	PART
ejpam-3587	140	17	connected	connect	VERB
ejpam-3587	140	18	,	,	PUNCT
ejpam-3587	140	19	not	not	PART
ejpam-3587	140	20	complete	complete	ADJ
ejpam-3587	140	21	and	and	CCONJ
ejpam-3587	140	22	not	not	PART
ejpam-3587	140	23	regular	regular	ADJ
ejpam-3587	140	24	by	by	ADP
ejpam-3587	140	25	definition	definition	NOUN
ejpam-3587	140	26	since	since	SCONJ
ejpam-3587	140	27	there	there	PRON
ejpam-3587	140	28	is	be	VERB
ejpam-3587	140	29	another	another	DET
ejpam-3587	140	30	element	element	NOUN
ejpam-3587	140	31	y	y	PROPN
ejpam-3587	140	32	∈	∈	PROPN
ejpam-3587	141	1	g	g	PROPN
ejpam-3587	141	2	3	3	NUM
ejpam-3587	141	3	yp	yp	NOUN
ejpam-3587	141	4	αi	αi	VERB
ejpam-3587	141	5	i	i	PRON
ejpam-3587	142	1	=	=	SYM
ejpam-3587	142	2	e	e	NOUN
ejpam-3587	142	3	,	,	PUNCT
ejpam-3587	142	4	then	then	ADV
ejpam-3587	142	5	deg(y	deg(y	PROPN
ejpam-3587	142	6	)	)	PUNCT
ejpam-3587	142	7	<	<	X
ejpam-3587	142	8	deg(x	deg(x	X
ejpam-3587	142	9	)	)	PUNCT
ejpam-3587	142	10	�	�	PROPN
ejpam-3587	142	11	the	the	DET
ejpam-3587	142	12	planarity	planarity	NOUN
ejpam-3587	142	13	of	of	ADP
ejpam-3587	142	14	the	the	DET
ejpam-3587	142	15	order	order	NOUN
ejpam-3587	142	16	product	product	NOUN
ejpam-3587	142	17	prime	prime	ADJ
ejpam-3587	142	18	graph	graph	NOUN
ejpam-3587	142	19	on	on	ADP
ejpam-3587	142	20	dihedral	dihedral	ADJ
ejpam-3587	142	21	group	group	NOUN
ejpam-3587	142	22	and	and	CCONJ
ejpam-3587	142	23	cyclic	cyclic	ADJ
ejpam-3587	142	24	group	group	NOUN
ejpam-3587	142	25	is	be	AUX
ejpam-3587	142	26	given	give	VERB
ejpam-3587	142	27	in	in	ADP
ejpam-3587	142	28	proposition	proposition	NOUN
ejpam-3587	142	29	1	1	NUM
ejpam-3587	142	30	and	and	CCONJ
ejpam-3587	142	31	proposition	proposition	NOUN
ejpam-3587	142	32	2	2	NUM
ejpam-3587	142	33	below	below	ADV
ejpam-3587	142	34	;	;	PUNCT
ejpam-3587	142	35	proposition	proposition	NOUN
ejpam-3587	142	36	1	1	NUM
ejpam-3587	142	37	.	.	PUNCT
ejpam-3587	143	1	let	let	VERB
ejpam-3587	143	2	g	g	PRON
ejpam-3587	143	3	be	be	AUX
ejpam-3587	143	4	a	a	DET
ejpam-3587	143	5	dihedral	dihedral	ADJ
ejpam-3587	143	6	group	group	NOUN
ejpam-3587	143	7	,	,	PUNCT
ejpam-3587	143	8	dn	dn	PROPN
ejpam-3587	143	9	,	,	PUNCT
ejpam-3587	143	10	then	then	ADV
ejpam-3587	143	11	γopp(g	γopp(g	NOUN
ejpam-3587	143	12	)	)	PUNCT
ejpam-3587	143	13	is	be	AUX
ejpam-3587	143	14	planar	planar	ADJ
ejpam-3587	143	15	only	only	ADV
ejpam-3587	143	16	if	if	SCONJ
ejpam-3587	143	17	n	n	NOUN
ejpam-3587	143	18	=	=	SYM
ejpam-3587	143	19	3	3	NUM
ejpam-3587	143	20	proof	proof	NOUN
ejpam-3587	143	21	:	:	PUNCT
ejpam-3587	143	22	by	by	ADP
ejpam-3587	143	23	theorem	theorem	NOUN
ejpam-3587	143	24	1	1	NUM
ejpam-3587	143	25	,	,	PUNCT
ejpam-3587	143	26	the	the	DET
ejpam-3587	143	27	size	size	NOUN
ejpam-3587	143	28	of	of	ADP
ejpam-3587	143	29	the	the	DET
ejpam-3587	143	30	maximum	maximum	ADJ
ejpam-3587	143	31	clique	clique	NOUN
ejpam-3587	143	32	is	be	AUX
ejpam-3587	143	33	n+	n+	ADP
ejpam-3587	143	34	1	1	NUM
ejpam-3587	143	35	,	,	PUNCT
ejpam-3587	143	36	so	so	ADV
ejpam-3587	143	37	the	the	DET
ejpam-3587	143	38	result	result	NOUN
ejpam-3587	143	39	follows	follow	VERB
ejpam-3587	143	40	since	since	ADV
ejpam-3587	143	41	,	,	PUNCT
ejpam-3587	143	42	the	the	DET
ejpam-3587	143	43	maximum	maximum	ADJ
ejpam-3587	143	44	complete	complete	ADJ
ejpam-3587	143	45	subgraph	subgraph	NOUN
ejpam-3587	143	46	is	be	AUX
ejpam-3587	143	47	less	less	ADJ
ejpam-3587	143	48	than	than	ADP
ejpam-3587	143	49	k5	k5	PROPN
ejpam-3587	143	50	�	�	PROPN
ejpam-3587	143	51	proposition	proposition	NOUN
ejpam-3587	143	52	2	2	NUM
ejpam-3587	143	53	.	.	PUNCT
ejpam-3587	144	1	let	let	VERB
ejpam-3587	144	2	g	g	PRON
ejpam-3587	144	3	be	be	AUX
ejpam-3587	144	4	a	a	DET
ejpam-3587	144	5	cyclic	cyclic	ADJ
ejpam-3587	144	6	group	group	NOUN
ejpam-3587	144	7	,	,	PUNCT
ejpam-3587	144	8	zn	zn	PROPN
ejpam-3587	144	9	,	,	PUNCT
ejpam-3587	144	10	then	then	ADV
ejpam-3587	144	11	γopp(g	γopp(g	NOUN
ejpam-3587	144	12	)	)	PUNCT
ejpam-3587	144	13	is	be	AUX
ejpam-3587	144	14	planar	planar	ADJ
ejpam-3587	144	15	if	if	SCONJ
ejpam-3587	144	16	n	n	ADV
ejpam-3587	144	17	=	=	PRON
ejpam-3587	144	18	{	{	PUNCT
ejpam-3587	144	19	pα	pα	INTJ
ejpam-3587	144	20	<	<	X
ejpam-3587	144	21	5,∏d	5,∏d	NUM
ejpam-3587	144	22	i=1	i=1	X
ejpam-3587	145	1	p	p	X
ejpam-3587	145	2	αi	αi	ADV
ejpam-3587	145	3	i	i	PRON
ejpam-3587	145	4	,	,	PUNCT
ejpam-3587	145	5	p	p	NOUN
ejpam-3587	145	6	αi	αi	VERB
ejpam-3587	145	7	i	i	PRON
ejpam-3587	145	8	<	<	X
ejpam-3587	145	9	5	5	NUM
ejpam-3587	145	10	.	.	PUNCT
ejpam-3587	145	11	m.	m.	PROPN
ejpam-3587	145	12	bello	bello	PROPN
ejpam-3587	145	13	,	,	PUNCT
ejpam-3587	145	14	n.	n.	PROPN
ejpam-3587	145	15	m.	m.	NOUN
ejpam-3587	145	16	mohd	mohd	PROPN
ejpam-3587	145	17	ali	ali	PROPN
ejpam-3587	145	18	,	,	PUNCT
ejpam-3587	145	19	n.	n.	PROPN
ejpam-3587	145	20	zulkifli	zulkifli	PROPN
ejpam-3587	145	21	/	/	SYM
ejpam-3587	145	22	eur	eur	PROPN
ejpam-3587	145	23	.	.	PUNCT
ejpam-3587	146	1	j.	j.	PROPN
ejpam-3587	146	2	pure	pure	PROPN
ejpam-3587	146	3	appl	appl	PROPN
ejpam-3587	146	4	.	.	PROPN
ejpam-3587	146	5	math	math	PROPN
ejpam-3587	146	6	,	,	PUNCT
ejpam-3587	146	7	13	13	NUM
ejpam-3587	146	8	(	(	PUNCT
ejpam-3587	146	9	1	1	NUM
ejpam-3587	146	10	)	)	PUNCT
ejpam-3587	146	11	(	(	PUNCT
ejpam-3587	146	12	2020	2020	NUM
ejpam-3587	146	13	)	)	PUNCT
ejpam-3587	146	14	,	,	PUNCT
ejpam-3587	146	15	84	84	NUM
ejpam-3587	146	16	-	-	SYM
ejpam-3587	146	17	95	95	NUM
ejpam-3587	146	18	90	90	NUM
ejpam-3587	146	19	proof	proof	NOUN
ejpam-3587	146	20	:	:	PUNCT
ejpam-3587	146	21	observe	observe	VERB
ejpam-3587	146	22	from	from	ADP
ejpam-3587	146	23	theorem	theorem	ADJ
ejpam-3587	146	24	3	3	NUM
ejpam-3587	146	25	and	and	CCONJ
ejpam-3587	146	26	the	the	DET
ejpam-3587	146	27	above	above	ADJ
ejpam-3587	146	28	hypothesis	hypothesis	NOUN
ejpam-3587	146	29	that	that	SCONJ
ejpam-3587	146	30	,	,	PUNCT
ejpam-3587	146	31	if	if	SCONJ
ejpam-3587	146	32	n	n	NUM
ejpam-3587	146	33	=	=	SYM
ejpam-3587	146	34	pα	pα	PROPN
ejpam-3587	146	35	,	,	PUNCT
ejpam-3587	146	36	then	then	ADV
ejpam-3587	146	37	the	the	DET
ejpam-3587	146	38	maximum	maximum	ADJ
ejpam-3587	146	39	complete	complete	ADJ
ejpam-3587	146	40	component	component	NOUN
ejpam-3587	146	41	is	be	AUX
ejpam-3587	146	42	less	less	ADJ
ejpam-3587	146	43	than	than	ADP
ejpam-3587	146	44	k5	k5	PROPN
ejpam-3587	146	45	and	and	CCONJ
ejpam-3587	146	46	so	so	ADV
ejpam-3587	146	47	γopp(g	γopp(g	NOUN
ejpam-3587	146	48	)	)	PUNCT
ejpam-3587	146	49	is	be	AUX
ejpam-3587	146	50	planar	planar	ADJ
ejpam-3587	146	51	,	,	PUNCT
ejpam-3587	146	52	since	since	SCONJ
ejpam-3587	146	53	the	the	DET
ejpam-3587	146	54	size	size	NOUN
ejpam-3587	146	55	of	of	ADP
ejpam-3587	146	56	the	the	DET
ejpam-3587	146	57	maximum	maximum	ADJ
ejpam-3587	146	58	clique	clique	NOUN
ejpam-3587	146	59	is	be	AUX
ejpam-3587	146	60	|g|	|g|	PROPN
ejpam-3587	146	61	=	=	SYM
ejpam-3587	146	62	pα	pα	AUX
ejpam-3587	146	63	.	.	PUNCT
ejpam-3587	146	64	suppose	suppose	VERB
ejpam-3587	146	65	n	n	PROPN
ejpam-3587	146	66	=	=	SYM
ejpam-3587	146	67	∏d	∏d	ADP
ejpam-3587	146	68	i=1	i=1	PROPN
ejpam-3587	147	1	p	p	X
ejpam-3587	147	2	αi	αi	ADV
ejpam-3587	147	3	i	i	PRON
ejpam-3587	147	4	,	,	PUNCT
ejpam-3587	147	5	then	then	ADV
ejpam-3587	147	6	still	still	ADV
ejpam-3587	147	7	by	by	ADP
ejpam-3587	147	8	theorem	theorem	NOUN
ejpam-3587	147	9	3	3	NUM
ejpam-3587	147	10	,	,	PUNCT
ejpam-3587	147	11	the	the	DET
ejpam-3587	147	12	maximum	maximum	ADJ
ejpam-3587	147	13	complete	complete	ADJ
ejpam-3587	147	14	component	component	NOUN
ejpam-3587	147	15	≯	≯	NOUN
ejpam-3587	147	16	k3	k3	VERB
ejpam-3587	147	17	since	since	SCONJ
ejpam-3587	147	18	pαii	pαii	NOUN
ejpam-3587	147	19	<	<	X
ejpam-3587	147	20	5	5	NUM
ejpam-3587	147	21	and	and	CCONJ
ejpam-3587	147	22	therefore	therefore	ADV
ejpam-3587	147	23	planar	planar	ADJ
ejpam-3587	147	24	.	.	PUNCT
ejpam-3587	148	1	�	�	NOUN
ejpam-3587	148	2	we	we	PRON
ejpam-3587	148	3	start	start	VERB
ejpam-3587	148	4	the	the	DET
ejpam-3587	148	5	investigation	investigation	NOUN
ejpam-3587	148	6	of	of	ADP
ejpam-3587	148	7	the	the	DET
ejpam-3587	148	8	invariants	invariant	NOUN
ejpam-3587	148	9	for	for	ADP
ejpam-3587	148	10	the	the	DET
ejpam-3587	148	11	order	order	NOUN
ejpam-3587	148	12	product	product	NOUN
ejpam-3587	148	13	prime	prime	ADJ
ejpam-3587	148	14	graph	graph	NOUN
ejpam-3587	148	15	.	.	PUNCT
ejpam-3587	149	1	the	the	DET
ejpam-3587	149	2	investigation	investigation	NOUN
ejpam-3587	149	3	begins	begin	VERB
ejpam-3587	149	4	with	with	ADP
ejpam-3587	149	5	the	the	DET
ejpam-3587	149	6	diameter	diameter	NOUN
ejpam-3587	149	7	of	of	ADP
ejpam-3587	149	8	the	the	DET
ejpam-3587	149	9	graph	graph	NOUN
ejpam-3587	149	10	on	on	ADP
ejpam-3587	149	11	dihedral	dihedral	ADJ
ejpam-3587	149	12	group	group	NOUN
ejpam-3587	149	13	which	which	PRON
ejpam-3587	149	14	is	be	AUX
ejpam-3587	149	15	given	give	VERB
ejpam-3587	149	16	in	in	ADP
ejpam-3587	149	17	propositions	proposition	NOUN
ejpam-3587	149	18	3	3	NUM
ejpam-3587	149	19	.	.	X
ejpam-3587	149	20	proposition	proposition	NOUN
ejpam-3587	149	21	3	3	X
ejpam-3587	149	22	.	.	PUNCT
ejpam-3587	150	1	let	let	VERB
ejpam-3587	150	2	g	g	PRON
ejpam-3587	150	3	be	be	AUX
ejpam-3587	150	4	a	a	DET
ejpam-3587	150	5	dihedral	dihedral	ADJ
ejpam-3587	150	6	group	group	NOUN
ejpam-3587	150	7	,	,	PUNCT
ejpam-3587	150	8	dn	dn	PROPN
ejpam-3587	150	9	,	,	PUNCT
ejpam-3587	150	10	then	then	ADV
ejpam-3587	150	11	diam(γopp(g	diam(γopp(g	NOUN
ejpam-3587	150	12	)	)	PUNCT
ejpam-3587	150	13	)	)	PUNCT
ejpam-3587	151	1	=	=	PUNCT
ejpam-3587	151	2			NUM
ejpam-3587	151	3	1	1	NUM
ejpam-3587	151	4	if	if	SCONJ
ejpam-3587	151	5	n	n	NOUN
ejpam-3587	151	6	=	=	SYM
ejpam-3587	151	7	2α	2α	NOUN
ejpam-3587	151	8	,	,	PUNCT
ejpam-3587	151	9	2	2	NUM
ejpam-3587	151	10	if	if	SCONJ
ejpam-3587	151	11	n	n	NUM
ejpam-3587	151	12	=	=	SYM
ejpam-3587	151	13	pα	pα	PROPN
ejpam-3587	151	14	,	,	PUNCT
ejpam-3587	151	15	p	p	X
ejpam-3587	151	16	6=	6=	PROPN
ejpam-3587	151	17	2	2	NUM
ejpam-3587	151	18	,	,	PUNCT
ejpam-3587	151	19	∞	∞	PROPN
ejpam-3587	151	20	if	if	SCONJ
ejpam-3587	151	21	n	n	ADV
ejpam-3587	151	22	=	=	SYM
ejpam-3587	151	23	∏d	∏d	ADP
ejpam-3587	151	24	i=1	i=1	PROPN
ejpam-3587	152	1	p	p	X
ejpam-3587	152	2	αi	αi	ADV
ejpam-3587	152	3	i	i	PRON
ejpam-3587	152	4	,	,	PUNCT
ejpam-3587	152	5	∀	∀	X
ejpam-3587	153	1	p.	p.	NOUN
ejpam-3587	153	2	proof	proof	NOUN
ejpam-3587	153	3	:	:	PUNCT
ejpam-3587	153	4	if	if	SCONJ
ejpam-3587	153	5	n	n	NOUN
ejpam-3587	153	6	=	=	SYM
ejpam-3587	153	7	2α	2α	NOUN
ejpam-3587	153	8	,	,	PUNCT
ejpam-3587	153	9	then	then	ADV
ejpam-3587	153	10	by	by	ADP
ejpam-3587	153	11	theorem	theorem	ADJ
ejpam-3587	153	12	4	4	NUM
ejpam-3587	153	13	,	,	PUNCT
ejpam-3587	153	14	γopp(g	γopp(g	NOUN
ejpam-3587	153	15	)	)	PUNCT
ejpam-3587	153	16	is	be	AUX
ejpam-3587	153	17	complete	complete	ADJ
ejpam-3587	153	18	,	,	PUNCT
ejpam-3587	153	19	and	and	CCONJ
ejpam-3587	153	20	therefore	therefore	ADV
ejpam-3587	153	21	each	each	PRON
ejpam-3587	153	22	of	of	ADP
ejpam-3587	153	23	its	its	PRON
ejpam-3587	153	24	vertices	vertex	NOUN
ejpam-3587	153	25	is	be	AUX
ejpam-3587	153	26	central	central	ADJ
ejpam-3587	153	27	,	,	PUNCT
ejpam-3587	153	28	hence	hence	ADV
ejpam-3587	153	29	diam(γopp(g	diam(γopp(g	NOUN
ejpam-3587	153	30	)	)	PUNCT
ejpam-3587	153	31	)	)	PUNCT
ejpam-3587	154	1	=	=	SYM
ejpam-3587	154	2	1	1	X
ejpam-3587	154	3	.	.	PUNCT
ejpam-3587	154	4	suppose	suppose	VERB
ejpam-3587	154	5	n	n	PROPN
ejpam-3587	154	6	=	=	SYM
ejpam-3587	154	7	pα	pα	PROPN
ejpam-3587	154	8	,	,	PUNCT
ejpam-3587	154	9	p	p	X
ejpam-3587	154	10	6=	6=	PROPN
ejpam-3587	154	11	2	2	NUM
ejpam-3587	154	12	,	,	PUNCT
ejpam-3587	154	13	then	then	ADV
ejpam-3587	154	14	recall	recall	VERB
ejpam-3587	154	15	that	that	SCONJ
ejpam-3587	154	16	by	by	ADP
ejpam-3587	154	17	definition	definition	NOUN
ejpam-3587	154	18	,	,	PUNCT
ejpam-3587	154	19	the	the	DET
ejpam-3587	154	20	vertices	vertex	NOUN
ejpam-3587	154	21	of	of	ADP
ejpam-3587	154	22	γopp(g	γopp(g	NOUN
ejpam-3587	154	23	)	)	PUNCT
ejpam-3587	154	24	are	be	AUX
ejpam-3587	154	25	the	the	DET
ejpam-3587	154	26	elements	element	NOUN
ejpam-3587	154	27	of	of	ADP
ejpam-3587	154	28	g	g	NOUN
ejpam-3587	154	29	,	,	PUNCT
ejpam-3587	154	30	and	and	CCONJ
ejpam-3587	154	31	|g|	|g|	PROPN
ejpam-3587	154	32	=	=	SYM
ejpam-3587	154	33	2pα	2pα	PROPN
ejpam-3587	154	34	.	.	PUNCT
ejpam-3587	155	1	so	so	ADV
ejpam-3587	155	2	pick	pick	VERB
ejpam-3587	155	3	x	x	PRON
ejpam-3587	155	4	,	,	PUNCT
ejpam-3587	155	5	y	y	PROPN
ejpam-3587	155	6	∈	∈	PROPN
ejpam-3587	155	7	g	g	PROPN
ejpam-3587	155	8	,	,	PUNCT
ejpam-3587	155	9	3	3	NUM
ejpam-3587	155	10	xpα	xpα	NOUN
ejpam-3587	155	11	=	=	SYM
ejpam-3587	155	12	e	e	X
ejpam-3587	155	13	=	=	SYM
ejpam-3587	155	14	y2	y2	PROPN
ejpam-3587	155	15	,	,	PUNCT
ejpam-3587	155	16	then	then	ADV
ejpam-3587	155	17	the	the	DET
ejpam-3587	155	18	maximum	maximum	ADJ
ejpam-3587	155	19	distance	distance	NOUN
ejpam-3587	155	20	between	between	ADP
ejpam-3587	155	21	pair	pair	NOUN
ejpam-3587	155	22	of	of	ADP
ejpam-3587	155	23	vertices	vertex	NOUN
ejpam-3587	155	24	of	of	ADP
ejpam-3587	155	25	γopp(g	γopp(g	NOUN
ejpam-3587	155	26	)	)	PUNCT
ejpam-3587	155	27	occur	occur	VERB
ejpam-3587	155	28	between	between	ADP
ejpam-3587	155	29	the	the	DET
ejpam-3587	155	30	vertices	vertex	NOUN
ejpam-3587	155	31	x	x	PUNCT
ejpam-3587	155	32	and	and	CCONJ
ejpam-3587	155	33	y	y	NOUN
ejpam-3587	155	34	,	,	PUNCT
ejpam-3587	155	35	but	but	CCONJ
ejpam-3587	155	36	x	x	X
ejpam-3587	155	37	∼	∼	NOUN
ejpam-3587	155	38	e	e	NOUN
ejpam-3587	155	39	∼	∼	NOUN
ejpam-3587	155	40	y	y	NOUN
ejpam-3587	155	41	,	,	PUNCT
ejpam-3587	155	42	that	that	PRON
ejpam-3587	155	43	is	be	AUX
ejpam-3587	155	44	the	the	DET
ejpam-3587	155	45	distance	distance	NOUN
ejpam-3587	155	46	to	to	PART
ejpam-3587	155	47	reach	reach	VERB
ejpam-3587	155	48	x	x	PUNCT
ejpam-3587	155	49	from	from	ADP
ejpam-3587	155	50	y	y	PROPN
ejpam-3587	155	51	is	be	AUX
ejpam-3587	155	52	2	2	NUM
ejpam-3587	155	53	,	,	PUNCT
ejpam-3587	155	54	hence	hence	ADV
ejpam-3587	155	55	diam(γopp(g	diam(γopp(g	NOUN
ejpam-3587	155	56	)	)	PUNCT
ejpam-3587	155	57	)	)	PUNCT
ejpam-3587	156	1	=	=	PUNCT
ejpam-3587	156	2	2	2	X
ejpam-3587	156	3	.	.	X
ejpam-3587	157	1	if	if	SCONJ
ejpam-3587	157	2	n	n	NOUN
ejpam-3587	157	3	=	=	SYM
ejpam-3587	157	4	∏d	∏d	ADP
ejpam-3587	157	5	i=1	i=1	PROPN
ejpam-3587	158	1	p	p	X
ejpam-3587	158	2	αi	αi	ADV
ejpam-3587	159	1	i	i	PRON
ejpam-3587	159	2	,	,	PUNCT
ejpam-3587	159	3	then	then	ADV
ejpam-3587	159	4	by	by	ADP
ejpam-3587	159	5	theorem	theorem	ADJ
ejpam-3587	159	6	4	4	NUM
ejpam-3587	159	7	,	,	PUNCT
ejpam-3587	159	8	γopp(g	γopp(g	NOUN
ejpam-3587	159	9	)	)	PUNCT
ejpam-3587	159	10	is	be	AUX
ejpam-3587	159	11	disconnected	disconnect	VERB
ejpam-3587	159	12	and	and	CCONJ
ejpam-3587	159	13	hence	hence	ADV
ejpam-3587	159	14	diam(γopp(g	diam(γopp(g	NOUN
ejpam-3587	159	15	)	)	PUNCT
ejpam-3587	159	16	)	)	PUNCT
ejpam-3587	160	1	=	=	NUM
ejpam-3587	160	2	∞	∞	PROPN
ejpam-3587	160	3	�	�	PROPN
ejpam-3587	160	4	the	the	DET
ejpam-3587	160	5	diameter	diameter	NOUN
ejpam-3587	160	6	of	of	ADP
ejpam-3587	160	7	the	the	DET
ejpam-3587	160	8	order	order	NOUN
ejpam-3587	160	9	product	product	NOUN
ejpam-3587	160	10	prime	prime	ADJ
ejpam-3587	160	11	graph	graph	NOUN
ejpam-3587	160	12	for	for	ADP
ejpam-3587	160	13	cyclic	cyclic	ADJ
ejpam-3587	160	14	groups	group	NOUN
ejpam-3587	160	15	are	be	AUX
ejpam-3587	160	16	given	give	VERB
ejpam-3587	160	17	in	in	ADP
ejpam-3587	160	18	proposition	proposition	NOUN
ejpam-3587	160	19	4	4	NUM
ejpam-3587	160	20	.	.	X
ejpam-3587	160	21	proposition	proposition	NOUN
ejpam-3587	160	22	4	4	NUM
ejpam-3587	160	23	.	.	PUNCT
ejpam-3587	161	1	let	let	VERB
ejpam-3587	161	2	g	g	PRON
ejpam-3587	161	3	be	be	AUX
ejpam-3587	161	4	a	a	DET
ejpam-3587	161	5	cyclic	cyclic	ADJ
ejpam-3587	161	6	group	group	NOUN
ejpam-3587	161	7	,	,	PUNCT
ejpam-3587	161	8	zn	zn	PROPN
ejpam-3587	161	9	,	,	PUNCT
ejpam-3587	161	10	then	then	ADV
ejpam-3587	161	11	diam(γopp(g	diam(γopp(g	NOUN
ejpam-3587	161	12	)	)	PUNCT
ejpam-3587	161	13	)	)	PUNCT
ejpam-3587	162	1	=	=	PRON
ejpam-3587	162	2	{	{	PUNCT
ejpam-3587	162	3	1	1	NUM
ejpam-3587	162	4	if	if	SCONJ
ejpam-3587	162	5	n	n	NUM
ejpam-3587	162	6	=	=	SYM
ejpam-3587	162	7	pα	pα	PROPN
ejpam-3587	162	8	,	,	PUNCT
ejpam-3587	162	9	∞	∞	PROPN
ejpam-3587	162	10	if	if	SCONJ
ejpam-3587	162	11	n	n	ADV
ejpam-3587	162	12	=	=	SYM
ejpam-3587	162	13	∏d	∏d	ADP
ejpam-3587	162	14	i=1	i=1	PROPN
ejpam-3587	163	1	p	p	X
ejpam-3587	163	2	αi	αi	ADV
ejpam-3587	163	3	i	i	PRON
ejpam-3587	163	4	.	.	PUNCT
ejpam-3587	164	1	proof	proof	NOUN
ejpam-3587	164	2	:	:	PUNCT
ejpam-3587	164	3	if	if	SCONJ
ejpam-3587	164	4	n	n	PRON
ejpam-3587	164	5	=	=	SYM
ejpam-3587	164	6	pα	pα	PROPN
ejpam-3587	164	7	,	,	PUNCT
ejpam-3587	164	8	then	then	ADV
ejpam-3587	164	9	by	by	ADP
ejpam-3587	164	10	theorem	theorem	NOUN
ejpam-3587	164	11	5	5	NUM
ejpam-3587	164	12	,	,	PUNCT
ejpam-3587	164	13	γopp(g	γopp(g	NOUN
ejpam-3587	164	14	)	)	PUNCT
ejpam-3587	164	15	is	be	AUX
ejpam-3587	164	16	complete	complete	ADJ
ejpam-3587	164	17	and	and	CCONJ
ejpam-3587	164	18	so	so	ADV
ejpam-3587	164	19	each	each	DET
ejpam-3587	164	20	vertex	vertex	NOUN
ejpam-3587	164	21	is	be	AUX
ejpam-3587	164	22	central	central	ADJ
ejpam-3587	164	23	,	,	PUNCT
ejpam-3587	164	24	therefore	therefore	ADV
ejpam-3587	164	25	diam(γopp(g	diam(γopp(g	NOUN
ejpam-3587	164	26	)	)	PUNCT
ejpam-3587	164	27	)	)	PUNCT
ejpam-3587	165	1	=	=	PUNCT
ejpam-3587	165	2	1	1	X
ejpam-3587	165	3	.	.	PUNCT
ejpam-3587	166	1	if	if	SCONJ
ejpam-3587	166	2	n	n	ADV
ejpam-3587	166	3	=	=	SYM
ejpam-3587	166	4	∏d	∏d	ADP
ejpam-3587	166	5	i=1	i=1	PROPN
ejpam-3587	167	1	p	p	X
ejpam-3587	167	2	αi	αi	ADV
ejpam-3587	167	3	i	i	PRON
ejpam-3587	167	4	,	,	PUNCT
ejpam-3587	167	5	then	then	ADV
ejpam-3587	167	6	still	still	ADV
ejpam-3587	167	7	by	by	ADP
ejpam-3587	167	8	theorem	theorem	NOUN
ejpam-3587	167	9	5	5	NUM
ejpam-3587	167	10	,	,	PUNCT
ejpam-3587	167	11	γopp(g	γopp(g	NOUN
ejpam-3587	167	12	)	)	PUNCT
ejpam-3587	167	13	is	be	AUX
ejpam-3587	167	14	disconnected	disconnect	VERB
ejpam-3587	167	15	and	and	CCONJ
ejpam-3587	167	16	so	so	ADV
ejpam-3587	167	17	diam(γopp(g	diam(γopp(g	NOUN
ejpam-3587	167	18	)	)	PUNCT
ejpam-3587	167	19	)	)	PUNCT
ejpam-3587	168	1	=	=	NUM
ejpam-3587	168	2	∞	∞	PROPN
ejpam-3587	168	3	�	�	PROPN
ejpam-3587	168	4	the	the	DET
ejpam-3587	168	5	girth	girth	NOUN
ejpam-3587	168	6	of	of	ADP
ejpam-3587	168	7	the	the	DET
ejpam-3587	168	8	order	order	NOUN
ejpam-3587	168	9	product	product	NOUN
ejpam-3587	168	10	prime	prime	ADJ
ejpam-3587	168	11	graph	graph	NOUN
ejpam-3587	168	12	of	of	ADP
ejpam-3587	168	13	the	the	DET
ejpam-3587	168	14	dihedral	dihedral	ADJ
ejpam-3587	168	15	group	group	NOUN
ejpam-3587	168	16	and	and	CCONJ
ejpam-3587	168	17	the	the	DET
ejpam-3587	168	18	cyclic	cyclic	ADJ
ejpam-3587	168	19	group	group	NOUN
ejpam-3587	168	20	is	be	AUX
ejpam-3587	168	21	given	give	VERB
ejpam-3587	168	22	in	in	ADP
ejpam-3587	168	23	proposition	proposition	NOUN
ejpam-3587	168	24	5	5	NUM
ejpam-3587	168	25	and	and	CCONJ
ejpam-3587	168	26	proposition	proposition	NOUN
ejpam-3587	168	27	6	6	NUM
ejpam-3587	168	28	.	.	PUNCT
ejpam-3587	168	29	proposition	proposition	NOUN
ejpam-3587	168	30	5	5	NUM
ejpam-3587	168	31	.	.	PUNCT
ejpam-3587	169	1	let	let	VERB
ejpam-3587	169	2	g	g	NOUN
ejpam-3587	169	3	be	be	AUX
ejpam-3587	169	4	the	the	DET
ejpam-3587	169	5	dihedral	dihedral	ADJ
ejpam-3587	169	6	group	group	NOUN
ejpam-3587	169	7	,	,	PUNCT
ejpam-3587	169	8	dn	dn	PROPN
ejpam-3587	169	9	,	,	PUNCT
ejpam-3587	169	10	then	then	ADV
ejpam-3587	169	11	girth(γopp(g	girth(γopp(g	NOUN
ejpam-3587	169	12	)	)	PUNCT
ejpam-3587	169	13	)	)	PUNCT
ejpam-3587	170	1	=	=	SYM
ejpam-3587	170	2	3	3	X
ejpam-3587	170	3	,	,	PUNCT
ejpam-3587	170	4	for	for	ADP
ejpam-3587	170	5	all	all	DET
ejpam-3587	170	6	n.	n.	PROPN
ejpam-3587	170	7	m.	m.	PROPN
ejpam-3587	170	8	bello	bello	PROPN
ejpam-3587	170	9	,	,	PUNCT
ejpam-3587	170	10	n.	n.	PROPN
ejpam-3587	170	11	m.	m.	NOUN
ejpam-3587	170	12	mohd	mohd	PROPN
ejpam-3587	170	13	ali	ali	PROPN
ejpam-3587	170	14	,	,	PUNCT
ejpam-3587	170	15	n.	n.	PROPN
ejpam-3587	170	16	zulkifli	zulkifli	PROPN
ejpam-3587	170	17	/	/	SYM
ejpam-3587	170	18	eur	eur	PROPN
ejpam-3587	170	19	.	.	PUNCT
ejpam-3587	171	1	j.	j.	PROPN
ejpam-3587	171	2	pure	pure	PROPN
ejpam-3587	171	3	appl	appl	PROPN
ejpam-3587	171	4	.	.	PROPN
ejpam-3587	171	5	math	math	PROPN
ejpam-3587	171	6	,	,	PUNCT
ejpam-3587	171	7	13	13	NUM
ejpam-3587	171	8	(	(	PUNCT
ejpam-3587	171	9	1	1	NUM
ejpam-3587	171	10	)	)	PUNCT
ejpam-3587	171	11	(	(	PUNCT
ejpam-3587	171	12	2020	2020	NUM
ejpam-3587	171	13	)	)	PUNCT
ejpam-3587	171	14	,	,	PUNCT
ejpam-3587	171	15	84	84	NUM
ejpam-3587	171	16	-	-	SYM
ejpam-3587	171	17	95	95	NUM
ejpam-3587	171	18	91	91	NUM
ejpam-3587	171	19	proof	proof	NOUN
ejpam-3587	171	20	:	:	PUNCT
ejpam-3587	171	21	if	if	SCONJ
ejpam-3587	171	22	n	n	PRON
ejpam-3587	171	23	=	=	SYM
ejpam-3587	171	24	pα	pα	PROPN
ejpam-3587	171	25	,	,	PUNCT
ejpam-3587	171	26	then	then	ADV
ejpam-3587	171	27	|g|	|g|	PROPN
ejpam-3587	171	28	=	=	SYM
ejpam-3587	171	29	2pα	2pα	PROPN
ejpam-3587	171	30	.	.	PUNCT
ejpam-3587	172	1	pick	pick	VERB
ejpam-3587	172	2	any	any	DET
ejpam-3587	172	3	two	two	NUM
ejpam-3587	172	4	elements	element	NOUN
ejpam-3587	172	5	x	x	X
ejpam-3587	172	6	,	,	PUNCT
ejpam-3587	172	7	y	y	PROPN
ejpam-3587	172	8	∈	∈	PROPN
ejpam-3587	172	9	g	g	PROPN
ejpam-3587	172	10	,	,	PUNCT
ejpam-3587	172	11	3	3	NUM
ejpam-3587	172	12	xp	xp	NOUN
ejpam-3587	172	13	α	α	NOUN
ejpam-3587	172	14	=	=	SYM
ejpam-3587	172	15	e	e	X
ejpam-3587	172	16	=	=	SYM
ejpam-3587	172	17	y2	y2	PROPN
ejpam-3587	172	18	,	,	PUNCT
ejpam-3587	172	19	then	then	ADV
ejpam-3587	172	20	x	x	PUNCT
ejpam-3587	172	21	∼	∼	NOUN
ejpam-3587	172	22	e	e	NOUN
ejpam-3587	172	23	∼	∼	NOUN
ejpam-3587	172	24	y	y	PROPN
ejpam-3587	172	25	is	be	AUX
ejpam-3587	172	26	a	a	DET
ejpam-3587	172	27	triangle	triangle	NOUN
ejpam-3587	172	28	in	in	ADP
ejpam-3587	172	29	γopp(g	γopp(g	NOUN
ejpam-3587	172	30	)	)	PUNCT
ejpam-3587	172	31	,	,	PUNCT
ejpam-3587	172	32	hence	hence	ADV
ejpam-3587	172	33	girth(γopp(g	girth(γopp(g	NOUN
ejpam-3587	172	34	)	)	PUNCT
ejpam-3587	172	35	)	)	PUNCT
ejpam-3587	173	1	=	=	SYM
ejpam-3587	173	2	3	3	X
ejpam-3587	173	3	.	.	X
ejpam-3587	174	1	if	if	SCONJ
ejpam-3587	174	2	n	n	ADV
ejpam-3587	174	3	=	=	SYM
ejpam-3587	174	4	∏d	∏d	ADP
ejpam-3587	174	5	i=1	i=1	PROPN
ejpam-3587	175	1	p	p	X
ejpam-3587	175	2	αi	αi	ADV
ejpam-3587	176	1	i	i	PRON
ejpam-3587	176	2	,	,	PUNCT
ejpam-3587	176	3	then	then	ADV
ejpam-3587	176	4	|g|	|g|	PROPN
ejpam-3587	176	5	=	=	SYM
ejpam-3587	176	6	2n	2n	NUM
ejpam-3587	176	7	=	=	SYM
ejpam-3587	176	8	2	2	NUM
ejpam-3587	176	9	∏d	∏d	ADP
ejpam-3587	176	10	i=1	i=1	PROPN
ejpam-3587	177	1	p	p	X
ejpam-3587	177	2	αi	αi	ADV
ejpam-3587	177	3	i	i	PRON
ejpam-3587	177	4	.	.	PUNCT
ejpam-3587	178	1	let	let	VERB
ejpam-3587	178	2	l	l	NOUN
ejpam-3587	178	3	,	,	PUNCT
ejpam-3587	178	4	m	m	VERB
ejpam-3587	178	5	∈	∈	NOUN
ejpam-3587	178	6	g	g	NOUN
ejpam-3587	178	7	,	,	PUNCT
ejpam-3587	178	8	3	3	NUM
ejpam-3587	178	9	lp	lp	NOUN
ejpam-3587	178	10	αi	αi	VERB
ejpam-3587	179	1	i	i	PRON
ejpam-3587	180	1	=	=	PUNCT
ejpam-3587	180	2	e	e	PROPN
ejpam-3587	180	3	=	=	PROPN
ejpam-3587	180	4	m2	m2	PROPN
ejpam-3587	180	5	,	,	PUNCT
ejpam-3587	180	6	then	then	ADV
ejpam-3587	180	7	also	also	ADV
ejpam-3587	180	8	l	l	NOUN
ejpam-3587	180	9	∼	∼	NOUN
ejpam-3587	180	10	e	e	NOUN
ejpam-3587	180	11	∼	∼	NOUN
ejpam-3587	180	12	m	m	VERB
ejpam-3587	180	13	is	be	AUX
ejpam-3587	180	14	a	a	DET
ejpam-3587	180	15	triangle	triangle	NOUN
ejpam-3587	180	16	in	in	ADP
ejpam-3587	180	17	γopp(g	γopp(g	PROPN
ejpam-3587	180	18	)	)	PUNCT
ejpam-3587	180	19	,	,	PUNCT
ejpam-3587	180	20	therefore	therefore	ADV
ejpam-3587	180	21	girth(γopp(g	girth(γopp(g	ADJ
ejpam-3587	180	22	)	)	PUNCT
ejpam-3587	180	23	)	)	PUNCT
ejpam-3587	181	1	=	=	SYM
ejpam-3587	181	2	3	3	NUM
ejpam-3587	181	3	�	�	PROPN
ejpam-3587	181	4	proposition	proposition	NOUN
ejpam-3587	181	5	6	6	NUM
ejpam-3587	181	6	.	.	PUNCT
ejpam-3587	182	1	let	let	VERB
ejpam-3587	182	2	g	g	PRON
ejpam-3587	182	3	be	be	AUX
ejpam-3587	182	4	a	a	DET
ejpam-3587	182	5	cyclic	cyclic	ADJ
ejpam-3587	182	6	group	group	NOUN
ejpam-3587	182	7	,	,	PUNCT
ejpam-3587	182	8	zn	zn	PROPN
ejpam-3587	182	9	,	,	PUNCT
ejpam-3587	182	10	n	n	PROPN
ejpam-3587	182	11	=	=	SYM
ejpam-3587	182	12	pα	pα	PROPN
ejpam-3587	182	13	,	,	PUNCT
ejpam-3587	182	14	then	then	ADV
ejpam-3587	182	15	girth(γopp(g	girth(γopp(g	NOUN
ejpam-3587	182	16	)	)	PUNCT
ejpam-3587	182	17	)	)	PUNCT
ejpam-3587	183	1	=	=	PRON
ejpam-3587	183	2	{	{	PUNCT
ejpam-3587	183	3	3	3	NUM
ejpam-3587	183	4	if	if	SCONJ
ejpam-3587	183	5	p	p	X
ejpam-3587	183	6	>	>	X
ejpam-3587	183	7	2	2	NUM
ejpam-3587	183	8	,	,	PUNCT
ejpam-3587	183	9	∞	∞	PROPN
ejpam-3587	183	10	if	if	SCONJ
ejpam-3587	183	11	p	p	NOUN
ejpam-3587	183	12	=	=	NOUN
ejpam-3587	183	13	2	2	NUM
ejpam-3587	183	14	,	,	PUNCT
ejpam-3587	183	15	α	α	NOUN
ejpam-3587	183	16	=	=	SYM
ejpam-3587	183	17	1	1	X
ejpam-3587	183	18	.	.	PUNCT
ejpam-3587	184	1	proof	proof	NOUN
ejpam-3587	184	2	:	:	PUNCT
ejpam-3587	184	3	since	since	SCONJ
ejpam-3587	184	4	|g|	|g|	PROPN
ejpam-3587	184	5	=	=	SYM
ejpam-3587	184	6	pα	pα	PROPN
ejpam-3587	184	7	,	,	PUNCT
ejpam-3587	184	8	then	then	ADV
ejpam-3587	184	9	all	all	DET
ejpam-3587	184	10	g1	g1	NOUN
ejpam-3587	184	11	,	,	PUNCT
ejpam-3587	184	12	g2	g2	PROPN
ejpam-3587	184	13	,	,	PUNCT
ejpam-3587	184	14	...	...	PUNCT
ejpam-3587	184	15	,	,	PUNCT
ejpam-3587	184	16	gpα	gpα	PROPN
ejpam-3587	184	17	form	form	VERB
ejpam-3587	184	18	single	single	ADJ
ejpam-3587	184	19	clique	clique	NOUN
ejpam-3587	184	20	in	in	ADP
ejpam-3587	184	21	γopp(g	γopp(g	PROPN
ejpam-3587	184	22	)	)	PUNCT
ejpam-3587	184	23	since	since	SCONJ
ejpam-3587	184	24	γopp(g	γopp(g	NOUN
ejpam-3587	184	25	)	)	PUNCT
ejpam-3587	184	26	is	be	AUX
ejpam-3587	184	27	complete	complete	ADJ
ejpam-3587	184	28	by	by	ADP
ejpam-3587	184	29	theorem	theorem	NOUN
ejpam-3587	184	30	5	5	NUM
ejpam-3587	184	31	.	.	PUNCT
ejpam-3587	184	32	that	that	PRON
ejpam-3587	184	33	is	be	AUX
ejpam-3587	184	34	γopp(g	γopp(g	NOUN
ejpam-3587	184	35	)	)	PUNCT
ejpam-3587	184	36	contains	contain	VERB
ejpam-3587	184	37	triangle	triangle	NOUN
ejpam-3587	184	38	and	and	CCONJ
ejpam-3587	184	39	hence	hence	ADV
ejpam-3587	184	40	girth(γopp(g	girth(γopp(g	NOUN
ejpam-3587	184	41	)	)	PUNCT
ejpam-3587	184	42	)	)	PUNCT
ejpam-3587	185	1	=	=	SYM
ejpam-3587	185	2	3	3	X
ejpam-3587	185	3	.	.	X
ejpam-3587	186	1	if	if	SCONJ
ejpam-3587	186	2	p	p	NOUN
ejpam-3587	186	3	=	=	NOUN
ejpam-3587	186	4	2	2	NUM
ejpam-3587	186	5	,	,	PUNCT
ejpam-3587	186	6	α	α	NOUN
ejpam-3587	186	7	=	=	SYM
ejpam-3587	186	8	1	1	NUM
ejpam-3587	186	9	,	,	PUNCT
ejpam-3587	186	10	then	then	ADV
ejpam-3587	186	11	|g|	|g|	PROPN
ejpam-3587	186	12	=	=	SYM
ejpam-3587	186	13	2	2	NUM
ejpam-3587	186	14	,	,	PUNCT
ejpam-3587	186	15	hence	hence	ADV
ejpam-3587	186	16	γopp(g	γopp(g	NOUN
ejpam-3587	186	17	)	)	PUNCT
ejpam-3587	186	18	is	be	AUX
ejpam-3587	186	19	triangle	triangle	NOUN
ejpam-3587	186	20	free	free	ADJ
ejpam-3587	186	21	,	,	PUNCT
ejpam-3587	186	22	infact	infact	PROPN
ejpam-3587	186	23	has	have	VERB
ejpam-3587	186	24	no	no	DET
ejpam-3587	186	25	any	any	DET
ejpam-3587	186	26	cycle	cycle	NOUN
ejpam-3587	186	27	,	,	PUNCT
ejpam-3587	186	28	therefore	therefore	ADV
ejpam-3587	186	29	girth(γopp(g	girth(γopp(g	ADJ
ejpam-3587	186	30	)	)	PUNCT
ejpam-3587	186	31	)	)	PUNCT
ejpam-3587	187	1	=	=	NUM
ejpam-3587	187	2	∞	∞	PROPN
ejpam-3587	187	3	�	�	PROPN
ejpam-3587	187	4	the	the	DET
ejpam-3587	187	5	clique	clique	ADJ
ejpam-3587	187	6	number	number	NOUN
ejpam-3587	187	7	for	for	ADP
ejpam-3587	187	8	the	the	DET
ejpam-3587	187	9	order	order	NOUN
ejpam-3587	187	10	product	product	NOUN
ejpam-3587	187	11	prime	prime	ADJ
ejpam-3587	187	12	graph	graph	NOUN
ejpam-3587	187	13	on	on	ADP
ejpam-3587	187	14	dihedral	dihedral	ADJ
ejpam-3587	187	15	group	group	NOUN
ejpam-3587	187	16	and	and	CCONJ
ejpam-3587	187	17	cyclic	cyclic	ADJ
ejpam-3587	187	18	groups	group	NOUN
ejpam-3587	187	19	is	be	AUX
ejpam-3587	187	20	given	give	VERB
ejpam-3587	187	21	in	in	ADP
ejpam-3587	187	22	proposition	proposition	NOUN
ejpam-3587	187	23	7	7	NUM
ejpam-3587	187	24	and	and	CCONJ
ejpam-3587	187	25	proposition	proposition	NOUN
ejpam-3587	187	26	8	8	NUM
ejpam-3587	187	27	.	.	PUNCT
ejpam-3587	188	1	proposition	proposition	NOUN
ejpam-3587	188	2	7	7	NUM
ejpam-3587	188	3	.	.	PUNCT
ejpam-3587	189	1	let	let	VERB
ejpam-3587	189	2	g	g	PRON
ejpam-3587	189	3	be	be	AUX
ejpam-3587	189	4	a	a	DET
ejpam-3587	189	5	dihedral	dihedral	ADJ
ejpam-3587	189	6	group	group	NOUN
ejpam-3587	189	7	,	,	PUNCT
ejpam-3587	189	8	dn	dn	PROPN
ejpam-3587	189	9	,	,	PUNCT
ejpam-3587	189	10	then	then	ADV
ejpam-3587	189	11	ω(γopp(g	ω(γopp(g	NUM
ejpam-3587	189	12	)	)	PUNCT
ejpam-3587	189	13	)	)	PUNCT
ejpam-3587	190	1	=	=	PUNCT
ejpam-3587	190	2			NUM
ejpam-3587	190	3	2n	2n	NOUN
ejpam-3587	190	4	if	if	SCONJ
ejpam-3587	190	5	n	n	NOUN
ejpam-3587	190	6	=	=	SYM
ejpam-3587	190	7	2α	2α	NOUN
ejpam-3587	190	8	,	,	PUNCT
ejpam-3587	190	9	(	(	PUNCT
ejpam-3587	190	10	n+	n+	NOUN
ejpam-3587	190	11	1	1	X
ejpam-3587	190	12	)	)	PUNCT
ejpam-3587	190	13	if	if	SCONJ
ejpam-3587	190	14	n	n	NOUN
ejpam-3587	190	15	=	=	VERB
ejpam-3587	190	16	pα	pα	NOUN
ejpam-3587	190	17	or	or	CCONJ
ejpam-3587	190	18	n	n	CCONJ
ejpam-3587	190	19	=	=	NOUN
ejpam-3587	190	20	∏d	∏d	ADP
ejpam-3587	190	21	i=1	i=1	PROPN
ejpam-3587	191	1	p	p	X
ejpam-3587	191	2	αi	αi	ADV
ejpam-3587	191	3	i	i	PRON
ejpam-3587	191	4	,	,	PUNCT
ejpam-3587	191	5	where	where	SCONJ
ejpam-3587	191	6	n	n	PRON
ejpam-3587	191	7	is	be	AUX
ejpam-3587	191	8	odd	odd	ADJ
ejpam-3587	191	9	in	in	ADP
ejpam-3587	191	10	each	each	DET
ejpam-3587	191	11	case	case	NOUN
ejpam-3587	191	12	,	,	PUNCT
ejpam-3587	191	13	(	(	PUNCT
ejpam-3587	191	14	n+	n+	X
ejpam-3587	191	15	2α	2α	NOUN
ejpam-3587	191	16	)	)	PUNCT
ejpam-3587	192	1	if	if	SCONJ
ejpam-3587	192	2	n	n	NOUN
ejpam-3587	192	3	=	=	SYM
ejpam-3587	192	4	∏d	∏d	ADP
ejpam-3587	192	5	i=1	i=1	PROPN
ejpam-3587	192	6	p	p	X
ejpam-3587	192	7	αi	αi	X
ejpam-3587	192	8	,	,	PUNCT
ejpam-3587	192	9	where	where	SCONJ
ejpam-3587	192	10	n	n	PRON
ejpam-3587	192	11	is	be	AUX
ejpam-3587	192	12	even	even	ADV
ejpam-3587	192	13	.	.	PUNCT
ejpam-3587	193	1	proof	proof	NOUN
ejpam-3587	193	2	:	:	PUNCT
ejpam-3587	193	3	if	if	SCONJ
ejpam-3587	193	4	n	n	NOUN
ejpam-3587	193	5	=	=	SYM
ejpam-3587	193	6	2α	2α	NOUN
ejpam-3587	193	7	,	,	PUNCT
ejpam-3587	193	8	then	then	ADV
ejpam-3587	193	9	by	by	ADP
ejpam-3587	193	10	theorem	theorem	NOUN
ejpam-3587	193	11	1	1	NUM
ejpam-3587	193	12	,	,	PUNCT
ejpam-3587	193	13	γopp(g	γopp(g	NOUN
ejpam-3587	193	14	)	)	PUNCT
ejpam-3587	193	15	=	=	SYM
ejpam-3587	193	16	k2n	k2n	PROPN
ejpam-3587	193	17	and	and	CCONJ
ejpam-3587	193	18	is	be	AUX
ejpam-3587	193	19	complete	complete	ADJ
ejpam-3587	193	20	by	by	ADP
ejpam-3587	193	21	theorem	theorem	NOUN
ejpam-3587	193	22	4	4	NUM
ejpam-3587	193	23	with	with	ADP
ejpam-3587	193	24	2n	2n	NUM
ejpam-3587	193	25	vertices	vertex	NOUN
ejpam-3587	193	26	,	,	PUNCT
ejpam-3587	193	27	hence	hence	ADV
ejpam-3587	193	28	ω(γopp(g	ω(γopp(g	NUM
ejpam-3587	193	29	)	)	PUNCT
ejpam-3587	193	30	)	)	PUNCT
ejpam-3587	194	1	=	=	SYM
ejpam-3587	194	2	2n	2n	X
ejpam-3587	194	3	.	.	PUNCT
ejpam-3587	195	1	suppose	suppose	VERB
ejpam-3587	195	2	n	n	NOUN
ejpam-3587	195	3	=	=	VERB
ejpam-3587	195	4	pα	pα	NOUN
ejpam-3587	195	5	or	or	CCONJ
ejpam-3587	195	6	∏d	∏d	ADP
ejpam-3587	195	7	i=1	i=1	PROPN
ejpam-3587	196	1	p	p	X
ejpam-3587	196	2	αi	αi	ADV
ejpam-3587	196	3	i	i	PRON
ejpam-3587	196	4	,	,	PUNCT
ejpam-3587	196	5	n	n	CCONJ
ejpam-3587	196	6	odd	odd	ADJ
ejpam-3587	196	7	,	,	PUNCT
ejpam-3587	196	8	then	then	ADV
ejpam-3587	196	9	by	by	ADP
ejpam-3587	196	10	theorem	theorem	NOUN
ejpam-3587	196	11	2	2	NUM
ejpam-3587	196	12	,	,	PUNCT
ejpam-3587	196	13	the	the	DET
ejpam-3587	196	14	size	size	NOUN
ejpam-3587	196	15	of	of	ADP
ejpam-3587	196	16	the	the	DET
ejpam-3587	196	17	maximum	maximum	ADJ
ejpam-3587	196	18	clique	clique	NOUN
ejpam-3587	196	19	is	be	AUX
ejpam-3587	196	20	n+	n+	ADP
ejpam-3587	197	1	1	1	X
ejpam-3587	197	2	.	.	PUNCT
ejpam-3587	197	3	therefore	therefore	ADV
ejpam-3587	197	4	ω(γopp(g	ω(γopp(g	NUM
ejpam-3587	197	5	)	)	PUNCT
ejpam-3587	197	6	)	)	PUNCT
ejpam-3587	198	1	=	=	SYM
ejpam-3587	198	2	n+	n+	PUNCT
ejpam-3587	199	1	1	1	X
ejpam-3587	199	2	.	.	PUNCT
ejpam-3587	200	1	if	if	SCONJ
ejpam-3587	200	2	n	n	ADV
ejpam-3587	200	3	=	=	SYM
ejpam-3587	200	4	∏d	∏d	ADP
ejpam-3587	200	5	i=1	i=1	PROPN
ejpam-3587	200	6	p	p	X
ejpam-3587	200	7	αi	αi	ADV
ejpam-3587	200	8	,	,	PUNCT
ejpam-3587	200	9	n	n	CCONJ
ejpam-3587	200	10	even	even	ADV
ejpam-3587	200	11	,	,	PUNCT
ejpam-3587	200	12	then	then	ADV
ejpam-3587	200	13	by	by	ADP
ejpam-3587	200	14	theorem	theorem	NOUN
ejpam-3587	200	15	2	2	NUM
ejpam-3587	200	16	,	,	PUNCT
ejpam-3587	200	17	the	the	DET
ejpam-3587	200	18	size	size	NOUN
ejpam-3587	200	19	of	of	ADP
ejpam-3587	200	20	the	the	DET
ejpam-3587	200	21	maximum	maximum	ADJ
ejpam-3587	200	22	clique	clique	NOUN
ejpam-3587	200	23	is	be	AUX
ejpam-3587	200	24	(	(	PUNCT
ejpam-3587	200	25	n+	n+	X
ejpam-3587	200	26	2α	2α	NOUN
ejpam-3587	200	27	)	)	PUNCT
ejpam-3587	200	28	,	,	PUNCT
ejpam-3587	200	29	so	so	ADV
ejpam-3587	200	30	ω(γopp(g	ω(γopp(g	NUM
ejpam-3587	200	31	)	)	PUNCT
ejpam-3587	200	32	)	)	PUNCT
ejpam-3587	201	1	=	=	PUNCT
ejpam-3587	202	1	(	(	PUNCT
ejpam-3587	202	2	n+	n+	NUM
ejpam-3587	202	3	2α	2α	NOUN
ejpam-3587	202	4	)	)	PUNCT
ejpam-3587	202	5	�	�	PROPN
ejpam-3587	202	6	proposition	proposition	NOUN
ejpam-3587	202	7	8	8	NUM
ejpam-3587	202	8	.	.	PUNCT
ejpam-3587	203	1	let	let	VERB
ejpam-3587	203	2	g	g	PRON
ejpam-3587	203	3	be	be	AUX
ejpam-3587	203	4	a	a	DET
ejpam-3587	203	5	cyclic	cyclic	ADJ
ejpam-3587	203	6	group	group	NOUN
ejpam-3587	203	7	,	,	PUNCT
ejpam-3587	203	8	zn	zn	PROPN
ejpam-3587	203	9	,	,	PUNCT
ejpam-3587	203	10	then	then	ADV
ejpam-3587	203	11	ω(γopp(g	ω(γopp(g	NUM
ejpam-3587	203	12	)	)	PUNCT
ejpam-3587	203	13	)	)	PUNCT
ejpam-3587	204	1	=	=	PRON
ejpam-3587	204	2	{	{	PUNCT
ejpam-3587	204	3	n	n	NOUN
ejpam-3587	204	4	if	if	SCONJ
ejpam-3587	204	5	n	n	PROPN
ejpam-3587	204	6	=	=	SYM
ejpam-3587	204	7	pα	pα	PROPN
ejpam-3587	204	8	,	,	PUNCT
ejpam-3587	204	9	max	max	PROPN
ejpam-3587	204	10	pαii	pαii	NOUN
ejpam-3587	204	11	if	if	SCONJ
ejpam-3587	204	12	n	n	NOUN
ejpam-3587	204	13	=	=	PUNCT
ejpam-3587	204	14	∏d	∏d	ADP
ejpam-3587	204	15	i=1	i=1	PROPN
ejpam-3587	205	1	p	p	X
ejpam-3587	205	2	αi	αi	ADV
ejpam-3587	205	3	i	i	PRON
ejpam-3587	205	4	.	.	PUNCT
ejpam-3587	206	1	proof	proof	NOUN
ejpam-3587	206	2	:	:	PUNCT
ejpam-3587	206	3	if	if	SCONJ
ejpam-3587	206	4	n	n	PRON
ejpam-3587	206	5	=	=	SYM
ejpam-3587	206	6	pα	pα	PROPN
ejpam-3587	206	7	,	,	PUNCT
ejpam-3587	206	8	then	then	ADV
ejpam-3587	206	9	γopp(g	γopp(g	NOUN
ejpam-3587	206	10	)	)	PUNCT
ejpam-3587	206	11	is	be	AUX
ejpam-3587	206	12	complete	complete	ADJ
ejpam-3587	206	13	by	by	ADP
ejpam-3587	206	14	theorem	theorem	NOUN
ejpam-3587	206	15	5	5	NUM
ejpam-3587	206	16	,	,	PUNCT
ejpam-3587	206	17	hence	hence	ADV
ejpam-3587	206	18	all	all	DET
ejpam-3587	206	19	the	the	DET
ejpam-3587	206	20	elements	element	NOUN
ejpam-3587	206	21	of	of	ADP
ejpam-3587	206	22	γopp(g	γopp(g	NOUN
ejpam-3587	206	23	)	)	PUNCT
ejpam-3587	206	24	form	form	VERB
ejpam-3587	206	25	a	a	DET
ejpam-3587	206	26	single	single	ADJ
ejpam-3587	206	27	clique	clique	NOUN
ejpam-3587	206	28	and	and	CCONJ
ejpam-3587	206	29	therefore	therefore	ADV
ejpam-3587	206	30	ω(γopp(g	ω(γopp(g	NUM
ejpam-3587	206	31	)	)	PUNCT
ejpam-3587	206	32	)	)	PUNCT
ejpam-3587	207	1	=	=	SYM
ejpam-3587	207	2	|g|	|g|	PROPN
ejpam-3587	207	3	=	=	SYM
ejpam-3587	207	4	n.	n.	PROPN
ejpam-3587	207	5	suppose	suppose	VERB
ejpam-3587	207	6	n	n	PROPN
ejpam-3587	207	7	=	=	SYM
ejpam-3587	207	8	∏d	∏d	ADP
ejpam-3587	207	9	i=1	i=1	PROPN
ejpam-3587	208	1	p	p	X
ejpam-3587	208	2	αi	αi	ADV
ejpam-3587	208	3	i	i	PRON
ejpam-3587	208	4	.	.	PUNCT
ejpam-3587	209	1	pick	pick	VERB
ejpam-3587	209	2	x	x	SYM
ejpam-3587	209	3	,	,	PUNCT
ejpam-3587	209	4	y	y	PROPN
ejpam-3587	209	5	∈	∈	PROPN
ejpam-3587	209	6	γopp(g	γopp(g	PROPN
ejpam-3587	209	7	)	)	PUNCT
ejpam-3587	209	8	3	3	NUM
ejpam-3587	209	9	xpt1	xpt1	NOUN
ejpam-3587	209	10	=	=	PUNCT
ejpam-3587	209	11	e	e	X
ejpam-3587	209	12	=	=	PUNCT
ejpam-3587	209	13	yp	yp	PROPN
ejpam-3587	209	14	t	t	PROPN
ejpam-3587	209	15	2	2	NUM
ejpam-3587	209	16	and	and	CCONJ
ejpam-3587	209	17	h	h	NOUN
ejpam-3587	209	18	∏d	∏d	ADP
ejpam-3587	209	19	i=1	i=1	PROPN
ejpam-3587	210	1	p	p	X
ejpam-3587	210	2	αi	αi	ADV
ejpam-3587	211	1	i	i	NOUN
ejpam-3587	211	2	=	=	SYM
ejpam-3587	211	3	e	e	NOUN
ejpam-3587	211	4	,	,	PUNCT
ejpam-3587	211	5	1	1	NUM
ejpam-3587	211	6	≤	≤	NOUN
ejpam-3587	211	7	t	t	NOUN
ejpam-3587	211	8	≤	≤	NUM
ejpam-3587	211	9	d	d	PROPN
ejpam-3587	211	10	,	,	PUNCT
ejpam-3587	211	11	m.	m.	NOUN
ejpam-3587	211	12	bello	bello	PROPN
ejpam-3587	211	13	,	,	PUNCT
ejpam-3587	211	14	n.	n.	PROPN
ejpam-3587	211	15	m.	m.	NOUN
ejpam-3587	211	16	mohd	mohd	PROPN
ejpam-3587	211	17	ali	ali	PROPN
ejpam-3587	211	18	,	,	PUNCT
ejpam-3587	211	19	n.	n.	PROPN
ejpam-3587	211	20	zulkifli	zulkifli	PROPN
ejpam-3587	211	21	/	/	SYM
ejpam-3587	211	22	eur	eur	PROPN
ejpam-3587	211	23	.	.	PUNCT
ejpam-3587	212	1	j.	j.	PROPN
ejpam-3587	212	2	pure	pure	PROPN
ejpam-3587	212	3	appl	appl	PROPN
ejpam-3587	212	4	.	.	PROPN
ejpam-3587	212	5	math	math	PROPN
ejpam-3587	212	6	,	,	PUNCT
ejpam-3587	212	7	13	13	NUM
ejpam-3587	212	8	(	(	PUNCT
ejpam-3587	212	9	1	1	NUM
ejpam-3587	212	10	)	)	PUNCT
ejpam-3587	212	11	(	(	PUNCT
ejpam-3587	212	12	2020	2020	NUM
ejpam-3587	212	13	)	)	PUNCT
ejpam-3587	212	14	,	,	PUNCT
ejpam-3587	212	15	84	84	NUM
ejpam-3587	212	16	-	-	SYM
ejpam-3587	212	17	95	95	NUM
ejpam-3587	212	18	92	92	NUM
ejpam-3587	213	1	then	then	ADV
ejpam-3587	213	2	h	h	NOUN
ejpam-3587	213	3	is	be	AUX
ejpam-3587	213	4	an	an	DET
ejpam-3587	213	5	isolated	isolated	ADJ
ejpam-3587	213	6	vertex	vertex	NOUN
ejpam-3587	213	7	and	and	CCONJ
ejpam-3587	213	8	the	the	DET
ejpam-3587	213	9	maximum	maximum	ADJ
ejpam-3587	213	10	clique	clique	ADJ
ejpam-3587	213	11	size	size	NOUN
ejpam-3587	213	12	is	be	AUX
ejpam-3587	213	13	the	the	DET
ejpam-3587	213	14	biggest	big	ADJ
ejpam-3587	213	15	among	among	ADP
ejpam-3587	213	16	pαii	pαii	NOUN
ejpam-3587	213	17	,	,	PUNCT
ejpam-3587	213	18	therefore	therefore	ADV
ejpam-3587	213	19	ω(γopp(g	ω(γopp(g	NUM
ejpam-3587	213	20	)	)	PUNCT
ejpam-3587	213	21	)	)	PUNCT
ejpam-3587	214	1	=	=	SYM
ejpam-3587	214	2	max	max	PROPN
ejpam-3587	214	3	pαii	pαii	NOUN
ejpam-3587	214	4	.	.	PUNCT
ejpam-3587	215	1	�	�	PROPN
ejpam-3587	215	2	in	in	ADP
ejpam-3587	215	3	proposition	proposition	NOUN
ejpam-3587	215	4	9	9	NUM
ejpam-3587	215	5	and	and	CCONJ
ejpam-3587	215	6	proposition	proposition	NOUN
ejpam-3587	215	7	10	10	NUM
ejpam-3587	215	8	,	,	PUNCT
ejpam-3587	215	9	we	we	PRON
ejpam-3587	215	10	give	give	VERB
ejpam-3587	215	11	the	the	DET
ejpam-3587	215	12	independent	independent	ADJ
ejpam-3587	215	13	number	number	NOUN
ejpam-3587	215	14	of	of	ADP
ejpam-3587	215	15	the	the	DET
ejpam-3587	215	16	order	order	NOUN
ejpam-3587	215	17	product	product	NOUN
ejpam-3587	215	18	prime	prime	ADJ
ejpam-3587	215	19	graphs	graph	NOUN
ejpam-3587	215	20	for	for	ADP
ejpam-3587	215	21	dihedral	dihedral	ADJ
ejpam-3587	215	22	group	group	NOUN
ejpam-3587	215	23	and	and	CCONJ
ejpam-3587	215	24	cyclic	cyclic	ADJ
ejpam-3587	215	25	group	group	NOUN
ejpam-3587	215	26	.	.	PUNCT
ejpam-3587	216	1	proposition	proposition	NOUN
ejpam-3587	216	2	9	9	NUM
ejpam-3587	216	3	.	.	PUNCT
ejpam-3587	217	1	let	let	VERB
ejpam-3587	217	2	g	g	PRON
ejpam-3587	217	3	be	be	AUX
ejpam-3587	217	4	a	a	DET
ejpam-3587	217	5	dihedral	dihedral	ADJ
ejpam-3587	217	6	group	group	NOUN
ejpam-3587	217	7	,	,	PUNCT
ejpam-3587	217	8	dn	dn	PROPN
ejpam-3587	217	9	,	,	PUNCT
ejpam-3587	217	10	then	then	ADV
ejpam-3587	217	11	α(γopp(g	α(γopp(g	NUM
ejpam-3587	217	12	)	)	PUNCT
ejpam-3587	217	13	)	)	PUNCT
ejpam-3587	218	1	=	=	PUNCT
ejpam-3587	218	2			NUM
ejpam-3587	218	3	1	1	NUM
ejpam-3587	218	4	if	if	SCONJ
ejpam-3587	218	5	n	n	NOUN
ejpam-3587	218	6	=	=	SYM
ejpam-3587	218	7	2α	2α	NOUN
ejpam-3587	218	8	,	,	PUNCT
ejpam-3587	218	9	2	2	NUM
ejpam-3587	218	10	if	if	SCONJ
ejpam-3587	218	11	n	n	ADV
ejpam-3587	218	12	=	=	VERB
ejpam-3587	218	13	pα	pα	PROPN
ejpam-3587	218	14	p	p	NOUN
ejpam-3587	218	15	6=	6=	ADP
ejpam-3587	218	16	2	2	NUM
ejpam-3587	218	17	,	,	PUNCT
ejpam-3587	218	18	n+	n+	PUNCT
ejpam-3587	219	1	2d−	2d−	PROPN
ejpam-3587	219	2	(	(	PUNCT
ejpam-3587	219	3	1	1	NUM
ejpam-3587	219	4	+	+	NUM
ejpam-3587	219	5	∑d	∑d	X
ejpam-3587	219	6	i=1	i=1	X
ejpam-3587	220	1	p	p	X
ejpam-3587	220	2	αi	αi	VERB
ejpam-3587	220	3	i	i	INTJ
ejpam-3587	220	4	)	)	PUNCT
ejpam-3587	221	1	if	if	SCONJ
ejpam-3587	221	2	n	n	ADV
ejpam-3587	221	3	=	=	SYM
ejpam-3587	221	4	∏d	∏d	ADP
ejpam-3587	221	5	i=1	i=1	PROPN
ejpam-3587	222	1	p	p	X
ejpam-3587	222	2	αi	αi	ADV
ejpam-3587	222	3	i	i	PRON
ejpam-3587	222	4	is	be	AUX
ejpam-3587	222	5	even	even	ADV
ejpam-3587	222	6	,	,	PUNCT
ejpam-3587	222	7	n+	n+	NUM
ejpam-3587	222	8	2d+	2d+	NUM
ejpam-3587	222	9	∑d	∑d	X
ejpam-3587	223	1	i=1	i=1	PRON
ejpam-3587	224	1	p	p	X
ejpam-3587	224	2	αi	αi	VERB
ejpam-3587	224	3	i	i	PRON
ejpam-3587	224	4	if	if	SCONJ
ejpam-3587	224	5	n	n	ADV
ejpam-3587	224	6	=	=	SYM
ejpam-3587	224	7	∏d	∏d	ADP
ejpam-3587	224	8	i=1	i=1	PROPN
ejpam-3587	225	1	p	p	X
ejpam-3587	225	2	αi	αi	ADV
ejpam-3587	225	3	i	i	PRON
ejpam-3587	225	4	is	be	AUX
ejpam-3587	225	5	odd	odd	ADJ
ejpam-3587	225	6	.	.	PUNCT
ejpam-3587	226	1	proof	proof	NOUN
ejpam-3587	226	2	:	:	PUNCT
ejpam-3587	226	3	if	if	SCONJ
ejpam-3587	226	4	n	n	NOUN
ejpam-3587	226	5	=	=	SYM
ejpam-3587	226	6	2α	2α	NOUN
ejpam-3587	226	7	,	,	PUNCT
ejpam-3587	226	8	then	then	ADV
ejpam-3587	226	9	by	by	ADP
ejpam-3587	226	10	theorem	theorem	ADJ
ejpam-3587	226	11	4	4	NUM
ejpam-3587	226	12	,	,	PUNCT
ejpam-3587	226	13	γopp(g	γopp(g	NOUN
ejpam-3587	226	14	)	)	PUNCT
ejpam-3587	226	15	is	be	AUX
ejpam-3587	226	16	complete	complete	ADJ
ejpam-3587	226	17	and	and	CCONJ
ejpam-3587	226	18	so	so	ADV
ejpam-3587	226	19	α(γopp(g	α(γopp(g	NUM
ejpam-3587	226	20	)	)	PUNCT
ejpam-3587	226	21	)	)	PUNCT
ejpam-3587	227	1	=	=	PUNCT
ejpam-3587	227	2	1	1	X
ejpam-3587	227	3	.	.	PUNCT
ejpam-3587	228	1	if	if	SCONJ
ejpam-3587	228	2	n	n	NUM
ejpam-3587	228	3	=	=	SYM
ejpam-3587	228	4	pα	pα	PROPN
ejpam-3587	228	5	,	,	PUNCT
ejpam-3587	228	6	p	p	X
ejpam-3587	228	7	6=	6=	PROPN
ejpam-3587	228	8	2	2	NUM
ejpam-3587	228	9	,	,	PUNCT
ejpam-3587	228	10	then	then	ADV
ejpam-3587	228	11	by	by	ADP
ejpam-3587	228	12	theorem	theorem	NOUN
ejpam-3587	228	13	1	1	NUM
ejpam-3587	228	14	,	,	PUNCT
ejpam-3587	228	15	there	there	PRON
ejpam-3587	228	16	are	be	VERB
ejpam-3587	228	17	only	only	ADV
ejpam-3587	228	18	two	two	NUM
ejpam-3587	228	19	non	non	ADJ
ejpam-3587	228	20	-	-	ADJ
ejpam-3587	228	21	trivial	trivial	ADJ
ejpam-3587	228	22	independent	independent	ADJ
ejpam-3587	228	23	cliques	clique	NOUN
ejpam-3587	228	24	whose	whose	DET
ejpam-3587	228	25	each	each	DET
ejpam-3587	228	26	member	member	NOUN
ejpam-3587	228	27	is	be	AUX
ejpam-3587	228	28	adjacent	adjacent	ADJ
ejpam-3587	228	29	to	to	ADP
ejpam-3587	228	30	e.	e.	PROPN
ejpam-3587	228	31	therefore	therefore	ADV
ejpam-3587	228	32	α(γopp(g	α(γopp(g	NUM
ejpam-3587	228	33	)	)	PUNCT
ejpam-3587	228	34	)	)	PUNCT
ejpam-3587	229	1	=	=	SYM
ejpam-3587	229	2	2	2	X
ejpam-3587	229	3	.	.	X
ejpam-3587	230	1	if	if	SCONJ
ejpam-3587	230	2	n	n	NOUN
ejpam-3587	230	3	=	=	SYM
ejpam-3587	230	4	∏d	∏d	ADP
ejpam-3587	230	5	i=1	i=1	PROPN
ejpam-3587	231	1	p	p	X
ejpam-3587	231	2	αi	αi	ADV
ejpam-3587	232	1	i	i	PRON
ejpam-3587	232	2	,	,	PUNCT
ejpam-3587	232	3	then	then	ADV
ejpam-3587	232	4	by	by	ADP
ejpam-3587	232	5	theorem	theorem	NOUN
ejpam-3587	232	6	2	2	NUM
ejpam-3587	232	7	,	,	PUNCT
ejpam-3587	232	8	the	the	DET
ejpam-3587	232	9	maximum	maximum	ADJ
ejpam-3587	232	10	independent	independent	ADJ
ejpam-3587	232	11	set	set	NOUN
ejpam-3587	232	12	is	be	AUX
ejpam-3587	232	13	n+	n+	ADP
ejpam-3587	232	14	2d−	2d−	PROPN
ejpam-3587	232	15	(	(	PUNCT
ejpam-3587	232	16	1	1	NUM
ejpam-3587	232	17	+	+	NUM
ejpam-3587	232	18	∑d	∑d	X
ejpam-3587	232	19	i=1	i=1	X
ejpam-3587	233	1	p	p	X
ejpam-3587	233	2	αi	αi	VERB
ejpam-3587	233	3	i	i	PRON
ejpam-3587	233	4	)	)	PUNCT
ejpam-3587	234	1	=	=	SYM
ejpam-3587	234	2	α(γopp(g	α(γopp(g	NUM
ejpam-3587	234	3	)	)	PUNCT
ejpam-3587	234	4	)	)	PUNCT
ejpam-3587	235	1	if	if	SCONJ
ejpam-3587	235	2	n	n	PRON
ejpam-3587	235	3	is	be	AUX
ejpam-3587	235	4	even	even	ADV
ejpam-3587	235	5	and	and	CCONJ
ejpam-3587	235	6	n+	n+	PUNCT
ejpam-3587	235	7	2d+	2d+	NOUN
ejpam-3587	235	8	∑d	∑d	X
ejpam-3587	235	9	i=1	i=1	PRON
ejpam-3587	236	1	p	p	X
ejpam-3587	236	2	αi	αi	VERB
ejpam-3587	236	3	i	i	PRON
ejpam-3587	236	4	if	if	SCONJ
ejpam-3587	236	5	n	n	ADV
ejpam-3587	236	6	if	if	SCONJ
ejpam-3587	236	7	n	n	PRON
ejpam-3587	236	8	is	be	AUX
ejpam-3587	236	9	odd	odd	ADJ
ejpam-3587	236	10	.	.	PUNCT
ejpam-3587	237	1	�	�	PROPN
ejpam-3587	237	2	proposition	proposition	NOUN
ejpam-3587	237	3	10	10	NUM
ejpam-3587	237	4	.	.	PUNCT
ejpam-3587	238	1	let	let	VERB
ejpam-3587	238	2	g	g	PRON
ejpam-3587	238	3	be	be	AUX
ejpam-3587	238	4	a	a	DET
ejpam-3587	238	5	cyclic	cyclic	ADJ
ejpam-3587	238	6	group	group	NOUN
ejpam-3587	238	7	,	,	PUNCT
ejpam-3587	238	8	zn	zn	PROPN
ejpam-3587	238	9	,	,	PUNCT
ejpam-3587	238	10	then	then	ADV
ejpam-3587	238	11	α(γopp(g	α(γopp(g	NUM
ejpam-3587	238	12	)	)	PUNCT
ejpam-3587	238	13	)	)	PUNCT
ejpam-3587	239	1	=	=	PRON
ejpam-3587	239	2	{	{	PUNCT
ejpam-3587	239	3	1	1	NUM
ejpam-3587	239	4	if	if	SCONJ
ejpam-3587	239	5	n	n	NUM
ejpam-3587	239	6	=	=	SYM
ejpam-3587	239	7	pα	pα	PROPN
ejpam-3587	239	8	,	,	PUNCT
ejpam-3587	239	9	n+	n+	PUNCT
ejpam-3587	240	1	2d−	2d−	PROPN
ejpam-3587	240	2	(	(	PUNCT
ejpam-3587	240	3	1	1	NUM
ejpam-3587	240	4	+	+	NUM
ejpam-3587	240	5	∑d	∑d	X
ejpam-3587	240	6	i=1	i=1	X
ejpam-3587	241	1	p	p	X
ejpam-3587	241	2	αi	αi	VERB
ejpam-3587	241	3	i	i	INTJ
ejpam-3587	241	4	)	)	PUNCT
ejpam-3587	242	1	if	if	SCONJ
ejpam-3587	242	2	n	n	ADV
ejpam-3587	242	3	=	=	SYM
ejpam-3587	242	4	∏d	∏d	ADP
ejpam-3587	242	5	i=1	i=1	PROPN
ejpam-3587	243	1	p	p	X
ejpam-3587	243	2	αi	αi	ADV
ejpam-3587	243	3	i	i	PRON
ejpam-3587	243	4	.	.	PUNCT
ejpam-3587	244	1	proof	proof	NOUN
ejpam-3587	244	2	:	:	PUNCT
ejpam-3587	244	3	if	if	SCONJ
ejpam-3587	244	4	n	n	PRON
ejpam-3587	244	5	=	=	SYM
ejpam-3587	244	6	pα	pα	PROPN
ejpam-3587	244	7	,	,	PUNCT
ejpam-3587	244	8	then	then	ADV
ejpam-3587	244	9	by	by	ADP
ejpam-3587	244	10	theorem	theorem	NOUN
ejpam-3587	244	11	5	5	NUM
ejpam-3587	244	12	,	,	PUNCT
ejpam-3587	244	13	γopp(g	γopp(g	NOUN
ejpam-3587	244	14	)	)	PUNCT
ejpam-3587	244	15	is	be	AUX
ejpam-3587	244	16	complete	complete	ADJ
ejpam-3587	244	17	and	and	CCONJ
ejpam-3587	244	18	so	so	ADV
ejpam-3587	244	19	all	all	DET
ejpam-3587	244	20	the	the	DET
ejpam-3587	244	21	vertices	vertex	NOUN
ejpam-3587	244	22	are	be	AUX
ejpam-3587	244	23	central	central	ADJ
ejpam-3587	244	24	,	,	PUNCT
ejpam-3587	244	25	therefore	therefore	ADV
ejpam-3587	244	26	α(γopp(g	α(γopp(g	NUM
ejpam-3587	244	27	)	)	PUNCT
ejpam-3587	244	28	)	)	PUNCT
ejpam-3587	245	1	=	=	PUNCT
ejpam-3587	245	2	1	1	X
ejpam-3587	245	3	.	.	PUNCT
ejpam-3587	246	1	if	if	SCONJ
ejpam-3587	246	2	n	n	ADV
ejpam-3587	246	3	=	=	SYM
ejpam-3587	246	4	∏d	∏d	ADP
ejpam-3587	246	5	i=1	i=1	PROPN
ejpam-3587	247	1	p	p	X
ejpam-3587	247	2	αi	αi	ADV
ejpam-3587	248	1	i	i	PRON
ejpam-3587	248	2	,	,	PUNCT
ejpam-3587	248	3	then	then	ADV
ejpam-3587	248	4	by	by	ADP
ejpam-3587	248	5	theorem	theorem	NOUN
ejpam-3587	248	6	3	3	NUM
ejpam-3587	248	7	,	,	PUNCT
ejpam-3587	248	8	the	the	DET
ejpam-3587	248	9	size	size	NOUN
ejpam-3587	248	10	of	of	ADP
ejpam-3587	248	11	the	the	DET
ejpam-3587	248	12	maximum	maximum	ADJ
ejpam-3587	248	13	independent	independent	ADJ
ejpam-3587	248	14	set	set	NOUN
ejpam-3587	248	15	is	be	AUX
ejpam-3587	248	16	n+	n+	ADP
ejpam-3587	248	17	2d−	2d−	PROPN
ejpam-3587	248	18	(	(	PUNCT
ejpam-3587	248	19	1	1	NUM
ejpam-3587	248	20	+	+	NUM
ejpam-3587	248	21	∑d	∑d	X
ejpam-3587	248	22	i=1	i=1	X
ejpam-3587	249	1	p	p	X
ejpam-3587	249	2	αi	αi	VERB
ejpam-3587	249	3	i	i	PRON
ejpam-3587	249	4	)	)	PUNCT
ejpam-3587	250	1	=	=	SYM
ejpam-3587	250	2	α(γopp(g	α(γopp(g	NUM
ejpam-3587	250	3	)	)	PUNCT
ejpam-3587	250	4	)	)	PUNCT
ejpam-3587	250	5	�	�	PROPN
ejpam-3587	250	6	the	the	DET
ejpam-3587	250	7	strength	strength	NOUN
ejpam-3587	250	8	for	for	ADP
ejpam-3587	250	9	the	the	DET
ejpam-3587	250	10	connectivity	connectivity	NOUN
ejpam-3587	250	11	of	of	ADP
ejpam-3587	250	12	the	the	DET
ejpam-3587	250	13	order	order	NOUN
ejpam-3587	250	14	product	product	NOUN
ejpam-3587	250	15	prime	prime	ADJ
ejpam-3587	250	16	graph	graph	NOUN
ejpam-3587	250	17	of	of	ADP
ejpam-3587	250	18	dihedral	dihedral	ADJ
ejpam-3587	250	19	and	and	CCONJ
ejpam-3587	250	20	cyclic	cyclic	ADJ
ejpam-3587	250	21	groups	group	NOUN
ejpam-3587	250	22	is	be	AUX
ejpam-3587	250	23	determined	determine	VERB
ejpam-3587	250	24	in	in	ADP
ejpam-3587	250	25	theorem	theorem	NOUN
ejpam-3587	250	26	6	6	NUM
ejpam-3587	250	27	to	to	PART
ejpam-3587	250	28	theorem	theorem	VERB
ejpam-3587	250	29	8	8	NUM
ejpam-3587	250	30	.	.	PUNCT
ejpam-3587	251	1	this	this	DET
ejpam-3587	251	2	strength	strength	NOUN
ejpam-3587	251	3	has	have	AUX
ejpam-3587	251	4	been	be	AUX
ejpam-3587	251	5	determined	determine	VERB
ejpam-3587	251	6	by	by	ADP
ejpam-3587	251	7	the	the	DET
ejpam-3587	251	8	vertex	vertex	NOUN
ejpam-3587	251	9	-	-	PUNCT
ejpam-3587	251	10	cut	cut	NOUN
ejpam-3587	251	11	of	of	ADP
ejpam-3587	251	12	the	the	DET
ejpam-3587	251	13	graphs	graph	NOUN
ejpam-3587	251	14	.	.	PUNCT
ejpam-3587	252	1	theorem	theorem	ADJ
ejpam-3587	252	2	6	6	NUM
ejpam-3587	252	3	.	.	PUNCT
ejpam-3587	253	1	let	let	VERB
ejpam-3587	253	2	g	g	PRON
ejpam-3587	253	3	be	be	AUX
ejpam-3587	253	4	a	a	DET
ejpam-3587	253	5	dihedral	dihedral	ADJ
ejpam-3587	253	6	group	group	NOUN
ejpam-3587	253	7	,	,	PUNCT
ejpam-3587	253	8	dn	dn	NOUN
ejpam-3587	253	9	or	or	CCONJ
ejpam-3587	253	10	cyclic	cyclic	ADJ
ejpam-3587	253	11	group	group	NOUN
ejpam-3587	253	12	,	,	PUNCT
ejpam-3587	253	13	zn	zn	PROPN
ejpam-3587	253	14	,	,	PUNCT
ejpam-3587	253	15	then	then	ADV
ejpam-3587	253	16	γopp(g	γopp(g	NOUN
ejpam-3587	253	17	)	)	PUNCT
ejpam-3587	253	18	is	be	AUX
ejpam-3587	253	19	0	0	NOUN
ejpam-3587	253	20	-	-	PUNCT
ejpam-3587	253	21	connected	connect	VERB
ejpam-3587	253	22	if	if	SCONJ
ejpam-3587	253	23	n	n	NOUN
ejpam-3587	253	24	=	=	SYM
ejpam-3587	253	25	∏d	∏d	ADP
ejpam-3587	253	26	i=1	i=1	PROPN
ejpam-3587	254	1	p	p	X
ejpam-3587	254	2	αi	αi	ADV
ejpam-3587	254	3	i	i	PRON
ejpam-3587	254	4	proof	proof	NOUN
ejpam-3587	254	5	:	:	PUNCT
ejpam-3587	254	6	by	by	ADP
ejpam-3587	254	7	theorem	theorem	NOUN
ejpam-3587	254	8	4	4	NUM
ejpam-3587	254	9	and	and	CCONJ
ejpam-3587	254	10	theorem	theorem	VERB
ejpam-3587	254	11	5	5	NUM
ejpam-3587	254	12	,	,	PUNCT
ejpam-3587	254	13	γopp(g	γopp(g	NOUN
ejpam-3587	254	14	)	)	PUNCT
ejpam-3587	254	15	is	be	AUX
ejpam-3587	254	16	disconnected	disconnect	VERB
ejpam-3587	254	17	,	,	PUNCT
ejpam-3587	254	18	therefore	therefore	ADV
ejpam-3587	254	19	γopp(g	γopp(g	NOUN
ejpam-3587	254	20	)	)	PUNCT
ejpam-3587	254	21	is	be	AUX
ejpam-3587	254	22	0connected	0connecte	VERB
ejpam-3587	254	23	�	�	PROPN
ejpam-3587	254	24	m.	m.	NOUN
ejpam-3587	254	25	bello	bello	PROPN
ejpam-3587	254	26	,	,	PUNCT
ejpam-3587	254	27	n.	n.	PROPN
ejpam-3587	254	28	m.	m.	NOUN
ejpam-3587	254	29	mohd	mohd	PROPN
ejpam-3587	254	30	ali	ali	PROPN
ejpam-3587	254	31	,	,	PUNCT
ejpam-3587	254	32	n.	n.	PROPN
ejpam-3587	254	33	zulkifli	zulkifli	PROPN
ejpam-3587	254	34	/	/	SYM
ejpam-3587	254	35	eur	eur	PROPN
ejpam-3587	254	36	.	.	PUNCT
ejpam-3587	255	1	j.	j.	PROPN
ejpam-3587	255	2	pure	pure	PROPN
ejpam-3587	255	3	appl	appl	PROPN
ejpam-3587	255	4	.	.	PROPN
ejpam-3587	255	5	math	math	PROPN
ejpam-3587	255	6	,	,	PUNCT
ejpam-3587	255	7	13	13	NUM
ejpam-3587	255	8	(	(	PUNCT
ejpam-3587	255	9	1	1	NUM
ejpam-3587	255	10	)	)	PUNCT
ejpam-3587	255	11	(	(	PUNCT
ejpam-3587	255	12	2020	2020	NUM
ejpam-3587	255	13	)	)	PUNCT
ejpam-3587	255	14	,	,	PUNCT
ejpam-3587	255	15	84	84	NUM
ejpam-3587	255	16	-	-	SYM
ejpam-3587	255	17	95	95	NUM
ejpam-3587	255	18	93	93	NUM
ejpam-3587	255	19	theorem	theorem	NOUN
ejpam-3587	255	20	7	7	NUM
ejpam-3587	255	21	.	.	PUNCT
ejpam-3587	256	1	let	let	VERB
ejpam-3587	256	2	g	g	PRON
ejpam-3587	256	3	be	be	AUX
ejpam-3587	256	4	a	a	DET
ejpam-3587	256	5	dihedral	dihedral	ADJ
ejpam-3587	256	6	group	group	NOUN
ejpam-3587	256	7	,	,	PUNCT
ejpam-3587	256	8	dpα	dpα	ADV
ejpam-3587	256	9	,	,	PUNCT
ejpam-3587	256	10	then	then	ADV
ejpam-3587	256	11	γopp(g	γopp(g	NOUN
ejpam-3587	256	12	)	)	PUNCT
ejpam-3587	256	13	is	be	AUX
ejpam-3587	256	14	(	(	PUNCT
ejpam-3587	256	15	n	n	CCONJ
ejpam-3587	256	16	−	−	PROPN
ejpam-3587	256	17	1)-connected	1)-connected	PROPN
ejpam-3587	256	18	if	if	SCONJ
ejpam-3587	256	19	n	n	PRON
ejpam-3587	256	20	is	be	AUX
ejpam-3587	256	21	even	even	ADV
ejpam-3587	256	22	and	and	CCONJ
ejpam-3587	256	23	1	1	NUM
ejpam-3587	256	24	-	-	PUNCT
ejpam-3587	256	25	connected	connect	VERB
ejpam-3587	256	26	if	if	SCONJ
ejpam-3587	256	27	n	n	NOUN
ejpam-3587	256	28	is	be	AUX
ejpam-3587	256	29	odd	odd	ADJ
ejpam-3587	256	30	proof	proof	NOUN
ejpam-3587	256	31	:	:	PUNCT
ejpam-3587	256	32	if	if	SCONJ
ejpam-3587	256	33	n	n	PRON
ejpam-3587	256	34	is	be	AUX
ejpam-3587	256	35	even	even	ADV
ejpam-3587	256	36	,	,	PUNCT
ejpam-3587	256	37	then	then	ADV
ejpam-3587	256	38	by	by	ADP
ejpam-3587	256	39	theorem	theorem	ADJ
ejpam-3587	256	40	4	4	NUM
ejpam-3587	256	41	,	,	PUNCT
ejpam-3587	256	42	γopp(g	γopp(g	NOUN
ejpam-3587	256	43	)	)	PUNCT
ejpam-3587	256	44	is	be	AUX
ejpam-3587	256	45	complete	complete	ADJ
ejpam-3587	256	46	,	,	PUNCT
ejpam-3587	256	47	so	so	ADV
ejpam-3587	256	48	we	we	PRON
ejpam-3587	256	49	have	have	VERB
ejpam-3587	256	50	n−1	n−1	PROPN
ejpam-3587	256	51	cut	cut	NOUN
ejpam-3587	256	52	-	-	PUNCT
ejpam-3587	256	53	vertices	vertex	NOUN
ejpam-3587	256	54	,	,	PUNCT
ejpam-3587	256	55	therefore	therefore	ADV
ejpam-3587	256	56	γopp(g	γopp(g	NOUN
ejpam-3587	256	57	)	)	PUNCT
ejpam-3587	256	58	is	be	AUX
ejpam-3587	256	59	(	(	PUNCT
ejpam-3587	256	60	n−	n−	NOUN
ejpam-3587	256	61	1)-connected	1)-connected	NUM
ejpam-3587	256	62	.	.	PUNCT
ejpam-3587	257	1	if	if	SCONJ
ejpam-3587	257	2	n	n	NOUN
ejpam-3587	257	3	is	be	AUX
ejpam-3587	257	4	odd	odd	ADJ
ejpam-3587	257	5	,	,	PUNCT
ejpam-3587	257	6	then	then	ADV
ejpam-3587	257	7	still	still	ADV
ejpam-3587	257	8	by	by	ADP
ejpam-3587	257	9	the	the	DET
ejpam-3587	257	10	theorem	theorem	PROPN
ejpam-3587	257	11	,	,	PUNCT
ejpam-3587	257	12	γopp(g	γopp(g	NOUN
ejpam-3587	257	13	)	)	PUNCT
ejpam-3587	257	14	has	have	VERB
ejpam-3587	257	15	one	one	NUM
ejpam-3587	257	16	vertex	vertex	NOUN
ejpam-3587	257	17	-cut	-cut	X
ejpam-3587	257	18	which	which	PRON
ejpam-3587	257	19	is	be	AUX
ejpam-3587	257	20	k1	k1	ADJ
ejpam-3587	257	21	and	and	CCONJ
ejpam-3587	257	22	so	so	ADV
ejpam-3587	257	23	γopp(g	γopp(g	NOUN
ejpam-3587	257	24	)	)	PUNCT
ejpam-3587	257	25	is	be	AUX
ejpam-3587	257	26	1	1	NUM
ejpam-3587	257	27	-	-	PUNCT
ejpam-3587	257	28	connected	connect	VERB
ejpam-3587	257	29	�	�	PROPN
ejpam-3587	257	30	theorem	theorem	VERB
ejpam-3587	257	31	8	8	NUM
ejpam-3587	257	32	.	.	PUNCT
ejpam-3587	258	1	let	let	VERB
ejpam-3587	258	2	g	g	PRON
ejpam-3587	258	3	be	be	AUX
ejpam-3587	258	4	a	a	DET
ejpam-3587	258	5	cyclic	cyclic	ADJ
ejpam-3587	258	6	group	group	NOUN
ejpam-3587	258	7	,	,	PUNCT
ejpam-3587	258	8	zn	zn	PROPN
ejpam-3587	258	9	,	,	PUNCT
ejpam-3587	258	10	n	n	PROPN
ejpam-3587	258	11	=	=	SYM
ejpam-3587	258	12	pα	pα	PROPN
ejpam-3587	258	13	,	,	PUNCT
ejpam-3587	258	14	α	α	PROPN
ejpam-3587	258	15	∈	∈	PROPN
ejpam-3587	258	16	n	n	CCONJ
ejpam-3587	258	17	,	,	PUNCT
ejpam-3587	258	18	then	then	ADV
ejpam-3587	258	19	γopp(g	γopp(g	X
ejpam-3587	258	20	)	)	PUNCT
ejpam-3587	258	21	is	be	AUX
ejpam-3587	258	22	(	(	PUNCT
ejpam-3587	258	23	n	n	CCONJ
ejpam-3587	258	24	−	−	PROPN
ejpam-3587	258	25	1)connected	1)connected	NUM
ejpam-3587	258	26	.	.	PUNCT
ejpam-3587	259	1	proof	proof	NOUN
ejpam-3587	259	2	:	:	PUNCT
ejpam-3587	259	3	the	the	DET
ejpam-3587	259	4	result	result	NOUN
ejpam-3587	259	5	follows	follow	VERB
ejpam-3587	259	6	,	,	PUNCT
ejpam-3587	259	7	since	since	SCONJ
ejpam-3587	259	8	by	by	ADP
ejpam-3587	259	9	theorem	theorem	NOUN
ejpam-3587	259	10	5	5	NUM
ejpam-3587	259	11	,	,	PUNCT
ejpam-3587	259	12	γopp(g	γopp(g	NOUN
ejpam-3587	259	13	)	)	PUNCT
ejpam-3587	259	14	is	be	AUX
ejpam-3587	259	15	complete	complete	ADJ
ejpam-3587	259	16	�	�	PROPN
ejpam-3587	259	17	the	the	DET
ejpam-3587	259	18	nilpotency	nilpotency	NOUN
ejpam-3587	259	19	of	of	ADP
ejpam-3587	259	20	dihedral	dihedral	ADJ
ejpam-3587	259	21	groups	group	NOUN
ejpam-3587	259	22	is	be	AUX
ejpam-3587	259	23	investigated	investigate	VERB
ejpam-3587	259	24	in	in	ADP
ejpam-3587	259	25	theorem	theorem	NOUN
ejpam-3587	259	26	9	9	NUM
ejpam-3587	259	27	using	use	VERB
ejpam-3587	259	28	the	the	DET
ejpam-3587	259	29	vertex	vertex	NOUN
ejpam-3587	259	30	-	-	PUNCT
ejpam-3587	259	31	cut	cut	NOUN
ejpam-3587	259	32	of	of	ADP
ejpam-3587	259	33	the	the	DET
ejpam-3587	259	34	graph	graph	NOUN
ejpam-3587	259	35	.	.	PUNCT
ejpam-3587	260	1	theorem	theorem	NOUN
ejpam-3587	260	2	9	9	NUM
ejpam-3587	260	3	.	.	PUNCT
ejpam-3587	261	1	let	let	VERB
ejpam-3587	261	2	g	g	PRON
ejpam-3587	261	3	be	be	AUX
ejpam-3587	261	4	a	a	DET
ejpam-3587	261	5	dihedral	dihedral	ADJ
ejpam-3587	261	6	group	group	NOUN
ejpam-3587	261	7	,	,	PUNCT
ejpam-3587	261	8	dn	dn	PROPN
ejpam-3587	261	9	,	,	PUNCT
ejpam-3587	261	10	then	then	ADV
ejpam-3587	261	11	g	g	PROPN
ejpam-3587	261	12	is	be	AUX
ejpam-3587	261	13	nilpotent	nilpotent	ADJ
ejpam-3587	261	14	if	if	SCONJ
ejpam-3587	261	15	k	k	PROPN
ejpam-3587	261	16	≥	≥	NUM
ejpam-3587	261	17	2	2	NUM
ejpam-3587	261	18	,	,	PUNCT
ejpam-3587	261	19	where	where	SCONJ
ejpam-3587	261	20	k	k	PROPN
ejpam-3587	261	21	is	be	AUX
ejpam-3587	261	22	vertex	vertex	NOUN
ejpam-3587	261	23	-	-	PUNCT
ejpam-3587	261	24	cut	cut	NOUN
ejpam-3587	261	25	of	of	ADP
ejpam-3587	261	26	γopp(g	γopp(g	NOUN
ejpam-3587	261	27	)	)	PUNCT
ejpam-3587	261	28	.	.	PUNCT
ejpam-3587	262	1	proof	proof	NOUN
ejpam-3587	262	2	:	:	PUNCT
ejpam-3587	262	3	we	we	PRON
ejpam-3587	262	4	need	need	VERB
ejpam-3587	262	5	to	to	PART
ejpam-3587	262	6	show	show	VERB
ejpam-3587	262	7	that	that	SCONJ
ejpam-3587	262	8	if	if	SCONJ
ejpam-3587	262	9	there	there	PRON
ejpam-3587	262	10	exist	exist	VERB
ejpam-3587	262	11	more	more	ADJ
ejpam-3587	262	12	than	than	ADP
ejpam-3587	262	13	1	1	NUM
ejpam-3587	262	14	vertices	vertex	NOUN
ejpam-3587	262	15	of	of	ADP
ejpam-3587	262	16	the	the	DET
ejpam-3587	262	17	graph	graph	NOUN
ejpam-3587	262	18	whose	whose	DET
ejpam-3587	262	19	all	all	DET
ejpam-3587	262	20	the	the	DET
ejpam-3587	262	21	non	non	ADJ
ejpam-3587	262	22	-	-	ADJ
ejpam-3587	262	23	isolated	isolated	ADJ
ejpam-3587	262	24	vertices	vertex	NOUN
ejpam-3587	262	25	of	of	ADP
ejpam-3587	262	26	the	the	DET
ejpam-3587	262	27	graph	graph	NOUN
ejpam-3587	262	28	are	be	AUX
ejpam-3587	262	29	adjacent	adjacent	ADJ
ejpam-3587	262	30	to	to	ADP
ejpam-3587	262	31	them	they	PRON
ejpam-3587	262	32	then	then	ADV
ejpam-3587	262	33	the	the	DET
ejpam-3587	262	34	group	group	NOUN
ejpam-3587	262	35	is	be	AUX
ejpam-3587	262	36	nilpotent	nilpotent	ADJ
ejpam-3587	262	37	.	.	PUNCT
ejpam-3587	263	1	suppose	suppose	VERB
ejpam-3587	263	2	k	k	PROPN
ejpam-3587	263	3	≥	≥	NUM
ejpam-3587	263	4	2	2	NUM
ejpam-3587	263	5	,	,	PUNCT
ejpam-3587	263	6	then	then	ADV
ejpam-3587	263	7	the	the	DET
ejpam-3587	263	8	central	central	ADJ
ejpam-3587	263	9	vertices	vertex	NOUN
ejpam-3587	263	10	of	of	ADP
ejpam-3587	263	11	γopp(g	γopp(g	NOUN
ejpam-3587	263	12	)	)	PUNCT
ejpam-3587	263	13	are	be	AUX
ejpam-3587	263	14	greater	great	ADJ
ejpam-3587	263	15	or	or	CCONJ
ejpam-3587	263	16	equals	equal	VERB
ejpam-3587	263	17	to	to	ADP
ejpam-3587	263	18	2	2	NUM
ejpam-3587	263	19	.	.	PUNCT
ejpam-3587	264	1	this	this	PRON
ejpam-3587	264	2	is	be	AUX
ejpam-3587	264	3	only	only	ADV
ejpam-3587	264	4	possible	possible	ADJ
ejpam-3587	264	5	if	if	SCONJ
ejpam-3587	264	6	z(g	z(g	NOUN
ejpam-3587	264	7	)	)	PUNCT
ejpam-3587	264	8	is	be	AUX
ejpam-3587	264	9	non	non	ADJ
ejpam-3587	264	10	-	-	ADJ
ejpam-3587	264	11	trivial	trivial	ADJ
ejpam-3587	264	12	and	and	CCONJ
ejpam-3587	264	13	the	the	DET
ejpam-3587	264	14	non	non	ADJ
ejpam-3587	264	15	-	-	ADJ
ejpam-3587	264	16	isolated	isolated	ADJ
ejpam-3587	264	17	vertices	vertex	NOUN
ejpam-3587	264	18	of	of	ADP
ejpam-3587	264	19	the	the	DET
ejpam-3587	264	20	graph	graph	NOUN
ejpam-3587	264	21	are	be	AUX
ejpam-3587	264	22	adjacent	adjacent	ADJ
ejpam-3587	264	23	to	to	ADP
ejpam-3587	264	24	z(g	z(g	NOUN
ejpam-3587	264	25	)	)	PUNCT
ejpam-3587	264	26	and	and	CCONJ
ejpam-3587	264	27	e	e	NOUN
ejpam-3587	264	28	since	since	SCONJ
ejpam-3587	264	29	g	g	PROPN
ejpam-3587	264	30	is	be	AUX
ejpam-3587	264	31	a	a	DET
ejpam-3587	264	32	group	group	NOUN
ejpam-3587	264	33	.	.	PUNCT
ejpam-3587	265	1	in	in	ADP
ejpam-3587	265	2	this	this	DET
ejpam-3587	265	3	case	case	NOUN
ejpam-3587	265	4	,	,	PUNCT
ejpam-3587	265	5	we	we	PRON
ejpam-3587	265	6	can	can	AUX
ejpam-3587	265	7	say	say	VERB
ejpam-3587	265	8	that	that	SCONJ
ejpam-3587	265	9	g	g	PROPN
ejpam-3587	265	10	has	have	VERB
ejpam-3587	265	11	even	even	ADV
ejpam-3587	265	12	degree	degree	NOUN
ejpam-3587	265	13	and	and	CCONJ
ejpam-3587	265	14	so	so	ADV
ejpam-3587	265	15	n	n	NOUN
ejpam-3587	265	16	=	=	SYM
ejpam-3587	265	17	2α	2α	NOUN
ejpam-3587	265	18	or	or	CCONJ
ejpam-3587	265	19	∏d	∏d	ADP
ejpam-3587	265	20	i=1	i=1	PROPN
ejpam-3587	265	21	2αii	2αii	NUM
ejpam-3587	265	22	.	.	PUNCT
ejpam-3587	266	1	if	if	SCONJ
ejpam-3587	266	2	n	n	ADV
ejpam-3587	266	3	=	=	SYM
ejpam-3587	266	4	∏d	∏d	ADP
ejpam-3587	266	5	i=1	i=1	PROPN
ejpam-3587	266	6	2αii	2αii	NUM
ejpam-3587	266	7	,	,	PUNCT
ejpam-3587	266	8	then	then	ADV
ejpam-3587	266	9	γopp(g	γopp(g	X
ejpam-3587	266	10	)	)	PUNCT
ejpam-3587	266	11	has	have	VERB
ejpam-3587	266	12	one	one	NUM
ejpam-3587	266	13	cut	cut	NOUN
ejpam-3587	266	14	-	-	PUNCT
ejpam-3587	266	15	vertex	vertex	NOUN
ejpam-3587	266	16	which	which	PRON
ejpam-3587	266	17	is	be	AUX
ejpam-3587	266	18	e	e	VERB
ejpam-3587	266	19	by	by	ADP
ejpam-3587	266	20	theorem	theorem	NOUN
ejpam-3587	266	21	1	1	NUM
ejpam-3587	266	22	.	.	PUNCT
ejpam-3587	267	1	suppose	suppose	VERB
ejpam-3587	267	2	n	n	PROPN
ejpam-3587	267	3	=	=	SYM
ejpam-3587	267	4	2α	2α	NOUN
ejpam-3587	267	5	then	then	ADV
ejpam-3587	267	6	still	still	ADV
ejpam-3587	267	7	by	by	ADP
ejpam-3587	267	8	theorem	theorem	NOUN
ejpam-3587	267	9	1	1	NUM
ejpam-3587	267	10	,	,	PUNCT
ejpam-3587	267	11	k	k	NOUN
ejpam-3587	267	12	=	=	SYM
ejpam-3587	267	13	2	2	NUM
ejpam-3587	267	14	and	and	CCONJ
ejpam-3587	267	15	|g|	|g|	PROPN
ejpam-3587	267	16	=	=	SYM
ejpam-3587	267	17	2α+1	2α+1	PROPN
ejpam-3587	267	18	,	,	PUNCT
ejpam-3587	267	19	so	so	SCONJ
ejpam-3587	267	20	g	g	PROPN
ejpam-3587	267	21	is	be	AUX
ejpam-3587	267	22	a	a	DET
ejpam-3587	267	23	p	p	NOUN
ejpam-3587	267	24	-	-	PUNCT
ejpam-3587	267	25	group	group	NOUN
ejpam-3587	267	26	,	,	PUNCT
ejpam-3587	267	27	therefore	therefore	ADV
ejpam-3587	267	28	g	g	PROPN
ejpam-3587	267	29	is	be	AUX
ejpam-3587	267	30	nilpotent	nilpotent	ADJ
ejpam-3587	267	31	�	�	PROPN
ejpam-3587	267	32	in	in	ADP
ejpam-3587	267	33	theorem	theorem	NOUN
ejpam-3587	267	34	10	10	NUM
ejpam-3587	267	35	,	,	PUNCT
ejpam-3587	267	36	we	we	PRON
ejpam-3587	267	37	give	give	VERB
ejpam-3587	267	38	the	the	DET
ejpam-3587	267	39	result	result	NOUN
ejpam-3587	267	40	that	that	PRON
ejpam-3587	267	41	shows	show	VERB
ejpam-3587	267	42	that	that	SCONJ
ejpam-3587	267	43	the	the	DET
ejpam-3587	267	44	order	order	NOUN
ejpam-3587	267	45	product	product	NOUN
ejpam-3587	267	46	prime	prime	ADJ
ejpam-3587	267	47	graph	graph	NOUN
ejpam-3587	267	48	of	of	ADP
ejpam-3587	267	49	any	any	DET
ejpam-3587	267	50	two	two	NUM
ejpam-3587	267	51	groups	group	NOUN
ejpam-3587	267	52	are	be	AUX
ejpam-3587	267	53	isormorphic	isormorphic	ADJ
ejpam-3587	267	54	if	if	SCONJ
ejpam-3587	267	55	the	the	DET
ejpam-3587	267	56	two	two	NUM
ejpam-3587	267	57	groups	group	NOUN
ejpam-3587	267	58	are	be	AUX
ejpam-3587	267	59	isomorphic	isomorphic	ADJ
ejpam-3587	267	60	.	.	PUNCT
ejpam-3587	268	1	theorem	theorem	ADJ
ejpam-3587	268	2	10	10	NUM
ejpam-3587	268	3	.	.	PUNCT
ejpam-3587	269	1	let	let	VERB
ejpam-3587	269	2	g	g	NOUN
ejpam-3587	269	3	and	and	CCONJ
ejpam-3587	269	4	h	h	NOUN
ejpam-3587	269	5	be	be	VERB
ejpam-3587	269	6	any	any	DET
ejpam-3587	269	7	two	two	NUM
ejpam-3587	269	8	groups	group	NOUN
ejpam-3587	269	9	,	,	PUNCT
ejpam-3587	269	10	such	such	ADJ
ejpam-3587	269	11	that	that	SCONJ
ejpam-3587	269	12	g	g	PROPN
ejpam-3587	269	13	∼=	∼=	PROPN
ejpam-3587	269	14	h	h	NOUN
ejpam-3587	269	15	,	,	PUNCT
ejpam-3587	269	16	then	then	ADV
ejpam-3587	269	17	γopp(g	γopp(g	PROPN
ejpam-3587	269	18	)	)	PUNCT
ejpam-3587	269	19	∼=	∼=	PROPN
ejpam-3587	269	20	γopp(h	γopp(h	NOUN
ejpam-3587	269	21	)	)	PUNCT
ejpam-3587	269	22	proof	proof	NOUN
ejpam-3587	269	23	:	:	PUNCT
ejpam-3587	269	24	let	let	VERB
ejpam-3587	269	25	φ	φ	PROPN
ejpam-3587	269	26	be	be	AUX
ejpam-3587	269	27	a	a	DET
ejpam-3587	269	28	map	map	NOUN
ejpam-3587	269	29	between	between	ADP
ejpam-3587	269	30	g	g	PROPN
ejpam-3587	269	31	and	and	CCONJ
ejpam-3587	269	32	h,3	h,3	NUM
ejpam-3587	269	33	φ	φ	PROPN
ejpam-3587	269	34	:	:	PUNCT
ejpam-3587	269	35	v	v	X
ejpam-3587	269	36	(	(	PUNCT
ejpam-3587	269	37	g	g	NOUN
ejpam-3587	269	38	)	)	PUNCT
ejpam-3587	269	39	−→	−→	NOUN
ejpam-3587	269	40	v	v	NOUN
ejpam-3587	269	41	(	(	PUNCT
ejpam-3587	269	42	h	h	NOUN
ejpam-3587	269	43	)	)	PUNCT
ejpam-3587	269	44	,	,	PUNCT
ejpam-3587	269	45	define	define	VERB
ejpam-3587	269	46	by	by	ADP
ejpam-3587	269	47	φ(ui	φ(ui	NOUN
ejpam-3587	269	48	)	)	PUNCT
ejpam-3587	269	49	∼	∼	NOUN
ejpam-3587	269	50	φ(uj	φ(uj	NOUN
ejpam-3587	269	51	)	)	PUNCT
ejpam-3587	269	52	in	in	ADP
ejpam-3587	269	53	h	h	NOUN
ejpam-3587	269	54	if	if	SCONJ
ejpam-3587	269	55	ui	ui	PROPN
ejpam-3587	269	56	∼	∼	NOUN
ejpam-3587	269	57	uj	uj	PROPN
ejpam-3587	269	58	in	in	ADP
ejpam-3587	269	59	g	g	PROPN
ejpam-3587	269	60	,	,	PUNCT
ejpam-3587	269	61	where	where	SCONJ
ejpam-3587	269	62	ui	ui	PROPN
ejpam-3587	269	63	,	,	PUNCT
ejpam-3587	269	64	vj	vj	INTJ
ejpam-3587	269	65	,	,	PUNCT
ejpam-3587	269	66	1	1	NUM
ejpam-3587	269	67	≤	≤	NUM
ejpam-3587	269	68	i	i	PRON
ejpam-3587	269	69	,	,	PUNCT
ejpam-3587	269	70	j	j	PROPN
ejpam-3587	269	71	≤	≤	PROPN
ejpam-3587	269	72	|g|	|g|	PROPN
ejpam-3587	269	73	are	be	AUX
ejpam-3587	269	74	the	the	DET
ejpam-3587	269	75	sets	set	NOUN
ejpam-3587	269	76	of	of	ADP
ejpam-3587	269	77	vertices	vertex	NOUN
ejpam-3587	269	78	of	of	ADP
ejpam-3587	269	79	g	g	NOUN
ejpam-3587	269	80	respectively	respectively	ADV
ejpam-3587	269	81	.	.	PUNCT
ejpam-3587	270	1	we	we	PRON
ejpam-3587	270	2	need	need	VERB
ejpam-3587	270	3	to	to	PART
ejpam-3587	270	4	show	show	VERB
ejpam-3587	270	5	that	that	SCONJ
ejpam-3587	270	6	φ	φ	PROPN
ejpam-3587	270	7	is	be	AUX
ejpam-3587	270	8	a	a	DET
ejpam-3587	270	9	bijection	bijection	NOUN
ejpam-3587	270	10	and	and	CCONJ
ejpam-3587	270	11	preserves	preserve	VERB
ejpam-3587	270	12	vertex	vertex	NOUN
ejpam-3587	270	13	adjacency	adjacency	NOUN
ejpam-3587	270	14	.	.	PUNCT
ejpam-3587	271	1	pick	pick	PROPN
ejpam-3587	271	2	u1	u1	PROPN
ejpam-3587	271	3	,	,	PUNCT
ejpam-3587	271	4	u2	u2	PROPN
ejpam-3587	271	5	∈	∈	PROPN
ejpam-3587	271	6	γopp(g	γopp(g	PROPN
ejpam-3587	271	7	)	)	PUNCT
ejpam-3587	271	8	,	,	PUNCT
ejpam-3587	271	9	3	3	NUM
ejpam-3587	271	10	u1	u1	NOUN
ejpam-3587	271	11	∼	∼	NOUN
ejpam-3587	271	12	u2	u2	NOUN
ejpam-3587	271	13	,	,	PUNCT
ejpam-3587	271	14	then	then	ADV
ejpam-3587	271	15	u1u2	u1u2	VERB
ejpam-3587	271	16	∈	∈	PROPN
ejpam-3587	271	17	e(γopp(g	e(γopp(g	NOUN
ejpam-3587	271	18	)	)	PUNCT
ejpam-3587	271	19	)	)	PUNCT
ejpam-3587	272	1	and	and	CCONJ
ejpam-3587	272	2	since	since	SCONJ
ejpam-3587	272	3	g	g	PROPN
ejpam-3587	272	4	∼=	∼=	PROPN
ejpam-3587	272	5	h	h	NOUN
ejpam-3587	272	6	,	,	PUNCT
ejpam-3587	272	7	then	then	ADV
ejpam-3587	272	8	φ(u1	φ(u1	NOUN
ejpam-3587	272	9	)	)	PUNCT
ejpam-3587	272	10	∼	∼	NOUN
ejpam-3587	272	11	φ(u2	φ(u2	NOUN
ejpam-3587	272	12	)	)	PUNCT
ejpam-3587	272	13	in	in	ADP
ejpam-3587	272	14	h	h	NOUN
ejpam-3587	272	15	,	,	PUNCT
ejpam-3587	272	16	that	that	PRON
ejpam-3587	272	17	is	is	ADV
ejpam-3587	272	18	φ(u1)φ(u2	φ(u1)φ(u2	PROPN
ejpam-3587	272	19	)	)	PUNCT
ejpam-3587	273	1	=	=	PUNCT
ejpam-3587	274	1	v1v2	v1v2	X
ejpam-3587	274	2	∈	∈	PROPN
ejpam-3587	274	3	e(γopp(h	e(γopp(h	NOUN
ejpam-3587	274	4	)	)	PUNCT
ejpam-3587	274	5	)	)	PUNCT
ejpam-3587	274	6	,	,	PUNCT
ejpam-3587	274	7	therefore	therefore	ADV
ejpam-3587	274	8	φ	φ	PROPN
ejpam-3587	274	9	preserves	preserve	VERB
ejpam-3587	274	10	vertex	vertex	NOUN
ejpam-3587	274	11	adjacency	adjacency	NOUN
ejpam-3587	274	12	.	.	PUNCT
ejpam-3587	275	1	φ	φ	PROPN
ejpam-3587	275	2	is	be	AUX
ejpam-3587	275	3	a	a	DET
ejpam-3587	275	4	bijection	bijection	NOUN
ejpam-3587	275	5	since	since	SCONJ
ejpam-3587	275	6	φ(u1	φ(u1	NOUN
ejpam-3587	275	7	)	)	PUNCT
ejpam-3587	275	8	=	=	SYM
ejpam-3587	275	9	φ(u2	φ(u2	NOUN
ejpam-3587	275	10	)	)	PUNCT
ejpam-3587	275	11	⇐	⇐	ADJ
ejpam-3587	275	12	⇒	⇒	PROPN
ejpam-3587	275	13	u1	u1	NOUN
ejpam-3587	275	14	=	=	SYM
ejpam-3587	275	15	u2	u2	PROPN
ejpam-3587	275	16	v1	v1	NOUN
ejpam-3587	275	17	=	=	SYM
ejpam-3587	275	18	v2	v2	PROPN
ejpam-3587	275	19	⇐	⇐	ADJ
ejpam-3587	275	20	⇒	⇒	PROPN
ejpam-3587	275	21	u1	u1	NOUN
ejpam-3587	275	22	=	=	SYM
ejpam-3587	275	23	v1	v1	NOUN
ejpam-3587	275	24	and	and	CCONJ
ejpam-3587	275	25	u2	u2	NOUN
ejpam-3587	275	26	=	=	PUNCT
ejpam-3587	275	27	v2	v2	PROPN
ejpam-3587	275	28	references	reference	NOUN
ejpam-3587	275	29	94	94	NUM
ejpam-3587	275	30	and	and	CCONJ
ejpam-3587	275	31	also	also	ADV
ejpam-3587	275	32	the	the	DET
ejpam-3587	275	33	vertices	vertex	NOUN
ejpam-3587	275	34	ui	ui	PROPN
ejpam-3587	275	35	∈	∈	PROPN
ejpam-3587	275	36	g	g	ADP
ejpam-3587	275	37	3	3	NUM
ejpam-3587	275	38	φ(ui	φ(ui	NOUN
ejpam-3587	275	39	)	)	PUNCT
ejpam-3587	275	40	=	=	SYM
ejpam-3587	275	41	vi	vi	NOUN
ejpam-3587	275	42	∈	∈	PROPN
ejpam-3587	275	43	h	h	NOUN
ejpam-3587	275	44	,	,	PUNCT
ejpam-3587	275	45	with	with	ADP
ejpam-3587	275	46	the	the	DET
ejpam-3587	275	47	condition	condition	NOUN
ejpam-3587	276	1	that	that	SCONJ
ejpam-3587	276	2	v1v2	v1v2	PUNCT
ejpam-3587	276	3	∈	∈	PROPN
ejpam-3587	276	4	e(γopp(h	e(γopp(h	NOUN
ejpam-3587	276	5	)	)	PUNCT
ejpam-3587	276	6	)	)	PUNCT
ejpam-3587	277	1	if	if	SCONJ
ejpam-3587	277	2	u1u2	u1u2	PRON
ejpam-3587	277	3	∈	∈	PROPN
ejpam-3587	277	4	e(γopp(g	e(γopp(g	NOUN
ejpam-3587	277	5	)	)	PUNCT
ejpam-3587	277	6	)	)	PUNCT
ejpam-3587	277	7	since	since	SCONJ
ejpam-3587	277	8	g	g	PROPN
ejpam-3587	277	9	∼=	∼=	PROPN
ejpam-3587	277	10	h	h	NOUN
ejpam-3587	277	11	�	�	NOUN
ejpam-3587	277	12	example	example	NOUN
ejpam-3587	277	13	2	2	X
ejpam-3587	277	14	.	.	X
ejpam-3587	277	15	consider	consider	VERB
ejpam-3587	277	16	the	the	DET
ejpam-3587	277	17	dihedral	dihedral	ADJ
ejpam-3587	277	18	group	group	NOUN
ejpam-3587	277	19	of	of	ADP
ejpam-3587	277	20	degree	degree	NOUN
ejpam-3587	277	21	six	six	NUM
ejpam-3587	277	22	and	and	CCONJ
ejpam-3587	277	23	symmetric	symmetric	ADJ
ejpam-3587	277	24	group	group	NOUN
ejpam-3587	277	25	of	of	ADP
ejpam-3587	277	26	degree	degree	NOUN
ejpam-3587	277	27	three	three	NUM
ejpam-3587	277	28	.	.	PUNCT
ejpam-3587	278	1	let	let	VERB
ejpam-3587	278	2	g	g	NOUN
ejpam-3587	278	3	=	=	PROPN
ejpam-3587	278	4	d6	d6	VERB
ejpam-3587	278	5	and	and	CCONJ
ejpam-3587	278	6	h	h	NOUN
ejpam-3587	278	7	=	=	SYM
ejpam-3587	278	8	s3	s3	PROPN
ejpam-3587	278	9	,	,	PUNCT
ejpam-3587	278	10	then	then	ADV
ejpam-3587	278	11	g	g	PROPN
ejpam-3587	278	12	∼=	∼=	PROPN
ejpam-3587	278	13	h	h	NOUN
ejpam-3587	278	14	,	,	PUNCT
ejpam-3587	278	15	it	it	PRON
ejpam-3587	278	16	can	can	AUX
ejpam-3587	278	17	be	be	AUX
ejpam-3587	278	18	easily	easily	ADV
ejpam-3587	278	19	seen	see	VERB
ejpam-3587	278	20	that	that	SCONJ
ejpam-3587	278	21	γopp(g	γopp(g	NOUN
ejpam-3587	278	22	)	)	PUNCT
ejpam-3587	278	23	∼=	∼=	PROPN
ejpam-3587	278	24	γopp(h	γopp(h	NOUN
ejpam-3587	278	25	)	)	PUNCT
ejpam-3587	278	26	since	since	SCONJ
ejpam-3587	278	27	the	the	DET
ejpam-3587	278	28	isomorphism	isomorphism	NOUN
ejpam-3587	278	29	preserves	preserve	VERB
ejpam-3587	278	30	the	the	DET
ejpam-3587	278	31	order	order	NOUN
ejpam-3587	278	32	of	of	ADP
ejpam-3587	278	33	the	the	DET
ejpam-3587	278	34	elements	element	NOUN
ejpam-3587	278	35	in	in	ADP
ejpam-3587	278	36	the	the	DET
ejpam-3587	278	37	groups	group	NOUN
ejpam-3587	278	38	.	.	PUNCT
ejpam-3587	279	1	observe	observe	VERB
ejpam-3587	279	2	that	that	SCONJ
ejpam-3587	279	3	the	the	DET
ejpam-3587	279	4	cycles	cycle	NOUN
ejpam-3587	279	5	of	of	ADP
ejpam-3587	279	6	length	length	NOUN
ejpam-3587	279	7	two	two	NUM
ejpam-3587	279	8	in	in	ADP
ejpam-3587	279	9	s3	s3	PROPN
ejpam-3587	279	10	correspond	correspond	ADV
ejpam-3587	279	11	to	to	ADP
ejpam-3587	279	12	the	the	DET
ejpam-3587	279	13	reflections	reflection	NOUN
ejpam-3587	279	14	of	of	ADP
ejpam-3587	279	15	d6	d6	NOUN
ejpam-3587	279	16	while	while	SCONJ
ejpam-3587	279	17	the	the	DET
ejpam-3587	279	18	cycles	cycle	NOUN
ejpam-3587	279	19	of	of	ADP
ejpam-3587	279	20	length	length	NOUN
ejpam-3587	279	21	three	three	NUM
ejpam-3587	279	22	corresponds	correspond	NOUN
ejpam-3587	279	23	to	to	ADP
ejpam-3587	279	24	the	the	DET
ejpam-3587	279	25	rotations	rotation	NOUN
ejpam-3587	279	26	.	.	PUNCT
ejpam-3587	280	1	therefore	therefore	ADV
ejpam-3587	280	2	γopp(g	γopp(g	NOUN
ejpam-3587	280	3	)	)	PUNCT
ejpam-3587	280	4	∼=	∼=	PROPN
ejpam-3587	280	5	γopp(h	γopp(h	NOUN
ejpam-3587	280	6	)	)	PUNCT
ejpam-3587	280	7	.	.	PUNCT
ejpam-3587	281	1	4	4	X
ejpam-3587	281	2	.	.	X
ejpam-3587	281	3	conclusion	conclusion	NOUN
ejpam-3587	281	4	in	in	ADP
ejpam-3587	281	5	this	this	DET
ejpam-3587	281	6	paper	paper	NOUN
ejpam-3587	281	7	,	,	PUNCT
ejpam-3587	281	8	new	new	ADJ
ejpam-3587	281	9	graph	graph	NOUN
ejpam-3587	281	10	that	that	PRON
ejpam-3587	281	11	relates	relate	VERB
ejpam-3587	281	12	the	the	DET
ejpam-3587	281	13	order	order	NOUN
ejpam-3587	281	14	of	of	ADP
ejpam-3587	281	15	the	the	DET
ejpam-3587	281	16	group	group	NOUN
ejpam-3587	281	17	elements	element	NOUN
ejpam-3587	281	18	by	by	ADP
ejpam-3587	281	19	prime	prime	ADJ
ejpam-3587	281	20	power	power	NOUN
ejpam-3587	281	21	is	be	AUX
ejpam-3587	281	22	defined	define	VERB
ejpam-3587	281	23	and	and	CCONJ
ejpam-3587	281	24	some	some	DET
ejpam-3587	281	25	properties	property	NOUN
ejpam-3587	281	26	of	of	ADP
ejpam-3587	281	27	the	the	DET
ejpam-3587	281	28	graph	graph	NOUN
ejpam-3587	281	29	which	which	PRON
ejpam-3587	281	30	include	include	VERB
ejpam-3587	281	31	some	some	PRON
ejpam-3587	281	32	of	of	ADP
ejpam-3587	281	33	its	its	PRON
ejpam-3587	281	34	invariants	invariant	NOUN
ejpam-3587	281	35	,	,	PUNCT
ejpam-3587	281	36	its	its	PRON
ejpam-3587	281	37	regularity	regularity	NOUN
ejpam-3587	281	38	,	,	PUNCT
ejpam-3587	281	39	planarity	planarity	NOUN
ejpam-3587	281	40	,	,	PUNCT
ejpam-3587	281	41	connectivity	connectivity	NOUN
ejpam-3587	281	42	and	and	CCONJ
ejpam-3587	281	43	the	the	DET
ejpam-3587	281	44	strength	strength	NOUN
ejpam-3587	281	45	of	of	ADP
ejpam-3587	281	46	the	the	DET
ejpam-3587	281	47	connectivity	connectivity	NOUN
ejpam-3587	281	48	have	have	AUX
ejpam-3587	281	49	been	be	AUX
ejpam-3587	281	50	investigated	investigate	VERB
ejpam-3587	281	51	and	and	CCONJ
ejpam-3587	281	52	the	the	DET
ejpam-3587	281	53	nilpotency	nilpotency	NOUN
ejpam-3587	281	54	of	of	ADP
ejpam-3587	281	55	the	the	DET
ejpam-3587	281	56	graph	graph	NOUN
ejpam-3587	281	57	is	be	AUX
ejpam-3587	281	58	checked	check	VERB
ejpam-3587	281	59	using	use	VERB
ejpam-3587	281	60	the	the	DET
ejpam-3587	281	61	vertex	vertex	NOUN
ejpam-3587	281	62	-	-	PUNCT
ejpam-3587	281	63	cut	cut	NOUN
ejpam-3587	281	64	of	of	ADP
ejpam-3587	281	65	the	the	DET
ejpam-3587	281	66	graph	graph	NOUN
ejpam-3587	281	67	.	.	PUNCT
ejpam-3587	282	1	acknowledgements	acknowledgement	NOUN
ejpam-3587	282	2	the	the	DET
ejpam-3587	282	3	first	first	ADJ
ejpam-3587	282	4	author	author	NOUN
ejpam-3587	282	5	would	would	AUX
ejpam-3587	282	6	like	like	VERB
ejpam-3587	282	7	to	to	PART
ejpam-3587	282	8	thank	thank	VERB
ejpam-3587	282	9	federal	federal	PROPN
ejpam-3587	282	10	university	university	PROPN
ejpam-3587	282	11	of	of	ADP
ejpam-3587	282	12	kashere	kashere	PROPN
ejpam-3587	282	13	(	(	PUNCT
ejpam-3587	282	14	fuk	fuk	ADV
ejpam-3587	282	15	)	)	PUNCT
ejpam-3587	282	16	for	for	ADP
ejpam-3587	282	17	their	their	PRON
ejpam-3587	282	18	total	total	ADJ
ejpam-3587	282	19	support	support	NOUN
ejpam-3587	282	20	.	.	PUNCT
ejpam-3587	283	1	he	he	PRON
ejpam-3587	283	2	also	also	ADV
ejpam-3587	283	3	like	like	VERB
ejpam-3587	283	4	to	to	PART
ejpam-3587	283	5	appreciate	appreciate	VERB
ejpam-3587	283	6	universiti	universiti	PROPN
ejpam-3587	283	7	teknologi	teknologi	PROPN
ejpam-3587	283	8	malaysia	malaysia	PROPN
ejpam-3587	283	9	(	(	PUNCT
ejpam-3587	283	10	utm	utm	PROPN
ejpam-3587	283	11	)	)	PUNCT
ejpam-3587	283	12	for	for	ADP
ejpam-3587	283	13	the	the	DET
ejpam-3587	283	14	financial	financial	ADJ
ejpam-3587	283	15	support	support	NOUN
ejpam-3587	283	16	of	of	ADP
ejpam-3587	283	17	international	international	ADJ
ejpam-3587	283	18	doctoral	doctoral	ADJ
ejpam-3587	283	19	fellowship	fellowship	NOUN
ejpam-3587	283	20	(	(	PUNCT
ejpam-3587	283	21	idf	idf	PROPN
ejpam-3587	283	22	)	)	PUNCT
ejpam-3587	283	23	.	.	PUNCT
ejpam-3587	284	1	the	the	DET
ejpam-3587	284	2	second	second	ADJ
ejpam-3587	284	3	and	and	CCONJ
ejpam-3587	284	4	third	third	ADJ
ejpam-3587	284	5	authors	author	NOUN
ejpam-3587	284	6	would	would	AUX
ejpam-3587	284	7	like	like	VERB
ejpam-3587	284	8	to	to	PART
ejpam-3587	284	9	thank	thank	VERB
ejpam-3587	284	10	universiti	universiti	PROPN
ejpam-3587	284	11	teknologi	teknologi	PROPN
ejpam-3587	284	12	malaysia	malaysia	PROPN
ejpam-3587	284	13	(	(	PUNCT
ejpam-3587	284	14	utm	utm	PROPN
ejpam-3587	284	15	)	)	PUNCT
ejpam-3587	284	16	for	for	ADP
ejpam-3587	284	17	its	its	PRON
ejpam-3587	284	18	support	support	NOUN
ejpam-3587	284	19	.	.	PUNCT
ejpam-3587	285	1	references	reference	NOUN
ejpam-3587	285	2	[	[	X
ejpam-3587	285	3	1	1	NUM
ejpam-3587	285	4	]	]	X
ejpam-3587	285	5	abd	abd	PROPN
ejpam-3587	285	6	rhani	rhani	NOUN
ejpam-3587	285	7	,	,	PUNCT
ejpam-3587	285	8	n.	n.	NOUN
ejpam-3587	285	9	,	,	PUNCT
ejpam-3587	285	10	muhainiah	muhainiah	PROPN
ejpam-3587	285	11	,	,	PUNCT
ejpam-3587	285	12	n.	n.	PROPN
ejpam-3587	285	13	m.	m.	PROPN
ejpam-3587	285	14	a.	a.	PROPN
ejpam-3587	285	15	,	,	PUNCT
ejpam-3587	285	16	sarmin	sarmin	NOUN
ejpam-3587	285	17	,	,	PUNCT
ejpam-3587	285	18	n.	n.	PROPN
ejpam-3587	285	19	h.	h.	PROPN
ejpam-3587	285	20	and	and	CCONJ
ejpam-3587	285	21	erfanian	erfanian	ADJ
ejpam-3587	285	22	,	,	PUNCT
ejpam-3587	285	23	a.	a.	NOUN
ejpam-3587	285	24	on	on	ADP
ejpam-3587	285	25	the	the	DET
ejpam-3587	285	26	domination	domination	NOUN
ejpam-3587	285	27	number	number	NOUN
ejpam-3587	285	28	and	and	CCONJ
ejpam-3587	285	29	regularity	regularity	NOUN
ejpam-3587	285	30	of	of	ADP
ejpam-3587	285	31	the	the	DET
ejpam-3587	285	32	relative	relative	ADJ
ejpam-3587	285	33	coprime	coprime	NOUN
ejpam-3587	285	34	graph	graph	NOUN
ejpam-3587	285	35	of	of	ADP
ejpam-3587	285	36	a	a	DET
ejpam-3587	285	37	group	group	NOUN
ejpam-3587	285	38	malaysian	malaysian	ADJ
ejpam-3587	285	39	journal	journal	NOUN
ejpam-3587	285	40	of	of	ADP
ejpam-3587	285	41	fundamental	fundamental	ADJ
ejpam-3587	285	42	and	and	CCONJ
ejpam-3587	285	43	applied	applied	ADJ
ejpam-3587	285	44	sciences	science	NOUN
ejpam-3587	285	45	,	,	PUNCT
ejpam-3587	285	46	13	13	NUM
ejpam-3587	285	47	(	(	PUNCT
ejpam-3587	285	48	2):(2017	2):(2017	NUM
ejpam-3587	285	49	)	)	PUNCT
ejpam-3587	285	50	,	,	PUNCT
ejpam-3587	285	51	72–74	72–74	NUM
ejpam-3587	285	52	.	.	PROPN
ejpam-3587	285	53	doi:10.2307/2369306	doi:10.2307/2369306	NOUN
ejpam-3587	286	1	2017	2017	NUM
ejpam-3587	286	2	[	[	SYM
ejpam-3587	286	3	2	2	NUM
ejpam-3587	286	4	]	]	X
ejpam-3587	286	5	arthur	arthur	PROPN
ejpam-3587	286	6	,	,	PUNCT
ejpam-3587	286	7	c.	c.	PROPN
ejpam-3587	286	8	desiderata	desiderata	PROPN
ejpam-3587	286	9	and	and	CCONJ
ejpam-3587	286	10	suggestions	suggestion	NOUN
ejpam-3587	286	11	:	:	PUNCT
ejpam-3587	286	12	no	no	INTJ
ejpam-3587	286	13	.	.	NOUN
ejpam-3587	286	14	2	2	X
ejpam-3587	286	15	.	.	X
ejpam-3587	287	1	the	the	DET
ejpam-3587	287	2	theory	theory	NOUN
ejpam-3587	287	3	of	of	ADP
ejpam-3587	287	4	groups	group	NOUN
ejpam-3587	287	5	:	:	PUNCT
ejpam-3587	287	6	graphical	graphical	ADJ
ejpam-3587	287	7	representation	representation	NOUN
ejpam-3587	287	8	american	american	PROPN
ejpam-3587	287	9	journal	journal	PROPN
ejpam-3587	287	10	of	of	ADP
ejpam-3587	287	11	mathematics	mathematic	NOUN
ejpam-3587	287	12	,	,	PUNCT
ejpam-3587	287	13	1	1	NUM
ejpam-3587	287	14	(	(	PUNCT
ejpam-3587	287	15	2):(1878	2):(1878	NUM
ejpam-3587	287	16	)	)	PUNCT
ejpam-3587	287	17	,	,	PUNCT
ejpam-3587	287	18	174–6	174–6	PROPN
ejpam-3587	287	19	.	.	PROPN
ejpam-3587	287	20	doi:10.2307/2369306	doi:10.2307/2369306	PROPN
ejpam-3587	287	21	1878	1878	NUM
ejpam-3587	287	22	[	[	X
ejpam-3587	287	23	3	3	NUM
ejpam-3587	287	24	]	]	X
ejpam-3587	287	25	akbari	akbari	PROPN
ejpam-3587	287	26	,	,	PUNCT
ejpam-3587	287	27	a.	a.	NOUN
ejpam-3587	287	28	and	and	CCONJ
ejpam-3587	287	29	eza	eza	PROPN
ejpam-3587	287	30	,	,	PUNCT
ejpam-3587	287	31	m.	m.	NOUN
ejpam-3587	287	32	a.	a.	NOUN
ejpam-3587	287	33	groups	group	NOUN
ejpam-3587	287	34	for	for	ADP
ejpam-3587	287	35	which	which	PRON
ejpam-3587	287	36	the	the	DET
ejpam-3587	287	37	non	non	ADJ
ejpam-3587	287	38	-	-	ADJ
ejpam-3587	287	39	commuting	commuting	ADJ
ejpam-3587	287	40	graph	graph	NOUN
ejpam-3587	287	41	is	be	AUX
ejpam-3587	287	42	a	a	DET
ejpam-3587	287	43	split	split	ADJ
ejpam-3587	287	44	graph	graph	NOUN
ejpam-3587	287	45	international	international	ADJ
ejpam-3587	287	46	journal	journal	NOUN
ejpam-3587	287	47	of	of	ADP
ejpam-3587	287	48	group	group	PROPN
ejpam-3587	287	49	theory	theory	NOUN
ejpam-3587	287	50	6(1	6(1	NUM
ejpam-3587	287	51	):	):	PUNCT
ejpam-3587	287	52	29	29	NUM
ejpam-3587	287	53	-	-	SYM
ejpam-3587	287	54	35	35	NUM
ejpam-3587	287	55	2017	2017	NUM
ejpam-3587	287	56	[	[	SYM
ejpam-3587	287	57	4	4	NUM
ejpam-3587	287	58	]	]	X
ejpam-3587	287	59	ganesan	ganesan	NOUN
ejpam-3587	287	60	,	,	PUNCT
ejpam-3587	287	61	a.	a.	NOUN
ejpam-3587	287	62	on	on	ADP
ejpam-3587	287	63	the	the	DET
ejpam-3587	287	64	automorphism	automorphism	NOUN
ejpam-3587	287	65	group	group	NOUN
ejpam-3587	287	66	of	of	ADP
ejpam-3587	287	67	cayley	cayley	ADJ
ejpam-3587	287	68	graphs	graph	NOUN
ejpam-3587	287	69	generated	generate	VERB
ejpam-3587	287	70	by	by	ADP
ejpam-3587	287	71	transposition	transposition	NOUN
ejpam-3587	287	72	australasian	australasian	ADJ
ejpam-3587	287	73	journal	journal	NOUN
ejpam-3587	287	74	of	of	ADP
ejpam-3587	287	75	combinatorics	combinatorics	PROPN
ejpam-3587	287	76	,	,	PUNCT
ejpam-3587	287	77	64(3	64(3	NUM
ejpam-3587	287	78	):	):	PUNCT
ejpam-3587	287	79	432	432	NUM
ejpam-3587	287	80	-	-	SYM
ejpam-3587	287	81	436	436	NUM
ejpam-3587	287	82	2016	2016	NUM
ejpam-3587	287	83	[	[	X
ejpam-3587	287	84	5	5	NUM
ejpam-3587	287	85	]	]	SYM
ejpam-3587	287	86	ghorbani	ghorbani	NOUN
ejpam-3587	287	87	,	,	PUNCT
ejpam-3587	287	88	m.	m.	NOUN
ejpam-3587	287	89	and	and	CCONJ
ejpam-3587	287	90	alkhansari	alkhansari	PROPN
ejpam-3587	287	91	,	,	PUNCT
ejpam-3587	287	92	g.	g.	PROPN
ejpam-3587	287	93	spectral	spectral	ADJ
ejpam-3587	287	94	properties	property	NOUN
ejpam-3587	287	95	of	of	ADP
ejpam-3587	287	96	nc	nc	NOUN
ejpam-3587	287	97	-	-	PUNCT
ejpam-3587	287	98	graph	graph	NOUN
ejpam-3587	287	99	kragujevac	kragujevac	PROPN
ejpam-3587	287	100	journal	journal	NOUN
ejpam-3587	287	101	of	of	ADP
ejpam-3587	287	102	mathematics	mathematic	NOUN
ejpam-3587	287	103	,	,	PUNCT
ejpam-3587	287	104	43(4	43(4	NOUN
ejpam-3587	287	105	):	):	PUNCT
ejpam-3587	287	106	523	523	NUM
ejpam-3587	287	107	-	-	SYM
ejpam-3587	287	108	534	534	NUM
ejpam-3587	287	109	2019	2019	NUM
ejpam-3587	287	110	[	[	SYM
ejpam-3587	287	111	6	6	NUM
ejpam-3587	287	112	]	]	X
ejpam-3587	287	113	kakeri	kakeri	PROPN
ejpam-3587	287	114	,	,	PUNCT
ejpam-3587	287	115	f.	f.	PROPN
ejpam-3587	287	116	,	,	PUNCT
ejpam-3587	287	117	erfanian	erfanian	ADJ
ejpam-3587	287	118	,	,	PUNCT
ejpam-3587	287	119	a.	a.	NOUN
ejpam-3587	287	120	and	and	CCONJ
ejpam-3587	287	121	mansoori	mansoori	PROPN
ejpam-3587	287	122	,	,	PUNCT
ejpam-3587	287	123	f.	f.	PROPN
ejpam-3587	287	124	generalization	generalization	NOUN
ejpam-3587	287	125	of	of	ADP
ejpam-3587	287	126	the	the	DET
ejpam-3587	287	127	non	non	ADJ
ejpam-3587	287	128	-	-	ADJ
ejpam-3587	287	129	commuting	commuting	ADJ
ejpam-3587	287	130	graph	graph	NOUN
ejpam-3587	287	131	of	of	ADP
ejpam-3587	287	132	a	a	DET
ejpam-3587	287	133	group	group	NOUN
ejpam-3587	287	134	via	via	ADP
ejpam-3587	287	135	normal	normal	ADJ
ejpam-3587	287	136	subgroup	subgroup	NOUN
ejpam-3587	287	137	scienceasia	scienceasia	PROPN
ejpam-3587	287	138	42(2016	42(2016	PROPN
ejpam-3587	287	139	):	):	PUNCT
ejpam-3587	287	140	231	231	NUM
ejpam-3587	287	141	-	-	SYM
ejpam-3587	287	142	235	235	NUM
ejpam-3587	287	143	2016	2016	NUM
ejpam-3587	287	144	references	reference	NOUN
ejpam-3587	287	145	95	95	NUM
ejpam-3587	288	1	[	[	X
ejpam-3587	288	2	7	7	NUM
ejpam-3587	288	3	]	]	X
ejpam-3587	288	4	kelarev	kelarev	X
ejpam-3587	288	5	,	,	PUNCT
ejpam-3587	288	6	a.	a.	NOUN
ejpam-3587	288	7	,	,	PUNCT
ejpam-3587	288	8	ryan	ryan	PROPN
ejpam-3587	288	9	,	,	PUNCT
ejpam-3587	288	10	j	j	PROPN
ejpam-3587	288	11	and	and	CCONJ
ejpam-3587	288	12	yearwood	yearwood	PROPN
ejpam-3587	288	13	,	,	PUNCT
ejpam-3587	288	14	j.	j.	PROPN
ejpam-3587	288	15	cayley	cayley	PROPN
ejpam-3587	288	16	graphs	graph	NOUN
ejpam-3587	288	17	as	as	ADP
ejpam-3587	288	18	classifiers	classifier	NOUN
ejpam-3587	288	19	for	for	ADP
ejpam-3587	288	20	data	datum	NOUN
ejpam-3587	288	21	mining	mining	NOUN
ejpam-3587	288	22	:	:	PUNCT
ejpam-3587	288	23	the	the	DET
ejpam-3587	288	24	influence	influence	NOUN
ejpam-3587	288	25	of	of	ADP
ejpam-3587	288	26	asymmetries	asymmetry	NOUN
ejpam-3587	288	27	.	.	PUNCT
ejpam-3587	289	1	:	:	PUNCT
ejpam-3587	289	2	discrete	discrete	ADJ
ejpam-3587	289	3	mathematics	mathematic	NOUN
ejpam-3587	289	4	2009	2009	NUM
ejpam-3587	289	5	309:(2009	309:(2009	NUM
ejpam-3587	289	6	)	)	PUNCT
ejpam-3587	289	7	5360	5360	NUM
ejpam-3587	289	8	-	-	SYM
ejpam-3587	289	9	5369	5369	NUM
ejpam-3587	289	10	.	.	PUNCT
ejpam-3587	290	1	[	[	X
ejpam-3587	290	2	8	8	NUM
ejpam-3587	290	3	]	]	X
ejpam-3587	290	4	selvakumar	selvakumar	PROPN
ejpam-3587	290	5	,	,	PUNCT
ejpam-3587	290	6	k.	k.	PROPN
ejpam-3587	290	7	and	and	CCONJ
ejpam-3587	290	8	subajini	subajini	PROPN
ejpam-3587	290	9	,	,	PUNCT
ejpam-3587	290	10	m.	m.	NOUN
ejpam-3587	290	11	classification	classification	NOUN
ejpam-3587	290	12	of	of	ADP
ejpam-3587	290	13	groups	group	NOUN
ejpam-3587	290	14	with	with	ADP
ejpam-3587	290	15	toroidal	toroidal	ADJ
ejpam-3587	290	16	coprime	coprime	NOUN
ejpam-3587	290	17	graphs	graph	NOUN
ejpam-3587	290	18	.	.	PUNCT
ejpam-3587	291	1	india	india	PROPN
ejpam-3587	291	2	:	:	PUNCT
ejpam-3587	291	3	australasian	australasian	ADJ
ejpam-3587	291	4	journal	journal	NOUN
ejpam-3587	291	5	of	of	ADP
ejpam-3587	291	6	combinatorics	combinatoric	NOUN
ejpam-3587	291	7	.	.	PUNCT
ejpam-3587	292	1	2017	2017	NUM
ejpam-3587	292	2	.	.	PUNCT
ejpam-3587	293	1	69(2):(2017	69(2):(2017	NUM
ejpam-3587	293	2	)	)	PUNCT
ejpam-3587	293	3	,	,	PUNCT
ejpam-3587	293	4	174–183	174–183	NUM
ejpam-3587	293	5	[	[	X
ejpam-3587	293	6	9	9	NUM
ejpam-3587	293	7	]	]	PUNCT
ejpam-3587	293	8	tamizh	tamizh	ADJ
ejpam-3587	293	9	,	,	PUNCT
ejpam-3587	293	10	t.	t.	PROPN
ejpam-3587	293	11	c.	c.	PROPN
ejpam-3587	293	12	,	,	PUNCT
ejpam-3587	293	13	selvakumar	selvakumar	PROPN
ejpam-3587	293	14	,	,	PUNCT
ejpam-3587	293	15	k.	k.	PROPN
ejpam-3587	293	16	and	and	CCONJ
ejpam-3587	293	17	raja	raja	PROPN
ejpam-3587	293	18	,	,	PUNCT
ejpam-3587	294	1	s.	s.	PROPN
ejpam-3587	294	2	commuting	commute	VERB
ejpam-3587	294	3	graphs	graph	NOUN
ejpam-3587	294	4	on	on	ADP
ejpam-3587	294	5	dihedral	dihedral	ADJ
ejpam-3587	294	6	groups	group	NOUN
ejpam-3587	294	7	the	the	DET
ejpam-3587	294	8	journal	journal	NOUN
ejpam-3587	294	9	of	of	ADP
ejpam-3587	294	10	mathematics	mathematic	NOUN
ejpam-3587	294	11	and	and	CCONJ
ejpam-3587	294	12	computer	computer	NOUN
ejpam-3587	294	13	science	science	NOUN
ejpam-3587	294	14	2011	2011	NUM
ejpam-3587	294	15	2(2011):402	2(2011):402	NOUN
ejpam-3587	294	16	-	-	PUNCT
ejpam-3587	294	17	406	406	NUM
ejpam-3587	294	18	[	[	SYM
ejpam-3587	294	19	10	10	NUM
ejpam-3587	294	20	]	]	PUNCT
ejpam-3587	294	21	sharafdini	sharafdini	PROPN
ejpam-3587	294	22	,	,	PUNCT
ejpam-3587	294	23	r.	r.	PROPN
ejpam-3587	294	24	and	and	CCONJ
ejpam-3587	294	25	darbandi	darbandi	PROPN
ejpam-3587	294	26	,	,	PUNCT
ejpam-3587	294	27	r.	r.	PROPN
ejpam-3587	294	28	energy	energy	NOUN
ejpam-3587	294	29	of	of	ADP
ejpam-3587	294	30	commuting	commute	VERB
ejpam-3587	294	31	graphs	graph	NOUN
ejpam-3587	294	32	of	of	ADP
ejpam-3587	294	33	finite	finite	ADJ
ejpam-3587	294	34	groups	group	NOUN
ejpam-3587	294	35	whose	whose	DET
ejpam-3587	294	36	centralizers	centralizer	NOUN
ejpam-3587	294	37	are	be	AUX
ejpam-3587	294	38	abelian	abelian	ADJ
ejpam-3587	294	39	arxiv:1704.06464v1[math.co	arxiv:1704.06464v1[math.co	ADP
ejpam-3587	294	40	]	]	X
ejpam-3587	294	41	2017	2017	NUM
ejpam-3587	294	42	[	[	SYM
ejpam-3587	294	43	11	11	NUM
ejpam-3587	294	44	]	]	PUNCT
ejpam-3587	294	45	vahidi	vahidi	NOUN
ejpam-3587	294	46	,	,	PUNCT
ejpam-3587	294	47	j.	j.	PROPN
ejpam-3587	294	48	and	and	CCONJ
ejpam-3587	294	49	asghar	asghar	PROPN
ejpam-3587	294	50	,	,	PUNCT
ejpam-3587	294	51	a.	a.	NOUN
ejpam-3587	294	52	t.	t.	NOUN
ejpam-3587	294	53	the	the	DET
ejpam-3587	294	54	commuting	commuting	NOUN
ejpam-3587	294	55	graphs	graph	NOUN
ejpam-3587	294	56	on	on	ADP
ejpam-3587	294	57	groups	group	NOUN
ejpam-3587	294	58	d2n	d2n	PROPN
ejpam-3587	294	59	,	,	PUNCT
ejpam-3587	294	60	qn	qn	INTJ
ejpam-3587	294	61	.	.	PUNCT
ejpam-3587	295	1	the	the	DET
ejpam-3587	295	2	journal	journal	NOUN
ejpam-3587	295	3	of	of	ADP
ejpam-3587	295	4	mathematics	mathematic	NOUN
ejpam-3587	295	5	and	and	CCONJ
ejpam-3587	295	6	computer	computer	NOUN
ejpam-3587	295	7	science	science	NOUN
ejpam-3587	295	8	2(2010):123	2(2010):123	NOUN
ejpam-3587	295	9	-	-	PUNCT
ejpam-3587	295	10	127	127	NUM
ejpam-3587	295	11	2010	2010	NUM