id	sid	tid	token	lemma	pos
iajs-3405	1	1	401	401	NUM
iajs-3405	1	2	©	©	ADP
iajs-3405	1	3	2024	2024	NUM
iajs-3405	1	4	the	the	DET
iajs-3405	1	5	author(s	author(s	NOUN
iajs-3405	1	6	)	)	PUNCT
iajs-3405	1	7	.	.	PUNCT
iajs-3405	2	1	published	publish	VERB
iajs-3405	2	2	by	by	ADP
iajs-3405	2	3	college	college	NOUN
iajs-3405	2	4	of	of	ADP
iajs-3405	2	5	education	education	NOUN
iajs-3405	2	6	for	for	ADP
iajs-3405	2	7	pure	pure	ADJ
iajs-3405	2	8	science	science	NOUN
iajs-3405	2	9	(	(	PUNCT
iajs-3405	2	10	ibn	ibn	PROPN
iajs-3405	2	11	al	al	PROPN
iajs-3405	2	12	-	-	PUNCT
iajs-3405	2	13	haitham	haitham	PROPN
iajs-3405	2	14	)	)	PUNCT
iajs-3405	2	15	,	,	PUNCT
iajs-3405	2	16	university	university	NOUN
iajs-3405	2	17	of	of	ADP
iajs-3405	2	18	baghdad	baghdad	PROPN
iajs-3405	2	19	.	.	PUNCT
iajs-3405	3	1	this	this	PRON
iajs-3405	3	2	is	be	AUX
iajs-3405	3	3	an	an	DET
iajs-3405	3	4	open	open	ADJ
iajs-3405	3	5	-	-	PUNCT
iajs-3405	3	6	access	access	NOUN
iajs-3405	3	7	article	article	NOUN
iajs-3405	3	8	distributed	distribute	VERB
iajs-3405	3	9	under	under	ADP
iajs-3405	3	10	the	the	DET
iajs-3405	3	11	terms	term	NOUN
iajs-3405	3	12	of	of	ADP
iajs-3405	3	13	the	the	DET
iajs-3405	3	14	creative	creative	ADJ
iajs-3405	3	15	commons	common	NOUN
iajs-3405	3	16	attribution	attribution	NOUN
iajs-3405	3	17	4.0	4.0	NUM
iajs-3405	3	18	international	international	ADJ
iajs-3405	3	19	license	license	NOUN
iajs-3405	3	20	ibn	ibn	PROPN
iajs-3405	3	21	al	al	PROPN
iajs-3405	3	22	-	-	PUNCT
iajs-3405	3	23	haitham	haitham	PROPN
iajs-3405	3	24	journal	journal	PROPN
iajs-3405	3	25	for	for	ADP
iajs-3405	3	26	pure	pure	ADJ
iajs-3405	3	27	and	and	CCONJ
iajs-3405	3	28	applied	applied	ADJ
iajs-3405	3	29	sciences	sciences	PROPN
iajs-3405	3	30	journal	journal	PROPN
iajs-3405	3	31	homepage	homepage	NOUN
iajs-3405	3	32	:	:	PUNCT
iajs-3405	3	33	jih.uobaghdad.edu.iq	jih.uobaghdad.edu.iq	NOUN
iajs-3405	3	34	pissn	pissn	ADJ
iajs-3405	3	35	:	:	PUNCT
iajs-3405	3	36	1609	1609	NUM
iajs-3405	3	37	-	-	SYM
iajs-3405	3	38	4042	4042	NUM
iajs-3405	3	39	,	,	PUNCT
iajs-3405	3	40	eissn	eissn	NOUN
iajs-3405	3	41	:	:	PUNCT
iajs-3405	3	42	2521	2521	NUM
iajs-3405	3	43	-	-	SYM
iajs-3405	3	44	3407	3407	NUM
iajs-3405	3	45	ihjpas	ihjpa	NOUN
iajs-3405	3	46	.	.	PUNCT
iajs-3405	4	1	2024	2024	NUM
iajs-3405	4	2	,	,	PUNCT
iajs-3405	4	3	37(4	37(4	NUM
iajs-3405	4	4	)	)	PUNCT
iajs-3405	4	5	analysing	analyse	VERB
iajs-3405	4	6	the	the	DET
iajs-3405	4	7	result	result	NOUN
iajs-3405	4	8	involution	involution	NOUN
iajs-3405	4	9	graph	graph	NOUN
iajs-3405	4	10	of	of	ADP
iajs-3405	4	11	the	the	DET
iajs-3405	4	12	group	group	NOUN
iajs-3405	4	13	j3	j3	PROPN
iajs-3405	4	14	ahmed	ahmed	AUX
iajs-3405	4	15	arkan	arkan	PROPN
iajs-3405	4	16	meteab1	meteab1	PROPN
iajs-3405	4	17	and	and	CCONJ
iajs-3405	4	18	ali	ali	PROPN
iajs-3405	4	19	abd	abd	PROPN
iajs-3405	4	20	aubad2	aubad2	PROPN
iajs-3405	4	21	,	,	PUNCT
iajs-3405	4	22	*	*	PROPN
iajs-3405	5	1	1,2department	1,2department	NUM
iajs-3405	5	2	of	of	ADP
iajs-3405	5	3	mathematics	mathematic	NOUN
iajs-3405	5	4	,	,	PUNCT
iajs-3405	5	5	college	college	NOUN
iajs-3405	5	6	of	of	ADP
iajs-3405	5	7	science	science	NOUN
iajs-3405	5	8	,	,	PUNCT
iajs-3405	5	9	university	university	NOUN
iajs-3405	5	10	of	of	ADP
iajs-3405	5	11	baghdad	baghdad	PROPN
iajs-3405	5	12	,	,	PUNCT
iajs-3405	5	13	baghdad	baghdad	PROPN
iajs-3405	5	14	,	,	PUNCT
iajs-3405	5	15	iraq	iraq	PROPN
iajs-3405	5	16	.	.	PUNCT
iajs-3405	6	1	*	*	PUNCT
iajs-3405	6	2	corresponding	correspond	VERB
iajs-3405	6	3	author	author	NOUN
iajs-3405	6	4	.	.	PUNCT
iajs-3405	7	1	received	receive	VERB
iajs-3405	7	2	:	:	PUNCT
iajs-3405	7	3	12	12	NUM
iajs-3405	7	4	april	april	PROPN
iajs-3405	7	5	2023	2023	NUM
iajs-3405	7	6	accepted	accept	VERB
iajs-3405	7	7	:	:	PUNCT
iajs-3405	7	8	18	18	NUM
iajs-3405	7	9	may	may	PROPN
iajs-3405	7	10	2023	2023	NUM
iajs-3405	7	11	published	publish	VERB
iajs-3405	7	12	:	:	PUNCT
iajs-3405	7	13	20	20	NUM
iajs-3405	7	14	october	october	NOUN
iajs-3405	7	15	2024	2024	NUM
iajs-3405	7	16	doi.org/10.30526/37.4.3405	doi.org/10.30526/37.4.3405	NOUN
iajs-3405	7	17	abstract	abstract	NOUN
iajs-3405	7	18	assume	assume	VERB
iajs-3405	7	19	that	that	SCONJ
iajs-3405	7	20	g	g	PROPN
iajs-3405	7	21	be	be	AUX
iajs-3405	7	22	a	a	DET
iajs-3405	7	23	finite	finite	ADJ
iajs-3405	7	24	group	group	NOUN
iajs-3405	7	25	and	and	CCONJ
iajs-3405	7	26	let	let	VERB
iajs-3405	7	27	i(g	i(g	NOUN
iajs-3405	7	28	)	)	PUNCT
iajs-3405	7	29	be	be	AUX
iajs-3405	7	30	the	the	DET
iajs-3405	7	31	set	set	NOUN
iajs-3405	7	32	of	of	ADP
iajs-3405	7	33	the	the	DET
iajs-3405	7	34	involution	involution	NOUN
iajs-3405	7	35	elements	element	NOUN
iajs-3405	7	36	in	in	ADP
iajs-3405	7	37	g.	g.	PROPN
iajs-3405	7	38	the	the	DET
iajs-3405	7	39	result	result	NOUN
iajs-3405	7	40	involution	involution	NOUN
iajs-3405	7	41	graph	graph	NOUN
iajs-3405	7	42	denoted	denote	VERB
iajs-3405	7	43	by	by	ADP
iajs-3405	7	44	,	,	PUNCT
iajs-3405	7	45	γ𝐺	γ𝐺	ADJ
iajs-3405	7	46	𝑅𝐼	𝑅𝐼	PROPN
iajs-3405	7	47	,	,	PUNCT
iajs-3405	7	48	is	be	AUX
iajs-3405	7	49	an	an	DET
iajs-3405	7	50	undirected	undirected	ADJ
iajs-3405	7	51	simple	simple	ADJ
iajs-3405	7	52	graph	graph	NOUN
iajs-3405	7	53	having	have	VERB
iajs-3405	7	54	the	the	DET
iajs-3405	7	55	elements	element	NOUN
iajs-3405	7	56	of	of	ADP
iajs-3405	7	57	g	g	PROPN
iajs-3405	7	58	as	as	ADP
iajs-3405	7	59	a	a	DET
iajs-3405	7	60	vertex	vertex	NOUN
iajs-3405	7	61	set	set	NOUN
iajs-3405	7	62	.	.	PUNCT
iajs-3405	8	1	moreover	moreover	ADV
iajs-3405	8	2	,	,	PUNCT
iajs-3405	8	3	two	two	NUM
iajs-3405	8	4	vertices	vertex	NOUN
iajs-3405	8	5	in	in	ADP
iajs-3405	8	6	γ𝐺	γ𝐺	PUNCT
iajs-3405	8	7	𝑅𝐼are	𝑅𝐼are	AUX
iajs-3405	8	8	connected	connect	VERB
iajs-3405	8	9	by	by	ADP
iajs-3405	8	10	an	an	DET
iajs-3405	8	11	edge	edge	NOUN
iajs-3405	8	12	if	if	SCONJ
iajs-3405	8	13	they	they	PRON
iajs-3405	8	14	are	be	AUX
iajs-3405	8	15	distinct	distinct	ADJ
iajs-3405	8	16	and	and	CCONJ
iajs-3405	8	17	their	their	PRON
iajs-3405	8	18	product	product	NOUN
iajs-3405	8	19	belong	belong	VERB
iajs-3405	8	20	to	to	ADP
iajs-3405	8	21	i(g	i(g	NOUN
iajs-3405	8	22	)	)	PUNCT
iajs-3405	8	23	.	.	PUNCT
iajs-3405	9	1	the	the	DET
iajs-3405	9	2	objective	objective	NOUN
iajs-3405	9	3	of	of	ADP
iajs-3405	9	4	this	this	DET
iajs-3405	9	5	work	work	NOUN
iajs-3405	9	6	is	be	AUX
iajs-3405	9	7	to	to	PART
iajs-3405	9	8	investigate	investigate	VERB
iajs-3405	9	9	the	the	DET
iajs-3405	9	10	result	result	NOUN
iajs-3405	9	11	involution	involution	NOUN
iajs-3405	9	12	graph	graph	NOUN
iajs-3405	9	13	for	for	ADP
iajs-3405	9	14	the	the	DET
iajs-3405	9	15	janko	janko	PROPN
iajs-3405	9	16	group	group	PROPN
iajs-3405	9	17	j3	j3	PROPN
iajs-3405	9	18	.	.	PUNCT
iajs-3405	10	1	in	in	ADP
iajs-3405	10	2	this	this	DET
iajs-3405	10	3	paper	paper	NOUN
iajs-3405	10	4	we	we	PRON
iajs-3405	10	5	compute	compute	VERB
iajs-3405	10	6	different	different	ADJ
iajs-3405	10	7	result	result	NOUN
iajs-3405	10	8	involution	involution	NOUN
iajs-3405	10	9	graph	graph	NOUN
iajs-3405	10	10	features	feature	NOUN
iajs-3405	10	11	,	,	PUNCT
iajs-3405	10	12	such	such	ADJ
iajs-3405	10	13	as	as	ADP
iajs-3405	10	14	the	the	DET
iajs-3405	10	15	radius	radius	NOUN
iajs-3405	10	16	,	,	PUNCT
iajs-3405	10	17	the	the	DET
iajs-3405	10	18	diameter	diameter	NOUN
iajs-3405	10	19	,	,	PUNCT
iajs-3405	10	20	the	the	DET
iajs-3405	10	21	clique	clique	NOUN
iajs-3405	10	22	number	number	NOUN
iajs-3405	10	23	,	,	PUNCT
iajs-3405	10	24	and	and	CCONJ
iajs-3405	10	25	the	the	DET
iajs-3405	10	26	girth	girth	NOUN
iajs-3405	10	27	.	.	PUNCT
iajs-3405	11	1	furthermore	furthermore	ADV
iajs-3405	11	2	,	,	PUNCT
iajs-3405	11	3	the	the	DET
iajs-3405	11	4	connectedness	connectedness	NOUN
iajs-3405	11	5	of	of	ADP
iajs-3405	11	6	the	the	DET
iajs-3405	11	7	result	result	NOUN
iajs-3405	11	8	involution	involution	NOUN
iajs-3405	11	9	graph	graph	NOUN
iajs-3405	11	10	is	be	AUX
iajs-3405	11	11	determined	determine	VERB
iajs-3405	11	12	.	.	PUNCT
iajs-3405	12	1	all	all	PRON
iajs-3405	12	2	of	of	ADP
iajs-3405	12	3	the	the	DET
iajs-3405	12	4	steps	step	NOUN
iajs-3405	12	5	needed	need	VERB
iajs-3405	12	6	for	for	ADP
iajs-3405	12	7	analyzing	analyze	VERB
iajs-3405	12	8	the	the	DET
iajs-3405	12	9	result	result	NOUN
iajs-3405	12	10	involution	involution	NOUN
iajs-3405	12	11	graph	graph	NOUN
iajs-3405	12	12	were	be	AUX
iajs-3405	12	13	carried	carry	VERB
iajs-3405	12	14	out	out	ADP
iajs-3405	12	15	using	use	VERB
iajs-3405	12	16	the	the	DET
iajs-3405	12	17	computational	computational	ADJ
iajs-3405	12	18	technique	technique	NOUN
iajs-3405	12	19	along	along	ADP
iajs-3405	12	20	with	with	ADP
iajs-3405	12	21	theoretical	theoretical	ADJ
iajs-3405	12	22	support	support	NOUN
iajs-3405	12	23	.	.	PUNCT
iajs-3405	13	1	keywords	keyword	NOUN
iajs-3405	13	2	:	:	PUNCT
iajs-3405	13	3	janko	janko	PROPN
iajs-3405	13	4	groups	group	NOUN
iajs-3405	13	5	,	,	PUNCT
iajs-3405	13	6	result	result	VERB
iajs-3405	13	7	involution	involution	NOUN
iajs-3405	13	8	graph	graph	NOUN
iajs-3405	13	9	,	,	PUNCT
iajs-3405	13	10	connectedness	connectedness	NOUN
iajs-3405	13	11	,	,	PUNCT
iajs-3405	13	12	girth	girth	NOUN
iajs-3405	13	13	.	.	PUNCT
iajs-3405	14	1	1	1	X
iajs-3405	14	2	.	.	X
iajs-3405	14	3	introduction	introduction	NOUN
iajs-3405	14	4	one	one	NUM
iajs-3405	14	5	of	of	ADP
iajs-3405	14	6	the	the	DET
iajs-3405	14	7	most	most	ADV
iajs-3405	14	8	important	important	ADJ
iajs-3405	14	9	techniques	technique	NOUN
iajs-3405	14	10	for	for	ADP
iajs-3405	14	11	examining	examine	VERB
iajs-3405	14	12	group	group	NOUN
iajs-3405	14	13	structure	structure	NOUN
iajs-3405	14	14	is	be	AUX
iajs-3405	14	15	possibly	possibly	ADV
iajs-3405	14	16	the	the	DET
iajs-3405	14	17	action	action	NOUN
iajs-3405	14	18	of	of	ADP
iajs-3405	14	19	a	a	DET
iajs-3405	14	20	group	group	NOUN
iajs-3405	14	21	on	on	ADP
iajs-3405	14	22	a	a	DET
iajs-3405	14	23	graph	graph	NOUN
iajs-3405	14	24	.	.	PUNCT
iajs-3405	15	1	the	the	DET
iajs-3405	15	2	numerous	numerous	ADJ
iajs-3405	15	3	and	and	CCONJ
iajs-3405	15	4	diverse	diverse	ADJ
iajs-3405	15	5	graphs	graph	NOUN
iajs-3405	15	6	that	that	PRON
iajs-3405	15	7	have	have	AUX
iajs-3405	15	8	been	be	AUX
iajs-3405	15	9	analyzed	analyze	VERB
iajs-3405	15	10	for	for	ADP
iajs-3405	15	11	various	various	ADJ
iajs-3405	15	12	groups	group	NOUN
iajs-3405	15	13	are	be	AUX
iajs-3405	15	14	highlighted	highlight	VERB
iajs-3405	15	15	by	by	ADP
iajs-3405	15	16	the	the	DET
iajs-3405	15	17	substantial	substantial	ADJ
iajs-3405	15	18	citations	citation	NOUN
iajs-3405	15	19	in	in	ADP
iajs-3405	15	20	[	[	PUNCT
iajs-3405	15	21	1	1	NUM
iajs-3405	15	22	-	-	SYM
iajs-3405	15	23	14	14	NUM
iajs-3405	15	24	]	]	PUNCT
iajs-3405	15	25	.	.	PUNCT
iajs-3405	16	1	if	if	SCONJ
iajs-3405	16	2	an	an	DET
iajs-3405	16	3	element	element	NOUN
iajs-3405	16	4	of	of	ADP
iajs-3405	16	5	a	a	DET
iajs-3405	16	6	group	group	NOUN
iajs-3405	16	7	has	have	VERB
iajs-3405	16	8	order	order	NOUN
iajs-3405	16	9	2	2	NUM
iajs-3405	16	10	,	,	PUNCT
iajs-3405	16	11	it	it	PRON
iajs-3405	16	12	is	be	AUX
iajs-3405	16	13	said	say	VERB
iajs-3405	16	14	to	to	PART
iajs-3405	16	15	be	be	AUX
iajs-3405	16	16	involution	involution	NOUN
iajs-3405	16	17	.	.	PUNCT
iajs-3405	17	1	involutions	involution	NOUN
iajs-3405	17	2	of	of	ADP
iajs-3405	17	3	groups	group	NOUN
iajs-3405	17	4	significantly	significantly	ADV
iajs-3405	17	5	affect	affect	VERB
iajs-3405	17	6	the	the	DET
iajs-3405	17	7	way	way	NOUN
iajs-3405	17	8	it	it	PRON
iajs-3405	17	9	is	be	AUX
iajs-3405	17	10	structured	structure	VERB
iajs-3405	17	11	.	.	PUNCT
iajs-3405	18	1	for	for	ADP
iajs-3405	18	2	instance	instance	NOUN
iajs-3405	18	3	,	,	PUNCT
iajs-3405	18	4	the	the	DET
iajs-3405	18	5	categorization	categorization	NOUN
iajs-3405	18	6	of	of	ADP
iajs-3405	18	7	finite	finite	ADJ
iajs-3405	18	8	simple	simple	ADJ
iajs-3405	18	9	groups	group	NOUN
iajs-3405	18	10	heavily	heavily	ADV
iajs-3405	18	11	depends	depend	VERB
iajs-3405	18	12	on	on	ADP
iajs-3405	18	13	the	the	DET
iajs-3405	18	14	study	study	NOUN
iajs-3405	18	15	of	of	ADP
iajs-3405	18	16	involutions	involution	NOUN
iajs-3405	18	17	.	.	PUNCT
iajs-3405	19	1	an	an	DET
iajs-3405	19	2	s3	s3	NOUN
iajs-3405	19	3	-	-	PUNCT
iajs-3405	19	4	involution	involution	NOUN
iajs-3405	19	5	graph	graph	NOUN
iajs-3405	19	6	for	for	ADP
iajs-3405	19	7	a	a	DET
iajs-3405	19	8	group	group	NOUN
iajs-3405	19	9	g	g	NOUN
iajs-3405	19	10	was	be	AUX
iajs-3405	19	11	first	first	ADV
iajs-3405	19	12	introduced	introduce	VERB
iajs-3405	19	13	by	by	ADP
iajs-3405	19	14	devillers	deviller	NOUN
iajs-3405	19	15	and	and	CCONJ
iajs-3405	19	16	giudici	giudici	NOUN
iajs-3405	19	17	in	in	ADP
iajs-3405	19	18	[	[	X
iajs-3405	19	19	15	15	NUM
iajs-3405	19	20	]	]	PUNCT
iajs-3405	19	21	as	as	ADP
iajs-3405	19	22	a	a	DET
iajs-3405	19	23	graph	graph	NOUN
iajs-3405	19	24	with	with	ADP
iajs-3405	19	25	a	a	DET
iajs-3405	19	26	g	g	NOUN
iajs-3405	19	27	-	-	PUNCT
iajs-3405	19	28	classes	class	NOUN
iajs-3405	19	29	of	of	ADP
iajs-3405	19	30	involution	involution	NOUN
iajs-3405	19	31	as	as	ADP
iajs-3405	19	32	a	a	DET
iajs-3405	19	33	vertex	vertex	NOUN
iajs-3405	19	34	set	set	NOUN
iajs-3405	19	35	,	,	PUNCT
iajs-3405	19	36	where	where	SCONJ
iajs-3405	19	37	two	two	NUM
iajs-3405	19	38	vertices	vertex	NOUN
iajs-3405	19	39	are	be	AUX
iajs-3405	19	40	adjacent	adjacent	ADJ
iajs-3405	19	41	if	if	SCONJ
iajs-3405	19	42	they	they	PRON
iajs-3405	19	43	generate	generate	VERB
iajs-3405	19	44	an	an	DET
iajs-3405	19	45	s3	s3	PROPN
iajs-3405	19	46	-	-	PUNCT
iajs-3405	19	47	subgroup	subgroup	NOUN
iajs-3405	19	48	in	in	ADP
iajs-3405	19	49	a	a	DET
iajs-3405	19	50	certain	certain	ADJ
iajs-3405	19	51	g	g	NOUN
iajs-3405	19	52	-	-	PUNCT
iajs-3405	19	53	class	class	NOUN
iajs-3405	19	54	.	.	PUNCT
iajs-3405	20	1	they	they	PRON
iajs-3405	20	2	looked	look	VERB
iajs-3405	20	3	at	at	ADP
iajs-3405	20	4	the	the	DET
iajs-3405	20	5	structure	structure	NOUN
iajs-3405	20	6	of	of	ADP
iajs-3405	20	7	s3	s3	NOUN
iajs-3405	20	8	-	-	PUNCT
iajs-3405	20	9	involution	involution	NOUN
iajs-3405	20	10	graph	graph	NOUN
iajs-3405	20	11	and	and	CCONJ
iajs-3405	20	12	general	general	ADJ
iajs-3405	20	13	characteristics	characteristic	NOUN
iajs-3405	20	14	for	for	ADP
iajs-3405	20	15	the	the	DET
iajs-3405	20	16	group	group	NOUN
iajs-3405	20	17	psl	psl	PROPN
iajs-3405	20	18	(	(	PUNCT
iajs-3405	20	19	2,q	2,q	NOUN
iajs-3405	20	20	)	)	PUNCT
iajs-3405	20	21	when	when	SCONJ
iajs-3405	20	22	q	q	NOUN
iajs-3405	20	23	is	be	AUX
iajs-3405	20	24	greater	great	ADJ
iajs-3405	20	25	than	than	ADP
iajs-3405	20	26	3	3	NUM
iajs-3405	20	27	.	.	PUNCT
iajs-3405	20	28	define	define	VERB
iajs-3405	20	29	i(g	i(g	NOUN
iajs-3405	20	30	)	)	PUNCT
iajs-3405	20	31	as	as	ADP
iajs-3405	20	32	a	a	DET
iajs-3405	20	33	set	set	NOUN
iajs-3405	20	34	of	of	ADP
iajs-3405	20	35	the	the	DET
iajs-3405	20	36	involution	involution	NOUN
iajs-3405	20	37	elements	element	NOUN
iajs-3405	20	38	in	in	ADP
iajs-3405	20	39	a	a	DET
iajs-3405	20	40	finite	finite	ADJ
iajs-3405	20	41	group	group	NOUN
iajs-3405	20	42	g.	g.	PROPN
iajs-3405	20	43	the	the	DET
iajs-3405	20	44	result	result	NOUN
iajs-3405	20	45	involution	involution	NOUN
iajs-3405	20	46	graph	graph	NOUN
iajs-3405	20	47	is	be	AUX
iajs-3405	20	48	known	know	VERB
iajs-3405	20	49	as	as	ADP
iajs-3405	20	50	the	the	DET
iajs-3405	20	51	simple	simple	ADJ
iajs-3405	20	52	undirected	undirected	ADJ
iajs-3405	20	53	graph	graph	NOUN
iajs-3405	20	54	with	with	ADP
iajs-3405	20	55	vertex	vertex	NOUN
iajs-3405	20	56	set	set	NOUN
iajs-3405	20	57	being	be	AUX
iajs-3405	20	58	the	the	DET
iajs-3405	20	59	elements	element	NOUN
iajs-3405	20	60	of	of	ADP
iajs-3405	20	61	g	g	NOUN
iajs-3405	20	62	with	with	ADP
iajs-3405	20	63	two	two	NUM
iajs-3405	20	64	vertices	vertex	NOUN
iajs-3405	20	65	x	x	X
iajs-3405	20	66	,	,	PUNCT
iajs-3405	20	67	y	y	PROPN
iajs-3405	20	68	g	g	PROPN
iajs-3405	20	69	are	be	AUX
iajs-3405	20	70	adjacent	adjacent	ADJ
iajs-3405	20	71	if	if	SCONJ
iajs-3405	20	72	x≠y	x≠y	PROPN
iajs-3405	20	73	and	and	CCONJ
iajs-3405	20	74	xy	xy	PROPN
iajs-3405	20	75	i(g	i(g	PROPN
iajs-3405	20	76	)	)	PUNCT
iajs-3405	20	77	,	,	PUNCT
iajs-3405	20	78	and	and	CCONJ
iajs-3405	20	79	is	be	AUX
iajs-3405	20	80	denoted	denote	VERB
iajs-3405	20	81	by	by	ADP
iajs-3405	20	82	γ𝐺	γ𝐺	ADJ
iajs-3405	20	83	𝑅𝐼.	𝑅𝐼.	PUNCT
iajs-3405	20	84	jund	jund	PROPN
iajs-3405	20	85	and	and	CCONJ
iajs-3405	20	86	salih	salih	PROPN
iajs-3405	20	87	reported	report	VERB
iajs-3405	20	88	the	the	DET
iajs-3405	20	89	result	result	NOUN
iajs-3405	20	90	involution	involution	NOUN
iajs-3405	20	91	graph	graph	NOUN
iajs-3405	20	92	and	and	CCONJ
iajs-3405	20	93	its	its	PRON
iajs-3405	20	94	attributes	attribute	NOUN
iajs-3405	20	95	for	for	ADP
iajs-3405	20	96	the	the	DET
iajs-3405	20	97	first	first	ADJ
iajs-3405	20	98	time	time	NOUN
iajs-3405	20	99	in	in	ADP
iajs-3405	20	100	[	[	X
iajs-3405	20	101	16	16	NUM
iajs-3405	20	102	]	]	PUNCT
iajs-3405	20	103	.	.	PUNCT
iajs-3405	21	1	in	in	ADP
iajs-3405	21	2	their	their	PRON
iajs-3405	21	3	analysis	analysis	NOUN
iajs-3405	21	4	,	,	PUNCT
iajs-3405	21	5	they	they	PRON
iajs-3405	21	6	demonstrated	demonstrate	VERB
iajs-3405	21	7	that	that	SCONJ
iajs-3405	21	8	the	the	DET
iajs-3405	21	9	graphs	graph	NOUN
iajs-3405	21	10	γ𝑆𝑛	γ𝑆𝑛	NOUN
iajs-3405	21	11	𝑅𝐼	𝑅𝐼	PROPN
iajs-3405	21	12	and	and	CCONJ
iajs-3405	21	13	γ𝐴𝑛	γ𝐴𝑛	PROPN
iajs-3405	21	14	𝑅𝐼	𝑅𝐼	PROPN
iajs-3405	21	15	are	be	AUX
iajs-3405	21	16	connected	connect	VERB
iajs-3405	21	17	graphs	graph	NOUN
iajs-3405	21	18	for	for	ADP
iajs-3405	21	19	n>4	n>4	NOUN
iajs-3405	21	20	and	and	CCONJ
iajs-3405	21	21	have	have	VERB
iajs-3405	21	22	a	a	DET
iajs-3405	21	23	maximum	maximum	ADJ
iajs-3405	21	24	diameter	diameter	NOUN
iajs-3405	21	25	,	,	PUNCT
iajs-3405	21	26	radius	radius	NOUN
iajs-3405	21	27	,	,	PUNCT
iajs-3405	21	28	and	and	CCONJ
iajs-3405	21	29	girth	girth	NOUN
iajs-3405	21	30	of	of	ADP
iajs-3405	21	31	3	3	NUM
iajs-3405	21	32	and	and	CCONJ
iajs-3405	21	33	3	3	NUM
iajs-3405	21	34	.	.	PUNCT
iajs-3405	22	1	also	also	ADV
iajs-3405	22	2	,	,	PUNCT
iajs-3405	22	3	they	they	PRON
iajs-3405	22	4	provide	provide	VERB
iajs-3405	22	5	some	some	DET
iajs-3405	22	6	really	really	ADV
iajs-3405	22	7	helpful	helpful	ADJ
iajs-3405	22	8	qualities	quality	NOUN
iajs-3405	22	9	for	for	ADP
iajs-3405	22	10	the	the	DET
iajs-3405	22	11	result	result	NOUN
iajs-3405	22	12	involution	involution	NOUN
iajs-3405	22	13	graphs	graph	NOUN
iajs-3405	22	14	of	of	ADP
iajs-3405	22	15	the	the	DET
iajs-3405	22	16	quaternion	quaternion	NOUN
iajs-3405	22	17	group	group	NOUN
iajs-3405	22	18	and	and	CCONJ
iajs-3405	22	19	the	the	DET
iajs-3405	22	20	dihedral	dihedral	ADJ
iajs-3405	22	21	group	group	NOUN
iajs-3405	22	22	.	.	PUNCT
iajs-3405	23	1	nevertheless	nevertheless	ADV
iajs-3405	23	2	,	,	PUNCT
iajs-3405	23	3	aubad	aubad	PROPN
iajs-3405	23	4	and	and	CCONJ
iajs-3405	23	5	salih	salih	PROPN
iajs-3405	23	6	looked	look	VERB
iajs-3405	23	7	at	at	ADP
iajs-3405	23	8	the	the	DET
iajs-3405	23	9	structure	structure	NOUN
iajs-3405	23	10	of	of	ADP
iajs-3405	23	11	the	the	DET
iajs-3405	23	12	https://creativecommons.org/licenses/by/4.0/	https://creativecommons.org/licenses/by/4.0/	PROPN
iajs-3405	23	13	https://creativecommons.org/licenses/by/4.0/	https://creativecommons.org/licenses/by/4.0/	PROPN
iajs-3405	23	14	https://orcid.org/0009-0001-4526-3790	https://orcid.org/0009-0001-4526-3790	PROPN
iajs-3405	23	15	mailto:ahmed.arkan1203a@sc.uobaghdad.edu.iq	mailto:ahmed.arkan1203a@sc.uobaghdad.edu.iq	PROPN
iajs-3405	23	16	https://orcid.org/0000-0002-4764-2946	https://orcid.org/0000-0002-4764-2946	PROPN
iajs-3405	23	17	mailto:ali.abd@sc.uobaghdad.edu.iq	mailto:ali.abd@sc.uobaghdad.edu.iq	NOUN
iajs-3405	23	18	ihjpas	ihjpas	PROPN
iajs-3405	23	19	.	.	PUNCT
iajs-3405	24	1	2024	2024	NUM
iajs-3405	24	2	,	,	PUNCT
iajs-3405	24	3	37(4	37(4	PRON
iajs-3405	24	4	)	)	PUNCT
iajs-3405	24	5	402	402	NUM
iajs-3405	24	6	involution	involution	NOUN
iajs-3405	24	7	graphs	graph	NOUN
iajs-3405	24	8	that	that	PRON
iajs-3405	24	9	were	be	AUX
iajs-3405	24	10	produced	produce	VERB
iajs-3405	24	11	for	for	ADP
iajs-3405	24	12	the	the	DET
iajs-3405	24	13	whole	whole	ADJ
iajs-3405	24	14	list	list	NOUN
iajs-3405	24	15	of	of	ADP
iajs-3405	24	16	the	the	DET
iajs-3405	24	17	mathieu	mathieu	PROPN
iajs-3405	24	18	sporadic	sporadic	ADJ
iajs-3405	24	19	simple	simple	ADJ
iajs-3405	24	20	groups	group	NOUN
iajs-3405	24	21	as	as	SCONJ
iajs-3405	24	22	mentioned	mention	VERB
iajs-3405	24	23	in	in	ADP
iajs-3405	24	24	[	[	X
iajs-3405	24	25	17	17	NUM
iajs-3405	24	26	]	]	PUNCT
iajs-3405	24	27	.	.	PUNCT
iajs-3405	25	1	furthermore	furthermore	ADV
iajs-3405	25	2	,	,	PUNCT
iajs-3405	25	3	the	the	DET
iajs-3405	25	4	result	result	NOUN
iajs-3405	25	5	involution	involution	NOUN
iajs-3405	25	6	graphs	graph	NOUN
iajs-3405	25	7	for	for	ADP
iajs-3405	25	8	the	the	DET
iajs-3405	25	9	conway	conway	PROPN
iajs-3405	25	10	group	group	NOUN
iajs-3405	25	11	co3	co3	ADV
iajs-3405	25	12	are	be	AUX
iajs-3405	25	13	analyzed	analyze	VERB
iajs-3405	25	14	with	with	ADP
iajs-3405	25	15	full	full	ADJ
iajs-3405	25	16	information	information	NOUN
iajs-3405	25	17	in	in	ADP
iajs-3405	25	18	[	[	X
iajs-3405	25	19	18	18	NUM
iajs-3405	25	20	]	]	PUNCT
iajs-3405	25	21	.	.	PUNCT
iajs-3405	26	1	examining	examine	VERB
iajs-3405	26	2	the	the	DET
iajs-3405	26	3	result	result	NOUN
iajs-3405	26	4	involution	involution	NOUN
iajs-3405	26	5	graph	graph	NOUN
iajs-3405	26	6	for	for	ADP
iajs-3405	26	7	the	the	DET
iajs-3405	26	8	janko	janko	PROPN
iajs-3405	26	9	group	group	PROPN
iajs-3405	26	10	j3	j3	PROPN
iajs-3405	26	11	,	,	PUNCT
iajs-3405	26	12	is	be	AUX
iajs-3405	26	13	the	the	DET
iajs-3405	26	14	aim	aim	NOUN
iajs-3405	26	15	of	of	ADP
iajs-3405	26	16	this	this	DET
iajs-3405	26	17	article	article	NOUN
iajs-3405	26	18	.	.	PUNCT
iajs-3405	27	1	together	together	ADV
iajs-3405	27	2	with	with	ADP
iajs-3405	27	3	the	the	DET
iajs-3405	27	4	connectedness	connectedness	NOUN
iajs-3405	27	5	of	of	ADP
iajs-3405	27	6	the	the	DET
iajs-3405	27	7	result	result	NOUN
iajs-3405	27	8	involution	involution	NOUN
iajs-3405	27	9	graph	graph	NOUN
iajs-3405	27	10	,	,	PUNCT
iajs-3405	27	11	we	we	PRON
iajs-3405	27	12	show	show	VERB
iajs-3405	27	13	many	many	ADJ
iajs-3405	27	14	graph	graph	NOUN
iajs-3405	27	15	properties	property	NOUN
iajs-3405	27	16	including	include	VERB
iajs-3405	27	17	the	the	DET
iajs-3405	27	18	radius	radius	NOUN
iajs-3405	27	19	,	,	PUNCT
iajs-3405	27	20	diameter	diameter	NOUN
iajs-3405	27	21	,	,	PUNCT
iajs-3405	27	22	clique	clique	ADJ
iajs-3405	27	23	number	number	NOUN
iajs-3405	27	24	,	,	PUNCT
iajs-3405	27	25	and	and	CCONJ
iajs-3405	27	26	girth	girth	NOUN
iajs-3405	27	27	.	.	PUNCT
iajs-3405	28	1	the	the	DET
iajs-3405	28	2	paper	paper	NOUN
iajs-3405	28	3	is	be	AUX
iajs-3405	28	4	set	set	VERB
iajs-3405	28	5	up	up	ADP
iajs-3405	28	6	like	like	SCONJ
iajs-3405	28	7	follows	follow	VERB
iajs-3405	28	8	:	:	PUNCT
iajs-3405	28	9	we	we	PRON
iajs-3405	28	10	offer	offer	VERB
iajs-3405	28	11	some	some	DET
iajs-3405	28	12	observations	observation	NOUN
iajs-3405	28	13	and	and	CCONJ
iajs-3405	28	14	graph	graph	NOUN
iajs-3405	28	15	notations	notation	NOUN
iajs-3405	28	16	for	for	ADP
iajs-3405	28	17	the	the	DET
iajs-3405	28	18	result	result	NOUN
iajs-3405	28	19	involution	involution	NOUN
iajs-3405	28	20	graph	graph	NOUN
iajs-3405	28	21	in	in	ADP
iajs-3405	28	22	section	section	NOUN
iajs-3405	28	23	2	2	NUM
iajs-3405	28	24	.	.	PUNCT
iajs-3405	29	1	a	a	DET
iajs-3405	29	2	number	number	NOUN
iajs-3405	29	3	of	of	ADP
iajs-3405	29	4	results	result	NOUN
iajs-3405	29	5	about	about	ADP
iajs-3405	29	6	γ𝐽3	γ𝐽3	PROPN
iajs-3405	29	7	𝑅𝐼	𝑅𝐼	PROPN
iajs-3405	29	8	are	be	AUX
iajs-3405	29	9	provided	provide	VERB
iajs-3405	29	10	in	in	ADP
iajs-3405	29	11	section	section	NOUN
iajs-3405	29	12	3	3	NUM
iajs-3405	29	13	.	.	PUNCT
iajs-3405	30	1	we	we	PRON
iajs-3405	30	2	draw	draw	VERB
iajs-3405	30	3	our	our	PRON
iajs-3405	30	4	concluding	conclude	VERB
iajs-3405	30	5	conclusions	conclusion	NOUN
iajs-3405	30	6	and	and	CCONJ
iajs-3405	30	7	make	make	VERB
iajs-3405	30	8	suggestions	suggestion	NOUN
iajs-3405	30	9	for	for	ADP
iajs-3405	30	10	more	more	ADJ
iajs-3405	30	11	study	study	NOUN
iajs-3405	30	12	in	in	ADP
iajs-3405	30	13	section	section	NOUN
iajs-3405	30	14	4	4	NUM
iajs-3405	30	15	.	.	NOUN
iajs-3405	31	1	2	2	NUM
iajs-3405	31	2	.	.	X
iajs-3405	31	3	preliminary	preliminary	ADJ
iajs-3405	31	4	we	we	PRON
iajs-3405	31	5	begin	begin	VERB
iajs-3405	31	6	the	the	DET
iajs-3405	31	7	section	section	NOUN
iajs-3405	31	8	by	by	ADP
iajs-3405	31	9	defining	define	VERB
iajs-3405	31	10	a	a	DET
iajs-3405	31	11	few	few	ADJ
iajs-3405	31	12	concepts	concept	NOUN
iajs-3405	31	13	and	and	CCONJ
iajs-3405	31	14	outlining	outline	VERB
iajs-3405	31	15	several	several	ADJ
iajs-3405	31	16	facts	fact	NOUN
iajs-3405	31	17	that	that	PRON
iajs-3405	31	18	will	will	AUX
iajs-3405	31	19	be	be	AUX
iajs-3405	31	20	important	important	ADJ
iajs-3405	31	21	to	to	ADP
iajs-3405	31	22	the	the	DET
iajs-3405	31	23	thesis	thesis	NOUN
iajs-3405	31	24	later	later	ADV
iajs-3405	31	25	on	on	ADV
iajs-3405	31	26	.	.	PUNCT
iajs-3405	32	1	first	first	ADV
iajs-3405	32	2	let	let	VERB
iajs-3405	32	3	g	g	NOUN
iajs-3405	32	4	be	be	AUX
iajs-3405	32	5	a	a	DET
iajs-3405	32	6	finite	finite	ADJ
iajs-3405	32	7	group	group	NOUN
iajs-3405	32	8	moving	move	VERB
iajs-3405	32	9	forward	forward	ADV
iajs-3405	32	10	.	.	PUNCT
iajs-3405	33	1	let	let	VERB
iajs-3405	33	2	sig=|i(g)|	sig=|i(g)|	PROPN
iajs-3405	33	3	be	be	AUX
iajs-3405	33	4	the	the	DET
iajs-3405	33	5	size	size	NOUN
iajs-3405	33	6	of	of	ADP
iajs-3405	33	7	the	the	DET
iajs-3405	33	8	set	set	NOUN
iajs-3405	33	9	i(g	i(g	NOUN
iajs-3405	33	10	)	)	PUNCT
iajs-3405	33	11	,	,	PUNCT
iajs-3405	33	12	where	where	SCONJ
iajs-3405	33	13	i(g	i(g	NOUN
iajs-3405	33	14	)	)	PUNCT
iajs-3405	33	15	be	be	VERB
iajs-3405	33	16	the	the	DET
iajs-3405	33	17	set	set	NOUN
iajs-3405	33	18	of	of	ADP
iajs-3405	33	19	the	the	DET
iajs-3405	33	20	involution	involution	NOUN
iajs-3405	33	21	elements	element	NOUN
iajs-3405	33	22	in	in	ADP
iajs-3405	33	23	g	g	PROPN
iajs-3405	33	24	as	as	SCONJ
iajs-3405	33	25	mentioned	mention	VERB
iajs-3405	33	26	in	in	ADP
iajs-3405	33	27	the	the	DET
iajs-3405	33	28	introduction	introduction	NOUN
iajs-3405	33	29	.	.	PUNCT
iajs-3405	34	1	we	we	PRON
iajs-3405	34	2	begin	begin	VERB
iajs-3405	34	3	with	with	ADP
iajs-3405	34	4	the	the	DET
iajs-3405	34	5	following	follow	VERB
iajs-3405	34	6	formula	formula	NOUN
iajs-3405	34	7	to	to	PART
iajs-3405	34	8	determine	determine	VERB
iajs-3405	34	9	how	how	SCONJ
iajs-3405	34	10	many	many	ADJ
iajs-3405	34	11	edges	edge	NOUN
iajs-3405	34	12	there	there	PRON
iajs-3405	34	13	are	be	VERB
iajs-3405	34	14	in	in	ADP
iajs-3405	34	15	the	the	DET
iajs-3405	34	16	result	result	NOUN
iajs-3405	34	17	involution	involution	NOUN
iajs-3405	34	18	graph	graph	NOUN
iajs-3405	34	19	:	:	PUNCT
iajs-3405	34	20	proposition	proposition	NOUN
iajs-3405	34	21	2.1	2.1	NUM
iajs-3405	35	1	[	[	X
iajs-3405	35	2	17	17	NUM
iajs-3405	35	3	]	]	PUNCT
iajs-3405	35	4	:	:	PUNCT
iajs-3405	35	5	let	let	VERB
iajs-3405	35	6	g	g	PRON
iajs-3405	35	7	be	be	AUX
iajs-3405	35	8	a	a	DET
iajs-3405	35	9	finite	finite	ADJ
iajs-3405	35	10	group	group	NOUN
iajs-3405	35	11	,	,	PUNCT
iajs-3405	35	12	and	and	CCONJ
iajs-3405	35	13	let	let	VERB
iajs-3405	35	14	f	f	PRON
iajs-3405	35	15	represent	represent	VERB
iajs-3405	35	16	the	the	DET
iajs-3405	35	17	number	number	NOUN
iajs-3405	35	18	of	of	ADP
iajs-3405	35	19	elements	element	NOUN
iajs-3405	35	20	of	of	ADP
iajs-3405	35	21	order	order	NOUN
iajs-3405	35	22	4	4	NUM
iajs-3405	35	23	in	in	ADP
iajs-3405	35	24	g.	g.	PROPN
iajs-3405	35	25	then	then	ADV
iajs-3405	35	26	the	the	DET
iajs-3405	35	27	number	number	NOUN
iajs-3405	35	28	of	of	ADP
iajs-3405	35	29	edges	edge	NOUN
iajs-3405	35	30	in	in	ADP
iajs-3405	35	31	the	the	DET
iajs-3405	35	32	result	result	NOUN
iajs-3405	35	33	involution	involution	NOUN
iajs-3405	35	34	graph	graph	NOUN
iajs-3405	35	35	is	be	AUX
iajs-3405	35	36	calculated	calculate	VERB
iajs-3405	35	37	using	use	VERB
iajs-3405	35	38	the	the	DET
iajs-3405	35	39	following	follow	VERB
iajs-3405	35	40	formula	formula	NOUN
iajs-3405	35	41	½	½	NOUN
iajs-3405	35	42	(	(	PUNCT
iajs-3405	35	43	𝒔𝐈𝑮	𝒔𝐈𝑮	PUNCT
iajs-3405	35	44	|𝐺|	|𝐺|	NOUN
iajs-3405	35	45	−	−	PROPN
iajs-3405	35	46	𝐹	𝐹	PROPN
iajs-3405	35	47	)	)	PUNCT
iajs-3405	35	48	.	.	PUNCT
iajs-3405	36	1	we	we	PRON
iajs-3405	36	2	should	should	AUX
iajs-3405	36	3	notice	notice	VERB
iajs-3405	36	4	that	that	SCONJ
iajs-3405	36	5	if	if	SCONJ
iajs-3405	36	6	g	g	PROPN
iajs-3405	36	7	is	be	AUX
iajs-3405	36	8	a	a	DET
iajs-3405	36	9	finite	finite	ADJ
iajs-3405	36	10	group	group	NOUN
iajs-3405	36	11	with	with	ADP
iajs-3405	36	12	large	large	ADJ
iajs-3405	36	13	number	number	NOUN
iajs-3405	36	14	of	of	ADP
iajs-3405	36	15	elements	element	NOUN
iajs-3405	36	16	,	,	PUNCT
iajs-3405	36	17	then	then	ADV
iajs-3405	36	18	the	the	DET
iajs-3405	36	19	γ𝐺	γ𝐺	ADJ
iajs-3405	36	20	𝑅𝐼	𝑅𝐼	PROPN
iajs-3405	36	21	has	have	VERB
iajs-3405	36	22	a	a	DET
iajs-3405	36	23	huge	huge	ADJ
iajs-3405	36	24	vertex	vertex	NOUN
iajs-3405	36	25	set	set	NOUN
iajs-3405	36	26	.	.	PUNCT
iajs-3405	37	1	the	the	DET
iajs-3405	37	2	result	result	NOUN
iajs-3405	37	3	involution	involution	NOUN
iajs-3405	37	4	graph	graph	NOUN
iajs-3405	37	5	of	of	ADP
iajs-3405	37	6	g	g	PROPN
iajs-3405	37	7	is	be	AUX
iajs-3405	37	8	then	then	ADV
iajs-3405	37	9	exceedingly	exceedingly	ADV
iajs-3405	37	10	difficult	difficult	ADJ
iajs-3405	37	11	to	to	PART
iajs-3405	37	12	handle	handle	VERB
iajs-3405	37	13	.	.	PUNCT
iajs-3405	38	1	to	to	PART
iajs-3405	38	2	resolve	resolve	VERB
iajs-3405	38	3	this	this	DET
iajs-3405	38	4	issue	issue	NOUN
iajs-3405	38	5	,	,	PUNCT
iajs-3405	38	6	we	we	PRON
iajs-3405	38	7	use	use	VERB
iajs-3405	38	8	the	the	DET
iajs-3405	38	9	resize	resize	NOUN
iajs-3405	38	10	graph	graph	NOUN
iajs-3405	38	11	idea	idea	NOUN
iajs-3405	38	12	,	,	PUNCT
iajs-3405	38	13	which	which	PRON
iajs-3405	38	14	define	define	VERB
iajs-3405	38	15	as	as	SCONJ
iajs-3405	38	16	follows	follow	VERB
iajs-3405	38	17	:	:	PUNCT
iajs-3405	38	18	definition	definition	NOUN
iajs-3405	38	19	2.2	2.2	NUM
iajs-3405	39	1	[	[	X
iajs-3405	39	2	17	17	NUM
iajs-3405	39	3	]	]	PUNCT
iajs-3405	39	4	:	:	PUNCT
iajs-3405	39	5	assume	assume	VERB
iajs-3405	39	6	that	that	SCONJ
iajs-3405	39	7	g	g	PROPN
iajs-3405	39	8	be	be	AUX
iajs-3405	39	9	a	a	DET
iajs-3405	39	10	finite	finite	ADJ
iajs-3405	39	11	group	group	NOUN
iajs-3405	39	12	,	,	PUNCT
iajs-3405	39	13	the	the	DET
iajs-3405	39	14	resize	resize	NOUN
iajs-3405	39	15	graph	graph	NOUN
iajs-3405	39	16	of	of	ADP
iajs-3405	39	17	g	g	NOUN
iajs-3405	39	18	,	,	PUNCT
iajs-3405	39	19	γ𝐺	γ𝐺	PUNCT
iajs-3405	39	20	𝑅𝑆	𝑅𝑆	ADJ
iajs-3405	39	21	,	,	PUNCT
iajs-3405	39	22	has	have	VERB
iajs-3405	39	23	a	a	DET
iajs-3405	39	24	vertex	vertex	NOUN
iajs-3405	39	25	set	set	VERB
iajs-3405	39	26	the	the	DET
iajs-3405	39	27	whole	whole	ADJ
iajs-3405	39	28	g	g	NOUN
iajs-3405	39	29	-	-	PUNCT
iajs-3405	39	30	conjugacy	conjugacy	ADJ
iajs-3405	39	31	classes	class	NOUN
iajs-3405	39	32	with	with	ADP
iajs-3405	39	33	two	two	NUM
iajs-3405	39	34	vertices	vertex	NOUN
iajs-3405	39	35	(	(	PUNCT
iajs-3405	39	36	g	g	NOUN
iajs-3405	39	37	-	-	PUNCT
iajs-3405	39	38	conjugacy	conjugacy	ADJ
iajs-3405	39	39	classes	class	NOUN
iajs-3405	39	40	)	)	PUNCT
iajs-3405	39	41	x	x	X
iajs-3405	39	42	,	,	PUNCT
iajs-3405	39	43	y	y	PROPN
iajs-3405	39	44			PROPN
iajs-3405	39	45	g	g	PROPN
iajs-3405	39	46	,	,	PUNCT
iajs-3405	39	47	are	be	AUX
iajs-3405	39	48	adjacent	adjacent	ADJ
iajs-3405	39	49	if	if	SCONJ
iajs-3405	39	50	x≠y	x≠y	PUNCT
iajs-3405	39	51	and	and	CCONJ
iajs-3405	39	52	there	there	PRON
iajs-3405	39	53	are	be	VERB
iajs-3405	39	54	v1	v1	NOUN
iajs-3405	39	55	x	x	NUM
iajs-3405	39	56	and	and	CCONJ
iajs-3405	39	57	v2	v2	PROPN
iajs-3405	39	58	y	y	PROPN
iajs-3405	39	59	such	such	ADJ
iajs-3405	39	60	that	that	DET
iajs-3405	39	61	v1	v1	NOUN
iajs-3405	39	62	,	,	PUNCT
iajs-3405	39	63	v2	v2	PROPN
iajs-3405	39	64	are	be	AUX
iajs-3405	39	65	adjacent	adjacent	ADJ
iajs-3405	39	66	vertices	vertex	NOUN
iajs-3405	39	67	in	in	ADP
iajs-3405	39	68	γ𝐺	γ𝐺	ADJ
iajs-3405	39	69	𝑅𝐼.	𝑅𝐼.	SCONJ
iajs-3405	39	70	the	the	DET
iajs-3405	39	71	following	follow	VERB
iajs-3405	39	72	results	result	NOUN
iajs-3405	39	73	displays	display	VERB
iajs-3405	39	74	a	a	DET
iajs-3405	39	75	relationship	relationship	NOUN
iajs-3405	39	76	between	between	ADP
iajs-3405	39	77	a	a	DET
iajs-3405	39	78	result	result	NOUN
iajs-3405	39	79	involution	involution	NOUN
iajs-3405	39	80	graph	graph	NOUN
iajs-3405	39	81	and	and	CCONJ
iajs-3405	39	82	a	a	DET
iajs-3405	39	83	resize	resize	NOUN
iajs-3405	39	84	graph	graph	NOUN
iajs-3405	39	85	:	:	PUNCT
iajs-3405	39	86	proposition	proposition	NOUN
iajs-3405	39	87	2.3	2.3	NUM
iajs-3405	40	1	[	[	X
iajs-3405	40	2	17	17	NUM
iajs-3405	40	3	]	]	PUNCT
iajs-3405	40	4	:	:	PUNCT
iajs-3405	40	5	let	let	VERB
iajs-3405	40	6	g	g	PRON
iajs-3405	40	7	be	be	AUX
iajs-3405	40	8	a	a	DET
iajs-3405	40	9	finite	finite	ADJ
iajs-3405	40	10	group	group	NOUN
iajs-3405	40	11	.	.	PUNCT
iajs-3405	41	1	then	then	ADV
iajs-3405	41	2	the	the	DET
iajs-3405	41	3	connectivity	connectivity	NOUN
iajs-3405	41	4	of	of	ADP
iajs-3405	41	5	the	the	DET
iajs-3405	41	6	graphs	graph	NOUN
iajs-3405	41	7	γ𝐺	γ𝐺	PUNCT
iajs-3405	41	8	𝑅𝐼	𝑅𝐼	PROPN
iajs-3405	41	9	and	and	CCONJ
iajs-3405	41	10	γ𝐺	γ𝐺	ADV
iajs-3405	41	11	𝑅𝑆	𝑅𝑆	PROPN
iajs-3405	41	12	are	be	AUX
iajs-3405	41	13	isomorphic	isomorphic	ADJ
iajs-3405	41	14	graphs	graph	NOUN
iajs-3405	41	15	.	.	PUNCT
iajs-3405	42	1	these	these	DET
iajs-3405	42	2	findings	finding	NOUN
iajs-3405	42	3	will	will	AUX
iajs-3405	42	4	be	be	AUX
iajs-3405	42	5	illustrated	illustrate	VERB
iajs-3405	42	6	by	by	ADP
iajs-3405	42	7	the	the	DET
iajs-3405	42	8	example	example	NOUN
iajs-3405	42	9	that	that	PRON
iajs-3405	42	10	follows	follow	VERB
iajs-3405	42	11	.	.	PUNCT
iajs-3405	43	1	we	we	PRON
iajs-3405	43	2	will	will	AUX
iajs-3405	43	3	mostly	mostly	ADV
iajs-3405	43	4	employ	employ	VERB
iajs-3405	43	5	gap	gap	NOUN
iajs-3405	43	6	[	[	X
iajs-3405	43	7	19	19	NUM
iajs-3405	43	8	]	]	PUNCT
iajs-3405	43	9	and	and	CCONJ
iajs-3405	43	10	yags	yag	NOUN
iajs-3405	43	11	[	[	X
iajs-3405	43	12	20	20	NUM
iajs-3405	43	13	]	]	PUNCT
iajs-3405	43	14	as	as	ADP
iajs-3405	43	15	a	a	DET
iajs-3405	43	16	computational	computational	ADJ
iajs-3405	43	17	approach	approach	NOUN
iajs-3405	43	18	in	in	ADP
iajs-3405	43	19	the	the	DET
iajs-3405	43	20	following	follow	VERB
iajs-3405	43	21	example	example	NOUN
iajs-3405	43	22	.	.	PUNCT
iajs-3405	44	1	example	example	NOUN
iajs-3405	44	2	2.4	2.4	NUM
iajs-3405	44	3	:	:	PUNCT
iajs-3405	44	4	let	let	VERB
iajs-3405	44	5	g	g	PRON
iajs-3405	44	6	be	be	AUX
iajs-3405	44	7	an	an	DET
iajs-3405	44	8	alternating	alternate	VERB
iajs-3405	44	9	group	group	NOUN
iajs-3405	44	10	of	of	ADP
iajs-3405	44	11	degree	degree	NOUN
iajs-3405	44	12	4	4	NUM
iajs-3405	44	13	.	.	PUNCT
iajs-3405	45	1	then	then	ADV
iajs-3405	45	2	the	the	DET
iajs-3405	45	3	result	result	NOUN
iajs-3405	45	4	involution	involution	NOUN
iajs-3405	45	5	graph	graph	NOUN
iajs-3405	45	6	γ𝐴4	γ𝐴4	ADP
iajs-3405	45	7	𝑅𝐼	𝑅𝐼	PROPN
iajs-3405	45	8	contains	contain	VERB
iajs-3405	45	9	the	the	DET
iajs-3405	45	10	following	follow	VERB
iajs-3405	45	11	vertices:{e,(2,3,4	vertices:{e,(2,3,4	NOUN
iajs-3405	45	12	)	)	PUNCT
iajs-3405	45	13	,	,	PUNCT
iajs-3405	45	14	(	(	PUNCT
iajs-3405	45	15	2,4,3	2,4,3	NUM
iajs-3405	45	16	)	)	PUNCT
iajs-3405	45	17	,	,	PUNCT
iajs-3405	45	18	(	(	PUNCT
iajs-3405	45	19	1,2)(3,4	1,2)(3,4	NUM
iajs-3405	45	20	)	)	PUNCT
iajs-3405	45	21	,	,	PUNCT
iajs-3405	45	22	(	(	PUNCT
iajs-3405	45	23	1,2,3	1,2,3	NOUN
iajs-3405	45	24	)	)	PUNCT
iajs-3405	45	25	,	,	PUNCT
iajs-3405	45	26	(	(	PUNCT
iajs-3405	45	27	1,2,4	1,2,4	NUM
iajs-3405	45	28	)	)	PUNCT
iajs-3405	45	29	,	,	PUNCT
iajs-3405	45	30	(	(	PUNCT
iajs-3405	45	31	1,3,2	1,3,2	NUM
iajs-3405	45	32	)	)	PUNCT
iajs-3405	45	33	,	,	PUNCT
iajs-3405	45	34	(	(	PUNCT
iajs-3405	45	35	1,3,4	1,3,4	NUM
iajs-3405	45	36	)	)	PUNCT
iajs-3405	45	37	,	,	PUNCT
iajs-3405	45	38	(	(	PUNCT
iajs-3405	45	39	1,3)(2,4	1,3)(2,4	NUM
iajs-3405	45	40	)	)	PUNCT
iajs-3405	45	41	,	,	PUNCT
iajs-3405	45	42	(	(	PUNCT
iajs-3405	45	43	1,4,2	1,4,2	NUM
iajs-3405	45	44	)	)	PUNCT
iajs-3405	45	45	,	,	PUNCT
iajs-3405	45	46	(	(	PUNCT
iajs-3405	45	47	1,4,3	1,4,3	NUM
iajs-3405	45	48	)	)	PUNCT
iajs-3405	45	49	,	,	PUNCT
iajs-3405	45	50	(	(	PUNCT
iajs-3405	45	51	1,4)(2,3)}.then	1,4)(2,3)}.then	ADV
iajs-3405	45	52	we	we	PRON
iajs-3405	45	53	can	can	AUX
iajs-3405	45	54	conclude	conclude	VERB
iajs-3405	45	55	the	the	DET
iajs-3405	45	56	figure	figure	NOUN
iajs-3405	45	57	below	below	ADP
iajs-3405	45	58	that	that	PRON
iajs-3405	45	59	the	the	DET
iajs-3405	45	60	graph	graph	NOUN
iajs-3405	45	61	γ𝐴4	γ𝐴4	ADP
iajs-3405	45	62	𝑅𝐼	𝑅𝐼	PROPN
iajs-3405	45	63	is	be	AUX
iajs-3405	45	64	disconnected	disconnect	VERB
iajs-3405	45	65	with	with	ADP
iajs-3405	45	66	two	two	NUM
iajs-3405	45	67	components	component	NOUN
iajs-3405	45	68	.	.	PUNCT
iajs-3405	46	1	one	one	NUM
iajs-3405	46	2	of	of	ADP
iajs-3405	46	3	these	these	DET
iajs-3405	46	4	components	component	NOUN
iajs-3405	46	5	has	have	VERB
iajs-3405	46	6	four	four	NUM
iajs-3405	46	7	vertices	vertex	NOUN
iajs-3405	46	8	labels	label	NOUN
iajs-3405	46	9	by	by	ADP
iajs-3405	46	10	the	the	DET
iajs-3405	46	11	numbers	number	NOUN
iajs-3405	46	12	{	{	PUNCT
iajs-3405	46	13	1,9,4,12	1,9,4,12	NUM
iajs-3405	46	14	}	}	PUNCT
iajs-3405	46	15	and	and	CCONJ
iajs-3405	46	16	the	the	DET
iajs-3405	46	17	subgraph	subgraph	NOUN
iajs-3405	46	18	induced	induce	VERB
iajs-3405	46	19	with	with	ADP
iajs-3405	46	20	this	this	DET
iajs-3405	46	21	vertex	vertex	NOUN
iajs-3405	46	22	is	be	AUX
iajs-3405	46	23	the	the	DET
iajs-3405	46	24	compete	compete	ADJ
iajs-3405	46	25	graph	graph	NOUN
iajs-3405	46	26	k4	k4	NOUN
iajs-3405	46	27	.	.	PUNCT
iajs-3405	47	1	on	on	ADP
iajs-3405	47	2	the	the	DET
iajs-3405	47	3	other	other	ADJ
iajs-3405	47	4	hand	hand	NOUN
iajs-3405	47	5	,	,	PUNCT
iajs-3405	47	6	the	the	DET
iajs-3405	47	7	subgraph	subgraph	NOUN
iajs-3405	47	8	induced	induce	VERB
iajs-3405	47	9	by	by	ADP
iajs-3405	47	10	the	the	DET
iajs-3405	47	11	vertices	vertex	NOUN
iajs-3405	47	12	labels	label	NOUN
iajs-3405	47	13	by	by	ADP
iajs-3405	47	14	{	{	PUNCT
iajs-3405	47	15	2,3,5,6,7,8,10,11	2,3,5,6,7,8,10,11	NUM
iajs-3405	47	16	}	}	PUNCT
iajs-3405	47	17	.	.	PUNCT
iajs-3405	48	1	this	this	DET
iajs-3405	48	2	graph	graph	NOUN
iajs-3405	48	3	is	be	AUX
iajs-3405	48	4	3regular	3regular	NUM
iajs-3405	48	5	graph	graph	NOUN
iajs-3405	48	6	with	with	ADP
iajs-3405	48	7	dimeter	dimeter	NOUN
iajs-3405	48	8	and	and	CCONJ
iajs-3405	48	9	radius	radius	NOUN
iajs-3405	48	10	of	of	ADP
iajs-3405	48	11	size	size	NOUN
iajs-3405	48	12	3	3	NUM
iajs-3405	48	13	.	.	PUNCT
iajs-3405	49	1	moreover	moreover	ADV
iajs-3405	49	2	,	,	PUNCT
iajs-3405	49	3	clique	clique	ADJ
iajs-3405	49	4	number	number	NOUN
iajs-3405	49	5	of	of	ADP
iajs-3405	49	6	size	size	NOUN
iajs-3405	49	7	2	2	NUM
iajs-3405	49	8	and	and	CCONJ
iajs-3405	49	9	girth	girth	NOUN
iajs-3405	49	10	4	4	NUM
iajs-3405	49	11	.	.	PUNCT
iajs-3405	50	1	this	this	DET
iajs-3405	50	2	information	information	NOUN
iajs-3405	50	3	can	can	AUX
iajs-3405	50	4	be	be	AUX
iajs-3405	50	5	seen	see	VERB
iajs-3405	50	6	the	the	DET
iajs-3405	50	7	following	follow	VERB
iajs-3405	50	8	figure	figure	NOUN
iajs-3405	50	9	:	:	PUNCT
iajs-3405	50	10	ihjpas	ihjpas	PROPN
iajs-3405	50	11	.	.	PUNCT
iajs-3405	51	1	2024	2024	NUM
iajs-3405	51	2	,	,	PUNCT
iajs-3405	51	3	37(4	37(4	NUM
iajs-3405	51	4	)	)	PUNCT
iajs-3405	52	1	403	403	NUM
iajs-3405	52	2	figure	figure	VERB
iajs-3405	52	3	1.the	1.the	DET
iajs-3405	52	4	structure	structure	NOUN
iajs-3405	52	5	of	of	ADP
iajs-3405	52	6	the	the	DET
iajs-3405	52	7	result	result	NOUN
iajs-3405	52	8	involution	involution	NOUN
iajs-3405	52	9	graph	graph	NOUN
iajs-3405	52	10	γ𝐺	γ𝐺	PUNCT
iajs-3405	52	11	𝑅𝐼	𝑅𝐼	PROPN
iajs-3405	52	12	,	,	PUNCT
iajs-3405	52	13	ga4	ga4	PROPN
iajs-3405	52	14	.	.	PUNCT
iajs-3405	53	1	on	on	ADP
iajs-3405	53	2	the	the	DET
iajs-3405	53	3	other	other	ADJ
iajs-3405	53	4	hand	hand	NOUN
iajs-3405	53	5	,	,	PUNCT
iajs-3405	53	6	the	the	DET
iajs-3405	53	7	resize	resize	NOUN
iajs-3405	53	8	graph	graph	NOUN
iajs-3405	53	9	of	of	ADP
iajs-3405	53	10	g	g	NOUN
iajs-3405	53	11	,	,	PUNCT
iajs-3405	53	12	γ𝐴4	γ𝐴4	PROPN
iajs-3405	53	13	𝑅𝑆	𝑅𝑆	PROPN
iajs-3405	53	14	has	have	VERB
iajs-3405	53	15	vertex	vertex	NOUN
iajs-3405	53	16	set	set	NOUN
iajs-3405	53	17	present	present	ADJ
iajs-3405	53	18	as	as	ADP
iajs-3405	53	19	{	{	PUNCT
iajs-3405	53	20	1a,2a,3a,3b	1a,2a,3a,3b	NOUN
iajs-3405	53	21	}	}	PUNCT
iajs-3405	53	22	.	.	PUNCT
iajs-3405	54	1	in	in	ADP
iajs-3405	54	2	the	the	DET
iajs-3405	54	3	next	next	ADJ
iajs-3405	54	4	figure	figure	NOUN
iajs-3405	54	5	we	we	PRON
iajs-3405	54	6	can	can	AUX
iajs-3405	54	7	see	see	VERB
iajs-3405	54	8	that	that	DET
iajs-3405	54	9	resize	resize	VERB
iajs-3405	54	10	graph	graph	NOUN
iajs-3405	54	11	of	of	ADP
iajs-3405	54	12	a4	a4	NOUN
iajs-3405	54	13	is	be	AUX
iajs-3405	54	14	(	(	PUNCT
iajs-3405	54	15	1,1)-biregular	1,1)-biregular	NUM
iajs-3405	54	16	disconnected	disconnected	ADJ
iajs-3405	54	17	graph	graph	NOUN
iajs-3405	54	18	has	have	VERB
iajs-3405	54	19	vertex	vertex	NOUN
iajs-3405	54	20	set	set	NOUN
iajs-3405	54	21	can	can	AUX
iajs-3405	54	22	be	be	AUX
iajs-3405	54	23	split	split	VERB
iajs-3405	54	24	into	into	ADP
iajs-3405	54	25	two	two	NUM
iajs-3405	54	26	disjoint	disjoint	NOUN
iajs-3405	54	27	vertices	vertex	NOUN
iajs-3405	54	28	can	can	AUX
iajs-3405	54	29	be	be	AUX
iajs-3405	54	30	labeled	label	VERB
iajs-3405	54	31	by	by	ADP
iajs-3405	54	32	x={1,2	x={1,2	ADJ
iajs-3405	54	33	}	}	PUNCT
iajs-3405	54	34	and	and	CCONJ
iajs-3405	54	35	y={3,4	y={3,4	ADJ
iajs-3405	54	36	}	}	PUNCT
iajs-3405	54	37	:	:	PUNCT
iajs-3405	54	38	figure	figure	NOUN
iajs-3405	54	39	2	2	NUM
iajs-3405	54	40	.	.	PUNCT
iajs-3405	55	1	the	the	DET
iajs-3405	55	2	structure	structure	NOUN
iajs-3405	55	3	of	of	ADP
iajs-3405	55	4	the	the	DET
iajs-3405	55	5	resize	resize	NOUN
iajs-3405	55	6	graph	graph	NOUN
iajs-3405	55	7	γ𝐺	γ𝐺	PUNCT
iajs-3405	55	8	𝑅𝑆	𝑅𝑆	ADJ
iajs-3405	55	9	,	,	PUNCT
iajs-3405	55	10	ga4	ga4	PROPN
iajs-3405	55	11	.	.	NOUN
iajs-3405	55	12	3	3	X
iajs-3405	55	13	.	.	NOUN
iajs-3405	55	14	results	result	NOUN
iajs-3405	55	15	in	in	ADP
iajs-3405	55	16	this	this	DET
iajs-3405	55	17	section	section	NOUN
iajs-3405	55	18	we	we	PRON
iajs-3405	55	19	will	will	AUX
iajs-3405	55	20	look	look	VERB
iajs-3405	55	21	at	at	ADP
iajs-3405	55	22	the	the	DET
iajs-3405	55	23	structure	structure	NOUN
iajs-3405	55	24	of	of	ADP
iajs-3405	55	25	the	the	DET
iajs-3405	55	26	result	result	NOUN
iajs-3405	55	27	involution	involution	NOUN
iajs-3405	55	28	graph	graph	NOUN
iajs-3405	55	29	for	for	ADP
iajs-3405	55	30	the	the	DET
iajs-3405	55	31	janko	janko	PROPN
iajs-3405	55	32	group	group	PROPN
iajs-3405	55	33	j3	j3	PROPN
iajs-3405	55	34	.	.	PUNCT
iajs-3405	56	1	to	to	PART
iajs-3405	56	2	achieve	achieve	VERB
iajs-3405	56	3	the	the	DET
iajs-3405	56	4	goal	goal	NOUN
iajs-3405	56	5	of	of	ADP
iajs-3405	56	6	the	the	DET
iajs-3405	56	7	study	study	NOUN
iajs-3405	56	8	,	,	PUNCT
iajs-3405	56	9	we	we	PRON
iajs-3405	56	10	will	will	AUX
iajs-3405	56	11	use	use	VERB
iajs-3405	56	12	gap	gap	NOUN
iajs-3405	56	13	and	and	CCONJ
iajs-3405	56	14	the	the	DET
iajs-3405	56	15	online	online	ADJ
iajs-3405	56	16	atlas	atlas	PROPN
iajs-3405	57	1	[	[	X
iajs-3405	57	2	21	21	NUM
iajs-3405	57	3	]	]	PUNCT
iajs-3405	57	4	.	.	PUNCT
iajs-3405	58	1	we	we	PRON
iajs-3405	58	2	should	should	AUX
iajs-3405	58	3	note	note	VERB
iajs-3405	58	4	that	that	SCONJ
iajs-3405	58	5	the	the	DET
iajs-3405	58	6	group	group	NOUN
iajs-3405	58	7	j3	j3	PROPN
iajs-3405	58	8	has	have	VERB
iajs-3405	58	9	only	only	ADV
iajs-3405	58	10	one	one	NUM
iajs-3405	58	11	class	class	NOUN
iajs-3405	58	12	of	of	ADP
iajs-3405	58	13	involution	involution	NOUN
iajs-3405	58	14	namely	namely	ADV
iajs-3405	58	15	2a	2a	NUM
iajs-3405	58	16	with	with	ADP
iajs-3405	58	17	size	size	NOUN
iajs-3405	58	18	equal	equal	ADJ
iajs-3405	58	19	to	to	ADP
iajs-3405	58	20	26163	26163	NUM
iajs-3405	58	21	.	.	PUNCT
iajs-3405	59	1	there	there	PRON
iajs-3405	59	2	are	be	VERB
iajs-3405	59	3	several	several	ADJ
iajs-3405	59	4	involutions	involution	NOUN
iajs-3405	59	5	to	to	PART
iajs-3405	59	6	take	take	VERB
iajs-3405	59	7	into	into	ADP
iajs-3405	59	8	account	account	NOUN
iajs-3405	59	9	as	as	ADP
iajs-3405	59	10	a	a	DET
iajs-3405	59	11	consequence	consequence	NOUN
iajs-3405	59	12	.	.	PUNCT
iajs-3405	60	1	hence	hence	ADV
iajs-3405	60	2	,	,	PUNCT
iajs-3405	60	3	in	in	ADP
iajs-3405	60	4	order	order	NOUN
iajs-3405	60	5	to	to	PART
iajs-3405	60	6	arrive	arrive	VERB
iajs-3405	60	7	at	at	ADP
iajs-3405	60	8	our	our	PRON
iajs-3405	60	9	observations	observation	NOUN
iajs-3405	60	10	,	,	PUNCT
iajs-3405	60	11	we	we	PRON
iajs-3405	60	12	will	will	AUX
iajs-3405	60	13	investigate	investigate	VERB
iajs-3405	60	14	the	the	DET
iajs-3405	60	15	resizing	resizing	NOUN
iajs-3405	60	16	graph	graph	NOUN
iajs-3405	60	17	γ𝐽3	γ𝐽3	PROPN
iajs-3405	60	18	𝑅𝑆.	𝑅𝑆.	NOUN
iajs-3405	60	19	3.1	3.1	NUM
iajs-3405	60	20	the	the	DET
iajs-3405	60	21	structures	structure	NOUN
iajs-3405	60	22	of	of	ADP
iajs-3405	60	23	𝚪𝑱𝟑	𝚪𝑱𝟑	PROPN
iajs-3405	60	24	𝑹𝑺	𝑹𝑺	PROPN
iajs-3405	60	25	the	the	DET
iajs-3405	60	26	online	online	PROPN
iajs-3405	60	27	atlas	atlas	PROPN
iajs-3405	60	28	reveals	reveal	VERB
iajs-3405	60	29	that	that	SCONJ
iajs-3405	60	30	j3	j3	PROPN
iajs-3405	60	31	has	have	VERB
iajs-3405	60	32	different	different	ADJ
iajs-3405	60	33	21	21	NUM
iajs-3405	60	34	conjugacy	conjugacy	ADJ
iajs-3405	60	35	classes	class	NOUN
iajs-3405	60	36	.	.	PUNCT
iajs-3405	61	1	therefore	therefore	ADV
iajs-3405	61	2	,	,	PUNCT
iajs-3405	61	3	the	the	DET
iajs-3405	61	4	resizing	resizing	NOUN
iajs-3405	61	5	graph	graph	NOUN
iajs-3405	61	6	γ𝐽3	γ𝐽3	PROPN
iajs-3405	61	7	𝑅𝑆	𝑅𝑆	PROPN
iajs-3405	61	8	has	have	VERB
iajs-3405	61	9	order	order	NOUN
iajs-3405	61	10	42	42	NUM
iajs-3405	61	11	.	.	PUNCT
iajs-3405	62	1	furthermore	furthermore	ADV
iajs-3405	62	2	,	,	PUNCT
iajs-3405	62	3	the	the	DET
iajs-3405	62	4	vertex	vertex	NOUN
iajs-3405	62	5	set	set	NOUN
iajs-3405	62	6	of	of	ADP
iajs-3405	62	7	γ𝐽3	γ𝐽3	PROPN
iajs-3405	62	8	𝑅𝑆	𝑅𝑆	PROPN
iajs-3405	62	9	could	could	AUX
iajs-3405	62	10	now	now	ADV
iajs-3405	62	11	be	be	AUX
iajs-3405	62	12	stated	state	VERB
iajs-3405	62	13	in	in	ADP
iajs-3405	62	14	the	the	DET
iajs-3405	62	15	following	follow	VERB
iajs-3405	62	16	manner:{1a	manner:{1a	NOUN
iajs-3405	62	17	,	,	PUNCT
iajs-3405	62	18	2a	2a	NUM
iajs-3405	62	19	,	,	PUNCT
iajs-3405	62	20	3a	3a	NUM
iajs-3405	62	21	,	,	PUNCT
iajs-3405	62	22	3b	3b	NUM
iajs-3405	62	23	,	,	PUNCT
iajs-3405	62	24	4a	4a	NUM
iajs-3405	62	25	,	,	PUNCT
iajs-3405	62	26	5a	5a	NUM
iajs-3405	62	27	,	,	PUNCT
iajs-3405	62	28	5b	5b	NUM
iajs-3405	62	29	,	,	PUNCT
iajs-3405	62	30	6a	6a	NOUN
iajs-3405	62	31	,	,	PUNCT
iajs-3405	62	32	8a	8a	NUM
iajs-3405	62	33	,	,	PUNCT
iajs-3405	62	34	9a	9a	NOUN
iajs-3405	62	35	,	,	PUNCT
iajs-3405	62	36	9b	9b	NOUN
iajs-3405	62	37	,	,	PUNCT
iajs-3405	62	38	9c	9c	NUM
iajs-3405	62	39	,	,	PUNCT
iajs-3405	62	40	10a	10a	NOUN
iajs-3405	62	41	,	,	PUNCT
iajs-3405	62	42	10b	10b	NOUN
iajs-3405	62	43	,	,	PUNCT
iajs-3405	62	44	12a	12a	NOUN
iajs-3405	62	45	,	,	PUNCT
iajs-3405	62	46	15a	15a	NOUN
iajs-3405	62	47	,	,	PUNCT
iajs-3405	62	48	15b	15b	NOUN
iajs-3405	62	49	,	,	PUNCT
iajs-3405	62	50	17a	17a	PROPN
iajs-3405	62	51	,	,	PUNCT
iajs-3405	62	52	17b	17b	NOUN
iajs-3405	62	53	,	,	PUNCT
iajs-3405	62	54	19a	19a	NOUN
iajs-3405	62	55	,	,	PUNCT
iajs-3405	62	56	19b	19b	NOUN
iajs-3405	62	57	}	}	PUNCT
iajs-3405	62	58	.	.	PUNCT
iajs-3405	63	1	in	in	ADP
iajs-3405	63	2	addition	addition	NOUN
iajs-3405	63	3	,	,	PUNCT
iajs-3405	63	4	the	the	DET
iajs-3405	63	5	vertex	vertex	NOUN
iajs-3405	63	6	degree	degree	NOUN
iajs-3405	63	7	sequence	sequence	NOUN
iajs-3405	63	8	is	be	AUX
iajs-3405	63	9	shown	show	VERB
iajs-3405	63	10	below	below	ADP
iajs-3405	63	11	:	:	PUNCT
iajs-3405	63	12	{	{	PUNCT
iajs-3405	63	13	1	1	NUM
iajs-3405	63	14	,	,	PUNCT
iajs-3405	63	15	18	18	NUM
iajs-3405	63	16	,	,	PUNCT
iajs-3405	63	17	14	14	NUM
iajs-3405	63	18	,	,	PUNCT
iajs-3405	63	19	17	17	NUM
iajs-3405	63	20	,	,	PUNCT
iajs-3405	63	21	18	18	NUM
iajs-3405	63	22	,	,	PUNCT
iajs-3405	63	23	19	19	NUM
iajs-3405	63	24	,	,	PUNCT
iajs-3405	63	25	19	19	NUM
iajs-3405	63	26	,	,	PUNCT
iajs-3405	63	27	18	18	NUM
iajs-3405	63	28	,	,	PUNCT
iajs-3405	63	29	19	19	NUM
iajs-3405	63	30	,	,	PUNCT
iajs-3405	63	31	18	18	NUM
iajs-3405	63	32	,	,	PUNCT
iajs-3405	63	33	18	18	NUM
iajs-3405	63	34	,	,	PUNCT
iajs-3405	63	35	18	18	NUM
iajs-3405	63	36	,	,	PUNCT
iajs-3405	63	37	19	19	NUM
iajs-3405	63	38	,	,	PUNCT
iajs-3405	63	39	19	19	NUM
iajs-3405	63	40	,	,	PUNCT
iajs-3405	63	41	19	19	NUM
iajs-3405	63	42	,	,	PUNCT
iajs-3405	63	43	19,19	19,19	NUM
iajs-3405	63	44	,	,	PUNCT
iajs-3405	63	45	19	19	NUM
iajs-3405	63	46	,	,	PUNCT
iajs-3405	63	47	19	19	NUM
iajs-3405	63	48	,	,	PUNCT
iajs-3405	63	49	18	18	NUM
iajs-3405	63	50	,	,	PUNCT
iajs-3405	63	51	18	18	NUM
iajs-3405	63	52	}	}	PUNCT
iajs-3405	63	53	ihjpas	ihjpa	NOUN
iajs-3405	63	54	.	.	PUNCT
iajs-3405	64	1	2024	2024	NUM
iajs-3405	64	2	,	,	PUNCT
iajs-3405	64	3	37(4	37(4	PRON
iajs-3405	64	4	)	)	PUNCT
iajs-3405	64	5	404	404	NUM
iajs-3405	64	6	figure	figure	NOUN
iajs-3405	64	7	3	3	NUM
iajs-3405	64	8	.	.	PUNCT
iajs-3405	65	1	the	the	DET
iajs-3405	65	2	structure	structure	NOUN
iajs-3405	65	3	of	of	ADP
iajs-3405	65	4	the	the	DET
iajs-3405	65	5	resize	resize	NOUN
iajs-3405	65	6	graph	graph	NOUN
iajs-3405	65	7	γ𝐺	γ𝐺	PUNCT
iajs-3405	65	8	𝑅𝑆	𝑅𝑆	ADJ
iajs-3405	65	9	,	,	PUNCT
iajs-3405	65	10	gj3	gj3	PROPN
iajs-3405	65	11	.	.	PUNCT
iajs-3405	66	1	according	accord	VERB
iajs-3405	66	2	to	to	ADP
iajs-3405	66	3	the	the	DET
iajs-3405	66	4	data	datum	NOUN
iajs-3405	66	5	in	in	ADP
iajs-3405	66	6	figure	figure	NOUN
iajs-3405	66	7	3	3	NUM
iajs-3405	66	8	,	,	PUNCT
iajs-3405	66	9	γ𝐽3	γ𝐽3	PROPN
iajs-3405	66	10	𝑅𝑆	𝑅𝑆	PROPN
iajs-3405	66	11	is	be	AUX
iajs-3405	66	12	connected	connect	VERB
iajs-3405	66	13	and	and	CCONJ
iajs-3405	66	14	has	have	VERB
iajs-3405	66	15	the	the	DET
iajs-3405	66	16	following	follow	VERB
iajs-3405	66	17	characteristics	characteristic	NOUN
iajs-3405	66	18	:	:	PUNCT
iajs-3405	66	19	table	table	NOUN
iajs-3405	66	20	1	1	NUM
iajs-3405	66	21	.	.	PUNCT
iajs-3405	67	1	properties	property	NOUN
iajs-3405	67	2	of	of	ADP
iajs-3405	67	3	the	the	DET
iajs-3405	67	4	resize	resize	NOUN
iajs-3405	67	5	graph	graph	NOUN
iajs-3405	67	6	γ𝐽3	γ𝐽3	PROPN
iajs-3405	67	7	𝑅𝑆	𝑅𝑆	PROPN
iajs-3405	67	8	.	.	PUNCT
iajs-3405	68	1	γ𝐺	γ𝐺	PUNCT
iajs-3405	68	2	𝑅𝑆	𝑅𝑆	PROPN
iajs-3405	68	3	e(γ𝐺	e(γ𝐺	PROPN
iajs-3405	68	4	𝑅𝑆	𝑅𝑆	ADJ
iajs-3405	68	5	)	)	PUNCT
iajs-3405	68	6	girth	girth	NOUN
iajs-3405	68	7	clique	clique	NOUN
iajs-3405	68	8	number	number	NOUN
iajs-3405	68	9	radius	radius	NOUN
iajs-3405	68	10	diameter	diameter	NOUN
iajs-3405	68	11	gj3	gj3	PROPN
iajs-3405	68	12	183	183	NUM
iajs-3405	68	13	3	3	NUM
iajs-3405	68	14	17	17	NUM
iajs-3405	68	15	2	2	NUM
iajs-3405	68	16	3	3	NUM
iajs-3405	68	17	3.2	3.2	NUM
iajs-3405	68	18	the	the	DET
iajs-3405	68	19	edges	edge	NOUN
iajs-3405	68	20	set	set	VERB
iajs-3405	68	21	of	of	ADP
iajs-3405	68	22	result	result	NOUN
iajs-3405	68	23	involution	involution	NOUN
iajs-3405	68	24	graphs	graph	NOUN
iajs-3405	68	25	in	in	ADP
iajs-3405	68	26	this	this	DET
iajs-3405	68	27	section	section	NOUN
iajs-3405	68	28	,	,	PUNCT
iajs-3405	68	29	we	we	PRON
iajs-3405	68	30	provide	provide	VERB
iajs-3405	68	31	comprehensive	comprehensive	ADJ
iajs-3405	68	32	information	information	NOUN
iajs-3405	68	33	about	about	ADP
iajs-3405	68	34	the	the	DET
iajs-3405	68	35	edges	edge	NOUN
iajs-3405	68	36	set	set	VERB
iajs-3405	68	37	of	of	ADP
iajs-3405	68	38	the	the	DET
iajs-3405	68	39	result	result	NOUN
iajs-3405	68	40	involution	involution	NOUN
iajs-3405	68	41	graph	graph	NOUN
iajs-3405	68	42	γ𝐽3	γ𝐽3	PROPN
iajs-3405	68	43	𝑅𝐼	𝑅𝐼	PROPN
iajs-3405	68	44	for	for	ADP
iajs-3405	68	45	the	the	DET
iajs-3405	68	46	janko	janko	PROPN
iajs-3405	68	47	group	group	PROPN
iajs-3405	68	48	j3	j3	PROPN
iajs-3405	68	49	.	.	PUNCT
iajs-3405	69	1	the	the	DET
iajs-3405	69	2	data	datum	NOUN
iajs-3405	69	3	concern	concern	NOUN
iajs-3405	69	4	the	the	DET
iajs-3405	69	5	number	number	NOUN
iajs-3405	69	6	of	of	ADP
iajs-3405	69	7	edges	edge	NOUN
iajs-3405	69	8	connecting	connect	VERB
iajs-3405	69	9	any	any	DET
iajs-3405	69	10	two	two	NUM
iajs-3405	69	11	g	g	NOUN
iajs-3405	69	12	-	-	PUNCT
iajs-3405	69	13	conjugacy	conjugacy	ADJ
iajs-3405	69	14	elements	element	NOUN
iajs-3405	69	15	.	.	PUNCT
iajs-3405	70	1	the	the	DET
iajs-3405	70	2	findings	finding	NOUN
iajs-3405	70	3	will	will	AUX
iajs-3405	70	4	be	be	AUX
iajs-3405	70	5	crucial	crucial	ADJ
iajs-3405	70	6	in	in	ADP
iajs-3405	70	7	assessing	assess	VERB
iajs-3405	70	8	the	the	DET
iajs-3405	70	9	construct	construct	NOUN
iajs-3405	70	10	of	of	ADP
iajs-3405	70	11	the	the	DET
iajs-3405	70	12	result	result	NOUN
iajs-3405	70	13	involution	involution	NOUN
iajs-3405	70	14	graph	graph	NOUN
iajs-3405	70	15	of	of	ADP
iajs-3405	70	16	j3	j3	PROPN
iajs-3405	70	17	.	.	PUNCT
iajs-3405	71	1	we	we	PRON
iajs-3405	71	2	will	will	AUX
iajs-3405	71	3	use	use	VERB
iajs-3405	71	4	gap	gap	NOUN
iajs-3405	71	5	and	and	CCONJ
iajs-3405	71	6	the	the	DET
iajs-3405	71	7	online	online	ADJ
iajs-3405	71	8	atlas	atlas	PROPN
iajs-3405	71	9	to	to	PART
iajs-3405	71	10	get	get	VERB
iajs-3405	71	11	the	the	DET
iajs-3405	71	12	intended	intend	VERB
iajs-3405	71	13	result	result	NOUN
iajs-3405	71	14	.	.	PUNCT
iajs-3405	72	1	we	we	PRON
iajs-3405	72	2	should	should	AUX
iajs-3405	72	3	be	be	AUX
iajs-3405	72	4	informed	inform	VERB
iajs-3405	72	5	of	of	ADP
iajs-3405	72	6	that	that	PRON
iajs-3405	72	7	,	,	PUNCT
iajs-3405	72	8	in	in	ADP
iajs-3405	72	9	the	the	DET
iajs-3405	72	10	elements	element	NOUN
iajs-3405	72	11	of	of	ADP
iajs-3405	72	12	the	the	DET
iajs-3405	72	13	class	class	NOUN
iajs-3405	72	14	5a	5a	NUM
iajs-3405	72	15	there	there	PRON
iajs-3405	72	16	are	be	VERB
iajs-3405	72	17	an	an	DET
iajs-3405	72	18	edges	edge	NOUN
iajs-3405	72	19	with	with	ADP
iajs-3405	72	20	the	the	DET
iajs-3405	72	21	remaining	remain	VERB
iajs-3405	72	22	j3conjugacy	j3conjugacy	NOUN
iajs-3405	72	23	classes	class	NOUN
iajs-3405	72	24	except	except	SCONJ
iajs-3405	72	25	the	the	DET
iajs-3405	72	26	identity	identity	NOUN
iajs-3405	72	27	element	element	NOUN
iajs-3405	72	28	.	.	PUNCT
iajs-3405	73	1	this	this	PRON
iajs-3405	73	2	can	can	AUX
iajs-3405	73	3	be	be	AUX
iajs-3405	73	4	seen	see	VERB
iajs-3405	73	5	in	in	ADP
iajs-3405	73	6	the	the	DET
iajs-3405	73	7	following	follow	VERB
iajs-3405	73	8	set	set	NOUN
iajs-3405	73	9	:	:	PUNCT
iajs-3405	73	10	{	{	PUNCT
iajs-3405	73	11	2a(33488640),3a(25116480),3b(167443200),4a(418608000),5a(598609440),5b(157396608	2a(33488640),3a(25116480),3b(167443200),4a(418608000),5a(598609440),5b(157396608	NUM
iajs-3405	73	12	0),6a(1783270080),8a(5425159680),9a(1557221760),9b(1557221760),9c(1557221760),10a	0),6a(1783270080),8a(5425159680),9a(1557221760),9b(1557221760),9c(1557221760),10a	NOUN
iajs-3405	73	13	(	(	PUNCT
iajs-3405	73	14	4651572096),10b(4470733440),12a(3717239040),15a(3265142400),15b(2662346880),17a(2	4651572096),10b(4470733440),12a(3717239040),15a(3265142400),15b(2662346880),17a(2	PROPN
iajs-3405	73	15	561880960),17b(2561880960),19a(2310716160),19b(2310716160	561880960),17b(2561880960),19a(2310716160),19b(2310716160	PROPN
iajs-3405	73	16	)	)	PUNCT
iajs-3405	73	17	}	}	PUNCT
iajs-3405	73	18	.	.	PUNCT
iajs-3405	74	1	in	in	ADP
iajs-3405	74	2	addition	addition	NOUN
iajs-3405	74	3	,	,	PUNCT
iajs-3405	74	4	we	we	PRON
iajs-3405	74	5	can	can	AUX
iajs-3405	74	6	find	find	VERB
iajs-3405	74	7	26163	26163	NUM
iajs-3405	74	8	edges	edge	NOUN
iajs-3405	74	9	between	between	ADP
iajs-3405	74	10	the	the	DET
iajs-3405	74	11	elements	element	NOUN
iajs-3405	74	12	of	of	ADP
iajs-3405	74	13	the	the	DET
iajs-3405	74	14	class	class	NOUN
iajs-3405	74	15	2a	2a	NUM
iajs-3405	74	16	.	.	PUNCT
iajs-3405	75	1	3.3	3.3	NUM
iajs-3405	75	2	the	the	DET
iajs-3405	75	3	structures	structure	NOUN
iajs-3405	75	4	of	of	ADP
iajs-3405	75	5	𝚪𝑱𝟑	𝚪𝑱𝟑	PROPN
iajs-3405	75	6	𝑹𝑰	𝑹𝑰	PROPN
iajs-3405	75	7	for	for	ADP
iajs-3405	75	8	the	the	DET
iajs-3405	75	9	janko	janko	PROPN
iajs-3405	75	10	group	group	PROPN
iajs-3405	75	11	j3	j3	PROPN
iajs-3405	75	12	,	,	PUNCT
iajs-3405	75	13	the	the	DET
iajs-3405	75	14	structures	structure	NOUN
iajs-3405	75	15	of	of	ADP
iajs-3405	75	16	the	the	DET
iajs-3405	75	17	result	result	NOUN
iajs-3405	75	18	involution	involution	NOUN
iajs-3405	75	19	graph	graph	NOUN
iajs-3405	75	20	are	be	AUX
iajs-3405	75	21	fully	fully	ADV
iajs-3405	75	22	described	describe	VERB
iajs-3405	75	23	in	in	ADP
iajs-3405	75	24	the	the	DET
iajs-3405	75	25	following	following	NOUN
iajs-3405	75	26	theorem	theorem	NOUN
iajs-3405	75	27	:	:	PUNCT
iajs-3405	75	28	theorem	theorem	ADJ
iajs-3405	75	29	3.1	3.1	NUM
iajs-3405	75	30	:	:	PUNCT
iajs-3405	75	31	the	the	DET
iajs-3405	75	32	result	result	NOUN
iajs-3405	75	33	involution	involution	NOUN
iajs-3405	75	34	graph	graph	NOUN
iajs-3405	75	35	for	for	ADP
iajs-3405	75	36	the	the	DET
iajs-3405	75	37	janko	janko	PROPN
iajs-3405	75	38	group	group	PROPN
iajs-3405	75	39	j3	j3	PROPN
iajs-3405	75	40	is	be	AUX
iajs-3405	75	41	connected	connect	VERB
iajs-3405	75	42	with	with	ADP
iajs-3405	75	43	diameter	diameter	NOUN
iajs-3405	75	44	3	3	NUM
iajs-3405	75	45	,	,	PUNCT
iajs-3405	75	46	radius	radius	NOUN
iajs-3405	75	47	2	2	NUM
iajs-3405	75	48	,	,	PUNCT
iajs-3405	75	49	and	and	CCONJ
iajs-3405	75	50	girth	girth	ADJ
iajs-3405	75	51	3	3	NUM
iajs-3405	75	52	.	.	PUNCT
iajs-3405	76	1	ihjpas	ihjpas	PROPN
iajs-3405	76	2	.	.	PUNCT
iajs-3405	77	1	2024	2024	NUM
iajs-3405	77	2	,	,	PUNCT
iajs-3405	77	3	37(4	37(4	PRON
iajs-3405	77	4	)	)	PUNCT
iajs-3405	78	1	405	405	NUM
iajs-3405	78	2	proof	proof	NOUN
iajs-3405	78	3	:	:	PUNCT
iajs-3405	78	4	the	the	DET
iajs-3405	78	5	resizing	resizing	NOUN
iajs-3405	78	6	graph	graph	NOUN
iajs-3405	78	7	of	of	ADP
iajs-3405	78	8	j3	j3	PROPN
iajs-3405	78	9	is	be	AUX
iajs-3405	78	10	connected	connect	VERB
iajs-3405	78	11	using	use	VERB
iajs-3405	78	12	table	table	NOUN
iajs-3405	78	13	1	1	NUM
iajs-3405	78	14	.	.	PUNCT
iajs-3405	79	1	as	as	ADP
iajs-3405	79	2	a	a	DET
iajs-3405	79	3	result	result	NOUN
iajs-3405	79	4	,	,	PUNCT
iajs-3405	79	5	by	by	ADP
iajs-3405	79	6	utilizing	utilize	VERB
iajs-3405	79	7	proposition	proposition	NOUN
iajs-3405	79	8	2.3	2.3	NUM
iajs-3405	79	9	,	,	PUNCT
iajs-3405	79	10	we	we	PRON
iajs-3405	79	11	are	be	AUX
iajs-3405	79	12	able	able	ADJ
iajs-3405	79	13	to	to	PART
iajs-3405	79	14	determine	determine	VERB
iajs-3405	79	15	how	how	SCONJ
iajs-3405	79	16	γ𝐽3	γ𝐽3	PROPN
iajs-3405	79	17	𝑅𝐼	𝑅𝐼	PROPN
iajs-3405	79	18	is	be	AUX
iajs-3405	79	19	connected	connect	VERB
iajs-3405	79	20	.	.	PUNCT
iajs-3405	80	1	in	in	ADP
iajs-3405	80	2	addition	addition	NOUN
iajs-3405	80	3	,	,	PUNCT
iajs-3405	80	4	between	between	ADP
iajs-3405	80	5	the	the	DET
iajs-3405	80	6	elements	element	NOUN
iajs-3405	80	7	of	of	ADP
iajs-3405	80	8	the	the	DET
iajs-3405	80	9	class	class	NOUN
iajs-3405	80	10	2a	2a	NUM
iajs-3405	80	11	there	there	PRON
iajs-3405	80	12	are	be	VERB
iajs-3405	80	13	26163	26163	NUM
iajs-3405	80	14	edges	edge	NOUN
iajs-3405	80	15	and	and	CCONJ
iajs-3405	80	16	these	these	DET
iajs-3405	80	17	elements	element	NOUN
iajs-3405	80	18	adjacent	adjacent	ADJ
iajs-3405	80	19	with	with	ADP
iajs-3405	80	20	the	the	DET
iajs-3405	80	21	identity	identity	NOUN
iajs-3405	80	22	element	element	NOUN
iajs-3405	80	23	of	of	ADP
iajs-3405	80	24	j3	j3	PROPN
iajs-3405	80	25	.	.	PUNCT
iajs-3405	81	1	hence	hence	ADV
iajs-3405	81	2	,	,	PUNCT
iajs-3405	81	3	we	we	PRON
iajs-3405	81	4	have	have	VERB
iajs-3405	81	5	a	a	DET
iajs-3405	81	6	cycle	cycle	NOUN
iajs-3405	81	7	with	with	ADP
iajs-3405	81	8	a	a	DET
iajs-3405	81	9	length	length	NOUN
iajs-3405	81	10	of	of	ADP
iajs-3405	81	11	3	3	NUM
iajs-3405	81	12	in	in	ADP
iajs-3405	81	13	the	the	DET
iajs-3405	81	14	graph	graph	NOUN
iajs-3405	81	15	γ𝐽3	γ𝐽3	PROPN
iajs-3405	81	16	𝑅𝐼.	𝑅𝐼.	NOUN
iajs-3405	81	17	therefore	therefore	ADV
iajs-3405	81	18	,	,	PUNCT
iajs-3405	81	19	the	the	DET
iajs-3405	81	20	result	result	NOUN
iajs-3405	81	21	involution	involution	NOUN
iajs-3405	81	22	graph	graph	NOUN
iajs-3405	81	23	has	have	VERB
iajs-3405	81	24	girth	girth	NOUN
iajs-3405	81	25	3	3	NUM
iajs-3405	81	26	in	in	ADP
iajs-3405	81	27	this	this	DET
iajs-3405	81	28	case	case	NOUN
iajs-3405	81	29	.	.	PUNCT
iajs-3405	82	1	furthermore	furthermore	ADV
iajs-3405	82	2	,	,	PUNCT
iajs-3405	82	3	the	the	DET
iajs-3405	82	4	class	class	NOUN
iajs-3405	82	5	5a	5a	NUM
iajs-3405	82	6	vertices	vertex	NOUN
iajs-3405	82	7	and	and	CCONJ
iajs-3405	82	8	the	the	DET
iajs-3405	82	9	identity	identity	NOUN
iajs-3405	82	10	element	element	NOUN
iajs-3405	82	11	are	be	AUX
iajs-3405	82	12	not	not	PART
iajs-3405	82	13	adjacent	adjacent	ADJ
iajs-3405	82	14	.	.	PUNCT
iajs-3405	83	1	but	but	CCONJ
iajs-3405	83	2	,	,	PUNCT
iajs-3405	83	3	during	during	ADP
iajs-3405	83	4	the	the	DET
iajs-3405	83	5	classes	class	NOUN
iajs-3405	83	6	2a	2a	NUM
iajs-3405	83	7	,	,	PUNCT
iajs-3405	83	8	these	these	DET
iajs-3405	83	9	vertices	vertex	NOUN
iajs-3405	83	10	were	be	AUX
iajs-3405	83	11	connected	connect	VERB
iajs-3405	83	12	to	to	ADP
iajs-3405	83	13	the	the	DET
iajs-3405	83	14	identity	identity	NOUN
iajs-3405	83	15	.	.	PUNCT
iajs-3405	84	1	as	as	ADP
iajs-3405	84	2	a	a	DET
iajs-3405	84	3	result	result	NOUN
iajs-3405	84	4	,	,	PUNCT
iajs-3405	84	5	in	in	ADP
iajs-3405	84	6	this	this	DET
iajs-3405	84	7	scenario	scenario	NOUN
iajs-3405	84	8	,	,	PUNCT
iajs-3405	84	9	the	the	DET
iajs-3405	84	10	radius	radius	NOUN
iajs-3405	84	11	is	be	AUX
iajs-3405	84	12	2	2	NUM
iajs-3405	84	13	.	.	PUNCT
iajs-3405	85	1	moreover	moreover	ADV
iajs-3405	85	2	,	,	PUNCT
iajs-3405	85	3	the	the	DET
iajs-3405	85	4	diameter	diameter	NOUN
iajs-3405	85	5	is	be	AUX
iajs-3405	85	6	3	3	NUM
iajs-3405	85	7	due	due	ADP
iajs-3405	85	8	to	to	ADP
iajs-3405	85	9	the	the	DET
iajs-3405	85	10	other	other	ADJ
iajs-3405	85	11	vertices	vertex	NOUN
iajs-3405	85	12	maximum	maximum	ADJ
iajs-3405	85	13	distance	distance	NOUN
iajs-3405	85	14	being	be	AUX
iajs-3405	85	15	3	3	NUM
iajs-3405	85	16	.	.	PUNCT
iajs-3405	86	1	we	we	PRON
iajs-3405	86	2	provide	provide	VERB
iajs-3405	86	3	the	the	DET
iajs-3405	86	4	following	follow	VERB
iajs-3405	86	5	significant	significant	ADJ
iajs-3405	86	6	corollaries	corollary	NOUN
iajs-3405	86	7	in	in	ADP
iajs-3405	86	8	light	light	NOUN
iajs-3405	86	9	of	of	ADP
iajs-3405	86	10	the	the	DET
iajs-3405	86	11	preceding	precede	VERB
iajs-3405	86	12	finding	finding	NOUN
iajs-3405	86	13	:	:	PUNCT
iajs-3405	86	14	corollary	corollary	ADJ
iajs-3405	86	15	3.2	3.2	NUM
iajs-3405	86	16	:	:	PUNCT
iajs-3405	86	17	suppose	suppose	VERB
iajs-3405	86	18	that	that	SCONJ
iajs-3405	86	19	g	g	PROPN
iajs-3405	86	20	be	be	VERB
iajs-3405	86	21	the	the	DET
iajs-3405	86	22	janko	janko	PROPN
iajs-3405	86	23	groups	group	NOUN
iajs-3405	86	24	j3	j3	PROPN
iajs-3405	86	25	.	.	PUNCT
iajs-3405	87	1	then	then	ADV
iajs-3405	87	2	for	for	ADP
iajs-3405	87	3	any	any	DET
iajs-3405	87	4	distinct	distinct	ADJ
iajs-3405	87	5	elements	element	NOUN
iajs-3405	87	6	x	x	X
iajs-3405	87	7	,	,	PUNCT
iajs-3405	87	8	y	y	PROPN
iajs-3405	87	9			PROPN
iajs-3405	87	10	g	g	PROPN
iajs-3405	87	11	,	,	PUNCT
iajs-3405	87	12	one	one	NUM
iajs-3405	87	13	of	of	ADP
iajs-3405	87	14	the	the	DET
iajs-3405	87	15	following	following	NOUN
iajs-3405	87	16	are	be	AUX
iajs-3405	87	17	holds	hold	NOUN
iajs-3405	87	18	:	:	PUNCT
iajs-3405	87	19	itheir	itheir	ADJ
iajs-3405	87	20	product	product	NOUN
iajs-3405	87	21	is	be	AUX
iajs-3405	87	22	an	an	DET
iajs-3405	87	23	involution	involution	NOUN
iajs-3405	87	24	element	element	NOUN
iajs-3405	87	25	.	.	PUNCT
iajs-3405	88	1	ii	ii	NOUN
iajs-3405	88	2	there	there	PRON
iajs-3405	88	3	exist	exist	VERB
iajs-3405	88	4	an	an	DET
iajs-3405	88	5	certain	certain	ADJ
iajs-3405	88	6	z	z	NOUN
iajs-3405	88	7			NOUN
iajs-3405	88	8	g	g	PROPN
iajs-3405	88	9	,	,	PUNCT
iajs-3405	88	10	satisfy	satisfy	VERB
iajs-3405	88	11	its	its	PRON
iajs-3405	88	12	product	product	NOUN
iajs-3405	88	13	with	with	ADP
iajs-3405	88	14	x	x	SYM
iajs-3405	88	15	and	and	CCONJ
iajs-3405	88	16	y	y	PROPN
iajs-3405	88	17	produce	produce	VERB
iajs-3405	88	18	an	an	DET
iajs-3405	88	19	involution	involution	NOUN
iajs-3405	88	20	elements	element	NOUN
iajs-3405	88	21	.	.	PUNCT
iajs-3405	89	1	iii	iii	X
iajs-3405	89	2	there	there	PRON
iajs-3405	89	3	are	be	VERB
iajs-3405	89	4	an	an	DET
iajs-3405	89	5	elements	element	NOUN
iajs-3405	89	6	z	z	NOUN
iajs-3405	89	7	,	,	PUNCT
iajs-3405	89	8	w	w	PROPN
iajs-3405	89	9			PROPN
iajs-3405	89	10	g	g	NOUN
iajs-3405	89	11	,	,	PUNCT
iajs-3405	89	12	satisfy	satisfy	PROPN
iajs-3405	89	13	(	(	PUNCT
iajs-3405	89	14	xz	xz	PROPN
iajs-3405	89	15	)	)	PUNCT
iajs-3405	89	16	,	,	PUNCT
iajs-3405	89	17	(	(	PUNCT
iajs-3405	89	18	zw	zw	PROPN
iajs-3405	89	19	)	)	PUNCT
iajs-3405	89	20	and	and	CCONJ
iajs-3405	89	21	(	(	PUNCT
iajs-3405	89	22	wy	wy	PROPN
iajs-3405	89	23	)	)	PUNCT
iajs-3405	89	24	are	be	AUX
iajs-3405	89	25	involution	involution	NOUN
iajs-3405	89	26	elements	element	NOUN
iajs-3405	89	27	.	.	PUNCT
iajs-3405	90	1	ivj3	ivj3	PROPN
iajs-3405	90	2	has	have	VERB
iajs-3405	90	3	three	three	NUM
iajs-3405	90	4	distinct	distinct	ADJ
iajs-3405	90	5	components	component	NOUN
iajs-3405	90	6	,	,	PUNCT
iajs-3405	90	7	any	any	DET
iajs-3405	90	8	one	one	NUM
iajs-3405	90	9	of	of	ADP
iajs-3405	90	10	them	they	PRON
iajs-3405	90	11	has	have	VERB
iajs-3405	90	12	an	an	DET
iajs-3405	90	13	involution	involution	NOUN
iajs-3405	90	14	product	product	NOUN
iajs-3405	90	15	with	with	ADP
iajs-3405	90	16	the	the	DET
iajs-3405	90	17	others	other	NOUN
iajs-3405	90	18	.	.	PUNCT
iajs-3405	91	1	proof	proof	NOUN
iajs-3405	91	2	:	:	PUNCT
iajs-3405	91	3	by	by	ADP
iajs-3405	91	4	applying	apply	VERB
iajs-3405	91	5	the	the	DET
iajs-3405	91	6	outcomes	outcome	NOUN
iajs-3405	91	7	of	of	ADP
iajs-3405	91	8	theorem	theorem	ADJ
iajs-3405	91	9	3.1	3.1	NUM
iajs-3405	91	10	we	we	PRON
iajs-3405	91	11	have	have	VERB
iajs-3405	91	12	the	the	DET
iajs-3405	91	13	diameter	diameter	NOUN
iajs-3405	91	14	2	2	NUM
iajs-3405	91	15	and	and	CCONJ
iajs-3405	91	16	the	the	DET
iajs-3405	91	17	radius	radius	NOUN
iajs-3405	91	18	2	2	NUM
iajs-3405	91	19	for	for	ADP
iajs-3405	91	20	the	the	DET
iajs-3405	91	21	result	result	NOUN
iajs-3405	91	22	involution	involution	NOUN
iajs-3405	91	23	graph	graph	NOUN
iajs-3405	91	24	of	of	ADP
iajs-3405	91	25	g	g	PROPN
iajs-3405	91	26	.	.	PUNCT
iajs-3405	92	1	therefore	therefore	ADV
iajs-3405	92	2	,	,	PUNCT
iajs-3405	92	3	when	when	SCONJ
iajs-3405	92	4	x	x	PRON
iajs-3405	92	5	and	and	CCONJ
iajs-3405	92	6	y	y	PROPN
iajs-3405	92	7	have	have	VERB
iajs-3405	92	8	distance	distance	NOUN
iajs-3405	92	9	one	one	NUM
iajs-3405	92	10	then	then	ADV
iajs-3405	92	11	their	their	PRON
iajs-3405	92	12	product	product	NOUN
iajs-3405	92	13	is	be	AUX
iajs-3405	92	14	an	an	DET
iajs-3405	92	15	involution	involution	NOUN
iajs-3405	92	16	element	element	NOUN
iajs-3405	92	17	so	so	SCONJ
iajs-3405	92	18	(	(	PUNCT
iajs-3405	92	19	i	i	NOUN
iajs-3405	92	20	)	)	PUNCT
iajs-3405	92	21	is	be	AUX
iajs-3405	92	22	hold	hold	ADJ
iajs-3405	92	23	.	.	PUNCT
iajs-3405	93	1	if	if	SCONJ
iajs-3405	93	2	the	the	DET
iajs-3405	93	3	distance	distance	NOUN
iajs-3405	93	4	between	between	ADP
iajs-3405	93	5	x	x	PUNCT
iajs-3405	93	6	and	and	CCONJ
iajs-3405	93	7	y	y	PROPN
iajs-3405	93	8	equal	equal	ADJ
iajs-3405	93	9	2	2	NUM
iajs-3405	93	10	,	,	PUNCT
iajs-3405	93	11	then	then	ADV
iajs-3405	93	12	one	one	PRON
iajs-3405	93	13	can	can	AUX
iajs-3405	93	14	find	find	VERB
iajs-3405	93	15	z	z	NOUN
iajs-3405	93	16	in	in	ADP
iajs-3405	93	17	g	g	PROPN
iajs-3405	93	18	satisfying	satisfy	VERB
iajs-3405	93	19	(	(	PUNCT
iajs-3405	93	20	ii	ii	NOUN
iajs-3405	93	21	)	)	PUNCT
iajs-3405	93	22	.	.	PUNCT
iajs-3405	94	1	finally	finally	ADV
iajs-3405	94	2	,	,	PUNCT
iajs-3405	94	3	to	to	PART
iajs-3405	94	4	prove	prove	VERB
iajs-3405	94	5	(	(	PUNCT
iajs-3405	94	6	iii	iii	NOUN
iajs-3405	94	7	)	)	PUNCT
iajs-3405	94	8	the	the	DET
iajs-3405	94	9	distance	distance	NOUN
iajs-3405	94	10	between	between	ADP
iajs-3405	94	11	x	x	PUNCT
iajs-3405	94	12	and	and	CCONJ
iajs-3405	94	13	y	y	PROPN
iajs-3405	94	14	equal	equal	ADJ
iajs-3405	94	15	to	to	ADP
iajs-3405	94	16	3	3	NUM
iajs-3405	94	17	,	,	PUNCT
iajs-3405	94	18	implies	imply	VERB
iajs-3405	94	19	there	there	PRON
iajs-3405	94	20	are	be	VERB
iajs-3405	94	21	such	such	ADJ
iajs-3405	94	22	z	z	PROPN
iajs-3405	94	23	,	,	PUNCT
iajs-3405	94	24	w	w	PROPN
iajs-3405	94	25			NOUN
iajs-3405	94	26	g	g	PROPN
iajs-3405	94	27	satisfy	satisfy	VERB
iajs-3405	94	28	the	the	DET
iajs-3405	94	29	conditions	condition	NOUN
iajs-3405	94	30	of	of	ADP
iajs-3405	94	31	(	(	PUNCT
iajs-3405	94	32	iii	iii	NOUN
iajs-3405	94	33	)	)	PUNCT
iajs-3405	94	34	.	.	PUNCT
iajs-3405	95	1	finally	finally	ADV
iajs-3405	95	2	,	,	PUNCT
iajs-3405	95	3	the	the	DET
iajs-3405	95	4	result	result	NOUN
iajs-3405	95	5	involution	involution	NOUN
iajs-3405	95	6	graph	graph	NOUN
iajs-3405	95	7	of	of	ADP
iajs-3405	95	8	g	g	NOUN
iajs-3405	95	9	with	with	ADP
iajs-3405	95	10	girth	girth	NOUN
iajs-3405	95	11	3	3	NUM
iajs-3405	95	12	.	.	PUNCT
iajs-3405	96	1	as	as	ADP
iajs-3405	96	2	a	a	DET
iajs-3405	96	3	result	result	NOUN
iajs-3405	96	4	,	,	PUNCT
iajs-3405	96	5	the	the	DET
iajs-3405	96	6	characterization	characterization	NOUN
iajs-3405	96	7	of	of	ADP
iajs-3405	96	8	the	the	DET
iajs-3405	96	9	result	result	NOUN
iajs-3405	96	10	involution	involution	NOUN
iajs-3405	96	11	graph	graph	NOUN
iajs-3405	96	12	normally	normally	ADV
iajs-3405	96	13	leads	lead	VERB
iajs-3405	96	14	to	to	ADP
iajs-3405	96	15	the	the	DET
iajs-3405	96	16	proof	proof	NOUN
iajs-3405	96	17	of	of	ADP
iajs-3405	96	18	iv	iv	NUM
iajs-3405	96	19	.	.	PROPN
iajs-3405	97	1	4	4	X
iajs-3405	97	2	.	.	X
iajs-3405	97	3	conclusion	conclusion	NOUN
iajs-3405	97	4	this	this	DET
iajs-3405	97	5	study	study	NOUN
iajs-3405	97	6	analyses	analyse	VERB
iajs-3405	97	7	the	the	DET
iajs-3405	97	8	result	result	NOUN
iajs-3405	97	9	involution	involution	NOUN
iajs-3405	97	10	graph	graph	NOUN
iajs-3405	97	11	for	for	ADP
iajs-3405	97	12	the	the	DET
iajs-3405	97	13	janko	janko	PROPN
iajs-3405	97	14	group	group	PROPN
iajs-3405	97	15	j3	j3	PROPN
iajs-3405	97	16	.	.	PUNCT
iajs-3405	98	1	the	the	DET
iajs-3405	98	2	computational	computational	ADJ
iajs-3405	98	3	method	method	NOUN
iajs-3405	98	4	used	use	VERB
iajs-3405	98	5	to	to	PART
iajs-3405	98	6	determine	determine	VERB
iajs-3405	98	7	certain	certain	ADJ
iajs-3405	98	8	graph	graph	NOUN
iajs-3405	98	9	properties	property	NOUN
iajs-3405	98	10	.	.	PUNCT
iajs-3405	99	1	detailed	detailed	ADJ
iajs-3405	99	2	information	information	NOUN
iajs-3405	99	3	about	about	ADP
iajs-3405	99	4	the	the	DET
iajs-3405	99	5	resize	resize	NOUN
iajs-3405	99	6	graph	graph	NOUN
iajs-3405	99	7	,	,	PUNCT
iajs-3405	99	8	for	for	ADP
iajs-3405	99	9	example	example	NOUN
iajs-3405	99	10	,	,	PUNCT
iajs-3405	99	11	as	as	ADV
iajs-3405	99	12	well	well	ADV
iajs-3405	99	13	as	as	ADP
iajs-3405	99	14	the	the	DET
iajs-3405	99	15	radius	radius	NOUN
iajs-3405	99	16	,	,	PUNCT
iajs-3405	99	17	diameter	diameter	NOUN
iajs-3405	99	18	and	and	CCONJ
iajs-3405	99	19	circumference	circumference	NOUN
iajs-3405	99	20	.	.	PUNCT
iajs-3405	100	1	the	the	DET
iajs-3405	100	2	results	result	NOUN
iajs-3405	100	3	of	of	ADP
iajs-3405	100	4	this	this	DET
iajs-3405	100	5	study	study	NOUN
iajs-3405	100	6	can	can	AUX
iajs-3405	100	7	be	be	AUX
iajs-3405	100	8	applied	apply	VERB
iajs-3405	100	9	to	to	ADP
iajs-3405	100	10	the	the	DET
iajs-3405	100	11	study	study	NOUN
iajs-3405	100	12	of	of	ADP
iajs-3405	100	13	more	more	ADV
iajs-3405	100	14	complicated	complicated	ADJ
iajs-3405	100	15	simple	simple	ADJ
iajs-3405	100	16	groups	group	NOUN
iajs-3405	100	17	,	,	PUNCT
iajs-3405	100	18	including	include	VERB
iajs-3405	100	19	monster	monster	NOUN
iajs-3405	100	20	groups	group	NOUN
iajs-3405	100	21	,	,	PUNCT
iajs-3405	100	22	pariah	pariah	NOUN
iajs-3405	100	23	groups	group	NOUN
iajs-3405	100	24	and	and	CCONJ
iajs-3405	100	25	lie	lie	NOUN
iajs-3405	100	26	-	-	PUNCT
iajs-3405	100	27	type	type	NOUN
iajs-3405	100	28	exceptional	exceptional	ADJ
iajs-3405	100	29	groups	group	NOUN
iajs-3405	100	30	.	.	PUNCT
iajs-3405	101	1	acknowledgment	acknowledgment	NOUN
iajs-3405	101	2	the	the	DET
iajs-3405	101	3	authors	author	NOUN
iajs-3405	101	4	would	would	AUX
iajs-3405	101	5	like	like	VERB
iajs-3405	101	6	to	to	PART
iajs-3405	101	7	thank	thank	VERB
iajs-3405	101	8	the	the	DET
iajs-3405	101	9	university	university	NOUN
iajs-3405	101	10	of	of	ADP
iajs-3405	101	11	baghdad	baghdad	PROPN
iajs-3405	101	12	(	(	PUNCT
iajs-3405	101	13	https://uobaghdad.edu.iq/	https://uobaghdad.edu.iq/	PROPN
iajs-3405	101	14	)	)	PUNCT
iajs-3405	101	15	,	,	PUNCT
iajs-3405	101	16	department	department	NOUN
iajs-3405	101	17	of	of	ADP
iajs-3405	101	18	mathematics	mathematics	PROPN
iajs-3405	101	19	in	in	ADP
iajs-3405	101	20	the	the	DET
iajs-3405	101	21	college	college	NOUN
iajs-3405	101	22	of	of	ADP
iajs-3405	101	23	sciences	science	NOUN
iajs-3405	101	24	for	for	ADP
iajs-3405	101	25	their	their	PRON
iajs-3405	101	26	motivation	motivation	NOUN
iajs-3405	101	27	and	and	CCONJ
iajs-3405	101	28	support	support	NOUN
iajs-3405	101	29	.	.	PUNCT
iajs-3405	102	1	conflict	conflict	NOUN
iajs-3405	102	2	of	of	ADP
iajs-3405	102	3	interest	interest	NOUN
iajs-3405	102	4	the	the	DET
iajs-3405	102	5	authors	author	NOUN
iajs-3405	102	6	declare	declare	VERB
iajs-3405	102	7	that	that	SCONJ
iajs-3405	102	8	they	they	PRON
iajs-3405	102	9	have	have	VERB
iajs-3405	102	10	no	no	DET
iajs-3405	102	11	conflicts	conflict	NOUN
iajs-3405	102	12	of	of	ADP
iajs-3405	102	13	interest	interest	NOUN
iajs-3405	102	14	.	.	PUNCT
iajs-3405	103	1	funding	fund	VERB
iajs-3405	103	2	no	no	DET
iajs-3405	103	3	funding	funding	NOUN
iajs-3405	103	4	.	.	PUNCT
iajs-3405	104	1	references	reference	NOUN
iajs-3405	104	2	1	1	NUM
iajs-3405	104	3	.	.	PUNCT
iajs-3405	104	4	aubad	aubad	PROPN
iajs-3405	104	5	,	,	PUNCT
iajs-3405	104	6	a.	a.	NOUN
iajs-3405	104	7	;	;	PUNCT
iajs-3405	104	8	rowley	rowley	NOUN
iajs-3405	104	9	,	,	PUNCT
iajs-3405	104	10	p.	p.	NOUN
iajs-3405	104	11	commuting	commute	VERB
iajs-3405	104	12	involution	involution	NOUN
iajs-3405	104	13	graphs	graph	NOUN
iajs-3405	104	14	for	for	ADP
iajs-3405	104	15	certain	certain	ADJ
iajs-3405	104	16	exceptional	exceptional	ADJ
iajs-3405	104	17	groups	group	NOUN
iajs-3405	104	18	of	of	ADP
iajs-3405	104	19	lie	lie	NOUN
iajs-3405	104	20	type	type	NOUN
iajs-3405	104	21	.	.	PUNCT
iajs-3405	105	1	graphs	graph	NOUN
iajs-3405	105	2	and	and	CCONJ
iajs-3405	105	3	combinatorics	combinatoric	NOUN
iajs-3405	105	4	2021	2021	NUM
iajs-3405	105	5	,	,	PUNCT
iajs-3405	105	6	37,1345–1355	37,1345–1355	NUM
iajs-3405	105	7	.	.	PUNCT
iajs-3405	106	1	https://doi.org/10.1007/s00373-021-02321-w	https://doi.org/10.1007/s00373-021-02321-w	NOUN
iajs-3405	106	2	.	.	PUNCT
iajs-3405	107	1	ihjpas	ihjpas	PROPN
iajs-3405	107	2	.	.	PUNCT
iajs-3405	108	1	2024	2024	NUM
iajs-3405	108	2	,	,	PUNCT
iajs-3405	108	3	37(4	37(4	PRON
iajs-3405	108	4	)	)	PUNCT
iajs-3405	108	5	406	406	NUM
iajs-3405	108	6	2	2	NUM
iajs-3405	108	7	.	.	X
iajs-3405	108	8	bhat	bhat	PROPN
iajs-3405	108	9	,	,	PUNCT
iajs-3405	108	10	v.k	v.k	PROPN
iajs-3405	108	11	;	;	PUNCT
iajs-3405	108	12	sharma	sharma	PROPN
iajs-3405	108	13	,	,	PUNCT
iajs-3405	108	14	k.	k.	PROPN
iajs-3405	108	15	on	on	ADP
iajs-3405	108	16	some	some	DET
iajs-3405	108	17	topological	topological	ADJ
iajs-3405	108	18	indices	index	NOUN
iajs-3405	108	19	for	for	ADP
iajs-3405	108	20	the	the	DET
iajs-3405	108	21	orbit	orbit	NOUN
iajs-3405	108	22	graph	graph	NOUN
iajs-3405	108	23	of	of	ADP
iajs-3405	108	24	dihedral	dihedral	ADJ
iajs-3405	108	25	groups	group	NOUN
iajs-3405	108	26	.	.	PUNCT
iajs-3405	109	1	journal	journal	NOUN
iajs-3405	109	2	of	of	ADP
iajs-3405	109	3	combinatorial	combinatorial	ADJ
iajs-3405	109	4	mathematics	mathematic	NOUN
iajs-3405	109	5	and	and	CCONJ
iajs-3405	109	6	combinatorial	combinatorial	ADJ
iajs-3405	109	7	computing	computing	NOUN
iajs-3405	109	8	2023	2023	NUM
iajs-3405	109	9	,	,	PUNCT
iajs-3405	109	10	117	117	NUM
iajs-3405	109	11	,	,	PUNCT
iajs-3405	109	12	195	195	NUM
iajs-3405	109	13	-	-	SYM
iajs-3405	109	14	208	208	NUM
iajs-3405	109	15	.	.	PUNCT
iajs-3405	109	16	https://doi.org/10.61091/jcmcc117-18	https://doi.org/10.61091/jcmcc117-18	NOUN
iajs-3405	109	17	.	.	PUNCT
iajs-3405	110	1	3	3	X
iajs-3405	110	2	.	.	X
iajs-3405	110	3	cameron	cameron	PROPN
iajs-3405	110	4	,	,	PUNCT
iajs-3405	110	5	p.	p.	PROPN
iajs-3405	110	6	j.	j.	PROPN
iajs-3405	110	7	;	;	PUNCT
iajs-3405	110	8	kuzma	kuzma	PROPN
iajs-3405	110	9	,	,	PUNCT
iajs-3405	110	10	b.	b.	PROPN
iajs-3405	110	11	between	between	ADP
iajs-3405	110	12	the	the	DET
iajs-3405	110	13	enhanced	enhanced	ADJ
iajs-3405	110	14	power	power	NOUN
iajs-3405	110	15	graph	graph	NOUN
iajs-3405	110	16	and	and	CCONJ
iajs-3405	110	17	the	the	DET
iajs-3405	110	18	commuting	commuting	NOUN
iajs-3405	110	19	graph	graph	NOUN
iajs-3405	110	20	.	.	PUNCT
iajs-3405	111	1	journal	journal	NOUN
iajs-3405	111	2	of	of	ADP
iajs-3405	111	3	graph	graph	NOUN
iajs-3405	111	4	theory	theory	NOUN
iajs-3405	111	5	,	,	PUNCT
iajs-3405	111	6	2023	2023	NUM
iajs-3405	111	7	,	,	PUNCT
iajs-3405	111	8	102(2	102(2	NUM
iajs-3405	111	9	)	)	PUNCT
iajs-3405	111	10	,	,	PUNCT
iajs-3405	111	11	295	295	NUM
iajs-3405	111	12	-	-	SYM
iajs-3405	111	13	303	303	NUM
iajs-3405	111	14	.	.	PUNCT
iajs-3405	112	1	https://doi.org/10.1002/jgt.22871	https://doi.org/10.1002/jgt.22871	PROPN
iajs-3405	112	2	.	.	PUNCT
iajs-3405	113	1	4	4	X
iajs-3405	113	2	.	.	X
iajs-3405	113	3	gaftan	gaftan	PROPN
iajs-3405	113	4	,	,	PUNCT
iajs-3405	113	5	a.m.	a.m.	ADV
iajs-3405	113	6	;	;	PUNCT
iajs-3405	113	7	mohammed	mohammed	PROPN
iajs-3405	113	8	,	,	PUNCT
iajs-3405	113	9	a.s	a.s	PROPN
iajs-3405	113	10	.	.	PROPN
iajs-3405	113	11	;	;	PUNCT
iajs-3405	113	12	subhi.o.h	subhi.o.h	NOUN
iajs-3405	113	13	.	.	PUNCT
iajs-3405	114	1	cryptography	cryptography	NOUN
iajs-3405	114	2	by	by	ADP
iajs-3405	114	3	using"hosoya"polynomials	using"hosoya"polynomial	NOUN
iajs-3405	114	4	for"graphs	for"graph	NOUN
iajs-3405	114	5	groups	group	NOUN
iajs-3405	114	6	of	of	ADP
iajs-3405	114	7	integer	integer	PROPN
iajs-3405	114	8	modulen	modulen	PROPN
iajs-3405	114	9	and"dihedral	and"dihedral	ADJ
iajs-3405	114	10	groups	group	NOUN
iajs-3405	114	11	with’immersion"property	with’immersion"property	NOUN
iajs-3405	114	12	.	.	PUNCT
iajs-3405	115	1	ibn	ibn	PROPN
iajs-3405	115	2	alhaitham	alhaitham	PROPN
iajs-3405	115	3	journal	journal	NOUN
iajs-3405	115	4	for	for	ADP
iajs-3405	115	5	pure	pure	ADJ
iajs-3405	115	6	and	and	CCONJ
iajs-3405	115	7	applied	applied	ADJ
iajs-3405	115	8	sciences	science	NOUN
iajs-3405	115	9	,	,	PUNCT
iajs-3405	115	10	2018	2018	NUM
iajs-3405	115	11	,	,	PUNCT
iajs-3405	115	12	31,151–159	31,151–159	NUM
iajs-3405	115	13	.	.	PUNCT
iajs-3405	116	1	https://doi.org/10.30526/31.3.2008	https://doi.org/10.30526/31.3.2008	NOUN
iajs-3405	116	2	.	.	PROPN
iajs-3405	117	1	5	5	NUM
iajs-3405	117	2	.	.	X
iajs-3405	117	3	hamdi	hamdi	PROPN
iajs-3405	117	4	,	,	PUNCT
iajs-3405	117	5	h.	h.	PROPN
iajs-3405	117	6	investigation	investigation	NOUN
iajs-3405	117	7	the	the	DET
iajs-3405	117	8	order	order	NOUN
iajs-3405	117	9	elements	element	VERB
iajs-3405	117	10	3	3	NUM
iajs-3405	117	11	in	in	ADP
iajs-3405	117	12	certain	certain	ADJ
iajs-3405	117	13	twisted	twisted	ADJ
iajs-3405	117	14	groups	group	NOUN
iajs-3405	117	15	of	of	ADP
iajs-3405	117	16	lie	lie	NOUN
iajs-3405	117	17	type	type	NOUN
iajs-3405	117	18	.	.	PUNCT
iajs-3405	118	1	italian	italian	ADJ
iajs-3405	118	2	journal	journal	NOUN
iajs-3405	118	3	of	of	ADP
iajs-3405	118	4	pure	pure	ADJ
iajs-3405	118	5	and	and	CCONJ
iajs-3405	118	6	applied	applied	ADJ
iajs-3405	118	7	mathematics	mathematic	NOUN
iajs-3405	118	8	,	,	PUNCT
iajs-3405	118	9	2022	2022	NUM
iajs-3405	118	10	,	,	PUNCT
iajs-3405	118	11	48	48	NUM
iajs-3405	118	12	,	,	PUNCT
iajs-3405	118	13	621	621	NUM
iajs-3405	118	14	-	-	SYM
iajs-3405	118	15	629	629	NUM
iajs-3405	118	16	.	.	PUNCT
iajs-3405	118	17	https://ijpam.uniud.it/onlineissue/202248/48%20hamdi.pdf	https://ijpam.uniud.it/onlineissue/202248/48%20hamdi.pdf	NOUN
iajs-3405	118	18	.	.	PUNCT
iajs-3405	119	1	6	6	X
iajs-3405	119	2	.	.	X
iajs-3405	119	3	khudhur	khudhur	PROPN
iajs-3405	119	4	,	,	PUNCT
iajs-3405	119	5	p.m.	p.m.	NOUN
iajs-3405	119	6	;	;	PUNCT
iajs-3405	119	7	haji	haji	PROPN
iajs-3405	119	8	,	,	PUNCT
iajs-3405	119	9	r.r	r.r	PROPN
iajs-3405	119	10	.	.	PROPN
iajs-3405	119	11	;	;	PUNCT
iajs-3405	119	12	khasraw	khasraw	PROPN
iajs-3405	119	13	,	,	PUNCT
iajs-3405	119	14	s.m	s.m	PROPN
iajs-3405	119	15	.	.	PUNCT
iajs-3405	120	1	the	the	DET
iajs-3405	120	2	intersection	intersection	NOUN
iajs-3405	120	3	graph	graph	NOUN
iajs-3405	120	4	of	of	ADP
iajs-3405	120	5	subgroups	subgroup	NOUN
iajs-3405	120	6	of	of	ADP
iajs-3405	120	7	the	the	DET
iajs-3405	120	8	dihedral	dihedral	ADJ
iajs-3405	120	9	group	group	NOUN
iajs-3405	120	10	of	of	ADP
iajs-3405	120	11	order	order	NOUN
iajs-3405	120	12	2pq	2pq	NOUN
iajs-3405	120	13	.	.	PUNCT
iajs-3405	121	1	iraqi	iraqi	ADJ
iajs-3405	121	2	journal	journal	PROPN
iajs-3405	121	3	of	of	ADP
iajs-3405	121	4	sciences	science	NOUN
iajs-3405	121	5	,	,	PUNCT
iajs-3405	121	6	2021	2021	NUM
iajs-3405	121	7	,	,	PUNCT
iajs-3405	121	8	62	62	NUM
iajs-3405	121	9	,	,	PUNCT
iajs-3405	121	10	4923–4929	4923–4929	NUM
iajs-3405	121	11	.	.	PUNCT
iajs-3405	121	12	https://doi.org/10.24996/ijs.2021.62.12.30	https://doi.org/10.24996/ijs.2021.62.12.30	PROPN
iajs-3405	121	13	.	.	PUNCT
iajs-3405	122	1	7	7	X
iajs-3405	122	2	.	.	NUM
iajs-3405	122	3	konstantinova	konstantinova	PROPN
iajs-3405	122	4	,	,	PUNCT
iajs-3405	122	5	e.v	e.v	PROPN
iajs-3405	122	6	.	.	PROPN
iajs-3405	122	7	;	;	PUNCT
iajs-3405	122	8	kravchuk	kravchuk	PROPN
iajs-3405	122	9	,	,	PUNCT
iajs-3405	122	10	a.	a.	NOUN
iajs-3405	122	11	spectrum	spectrum	NOUN
iajs-3405	122	12	of	of	ADP
iajs-3405	122	13	the	the	DET
iajs-3405	122	14	transposition	transposition	NOUN
iajs-3405	122	15	graph	graph	NOUN
iajs-3405	122	16	.	.	PUNCT
iajs-3405	123	1	linear	linear	ADJ
iajs-3405	123	2	algebra	algebra	NOUN
iajs-3405	123	3	and	and	CCONJ
iajs-3405	123	4	its	its	PRON
iajs-3405	123	5	applications	application	NOUN
iajs-3405	123	6	,	,	PUNCT
iajs-3405	123	7	2022	2022	NUM
iajs-3405	123	8	,	,	PUNCT
iajs-3405	123	9	654	654	NUM
iajs-3405	123	10	,	,	PUNCT
iajs-3405	123	11	379	379	NUM
iajs-3405	123	12	–	–	PUNCT
iajs-3405	123	13	389	389	NUM
iajs-3405	123	14	.	.	PUNCT
iajs-3405	124	1	https://doi.org/10.1016/j.laa.2022.08.033	https://doi.org/10.1016/j.laa.2022.08.033	NOUN
iajs-3405	124	2	.	.	PUNCT
iajs-3405	125	1	8	8	NUM
iajs-3405	125	2	.	.	PUNCT
iajs-3405	126	1	kumari	kumari	PROPN
iajs-3405	126	2	,	,	PUNCT
iajs-3405	126	3	m.l	m.l	PROPN
iajs-3405	126	4	.	.	PROPN
iajs-3405	126	5	;	;	PUNCT
iajs-3405	126	6	pandiselvi	pandiselvi	PROPN
iajs-3405	126	7	,	,	PUNCT
iajs-3405	126	8	l.	l.	PROPN
iajs-3405	126	9	;	;	PUNCT
iajs-3405	126	10	palani	palani	PROPN
iajs-3405	126	11	,	,	PUNCT
iajs-3405	126	12	k.	k.	PROPN
iajs-3405	126	13	quotient	quotient	VERB
iajs-3405	126	14	energy	energy	NOUN
iajs-3405	126	15	of	of	ADP
iajs-3405	126	16	zero	zero	NUM
iajs-3405	126	17	divisor	divisor	NOUN
iajs-3405	126	18	graphs	graph	NOUN
iajs-3405	126	19	and	and	CCONJ
iajs-3405	126	20	identity	identity	NOUN
iajs-3405	126	21	graphs	graph	NOUN
iajs-3405	126	22	.	.	PUNCT
iajs-3405	127	1	baghdad	baghdad	PROPN
iajs-3405	127	2	sci.j	sci.j	NUM
iajs-3405	127	3	,	,	PUNCT
iajs-3405	127	4	2023	2023	NUM
iajs-3405	127	5	,	,	PUNCT
iajs-3405	127	6	20	20	NUM
iajs-3405	127	7	,	,	PUNCT
iajs-3405	127	8	0277	0277	NUM
iajs-3405	127	9	.	.	PUNCT
iajs-3405	128	1	https://doi.org/10.21123/bsj.2023.8408	https://doi.org/10.21123/bsj.2023.8408	ADJ
iajs-3405	128	2	.	.	PROPN
iajs-3405	128	3	9	9	NUM
iajs-3405	128	4	.	.	X
iajs-3405	128	5	nawaf	nawaf	PROPN
iajs-3405	128	6	,	,	PUNCT
iajs-3405	128	7	a.	a.	PROPN
iajs-3405	128	8	j.	j.	PROPN
iajs-3405	128	9	;	;	PUNCT
iajs-3405	128	10	mohammad	mohammad	PROPN
iajs-3405	128	11	,	,	PUNCT
iajs-3405	128	12	a.	a.	PROPN
iajs-3405	128	13	s.	s.	PROPN
iajs-3405	129	1	some	some	DET
iajs-3405	129	2	topological	topological	ADJ
iajs-3405	129	3	and	and	CCONJ
iajs-3405	129	4	polynomial	polynomial	ADJ
iajs-3405	129	5	indices	index	NOUN
iajs-3405	129	6	(	(	PUNCT
iajs-3405	129	7	hosoya	hosoya	NOUN
iajs-3405	129	8	and	and	CCONJ
iajs-3405	129	9	schultz	schultz	PROPN
iajs-3405	129	10	)	)	PUNCT
iajs-3405	129	11	for	for	ADP
iajs-3405	129	12	the	the	DET
iajs-3405	129	13	intersection	intersection	NOUN
iajs-3405	129	14	graph	graph	NOUN
iajs-3405	129	15	of	of	ADP
iajs-3405	129	16	the	the	DET
iajs-3405	129	17	subgroup	subgroup	NOUN
iajs-3405	129	18	ofã€	ofã€	PROPN
iajs-3405	129	19	–	–	PUNCT
iajs-3405	129	20	z〗_(r^n	z〗_(r^n	NOUN
iajs-3405	129	21	)	)	PUNCT
iajs-3405	129	22	.	.	PUNCT
iajs-3405	129	23	)	)	PUNCT
iajs-3405	129	24	.	.	PUNCT
iajs-3405	130	1	ibn	ibn	PROPN
iajs-3405	130	2	al	al	PROPN
iajs-3405	130	3	-	-	PUNCT
iajs-3405	130	4	haitham	haitham	PROPN
iajs-3405	130	5	journal	journal	PROPN
iajs-3405	130	6	for	for	ADP
iajs-3405	130	7	pure	pure	ADJ
iajs-3405	130	8	and	and	CCONJ
iajs-3405	130	9	applied	applied	ADJ
iajs-3405	130	10	sciences	science	NOUN
iajs-3405	130	11	,	,	PUNCT
iajs-3405	130	12	2021	2021	NUM
iajs-3405	130	13	,	,	PUNCT
iajs-3405	130	14	34	34	NUM
iajs-3405	130	15	,	,	PUNCT
iajs-3405	130	16	68	68	NUM
iajs-3405	130	17	-	-	SYM
iajs-3405	130	18	77	77	NUM
iajs-3405	130	19	.	.	PUNCT
iajs-3405	131	1	https://doi.org/10.30526/34.4.2704	https://doi.org/10.30526/34.4.2704	PROPN
iajs-3405	131	2	.	.	PROPN
iajs-3405	131	3	10	10	NUM
iajs-3405	131	4	.	.	PUNCT
iajs-3405	132	1	neamah	neamah	PROPN
iajs-3405	132	2	,	,	PUNCT
iajs-3405	132	3	a.	a.	NOUN
iajs-3405	132	4	a.	a.	PROPN
iajs-3405	132	5	;	;	PUNCT
iajs-3405	132	6	majeed	majeed	PROPN
iajs-3405	132	7	,	,	PUNCT
iajs-3405	132	8	a.	a.	PROPN
iajs-3405	132	9	h.	h.	PROPN
iajs-3405	132	10	;	;	PUNCT
iajs-3405	133	1	erfanian	erfanian	ADJ
iajs-3405	133	2	,	,	PUNCT
iajs-3405	133	3	a.	a.	NOUN
iajs-3405	133	4	the	the	DET
iajs-3405	133	5	generalized	generalize	VERB
iajs-3405	133	6	cayley	cayley	ADJ
iajs-3405	133	7	graph	graph	NOUN
iajs-3405	133	8	of	of	ADP
iajs-3405	133	9	complete	complete	ADJ
iajs-3405	133	10	graph	graph	NOUN
iajs-3405	133	11	kn	kn	PROPN
iajs-3405	133	12	and	and	CCONJ
iajs-3405	133	13	complete	complete	ADJ
iajs-3405	133	14	multipartite	multipartite	ADJ
iajs-3405	133	15	graphs	graph	NOUN
iajs-3405	133	16	k	k	X
iajs-3405	133	17	(	(	PUNCT
iajs-3405	133	18	n	n	CCONJ
iajs-3405	133	19	,	,	PUNCT
iajs-3405	133	20	n	n	CCONJ
iajs-3405	133	21	)	)	PUNCT
iajs-3405	133	22	and	and	CCONJ
iajs-3405	133	23	k(n	k(n	PROPN
iajs-3405	133	24	,	,	PUNCT
iajs-3405	133	25	n	n	CCONJ
iajs-3405	133	26	,	,	PUNCT
iajs-3405	133	27	n	n	CCONJ
iajs-3405	133	28	)	)	PUNCT
iajs-3405	133	29	.	.	PUNCT
iajs-3405	134	1	iraqi	iraqi	ADJ
iajs-3405	134	2	journal	journal	PROPN
iajs-3405	134	3	of	of	ADP
iajs-3405	134	4	science	science	NOUN
iajs-3405	134	5	,	,	PUNCT
iajs-3405	134	6	2022	2022	NUM
iajs-3405	134	7	,	,	PUNCT
iajs-3405	134	8	63(7	63(7	NUM
iajs-3405	134	9	)	)	PUNCT
iajs-3405	134	10	,	,	PUNCT
iajs-3405	134	11	3103–3110	3103–3110	NUM
iajs-3405	134	12	.	.	PUNCT
iajs-3405	135	1	https://doi.org/10.24996/ijs.2022.63.7.31	https://doi.org/10.24996/ijs.2022.63.7.31	PROPN
iajs-3405	135	2	.	.	PUNCT
iajs-3405	136	1	11	11	NUM
iajs-3405	136	2	.	.	X
iajs-3405	137	1	newman	newman	PROPN
iajs-3405	137	2	,	,	PUNCT
iajs-3405	137	3	a.	a.	NOUN
iajs-3405	137	4	abelian	abelian	PROPN
iajs-3405	137	5	groups	group	NOUN
iajs-3405	137	6	from	from	ADP
iajs-3405	137	7	random	random	ADJ
iajs-3405	137	8	hypergraphs	hypergraph	NOUN
iajs-3405	137	9	.	.	PUNCT
iajs-3405	138	1	combinatorics	combinatoric	NOUN
iajs-3405	138	2	probability	probability	PROPN
iajs-3405	138	3	computing	computing	PROPN
iajs-3405	138	4	,	,	PUNCT
iajs-3405	138	5	cambridge	cambridge	PROPN
iajs-3405	138	6	university	university	PROPN
iajs-3405	138	7	press	press	NOUN
iajs-3405	138	8	,	,	PUNCT
iajs-3405	138	9	2023	2023	NUM
iajs-3405	138	10	,	,	PUNCT
iajs-3405	138	11	32	32	NUM
iajs-3405	138	12	,	,	PUNCT
iajs-3405	138	13	654	654	NUM
iajs-3405	138	14	–	–	PUNCT
iajs-3405	138	15	664	664	NUM
iajs-3405	138	16	.	.	PUNCT
iajs-3405	138	17	https://doi.org/10.1017/s0963548323000056	https://doi.org/10.1017/s0963548323000056	NUM
iajs-3405	138	18	.	.	PUNCT
iajs-3405	138	19	12	12	NUM
iajs-3405	138	20	.	.	PUNCT
iajs-3405	139	1	romdhini	romdhini	PROPN
iajs-3405	139	2	,	,	PUNCT
iajs-3405	139	3	m.	m.	NOUN
iajs-3405	139	4	u.	u.	PROPN
iajs-3405	139	5	;	;	PUNCT
iajs-3405	139	6	nawawi	nawawi	PROPN
iajs-3405	139	7	,	,	PUNCT
iajs-3405	139	8	a.	a.	NOUN
iajs-3405	139	9	;	;	PUNCT
iajs-3405	139	10	chen	chen	PROPN
iajs-3405	139	11	,	,	PUNCT
iajs-3405	139	12	c.	c.	PROPN
iajs-3405	139	13	y.	y.	PROPN
iajs-3405	139	14	neighbors	neighbor	NOUN
iajs-3405	139	15	degree	degree	NOUN
iajs-3405	139	16	sum	sum	NOUN
iajs-3405	139	17	energy	energy	NOUN
iajs-3405	139	18	of	of	ADP
iajs-3405	139	19	commuting	commute	VERB
iajs-3405	139	20	and	and	CCONJ
iajs-3405	139	21	noncommuting	noncommute	VERB
iajs-3405	139	22	graphs	graph	NOUN
iajs-3405	139	23	for	for	ADP
iajs-3405	139	24	dihedral	dihedral	ADJ
iajs-3405	139	25	groups	group	NOUN
iajs-3405	139	26	.	.	PUNCT
iajs-3405	140	1	malaysian	malaysian	ADJ
iajs-3405	140	2	journal	journal	PROPN
iajs-3405	140	3	of	of	ADP
iajs-3405	140	4	mathematical	mathematical	ADJ
iajs-3405	140	5	sciences	science	NOUN
iajs-3405	140	6	,	,	PUNCT
iajs-3405	140	7	2023	2023	NUM
iajs-3405	140	8	,	,	PUNCT
iajs-3405	140	9	17(1	17(1	NUM
iajs-3405	140	10	)	)	PUNCT
iajs-3405	140	11	,	,	PUNCT
iajs-3405	140	12	53–65	53–65	NUM
iajs-3405	140	13	.	.	PUNCT
iajs-3405	141	1	https://doi.org/10.47836/mjms.17.1.05	https://doi.org/10.47836/mjms.17.1.05	NOUN
iajs-3405	141	2	.	.	PUNCT
iajs-3405	142	1	13	13	NUM
iajs-3405	142	2	.	.	PUNCT
iajs-3405	143	1	roslly	roslly	ADV
iajs-3405	143	2	,	,	PUNCT
iajs-3405	143	3	s.	s.	PROPN
iajs-3405	143	4	r.	r.	PROPN
iajs-3405	143	5	d.	d.	PROPN
iajs-3405	143	6	;	;	PUNCT
iajs-3405	143	7	ab	ab	PROPN
iajs-3405	143	8	halem	halem	PROPN
iajs-3405	143	9	,	,	PUNCT
iajs-3405	143	10	n.	n.	PROPN
iajs-3405	143	11	f.	f.	PROPN
iajs-3405	143	12	a.	a.	PROPN
iajs-3405	143	13	z.	z.	PROPN
iajs-3405	143	14	;	;	PUNCT
iajs-3405	143	15	zailani	zailani	NOUN
iajs-3405	143	16	,	,	PUNCT
iajs-3405	143	17	n.	n.	PROPN
iajs-3405	143	18	s.	s.	PROPN
iajs-3405	143	19	s.	s.	PROPN
iajs-3405	143	20	;	;	PUNCT
iajs-3405	143	21	alimon	alimon	PROPN
iajs-3405	143	22	,	,	PUNCT
iajs-3405	143	23	n.	n.	PROPN
iajs-3405	143	24	i.	i.	PROPN
iajs-3405	143	25	;	;	PUNCT
iajs-3405	143	26	mohammad	mohammad	PROPN
iajs-3405	143	27	,	,	PUNCT
iajs-3405	143	28	s.	s.	PROPN
iajs-3405	143	29	a.	a.	PROPN
iajs-3405	143	30	generalization	generalization	NOUN
iajs-3405	143	31	of	of	ADP
iajs-3405	143	32	randic	randic	ADJ
iajs-3405	143	33	́	́	PROPN
iajs-3405	143	34	index	index	NOUN
iajs-3405	143	35	of	of	ADP
iajs-3405	143	36	the	the	DET
iajs-3405	143	37	non	non	ADJ
iajs-3405	143	38	-	-	ADJ
iajs-3405	143	39	commuting	commuting	ADJ
iajs-3405	143	40	graph	graph	NOUN
iajs-3405	143	41	for	for	ADP
iajs-3405	143	42	some	some	DET
iajs-3405	143	43	finite	finite	ADJ
iajs-3405	143	44	groups	group	NOUN
iajs-3405	143	45	.	.	PUNCT
iajs-3405	144	1	malaysian	malaysian	ADJ
iajs-3405	144	2	journal	journal	PROPN
iajs-3405	144	3	of	of	ADP
iajs-3405	144	4	fundamental	fundamental	ADJ
iajs-3405	144	5	and	and	CCONJ
iajs-3405	144	6	applied	applied	ADJ
iajs-3405	144	7	sciences	science	NOUN
iajs-3405	144	8	,	,	PUNCT
iajs-3405	144	9	2023	2023	NUM
iajs-3405	144	10	,	,	PUNCT
iajs-3405	144	11	19(5	19(5	NUM
iajs-3405	144	12	)	)	PUNCT
iajs-3405	144	13	,	,	PUNCT
iajs-3405	144	14	762	762	NUM
iajs-3405	144	15	-	-	SYM
iajs-3405	144	16	768	768	NUM
iajs-3405	144	17	.	.	PUNCT
iajs-3405	145	1	https://doi.org/10.11113/mjfas.v19n5.3047	https://doi.org/10.11113/mjfas.v19n5.3047	NOUN
iajs-3405	145	2	.	.	PUNCT
iajs-3405	146	1	14	14	NUM
iajs-3405	146	2	.	.	X
iajs-3405	146	3	tolue	tolue	NOUN
iajs-3405	146	4	,	,	PUNCT
iajs-3405	146	5	b.	b.	PROPN
iajs-3405	147	1	the	the	DET
iajs-3405	147	2	twin	twin	ADJ
iajs-3405	147	3	non	non	ADJ
iajs-3405	147	4	-	-	ADJ
iajs-3405	147	5	commuting	commuting	ADJ
iajs-3405	147	6	graph	graph	NOUN
iajs-3405	147	7	of	of	ADP
iajs-3405	147	8	a	a	DET
iajs-3405	147	9	group	group	NOUN
iajs-3405	147	10	.	.	PUNCT
iajs-3405	148	1	rendiconti	rendiconti	PROPN
iajs-3405	148	2	del	del	PROPN
iajs-3405	148	3	circolo	circolo	PROPN
iajs-3405	148	4	matematico	matematico	NOUN
iajs-3405	148	5	di	di	PROPN
iajs-3405	148	6	palermo	palermo	PROPN
iajs-3405	148	7	series	series	PROPN
iajs-3405	148	8	2	2	NUM
iajs-3405	148	9	2020	2020	NUM
iajs-3405	148	10	,	,	PUNCT
iajs-3405	148	11	69(2	69(2	NOUN
iajs-3405	148	12	)	)	PUNCT
iajs-3405	148	13	,	,	PUNCT
iajs-3405	148	14	591–599	591–599	NUM
iajs-3405	148	15	.	.	PUNCT
iajs-3405	149	1	https://doi.org/10.1007/s12215-019-00421-4	https://doi.org/10.1007/s12215-019-00421-4	NUM
iajs-3405	149	2	.	.	PUNCT
iajs-3405	150	1	15	15	NUM
iajs-3405	150	2	.	.	PUNCT
iajs-3405	151	1	devillers	deviller	NOUN
iajs-3405	151	2	,	,	PUNCT
iajs-3405	151	3	a.	a.	NOUN
iajs-3405	151	4	;	;	PUNCT
iajs-3405	151	5	giudici	giudici	NOUN
iajs-3405	151	6	,	,	PUNCT
iajs-3405	151	7	m.	m.	NOUN
iajs-3405	151	8	involution	involution	NOUN
iajs-3405	151	9	graphs	graph	NOUN
iajs-3405	151	10	where	where	SCONJ
iajs-3405	151	11	the	the	DET
iajs-3405	151	12	product	product	NOUN
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iajs-3405	152	13	doi:10.1017	doi:10.1017	NOUN
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iajs-3405	159	8	,	,	PUNCT
iajs-3405	159	9	331–240	331–240	NUM
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iajs-3405	160	1	https://doi.org/10.24996/ijs.2023.64.1.30	https://doi.org/10.24996/ijs.2023.64.1.30	PROPN
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iajs-3405	171	13	.	.	PUNCT
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iajs-3405	173	5	1	1	NUM
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iajs-3405	174	2	.	.	X
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iajs-3405	174	5	r.	r.	PROPN
iajs-3405	174	6	a.	a.	PROPN
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iajs-3405	174	8	walsh	walsh	PROPN
iajs-3405	174	9	.p	.p	PROPN
iajs-3405	174	10	.	.	PUNCT
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iajs-3405	174	21	;	;	PUNCT
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iajs-3405	175	4	online	online	ADV
iajs-3405	175	5	:	:	PUNCT
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iajs-3405	176	1	http://brauer.maths/	http://brauer.maths/	PROPN