id	sid	tid	token	lemma	pos
ejpam-4863	1	1	european	european	PROPN
ejpam-4863	1	2	journal	journal	PROPN
ejpam-4863	1	3	of	of	ADP
ejpam-4863	1	4	pure	pure	ADJ
ejpam-4863	1	5	and	and	CCONJ
ejpam-4863	1	6	applied	apply	VERB
ejpam-4863	1	7	mathematics	mathematic	NOUN
ejpam-4863	1	8	vol	vol	NOUN
ejpam-4863	1	9	.	.	PUNCT
ejpam-4863	2	1	16	16	NUM
ejpam-4863	2	2	,	,	PUNCT
ejpam-4863	2	3	no	no	INTJ
ejpam-4863	2	4	.	.	NOUN
ejpam-4863	2	5	3	3	NUM
ejpam-4863	2	6	,	,	PUNCT
ejpam-4863	2	7	2023	2023	NUM
ejpam-4863	2	8	,	,	PUNCT
ejpam-4863	2	9	1894	1894	NUM
ejpam-4863	2	10	-	-	SYM
ejpam-4863	2	11	1901	1901	NUM
ejpam-4863	2	12	issn	issn	PROPN
ejpam-4863	2	13	1307	1307	NUM
ejpam-4863	2	14	-	-	SYM
ejpam-4863	2	15	5543	5543	NUM
ejpam-4863	2	16	–	–	PUNCT
ejpam-4863	2	17	ejpam.com	ejpam.com	X
ejpam-4863	2	18	published	publish	VERB
ejpam-4863	2	19	by	by	ADP
ejpam-4863	2	20	new	new	PROPN
ejpam-4863	2	21	york	york	PROPN
ejpam-4863	2	22	business	business	PROPN
ejpam-4863	2	23	global	global	PROPN
ejpam-4863	3	1	the	the	DET
ejpam-4863	3	2	generator	generator	NOUN
ejpam-4863	3	3	graph	graph	NOUN
ejpam-4863	3	4	of	of	ADP
ejpam-4863	3	5	a	a	DET
ejpam-4863	3	6	group	group	NOUN
ejpam-4863	3	7	teresa	teresa	PROPN
ejpam-4863	3	8	l.	l.	PROPN
ejpam-4863	3	9	tacbobo	tacbobo	PROPN
ejpam-4863	3	10	mathematics	mathematics	PROPN
ejpam-4863	3	11	department	department	PROPN
ejpam-4863	3	12	,	,	PUNCT
ejpam-4863	3	13	college	college	NOUN
ejpam-4863	3	14	of	of	ADP
ejpam-4863	3	15	arts	art	NOUN
ejpam-4863	3	16	and	and	CCONJ
ejpam-4863	3	17	sciences	sciences	PROPN
ejpam-4863	3	18	,	,	PUNCT
ejpam-4863	3	19	bukidnon	bukidnon	NOUN
ejpam-4863	3	20	state	state	PROPN
ejpam-4863	3	21	university	university	PROPN
ejpam-4863	3	22	,	,	PUNCT
ejpam-4863	3	23	malaybalay	malaybalay	NOUN
ejpam-4863	3	24	city	city	NOUN
ejpam-4863	3	25	,	,	PUNCT
ejpam-4863	3	26	bukidnon	bukidnon	NOUN
ejpam-4863	3	27	,	,	PUNCT
ejpam-4863	3	28	philippines	philippine	NOUN
ejpam-4863	3	29	abstract	abstract	ADJ
ejpam-4863	3	30	.	.	PUNCT
ejpam-4863	4	1	this	this	DET
ejpam-4863	4	2	paper	paper	NOUN
ejpam-4863	4	3	presents	present	VERB
ejpam-4863	4	4	a	a	DET
ejpam-4863	4	5	way	way	NOUN
ejpam-4863	4	6	to	to	PART
ejpam-4863	4	7	represent	represent	VERB
ejpam-4863	4	8	a	a	DET
ejpam-4863	4	9	group	group	NOUN
ejpam-4863	4	10	using	use	VERB
ejpam-4863	4	11	a	a	DET
ejpam-4863	4	12	graph	graph	NOUN
ejpam-4863	4	13	,	,	PUNCT
ejpam-4863	4	14	which	which	PRON
ejpam-4863	4	15	involves	involve	VERB
ejpam-4863	4	16	the	the	DET
ejpam-4863	4	17	concept	concept	NOUN
ejpam-4863	4	18	of	of	ADP
ejpam-4863	4	19	a	a	DET
ejpam-4863	4	20	generator	generator	NOUN
ejpam-4863	4	21	element	element	NOUN
ejpam-4863	4	22	of	of	ADP
ejpam-4863	4	23	a	a	DET
ejpam-4863	4	24	group	group	NOUN
ejpam-4863	4	25	.	.	PUNCT
ejpam-4863	5	1	the	the	DET
ejpam-4863	5	2	graph	graph	NOUN
ejpam-4863	5	3	representing	represent	VERB
ejpam-4863	5	4	a	a	DET
ejpam-4863	5	5	group	group	NOUN
ejpam-4863	5	6	is	be	AUX
ejpam-4863	5	7	called	call	VERB
ejpam-4863	5	8	the	the	DET
ejpam-4863	5	9	generator	generator	NOUN
ejpam-4863	5	10	graph	graph	NOUN
ejpam-4863	5	11	.	.	PUNCT
ejpam-4863	6	1	in	in	ADP
ejpam-4863	6	2	the	the	DET
ejpam-4863	6	3	generator	generator	NOUN
ejpam-4863	6	4	graph	graph	NOUN
ejpam-4863	6	5	,	,	PUNCT
ejpam-4863	6	6	the	the	DET
ejpam-4863	6	7	vertices	vertex	NOUN
ejpam-4863	6	8	correspond	correspond	VERB
ejpam-4863	6	9	to	to	ADP
ejpam-4863	6	10	the	the	DET
ejpam-4863	6	11	elements	element	NOUN
ejpam-4863	6	12	of	of	ADP
ejpam-4863	6	13	the	the	DET
ejpam-4863	6	14	group	group	NOUN
ejpam-4863	6	15	,	,	PUNCT
ejpam-4863	6	16	and	and	CCONJ
ejpam-4863	6	17	two	two	NUM
ejpam-4863	6	18	vertices	vertex	NOUN
ejpam-4863	6	19	,	,	PUNCT
ejpam-4863	6	20	x	x	PUNCT
ejpam-4863	6	21	and	and	CCONJ
ejpam-4863	6	22	y	y	PROPN
ejpam-4863	6	23	,	,	PUNCT
ejpam-4863	6	24	are	be	AUX
ejpam-4863	6	25	connected	connect	VERB
ejpam-4863	6	26	by	by	ADP
ejpam-4863	6	27	an	an	DET
ejpam-4863	6	28	edge	edge	NOUN
ejpam-4863	6	29	if	if	SCONJ
ejpam-4863	6	30	either	either	CCONJ
ejpam-4863	6	31	x	x	SYM
ejpam-4863	6	32	or	or	CCONJ
ejpam-4863	6	33	y	y	PROPN
ejpam-4863	6	34	serves	serve	VERB
ejpam-4863	6	35	as	as	ADP
ejpam-4863	6	36	a	a	DET
ejpam-4863	6	37	generator	generator	NOUN
ejpam-4863	6	38	for	for	ADP
ejpam-4863	6	39	the	the	DET
ejpam-4863	6	40	group	group	NOUN
ejpam-4863	6	41	.	.	PUNCT
ejpam-4863	7	1	the	the	DET
ejpam-4863	7	2	paper	paper	NOUN
ejpam-4863	7	3	investigates	investigate	VERB
ejpam-4863	7	4	some	some	DET
ejpam-4863	7	5	properties	property	NOUN
ejpam-4863	7	6	of	of	ADP
ejpam-4863	7	7	these	these	DET
ejpam-4863	7	8	generator	generator	NOUN
ejpam-4863	7	9	graphs	graph	NOUN
ejpam-4863	7	10	and	and	CCONJ
ejpam-4863	7	11	obtains	obtain	VERB
ejpam-4863	7	12	the	the	DET
ejpam-4863	7	13	generator	generator	NOUN
ejpam-4863	7	14	graphs	graph	NOUN
ejpam-4863	7	15	for	for	ADP
ejpam-4863	7	16	specific	specific	ADJ
ejpam-4863	7	17	groups	group	NOUN
ejpam-4863	7	18	.	.	PUNCT
ejpam-4863	8	1	additionally	additionally	ADV
ejpam-4863	8	2	,	,	PUNCT
ejpam-4863	8	3	it	it	PRON
ejpam-4863	8	4	explores	explore	VERB
ejpam-4863	8	5	the	the	DET
ejpam-4863	8	6	relationship	relationship	NOUN
ejpam-4863	8	7	between	between	ADP
ejpam-4863	8	8	the	the	DET
ejpam-4863	8	9	generator	generator	NOUN
ejpam-4863	8	10	graph	graph	NOUN
ejpam-4863	8	11	of	of	ADP
ejpam-4863	8	12	a	a	DET
ejpam-4863	8	13	group	group	NOUN
ejpam-4863	8	14	and	and	CCONJ
ejpam-4863	8	15	the	the	DET
ejpam-4863	8	16	generating	generate	VERB
ejpam-4863	8	17	graph	graph	NOUN
ejpam-4863	8	18	introduced	introduce	VERB
ejpam-4863	8	19	by	by	ADP
ejpam-4863	8	20	lucchini	lucchini	PROPN
ejpam-4863	8	21	et	et	PROPN
ejpam-4863	8	22	al	al	PROPN
ejpam-4863	8	23	.	.	PROPN
ejpam-4863	9	1	in	in	ADP
ejpam-4863	9	2	their	their	PRON
ejpam-4863	9	3	work	work	NOUN
ejpam-4863	9	4	[	[	X
ejpam-4863	9	5	7	7	NUM
ejpam-4863	9	6	]	]	PUNCT
ejpam-4863	9	7	.	.	PUNCT
ejpam-4863	10	1	2020	2020	NUM
ejpam-4863	10	2	mathematics	mathematic	NOUN
ejpam-4863	10	3	subject	subject	NOUN
ejpam-4863	10	4	classifications	classification	NOUN
ejpam-4863	10	5	:	:	PUNCT
ejpam-4863	10	6	05c25	05c25	NUM
ejpam-4863	10	7	key	key	ADJ
ejpam-4863	10	8	words	word	NOUN
ejpam-4863	10	9	and	and	CCONJ
ejpam-4863	10	10	phrases	phrase	NOUN
ejpam-4863	10	11	:	:	PUNCT
ejpam-4863	10	12	graph	graph	NOUN
ejpam-4863	10	13	,	,	PUNCT
ejpam-4863	10	14	group	group	NOUN
ejpam-4863	10	15	,	,	PUNCT
ejpam-4863	10	16	generator	generator	NOUN
ejpam-4863	10	17	graph	graph	NOUN
ejpam-4863	10	18	,	,	PUNCT
ejpam-4863	10	19	generating	generating	NOUN
ejpam-4863	10	20	graph	graph	NOUN
ejpam-4863	10	21	1	1	NUM
ejpam-4863	10	22	.	.	PUNCT
ejpam-4863	10	23	introduction	introduction	NOUN
ejpam-4863	10	24	in	in	ADP
ejpam-4863	10	25	graph	graph	NOUN
ejpam-4863	10	26	theory	theory	NOUN
ejpam-4863	10	27	,	,	PUNCT
ejpam-4863	10	28	a	a	DET
ejpam-4863	10	29	graph	graph	NOUN
ejpam-4863	10	30	is	be	AUX
ejpam-4863	10	31	a	a	DET
ejpam-4863	10	32	collection	collection	NOUN
ejpam-4863	10	33	of	of	ADP
ejpam-4863	10	34	points	point	NOUN
ejpam-4863	10	35	called	call	VERB
ejpam-4863	10	36	vertices	vertex	NOUN
ejpam-4863	10	37	,	,	PUNCT
ejpam-4863	10	38	and	and	CCONJ
ejpam-4863	10	39	edges	edge	NOUN
ejpam-4863	10	40	that	that	PRON
ejpam-4863	10	41	connect	connect	VERB
ejpam-4863	10	42	the	the	DET
ejpam-4863	10	43	vertices	vertex	NOUN
ejpam-4863	10	44	.	.	PUNCT
ejpam-4863	11	1	it	it	PRON
ejpam-4863	11	2	is	be	AUX
ejpam-4863	11	3	widely	widely	ADV
ejpam-4863	11	4	known	know	VERB
ejpam-4863	11	5	for	for	ADP
ejpam-4863	11	6	its	its	PRON
ejpam-4863	11	7	applications	application	NOUN
ejpam-4863	11	8	in	in	ADP
ejpam-4863	11	9	networks	network	NOUN
ejpam-4863	11	10	such	such	ADJ
ejpam-4863	11	11	as	as	ADP
ejpam-4863	11	12	facebook	facebook	PROPN
ejpam-4863	11	13	.	.	PUNCT
ejpam-4863	12	1	graphs	graph	NOUN
ejpam-4863	12	2	can	can	AUX
ejpam-4863	12	3	be	be	AUX
ejpam-4863	12	4	used	use	VERB
ejpam-4863	12	5	to	to	PART
ejpam-4863	12	6	model	model	VERB
ejpam-4863	12	7	relationships	relationship	NOUN
ejpam-4863	12	8	or	or	CCONJ
ejpam-4863	12	9	connections	connection	NOUN
ejpam-4863	12	10	between	between	ADP
ejpam-4863	12	11	objects	object	NOUN
ejpam-4863	12	12	,	,	PUNCT
ejpam-4863	12	13	describe	describe	VERB
ejpam-4863	12	14	events	event	NOUN
ejpam-4863	12	15	and	and	CCONJ
ejpam-4863	12	16	even	even	ADV
ejpam-4863	12	17	in	in	ADP
ejpam-4863	12	18	analysis	analysis	NOUN
ejpam-4863	12	19	and	and	CCONJ
ejpam-4863	12	20	problem	problem	NOUN
ejpam-4863	12	21	solving	solving	NOUN
ejpam-4863	12	22	.	.	PUNCT
ejpam-4863	13	1	in	in	ADP
ejpam-4863	13	2	most	most	ADJ
ejpam-4863	13	3	cases	case	NOUN
ejpam-4863	13	4	,	,	PUNCT
ejpam-4863	13	5	objects	object	NOUN
ejpam-4863	13	6	are	be	AUX
ejpam-4863	13	7	represented	represent	VERB
ejpam-4863	13	8	by	by	ADP
ejpam-4863	13	9	vertices	vertex	NOUN
ejpam-4863	13	10	while	while	SCONJ
ejpam-4863	13	11	the	the	DET
ejpam-4863	13	12	relationship	relationship	NOUN
ejpam-4863	13	13	between	between	ADP
ejpam-4863	13	14	two	two	NUM
ejpam-4863	13	15	objects	object	NOUN
ejpam-4863	13	16	is	be	AUX
ejpam-4863	13	17	represented	represent	VERB
ejpam-4863	13	18	by	by	ADP
ejpam-4863	13	19	an	an	DET
ejpam-4863	13	20	edge	edge	NOUN
ejpam-4863	13	21	in	in	ADP
ejpam-4863	13	22	the	the	DET
ejpam-4863	13	23	graph	graph	NOUN
ejpam-4863	13	24	.	.	PUNCT
ejpam-4863	14	1	a	a	DET
ejpam-4863	14	2	group	group	NOUN
ejpam-4863	14	3	can	can	AUX
ejpam-4863	14	4	be	be	AUX
ejpam-4863	14	5	briefly	briefly	ADV
ejpam-4863	14	6	defined	define	VERB
ejpam-4863	14	7	as	as	ADP
ejpam-4863	14	8	a	a	DET
ejpam-4863	14	9	set	set	NOUN
ejpam-4863	14	10	with	with	ADP
ejpam-4863	14	11	an	an	DET
ejpam-4863	14	12	associative	associative	ADJ
ejpam-4863	14	13	binary	binary	ADJ
ejpam-4863	14	14	operation	operation	NOUN
ejpam-4863	14	15	,	,	PUNCT
ejpam-4863	14	16	an	an	DET
ejpam-4863	14	17	identity	identity	NOUN
ejpam-4863	14	18	element	element	NOUN
ejpam-4863	14	19	,	,	PUNCT
ejpam-4863	14	20	and	and	CCONJ
ejpam-4863	14	21	inverses	inverse	VERB
ejpam-4863	14	22	with	with	ADP
ejpam-4863	14	23	respect	respect	NOUN
ejpam-4863	14	24	to	to	ADP
ejpam-4863	14	25	that	that	DET
ejpam-4863	14	26	identity	identity	NOUN
ejpam-4863	14	27	element	element	NOUN
ejpam-4863	14	28	.	.	PUNCT
ejpam-4863	15	1	for	for	ADP
ejpam-4863	15	2	example	example	NOUN
ejpam-4863	15	3	,	,	PUNCT
ejpam-4863	15	4	the	the	DET
ejpam-4863	15	5	set	set	NOUN
ejpam-4863	15	6	of	of	ADP
ejpam-4863	15	7	real	real	ADJ
ejpam-4863	15	8	numbers	number	NOUN
ejpam-4863	15	9	is	be	AUX
ejpam-4863	15	10	a	a	DET
ejpam-4863	15	11	group	group	NOUN
ejpam-4863	15	12	under	under	ADP
ejpam-4863	15	13	the	the	DET
ejpam-4863	15	14	usual	usual	ADJ
ejpam-4863	15	15	addition	addition	NOUN
ejpam-4863	15	16	operation	operation	NOUN
ejpam-4863	15	17	.	.	PUNCT
ejpam-4863	16	1	group	group	NOUN
ejpam-4863	16	2	theory	theory	NOUN
ejpam-4863	16	3	also	also	ADV
ejpam-4863	16	4	finds	find	VERB
ejpam-4863	16	5	application	application	NOUN
ejpam-4863	16	6	in	in	ADP
ejpam-4863	16	7	chemistry	chemistry	NOUN
ejpam-4863	16	8	in	in	ADP
ejpam-4863	16	9	the	the	DET
ejpam-4863	16	10	study	study	NOUN
ejpam-4863	16	11	of	of	ADP
ejpam-4863	16	12	the	the	DET
ejpam-4863	16	13	group	group	NOUN
ejpam-4863	16	14	of	of	ADP
ejpam-4863	16	15	symmetries	symmetry	NOUN
ejpam-4863	16	16	of	of	ADP
ejpam-4863	16	17	crystals	crystal	NOUN
ejpam-4863	16	18	and	and	CCONJ
ejpam-4863	16	19	molecules	molecule	NOUN
ejpam-4863	16	20	.	.	PUNCT
ejpam-4863	17	1	basic	basic	ADJ
ejpam-4863	17	2	concepts	concept	NOUN
ejpam-4863	17	3	in	in	ADP
ejpam-4863	17	4	graph	graph	NOUN
ejpam-4863	17	5	theory	theory	NOUN
ejpam-4863	17	6	and	and	CCONJ
ejpam-4863	17	7	group	group	NOUN
ejpam-4863	17	8	theory	theory	NOUN
ejpam-4863	17	9	may	may	AUX
ejpam-4863	17	10	be	be	AUX
ejpam-4863	17	11	found	find	VERB
ejpam-4863	17	12	in	in	ADP
ejpam-4863	17	13	[	[	X
ejpam-4863	17	14	4	4	NUM
ejpam-4863	17	15	]	]	PUNCT
ejpam-4863	17	16	,	,	PUNCT
ejpam-4863	17	17	and	and	CCONJ
ejpam-4863	17	18	in	in	ADP
ejpam-4863	17	19	[	[	X
ejpam-4863	17	20	3	3	NUM
ejpam-4863	17	21	]	]	PUNCT
ejpam-4863	17	22	and	and	CCONJ
ejpam-4863	17	23	[	[	X
ejpam-4863	17	24	5	5	NUM
ejpam-4863	17	25	]	]	PUNCT
ejpam-4863	17	26	respectively	respectively	ADV
ejpam-4863	17	27	.	.	PUNCT
ejpam-4863	18	1	the	the	DET
ejpam-4863	18	2	interplay	interplay	NOUN
ejpam-4863	18	3	between	between	ADP
ejpam-4863	18	4	group	group	NOUN
ejpam-4863	18	5	theory	theory	NOUN
ejpam-4863	18	6	and	and	CCONJ
ejpam-4863	18	7	graph	graph	NOUN
ejpam-4863	18	8	theory	theory	NOUN
ejpam-4863	18	9	has	have	AUX
ejpam-4863	18	10	been	be	AUX
ejpam-4863	18	11	explored	explore	VERB
ejpam-4863	18	12	in	in	ADP
ejpam-4863	18	13	literature	literature	NOUN
ejpam-4863	18	14	for	for	ADP
ejpam-4863	18	15	many	many	ADJ
ejpam-4863	18	16	years	year	NOUN
ejpam-4863	18	17	.	.	PUNCT
ejpam-4863	19	1	some	some	DET
ejpam-4863	19	2	researchers	researcher	NOUN
ejpam-4863	19	3	represent	represent	VERB
ejpam-4863	19	4	groups	group	NOUN
ejpam-4863	19	5	as	as	ADP
ejpam-4863	19	6	graphs	graph	NOUN
ejpam-4863	19	7	,	,	PUNCT
ejpam-4863	19	8	while	while	SCONJ
ejpam-4863	19	9	others	other	NOUN
ejpam-4863	19	10	do	do	VERB
ejpam-4863	19	11	it	it	PRON
ejpam-4863	19	12	the	the	DET
ejpam-4863	19	13	other	other	ADJ
ejpam-4863	19	14	way	way	NOUN
ejpam-4863	19	15	around	around	ADV
ejpam-4863	19	16	.	.	PUNCT
ejpam-4863	20	1	the	the	DET
ejpam-4863	20	2	concept	concept	NOUN
ejpam-4863	20	3	of	of	ADP
ejpam-4863	20	4	identity	identity	NOUN
ejpam-4863	20	5	graph	graph	NOUN
ejpam-4863	20	6	of	of	ADP
ejpam-4863	20	7	a	a	DET
ejpam-4863	20	8	group	group	NOUN
ejpam-4863	20	9	is	be	AUX
ejpam-4863	20	10	introduced	introduce	VERB
ejpam-4863	20	11	in	in	ADP
ejpam-4863	20	12	[	[	X
ejpam-4863	20	13	6	6	NUM
ejpam-4863	20	14	]	]	PUNCT
ejpam-4863	20	15	.	.	PUNCT
ejpam-4863	21	1	the	the	DET
ejpam-4863	21	2	identity	identity	NOUN
ejpam-4863	21	3	graph	graph	NOUN
ejpam-4863	21	4	is	be	AUX
ejpam-4863	21	5	a	a	DET
ejpam-4863	21	6	graph	graph	NOUN
ejpam-4863	21	7	with	with	ADP
ejpam-4863	21	8	elements	element	NOUN
ejpam-4863	21	9	of	of	ADP
ejpam-4863	21	10	group	group	NOUN
ejpam-4863	21	11	as	as	SCONJ
ejpam-4863	21	12	vertices	vertex	NOUN
ejpam-4863	21	13	and	and	CCONJ
ejpam-4863	21	14	adjacency	adjacency	NOUN
ejpam-4863	21	15	of	of	ADP
ejpam-4863	21	16	vertices	vertex	NOUN
ejpam-4863	21	17	is	be	AUX
ejpam-4863	21	18	defined	define	VERB
ejpam-4863	21	19	in	in	ADP
ejpam-4863	21	20	terms	term	NOUN
ejpam-4863	21	21	of	of	ADP
ejpam-4863	21	22	the	the	DET
ejpam-4863	21	23	identity	identity	NOUN
ejpam-4863	21	24	element	element	NOUN
ejpam-4863	21	25	of	of	ADP
ejpam-4863	21	26	a	a	DET
ejpam-4863	21	27	group	group	NOUN
ejpam-4863	21	28	.	.	PUNCT
ejpam-4863	22	1	two	two	NUM
ejpam-4863	22	2	vertices	vertex	NOUN
ejpam-4863	22	3	x	x	PUNCT
ejpam-4863	22	4	and	and	CCONJ
ejpam-4863	22	5	y	y	PROPN
ejpam-4863	22	6	can	can	AUX
ejpam-4863	22	7	be	be	AUX
ejpam-4863	22	8	joined	join	VERB
ejpam-4863	22	9	by	by	ADP
ejpam-4863	22	10	an	an	DET
ejpam-4863	22	11	doi	doi	NOUN
ejpam-4863	22	12	:	:	PUNCT
ejpam-4863	22	13	https://doi.org/10.29020/nybg.ejpam.v16i3.4863	https://doi.org/10.29020/nybg.ejpam.v16i3.4863	NOUN
ejpam-4863	22	14	email	email	NOUN
ejpam-4863	22	15	address	address	NOUN
ejpam-4863	22	16	:	:	PUNCT
ejpam-4863	22	17	teresatacbobo@buksu.edu.ph	teresatacbobo@buksu.edu.ph	PROPN
ejpam-4863	22	18	(	(	PUNCT
ejpam-4863	22	19	t.	t.	PROPN
ejpam-4863	22	20	l.	l.	PROPN
ejpam-4863	22	21	tacbobo	tacbobo	PROPN
ejpam-4863	22	22	)	)	PUNCT
ejpam-4863	22	23	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-4863	22	24	1894	1894	NUM
ejpam-4863	22	25	©	©	ADP
ejpam-4863	22	26	2023	2023	NUM
ejpam-4863	22	27	ejpam	ejpam	NOUN
ejpam-4863	22	28	all	all	DET
ejpam-4863	22	29	rights	right	NOUN
ejpam-4863	22	30	reserved	reserve	VERB
ejpam-4863	22	31	.	.	PUNCT
ejpam-4863	23	1	t.	t.	PROPN
ejpam-4863	23	2	l.	l.	PROPN
ejpam-4863	23	3	tacbobo	tacbobo	PROPN
ejpam-4863	23	4	/	/	SYM
ejpam-4863	23	5	eur	eur	PROPN
ejpam-4863	23	6	.	.	PUNCT
ejpam-4863	24	1	j.	j.	PROPN
ejpam-4863	24	2	pure	pure	PROPN
ejpam-4863	24	3	appl	appl	PROPN
ejpam-4863	24	4	.	.	PROPN
ejpam-4863	24	5	math	math	PROPN
ejpam-4863	24	6	,	,	PUNCT
ejpam-4863	24	7	16	16	NUM
ejpam-4863	24	8	(	(	PUNCT
ejpam-4863	24	9	3	3	NUM
ejpam-4863	24	10	)	)	PUNCT
ejpam-4863	24	11	(	(	PUNCT
ejpam-4863	24	12	2023	2023	NUM
ejpam-4863	24	13	)	)	PUNCT
ejpam-4863	24	14	,	,	PUNCT
ejpam-4863	24	15	1894	1894	NUM
ejpam-4863	24	16	-	-	SYM
ejpam-4863	24	17	1901	1901	NUM
ejpam-4863	24	18	1895	1895	NUM
ejpam-4863	24	19	edge	edge	NOUN
ejpam-4863	24	20	in	in	ADP
ejpam-4863	24	21	the	the	DET
ejpam-4863	24	22	identity	identity	NOUN
ejpam-4863	24	23	graph	graph	NOUN
ejpam-4863	24	24	if	if	SCONJ
ejpam-4863	24	25	xy	xy	PROPN
ejpam-4863	24	26	=	=	SYM
ejpam-4863	24	27	e	e	PROPN
ejpam-4863	24	28	(	(	PUNCT
ejpam-4863	24	29	e−	e−	X
ejpam-4863	24	30	being	be	AUX
ejpam-4863	24	31	the	the	DET
ejpam-4863	24	32	identity	identity	NOUN
ejpam-4863	24	33	of	of	ADP
ejpam-4863	24	34	a	a	DET
ejpam-4863	24	35	group	group	NOUN
ejpam-4863	24	36	)	)	PUNCT
ejpam-4863	24	37	.	.	PUNCT
ejpam-4863	25	1	lucchini	lucchini	PROPN
ejpam-4863	25	2	et	et	PROPN
ejpam-4863	25	3	al	al	PROPN
ejpam-4863	25	4	.	.	PROPN
ejpam-4863	25	5	introduced	introduce	VERB
ejpam-4863	25	6	the	the	DET
ejpam-4863	25	7	concept	concept	NOUN
ejpam-4863	25	8	of	of	ADP
ejpam-4863	25	9	generating	generate	VERB
ejpam-4863	25	10	graph	graph	NOUN
ejpam-4863	25	11	of	of	ADP
ejpam-4863	25	12	a	a	DET
ejpam-4863	25	13	group	group	NOUN
ejpam-4863	25	14	in	in	ADP
ejpam-4863	25	15	[	[	X
ejpam-4863	25	16	7	7	NUM
ejpam-4863	25	17	]	]	PUNCT
ejpam-4863	25	18	.	.	PUNCT
ejpam-4863	26	1	the	the	DET
ejpam-4863	26	2	generating	generate	VERB
ejpam-4863	26	3	graph	graph	NOUN
ejpam-4863	26	4	of	of	ADP
ejpam-4863	26	5	a	a	DET
ejpam-4863	26	6	group	group	NOUN
ejpam-4863	26	7	is	be	AUX
ejpam-4863	26	8	also	also	ADV
ejpam-4863	26	9	a	a	DET
ejpam-4863	26	10	graph	graph	NOUN
ejpam-4863	26	11	with	with	ADP
ejpam-4863	26	12	the	the	DET
ejpam-4863	26	13	elements	element	NOUN
ejpam-4863	26	14	of	of	ADP
ejpam-4863	26	15	group	group	NOUN
ejpam-4863	26	16	as	as	ADP
ejpam-4863	26	17	vertices	vertex	NOUN
ejpam-4863	26	18	,	,	PUNCT
ejpam-4863	26	19	and	and	CCONJ
ejpam-4863	26	20	adjacency	adjacency	NOUN
ejpam-4863	26	21	of	of	ADP
ejpam-4863	26	22	vertices	vertex	NOUN
ejpam-4863	26	23	is	be	AUX
ejpam-4863	26	24	restricted	restrict	VERB
ejpam-4863	26	25	to	to	ADP
ejpam-4863	26	26	subgroup	subgroup	NOUN
ejpam-4863	26	27	generated	generate	VERB
ejpam-4863	26	28	by	by	ADP
ejpam-4863	26	29	the	the	DET
ejpam-4863	26	30	given	give	VERB
ejpam-4863	26	31	pair	pair	NOUN
ejpam-4863	26	32	of	of	ADP
ejpam-4863	26	33	vertices	vertex	NOUN
ejpam-4863	26	34	.	.	PUNCT
ejpam-4863	27	1	the	the	DET
ejpam-4863	27	2	generating	generate	VERB
ejpam-4863	27	3	graph	graph	NOUN
ejpam-4863	27	4	of	of	ADP
ejpam-4863	27	5	symmetric	symmetric	ADJ
ejpam-4863	27	6	groups	group	NOUN
ejpam-4863	27	7	is	be	AUX
ejpam-4863	27	8	considered	consider	VERB
ejpam-4863	27	9	in	in	ADP
ejpam-4863	27	10	[	[	X
ejpam-4863	27	11	2	2	NUM
ejpam-4863	27	12	]	]	PUNCT
ejpam-4863	27	13	.	.	PUNCT
ejpam-4863	28	1	other	other	ADJ
ejpam-4863	28	2	graphs	graph	NOUN
ejpam-4863	28	3	associated	associate	VERB
ejpam-4863	28	4	with	with	ADP
ejpam-4863	28	5	finite	finite	ADJ
ejpam-4863	28	6	groups	group	NOUN
ejpam-4863	28	7	are	be	AUX
ejpam-4863	28	8	discussed	discuss	VERB
ejpam-4863	28	9	in	in	ADP
ejpam-4863	28	10	[	[	X
ejpam-4863	28	11	8	8	NUM
ejpam-4863	28	12	]	]	PUNCT
ejpam-4863	28	13	.	.	PUNCT
ejpam-4863	29	1	the	the	DET
ejpam-4863	29	2	above	above	ADJ
ejpam-4863	29	3	ideas	idea	NOUN
ejpam-4863	29	4	of	of	ADP
ejpam-4863	29	5	group	group	NOUN
ejpam-4863	29	6	representations	representation	NOUN
ejpam-4863	29	7	have	have	AUX
ejpam-4863	29	8	motivated	motivate	VERB
ejpam-4863	29	9	the	the	DET
ejpam-4863	29	10	present	present	ADJ
ejpam-4863	29	11	paper	paper	NOUN
ejpam-4863	29	12	to	to	PART
ejpam-4863	29	13	introduce	introduce	VERB
ejpam-4863	29	14	a	a	DET
ejpam-4863	29	15	graph	graph	NOUN
ejpam-4863	29	16	with	with	ADP
ejpam-4863	29	17	the	the	DET
ejpam-4863	29	18	elements	element	NOUN
ejpam-4863	29	19	of	of	ADP
ejpam-4863	29	20	the	the	DET
ejpam-4863	29	21	group	group	NOUN
ejpam-4863	29	22	as	as	ADP
ejpam-4863	29	23	vertices	vertex	NOUN
ejpam-4863	29	24	,	,	PUNCT
ejpam-4863	29	25	and	and	CCONJ
ejpam-4863	29	26	adjacency	adjacency	NOUN
ejpam-4863	29	27	of	of	ADP
ejpam-4863	29	28	vertices	vertex	NOUN
ejpam-4863	29	29	is	be	AUX
ejpam-4863	29	30	defined	define	VERB
ejpam-4863	29	31	in	in	ADP
ejpam-4863	29	32	terms	term	NOUN
ejpam-4863	29	33	of	of	ADP
ejpam-4863	29	34	the	the	DET
ejpam-4863	29	35	generator	generator	NOUN
ejpam-4863	29	36	element	element	NOUN
ejpam-4863	29	37	of	of	ADP
ejpam-4863	29	38	the	the	DET
ejpam-4863	29	39	group	group	NOUN
ejpam-4863	29	40	.	.	PUNCT
ejpam-4863	30	1	the	the	DET
ejpam-4863	30	2	graph	graph	NOUN
ejpam-4863	30	3	will	will	AUX
ejpam-4863	30	4	be	be	AUX
ejpam-4863	30	5	called	call	VERB
ejpam-4863	30	6	the	the	DET
ejpam-4863	30	7	generator	generator	NOUN
ejpam-4863	30	8	graph	graph	NOUN
ejpam-4863	30	9	of	of	ADP
ejpam-4863	30	10	a	a	DET
ejpam-4863	30	11	group	group	NOUN
ejpam-4863	30	12	.	.	PUNCT
ejpam-4863	31	1	2	2	NUM
ejpam-4863	31	2	.	.	NUM
ejpam-4863	31	3	basic	basic	ADJ
ejpam-4863	31	4	concepts	concept	NOUN
ejpam-4863	31	5	2.1	2.1	NUM
ejpam-4863	31	6	.	.	PUNCT
ejpam-4863	32	1	graphs	graph	NOUN
ejpam-4863	32	2	althroughout	althroughout	ADP
ejpam-4863	32	3	this	this	DET
ejpam-4863	32	4	paper	paper	NOUN
ejpam-4863	32	5	,	,	PUNCT
ejpam-4863	32	6	we	we	PRON
ejpam-4863	32	7	only	only	ADV
ejpam-4863	32	8	consider	consider	VERB
ejpam-4863	32	9	undirected	undirected	ADJ
ejpam-4863	32	10	graphs	graph	NOUN
ejpam-4863	32	11	with	with	ADP
ejpam-4863	32	12	no	no	DET
ejpam-4863	32	13	loops	loop	NOUN
ejpam-4863	32	14	.	.	PUNCT
ejpam-4863	33	1	the	the	DET
ejpam-4863	33	2	basic	basic	ADJ
ejpam-4863	33	3	definitions	definition	NOUN
ejpam-4863	33	4	and	and	CCONJ
ejpam-4863	33	5	concepts	concept	NOUN
ejpam-4863	33	6	used	use	VERB
ejpam-4863	33	7	in	in	ADP
ejpam-4863	33	8	this	this	DET
ejpam-4863	33	9	study	study	NOUN
ejpam-4863	33	10	are	be	AUX
ejpam-4863	33	11	adopted	adopt	VERB
ejpam-4863	33	12	from	from	ADP
ejpam-4863	33	13	[	[	X
ejpam-4863	33	14	1	1	NUM
ejpam-4863	33	15	]	]	PUNCT
ejpam-4863	33	16	.	.	PUNCT
ejpam-4863	34	1	given	give	VERB
ejpam-4863	34	2	a	a	DET
ejpam-4863	34	3	graph	graph	NOUN
ejpam-4863	34	4	g	g	NOUN
ejpam-4863	34	5	=	=	PUNCT
ejpam-4863	34	6	(	(	PUNCT
ejpam-4863	34	7	v	v	NOUN
ejpam-4863	34	8	(	(	PUNCT
ejpam-4863	34	9	g	g	NOUN
ejpam-4863	34	10	)	)	PUNCT
ejpam-4863	34	11	,	,	PUNCT
ejpam-4863	34	12	e(g	e(g	PROPN
ejpam-4863	34	13	)	)	PUNCT
ejpam-4863	34	14	)	)	PUNCT
ejpam-4863	34	15	,	,	PUNCT
ejpam-4863	34	16	the	the	DET
ejpam-4863	34	17	sets	set	NOUN
ejpam-4863	34	18	v	v	ADP
ejpam-4863	34	19	(	(	PUNCT
ejpam-4863	34	20	g	g	NOUN
ejpam-4863	34	21	)	)	PUNCT
ejpam-4863	34	22	and	and	CCONJ
ejpam-4863	34	23	e(g	e(g	PROPN
ejpam-4863	34	24	)	)	PUNCT
ejpam-4863	34	25	are	be	AUX
ejpam-4863	34	26	,	,	PUNCT
ejpam-4863	34	27	respectively	respectively	ADV
ejpam-4863	34	28	,	,	PUNCT
ejpam-4863	34	29	the	the	DET
ejpam-4863	34	30	vertex	vertex	NOUN
ejpam-4863	34	31	set	set	NOUN
ejpam-4863	34	32	and	and	CCONJ
ejpam-4863	34	33	edge	edge	NOUN
ejpam-4863	34	34	set	set	NOUN
ejpam-4863	34	35	of	of	ADP
ejpam-4863	34	36	g.	g.	PROPN
ejpam-4863	34	37	the	the	DET
ejpam-4863	34	38	cardinality	cardinality	NOUN
ejpam-4863	34	39	of	of	ADP
ejpam-4863	34	40	v	v	NOUN
ejpam-4863	34	41	(	(	PUNCT
ejpam-4863	34	42	g	g	NOUN
ejpam-4863	34	43	)	)	PUNCT
ejpam-4863	34	44	,	,	PUNCT
ejpam-4863	34	45	denoted	denote	VERB
ejpam-4863	34	46	|v	|v	PROPN
ejpam-4863	34	47	(	(	PUNCT
ejpam-4863	34	48	g)|	g)|	NOUN
ejpam-4863	34	49	,	,	PUNCT
ejpam-4863	34	50	is	be	AUX
ejpam-4863	34	51	called	call	VERB
ejpam-4863	34	52	the	the	DET
ejpam-4863	34	53	order	order	NOUN
ejpam-4863	34	54	of	of	ADP
ejpam-4863	34	55	g	g	PROPN
ejpam-4863	34	56	and	and	CCONJ
ejpam-4863	34	57	the	the	DET
ejpam-4863	34	58	cardinality	cardinality	NOUN
ejpam-4863	34	59	|e(g)|	|e(g)|	PROPN
ejpam-4863	34	60	of	of	ADP
ejpam-4863	34	61	e(g	e(g	PROPN
ejpam-4863	34	62	)	)	PUNCT
ejpam-4863	34	63	is	be	AUX
ejpam-4863	34	64	the	the	DET
ejpam-4863	34	65	size	size	NOUN
ejpam-4863	34	66	of	of	ADP
ejpam-4863	34	67	g.	g.	PROPN
ejpam-4863	34	68	each	each	DET
ejpam-4863	34	69	element	element	NOUN
ejpam-4863	34	70	of	of	ADP
ejpam-4863	34	71	v	v	NOUN
ejpam-4863	34	72	(	(	PUNCT
ejpam-4863	34	73	g	g	NOUN
ejpam-4863	34	74	)	)	PUNCT
ejpam-4863	34	75	is	be	AUX
ejpam-4863	34	76	considered	consider	VERB
ejpam-4863	34	77	a	a	DET
ejpam-4863	34	78	vertex	vertex	NOUN
ejpam-4863	34	79	of	of	ADP
ejpam-4863	34	80	g.	g.	PROPN
ejpam-4863	35	1	if	if	SCONJ
ejpam-4863	35	2	u	u	PROPN
ejpam-4863	35	3	,	,	PUNCT
ejpam-4863	35	4	v	v	PROPN
ejpam-4863	35	5	∈	∈	PROPN
ejpam-4863	35	6	v	v	NOUN
ejpam-4863	35	7	(	(	PUNCT
ejpam-4863	35	8	g	g	NOUN
ejpam-4863	35	9	)	)	PUNCT
ejpam-4863	35	10	and	and	CCONJ
ejpam-4863	35	11	e	e	X
ejpam-4863	35	12	=	=	PUNCT
ejpam-4863	36	1	[	[	X
ejpam-4863	36	2	u	u	NOUN
ejpam-4863	36	3	,	,	PUNCT
ejpam-4863	36	4	v	v	NOUN
ejpam-4863	36	5	]	]	PUNCT
ejpam-4863	36	6	is	be	AUX
ejpam-4863	36	7	in	in	ADP
ejpam-4863	36	8	e(g	e(g	PROPN
ejpam-4863	36	9	)	)	PUNCT
ejpam-4863	36	10	,	,	PUNCT
ejpam-4863	36	11	then	then	ADV
ejpam-4863	36	12	e	e	PROPN
ejpam-4863	36	13	is	be	AUX
ejpam-4863	36	14	an	an	DET
ejpam-4863	36	15	edge	edge	NOUN
ejpam-4863	36	16	of	of	ADP
ejpam-4863	36	17	g	g	NOUN
ejpam-4863	36	18	,	,	PUNCT
ejpam-4863	36	19	and	and	CCONJ
ejpam-4863	36	20	e	e	NOUN
ejpam-4863	36	21	is	be	AUX
ejpam-4863	36	22	said	say	VERB
ejpam-4863	36	23	to	to	PART
ejpam-4863	36	24	join	join	VERB
ejpam-4863	36	25	u	u	NOUN
ejpam-4863	36	26	and	and	CCONJ
ejpam-4863	36	27	v.	v.	ADP
ejpam-4863	36	28	in	in	ADP
ejpam-4863	36	29	this	this	DET
ejpam-4863	36	30	case	case	NOUN
ejpam-4863	36	31	,	,	PUNCT
ejpam-4863	36	32	it	it	PRON
ejpam-4863	36	33	is	be	AUX
ejpam-4863	36	34	customary	customary	ADJ
ejpam-4863	36	35	to	to	PART
ejpam-4863	36	36	write	write	VERB
ejpam-4863	36	37	e	e	NOUN
ejpam-4863	36	38	=	=	NOUN
ejpam-4863	36	39	uv	uv	NOUN
ejpam-4863	36	40	and	and	CCONJ
ejpam-4863	36	41	say	say	VERB
ejpam-4863	36	42	that	that	SCONJ
ejpam-4863	36	43	u	u	PROPN
ejpam-4863	36	44	and	and	CCONJ
ejpam-4863	36	45	v	v	NOUN
ejpam-4863	36	46	are	be	AUX
ejpam-4863	36	47	adjacent	adjacent	ADJ
ejpam-4863	36	48	,	,	PUNCT
ejpam-4863	36	49	while	while	SCONJ
ejpam-4863	36	50	u	u	PRON
ejpam-4863	36	51	and	and	CCONJ
ejpam-4863	36	52	e	e	PROPN
ejpam-4863	36	53	are	be	AUX
ejpam-4863	36	54	incident	incident	NOUN
ejpam-4863	36	55	,	,	PUNCT
ejpam-4863	36	56	as	as	SCONJ
ejpam-4863	36	57	v	v	NOUN
ejpam-4863	36	58	and	and	CCONJ
ejpam-4863	36	59	e	e	NOUN
ejpam-4863	36	60	are	be	AUX
ejpam-4863	36	61	.	.	PUNCT
ejpam-4863	37	1	adjacent	adjacent	ADJ
ejpam-4863	37	2	vertices	vertex	NOUN
ejpam-4863	37	3	are	be	AUX
ejpam-4863	37	4	also	also	ADV
ejpam-4863	37	5	called	call	VERB
ejpam-4863	37	6	neighbors	neighbor	NOUN
ejpam-4863	37	7	.	.	PUNCT
ejpam-4863	38	1	the	the	DET
ejpam-4863	38	2	degree	degree	NOUN
ejpam-4863	38	3	degg(v	degg(v	PROPN
ejpam-4863	38	4	)	)	PUNCT
ejpam-4863	38	5	of	of	ADP
ejpam-4863	38	6	a	a	DET
ejpam-4863	38	7	vertex	vertex	NOUN
ejpam-4863	38	8	v	v	NOUN
ejpam-4863	38	9	is	be	AUX
ejpam-4863	38	10	the	the	DET
ejpam-4863	38	11	number	number	NOUN
ejpam-4863	38	12	of	of	ADP
ejpam-4863	38	13	edges	edge	NOUN
ejpam-4863	38	14	incident	incident	NOUN
ejpam-4863	38	15	to	to	ADP
ejpam-4863	38	16	v.	v.	ADP
ejpam-4863	38	17	a	a	DET
ejpam-4863	38	18	subgraph	subgraph	NOUN
ejpam-4863	38	19	of	of	ADP
ejpam-4863	38	20	a	a	DET
ejpam-4863	38	21	graph	graph	NOUN
ejpam-4863	38	22	g	g	NOUN
ejpam-4863	38	23	is	be	AUX
ejpam-4863	38	24	a	a	DET
ejpam-4863	38	25	graph	graph	NOUN
ejpam-4863	38	26	having	have	VERB
ejpam-4863	38	27	all	all	DET
ejpam-4863	38	28	its	its	PRON
ejpam-4863	38	29	vertices	vertex	NOUN
ejpam-4863	38	30	and	and	CCONJ
ejpam-4863	38	31	edges	edge	NOUN
ejpam-4863	38	32	in	in	ADP
ejpam-4863	38	33	g.	g.	PROPN
ejpam-4863	39	1	it	it	PRON
ejpam-4863	39	2	is	be	AUX
ejpam-4863	39	3	a	a	DET
ejpam-4863	39	4	spanning	span	VERB
ejpam-4863	39	5	subgraph	subgraph	NOUN
ejpam-4863	39	6	if	if	SCONJ
ejpam-4863	39	7	it	it	PRON
ejpam-4863	39	8	contains	contain	VERB
ejpam-4863	39	9	all	all	DET
ejpam-4863	39	10	the	the	DET
ejpam-4863	39	11	vertices	vertex	NOUN
ejpam-4863	39	12	of	of	ADP
ejpam-4863	39	13	g.	g.	PROPN
ejpam-4863	39	14	the	the	DET
ejpam-4863	39	15	induced	induce	VERB
ejpam-4863	39	16	subgraph	subgraph	NOUN
ejpam-4863	39	17	⟨s⟩	⟨s⟩	PROPN
ejpam-4863	39	18	is	be	AUX
ejpam-4863	39	19	the	the	DET
ejpam-4863	39	20	maximal	maximal	ADJ
ejpam-4863	39	21	subgraph	subgraph	NOUN
ejpam-4863	39	22	with	with	ADP
ejpam-4863	39	23	vertex	vertex	NOUN
ejpam-4863	39	24	set	set	VERB
ejpam-4863	39	25	s.	s.	PROPN
ejpam-4863	40	1	the	the	DET
ejpam-4863	40	2	path	path	NOUN
ejpam-4863	40	3	of	of	ADP
ejpam-4863	40	4	order	order	NOUN
ejpam-4863	40	5	n	n	CCONJ
ejpam-4863	40	6	,	,	PUNCT
ejpam-4863	40	7	denoted	denote	VERB
ejpam-4863	40	8	by	by	ADP
ejpam-4863	40	9	pn	pn	NOUN
ejpam-4863	40	10	=	=	PUNCT
ejpam-4863	41	1	[	[	X
ejpam-4863	41	2	v1	v1	NOUN
ejpam-4863	41	3	,	,	PUNCT
ejpam-4863	41	4	v2	v2	PROPN
ejpam-4863	41	5	,	,	PUNCT
ejpam-4863	41	6	...	...	PUNCT
ejpam-4863	41	7	,	,	PUNCT
ejpam-4863	41	8	vn	vn	X
ejpam-4863	41	9	]	]	PUNCT
ejpam-4863	41	10	,	,	PUNCT
ejpam-4863	41	11	is	be	AUX
ejpam-4863	41	12	the	the	DET
ejpam-4863	41	13	graph	graph	NOUN
ejpam-4863	41	14	with	with	ADP
ejpam-4863	41	15	vertices	vertex	NOUN
ejpam-4863	41	16	v1	v1	NOUN
ejpam-4863	41	17	,	,	PUNCT
ejpam-4863	41	18	v2	v2	PROPN
ejpam-4863	41	19	,	,	PUNCT
ejpam-4863	41	20	...	...	PUNCT
ejpam-4863	41	21	,	,	PUNCT
ejpam-4863	41	22	vn	vn	NOUN
ejpam-4863	41	23	,	,	PUNCT
ejpam-4863	41	24	and	and	CCONJ
ejpam-4863	41	25	edges	edge	NOUN
ejpam-4863	41	26	v1v2	v1v2	NOUN
ejpam-4863	41	27	,	,	PUNCT
ejpam-4863	41	28	v2v3	v2v3	NUM
ejpam-4863	41	29	,	,	PUNCT
ejpam-4863	41	30	...	...	PUNCT
ejpam-4863	41	31	,	,	PUNCT
ejpam-4863	41	32	vn−1vn	vn−1vn	NUM
ejpam-4863	41	33	.	.	PUNCT
ejpam-4863	42	1	we	we	PRON
ejpam-4863	42	2	also	also	ADV
ejpam-4863	42	3	call	call	VERB
ejpam-4863	42	4	pn	pn	PROPN
ejpam-4863	42	5	as	as	ADP
ejpam-4863	42	6	a	a	DET
ejpam-4863	42	7	u	u	NOUN
ejpam-4863	42	8	-	-	NOUN
ejpam-4863	42	9	v	v	ADJ
ejpam-4863	42	10	path	path	NOUN
ejpam-4863	42	11	of	of	ADP
ejpam-4863	42	12	length	length	NOUN
ejpam-4863	42	13	n−	n−	NOUN
ejpam-4863	42	14	1	1	NUM
ejpam-4863	42	15	,	,	PUNCT
ejpam-4863	42	16	where	where	SCONJ
ejpam-4863	42	17	u	u	NOUN
ejpam-4863	42	18	=	=	SYM
ejpam-4863	42	19	v1	v1	PROPN
ejpam-4863	42	20	and	and	CCONJ
ejpam-4863	42	21	v	v	NOUN
ejpam-4863	42	22	=	=	SYM
ejpam-4863	42	23	vn	vn	PROPN
ejpam-4863	42	24	.	.	PUNCT
ejpam-4863	43	1	a	a	DET
ejpam-4863	43	2	graph	graph	NOUN
ejpam-4863	43	3	g	g	NOUN
ejpam-4863	43	4	is	be	AUX
ejpam-4863	43	5	connected	connect	VERB
ejpam-4863	43	6	if	if	SCONJ
ejpam-4863	43	7	there	there	PRON
ejpam-4863	43	8	is	be	VERB
ejpam-4863	43	9	a	a	DET
ejpam-4863	43	10	path	path	NOUN
ejpam-4863	43	11	that	that	PRON
ejpam-4863	43	12	joins	join	VERB
ejpam-4863	43	13	each	each	DET
ejpam-4863	43	14	pair	pair	NOUN
ejpam-4863	43	15	of	of	ADP
ejpam-4863	43	16	vertices	vertex	NOUN
ejpam-4863	43	17	.	.	PUNCT
ejpam-4863	44	1	a	a	DET
ejpam-4863	44	2	graph	graph	NOUN
ejpam-4863	44	3	g	g	NOUN
ejpam-4863	44	4	is	be	AUX
ejpam-4863	44	5	called	call	VERB
ejpam-4863	44	6	complete	complete	ADJ
ejpam-4863	44	7	if	if	SCONJ
ejpam-4863	44	8	every	every	DET
ejpam-4863	44	9	pair	pair	NOUN
ejpam-4863	44	10	of	of	ADP
ejpam-4863	44	11	its	its	PRON
ejpam-4863	44	12	vertices	vertex	NOUN
ejpam-4863	44	13	is	be	AUX
ejpam-4863	44	14	adjacent	adjacent	ADJ
ejpam-4863	44	15	.	.	PUNCT
ejpam-4863	45	1	kn	kn	PROPN
ejpam-4863	45	2	denotes	denote	VERB
ejpam-4863	45	3	the	the	DET
ejpam-4863	45	4	complete	complete	ADJ
ejpam-4863	45	5	graph	graph	NOUN
ejpam-4863	45	6	of	of	ADP
ejpam-4863	45	7	order	order	NOUN
ejpam-4863	45	8	n.	n.	VERB
ejpam-4863	45	9	the	the	DET
ejpam-4863	45	10	graph	graph	NOUN
ejpam-4863	45	11	k1	k1	NOUN
ejpam-4863	45	12	is	be	AUX
ejpam-4863	45	13	the	the	DET
ejpam-4863	45	14	trivial	trivial	ADJ
ejpam-4863	45	15	graph	graph	NOUN
ejpam-4863	45	16	.	.	PUNCT
ejpam-4863	46	1	it	it	PRON
ejpam-4863	46	2	is	be	AUX
ejpam-4863	46	3	trivial	trivial	ADJ
ejpam-4863	46	4	to	to	PART
ejpam-4863	46	5	see	see	VERB
ejpam-4863	46	6	that	that	SCONJ
ejpam-4863	46	7	kn	kn	PROPN
ejpam-4863	46	8	contains	contain	VERB
ejpam-4863	46	9	n(n−	n(n−	PROPN
ejpam-4863	46	10	1)/2	1)/2	NUM
ejpam-4863	46	11	edges	edge	VERB
ejpam-4863	46	12	.	.	PUNCT
ejpam-4863	47	1	a	a	DET
ejpam-4863	47	2	graph	graph	NOUN
ejpam-4863	47	3	with	with	ADP
ejpam-4863	47	4	an	an	DET
ejpam-4863	47	5	empty	empty	ADJ
ejpam-4863	47	6	edge	edge	NOUN
ejpam-4863	47	7	set	set	NOUN
ejpam-4863	47	8	is	be	AUX
ejpam-4863	47	9	called	call	VERB
ejpam-4863	47	10	a	a	DET
ejpam-4863	47	11	null	null	ADJ
ejpam-4863	47	12	graph	graph	NOUN
ejpam-4863	47	13	.	.	PUNCT
ejpam-4863	48	1	a	a	DET
ejpam-4863	48	2	null	null	ADJ
ejpam-4863	48	3	graph	graph	NOUN
ejpam-4863	48	4	of	of	ADP
ejpam-4863	48	5	order	order	NOUN
ejpam-4863	48	6	n	n	NOUN
ejpam-4863	48	7	is	be	AUX
ejpam-4863	48	8	denoted	denote	VERB
ejpam-4863	48	9	kn	kn	PROPN
ejpam-4863	48	10	.	.	PUNCT
ejpam-4863	49	1	the	the	DET
ejpam-4863	49	2	join	join	NOUN
ejpam-4863	49	3	g1	g1	PROPN
ejpam-4863	49	4	+	+	PROPN
ejpam-4863	49	5	g2	g2	PROPN
ejpam-4863	49	6	of	of	ADP
ejpam-4863	49	7	two	two	NUM
ejpam-4863	49	8	graphs	graph	NOUN
ejpam-4863	49	9	g1	g1	NOUN
ejpam-4863	49	10	and	and	CCONJ
ejpam-4863	49	11	g2	g2	PROPN
ejpam-4863	49	12	is	be	AUX
ejpam-4863	49	13	their	their	PRON
ejpam-4863	49	14	disjoint	disjoint	NOUN
ejpam-4863	49	15	union	union	NOUN
ejpam-4863	49	16	together	together	ADV
ejpam-4863	49	17	with	with	ADP
ejpam-4863	49	18	all	all	DET
ejpam-4863	49	19	the	the	DET
ejpam-4863	49	20	edges	edge	NOUN
ejpam-4863	49	21	that	that	PRON
ejpam-4863	49	22	connect	connect	VERB
ejpam-4863	49	23	all	all	DET
ejpam-4863	49	24	the	the	DET
ejpam-4863	49	25	vertices	vertex	NOUN
ejpam-4863	49	26	of	of	ADP
ejpam-4863	49	27	g1	g1	NOUN
ejpam-4863	49	28	with	with	ADP
ejpam-4863	49	29	all	all	DET
ejpam-4863	49	30	the	the	DET
ejpam-4863	49	31	vertices	vertex	NOUN
ejpam-4863	49	32	of	of	ADP
ejpam-4863	49	33	g2	g2	PROPN
ejpam-4863	49	34	.	.	PUNCT
ejpam-4863	50	1	2.2	2.2	NUM
ejpam-4863	50	2	.	.	PUNCT
ejpam-4863	50	3	groups	group	NOUN
ejpam-4863	50	4	a	a	DET
ejpam-4863	50	5	binary	binary	ADJ
ejpam-4863	50	6	operation	operation	NOUN
ejpam-4863	50	7	or	or	CCONJ
ejpam-4863	50	8	law	law	NOUN
ejpam-4863	50	9	of	of	ADP
ejpam-4863	50	10	composition	composition	NOUN
ejpam-4863	50	11	on	on	ADP
ejpam-4863	50	12	a	a	DET
ejpam-4863	50	13	set	set	NOUN
ejpam-4863	50	14	g	g	NOUN
ejpam-4863	50	15	is	be	AUX
ejpam-4863	50	16	a	a	DET
ejpam-4863	50	17	function	function	NOUN
ejpam-4863	50	18	g	g	ADP
ejpam-4863	50	19	×	×	NOUN
ejpam-4863	50	20	g	g	NOUN
ejpam-4863	50	21	→	→	SYM
ejpam-4863	50	22	g	g	PROPN
ejpam-4863	50	23	that	that	PRON
ejpam-4863	50	24	assigns	assign	VERB
ejpam-4863	50	25	to	to	ADP
ejpam-4863	50	26	each	each	DET
ejpam-4863	50	27	pair	pair	NOUN
ejpam-4863	50	28	(	(	PUNCT
ejpam-4863	50	29	a	a	PRON
ejpam-4863	50	30	,	,	PUNCT
ejpam-4863	50	31	b	b	NOUN
ejpam-4863	50	32	)	)	PUNCT
ejpam-4863	50	33	∈	∈	PROPN
ejpam-4863	50	34	g×g	g×g	PROPN
ejpam-4863	50	35	a	a	DET
ejpam-4863	50	36	unique	unique	ADJ
ejpam-4863	50	37	element	element	NOUN
ejpam-4863	50	38	a	a	DET
ejpam-4863	50	39	◦	◦	NOUN
ejpam-4863	50	40	b	b	NOUN
ejpam-4863	50	41	,	,	PUNCT
ejpam-4863	50	42	or	or	CCONJ
ejpam-4863	50	43	ab	ab	PROPN
ejpam-4863	50	44	∈	∈	PROPN
ejpam-4863	50	45	g	g	PROPN
ejpam-4863	50	46	,	,	PUNCT
ejpam-4863	50	47	called	call	VERB
ejpam-4863	50	48	the	the	DET
ejpam-4863	50	49	composition	composition	NOUN
ejpam-4863	50	50	of	of	ADP
ejpam-4863	50	51	a	a	PRON
ejpam-4863	50	52	and	and	CCONJ
ejpam-4863	50	53	b.	b.	PROPN
ejpam-4863	50	54	a	a	DET
ejpam-4863	50	55	group	group	NOUN
ejpam-4863	50	56	(	(	PUNCT
ejpam-4863	50	57	g	g	NOUN
ejpam-4863	50	58	,	,	PUNCT
ejpam-4863	50	59	◦	◦	NOUN
ejpam-4863	50	60	)	)	PUNCT
ejpam-4863	50	61	is	be	AUX
ejpam-4863	50	62	a	a	DET
ejpam-4863	50	63	set	set	NOUN
ejpam-4863	50	64	g	g	NOUN
ejpam-4863	50	65	together	together	ADV
ejpam-4863	50	66	with	with	ADP
ejpam-4863	50	67	a	a	DET
ejpam-4863	50	68	law	law	NOUN
ejpam-4863	50	69	of	of	ADP
ejpam-4863	50	70	composition	composition	NOUN
ejpam-4863	50	71	(	(	PUNCT
ejpam-4863	50	72	a	a	DET
ejpam-4863	50	73	,	,	PUNCT
ejpam-4863	50	74	b	b	NOUN
ejpam-4863	50	75	)	)	PUNCT
ejpam-4863	50	76	7→	7→	NOUN
ejpam-4863	50	77	a	a	DET
ejpam-4863	50	78	◦	◦	NOUN
ejpam-4863	50	79	b	b	NOUN
ejpam-4863	50	80	that	that	PRON
ejpam-4863	50	81	satisfies	satisfy	VERB
ejpam-4863	50	82	the	the	DET
ejpam-4863	50	83	following	follow	VERB
ejpam-4863	50	84	axioms	axiom	NOUN
ejpam-4863	50	85	:	:	PUNCT
ejpam-4863	50	86	(	(	PUNCT
ejpam-4863	50	87	i	i	NOUN
ejpam-4863	50	88	)	)	PUNCT
ejpam-4863	50	89	the	the	DET
ejpam-4863	50	90	law	law	NOUN
ejpam-4863	50	91	of	of	ADP
ejpam-4863	50	92	composition	composition	NOUN
ejpam-4863	50	93	is	be	AUX
ejpam-4863	50	94	associative	associative	ADJ
ejpam-4863	50	95	,	,	PUNCT
ejpam-4863	50	96	i.e.	i.e.	X
ejpam-4863	50	97	,	,	PUNCT
ejpam-4863	51	1	(	(	PUNCT
ejpam-4863	51	2	a	a	DET
ejpam-4863	51	3	◦	◦	NOUN
ejpam-4863	51	4	b	b	NOUN
ejpam-4863	51	5	)	)	PUNCT
ejpam-4863	51	6	◦	◦	NOUN
ejpam-4863	51	7	c	c	NOUN
ejpam-4863	51	8	=	=	PUNCT
ejpam-4863	51	9	a	a	DET
ejpam-4863	51	10	◦	◦	NOUN
ejpam-4863	51	11	(	(	PUNCT
ejpam-4863	51	12	b	b	X
ejpam-4863	51	13	◦	◦	NOUN
ejpam-4863	51	14	c	c	NOUN
ejpam-4863	51	15	)	)	PUNCT
ejpam-4863	51	16	for	for	ADP
ejpam-4863	51	17	a	a	DET
ejpam-4863	51	18	,	,	PUNCT
ejpam-4863	51	19	b	b	NOUN
ejpam-4863	51	20	,	,	PUNCT
ejpam-4863	51	21	c	c	PROPN
ejpam-4863	51	22	∈	∈	PROPN
ejpam-4863	51	23	g	g	PROPN
ejpam-4863	51	24	;	;	PUNCT
ejpam-4863	51	25	(	(	PUNCT
ejpam-4863	51	26	ii	ii	NOUN
ejpam-4863	51	27	)	)	PUNCT
ejpam-4863	51	28	there	there	PRON
ejpam-4863	51	29	exists	exist	VERB
ejpam-4863	51	30	an	an	DET
ejpam-4863	51	31	element	element	NOUN
ejpam-4863	51	32	e	e	PROPN
ejpam-4863	51	33	∈	∈	PROPN
ejpam-4863	51	34	g	g	PROPN
ejpam-4863	51	35	called	call	VERB
ejpam-4863	51	36	the	the	DET
ejpam-4863	51	37	identity	identity	NOUN
ejpam-4863	51	38	element	element	NOUN
ejpam-4863	51	39	,	,	PUNCT
ejpam-4863	51	40	such	such	ADJ
ejpam-4863	51	41	t.	t.	PROPN
ejpam-4863	51	42	l.	l.	PROPN
ejpam-4863	51	43	tacbobo	tacbobo	PROPN
ejpam-4863	51	44	/	/	SYM
ejpam-4863	51	45	eur	eur	PROPN
ejpam-4863	51	46	.	.	PUNCT
ejpam-4863	52	1	j.	j.	PROPN
ejpam-4863	52	2	pure	pure	PROPN
ejpam-4863	52	3	appl	appl	PROPN
ejpam-4863	52	4	.	.	PROPN
ejpam-4863	52	5	math	math	PROPN
ejpam-4863	52	6	,	,	PUNCT
ejpam-4863	52	7	16	16	NUM
ejpam-4863	52	8	(	(	PUNCT
ejpam-4863	52	9	3	3	NUM
ejpam-4863	52	10	)	)	PUNCT
ejpam-4863	52	11	(	(	PUNCT
ejpam-4863	52	12	2023	2023	NUM
ejpam-4863	52	13	)	)	PUNCT
ejpam-4863	52	14	,	,	PUNCT
ejpam-4863	52	15	1894	1894	NUM
ejpam-4863	52	16	-	-	SYM
ejpam-4863	52	17	1901	1901	NUM
ejpam-4863	52	18	1896	1896	NUM
ejpam-4863	52	19	that	that	SCONJ
ejpam-4863	52	20	for	for	ADP
ejpam-4863	52	21	any	any	DET
ejpam-4863	52	22	element	element	NOUN
ejpam-4863	52	23	a	a	DET
ejpam-4863	52	24	∈	∈	PROPN
ejpam-4863	52	25	g	g	NOUN
ejpam-4863	52	26	,	,	PUNCT
ejpam-4863	52	27	e	e	AUX
ejpam-4863	52	28	◦	◦	VERB
ejpam-4863	52	29	a	a	DET
ejpam-4863	52	30	=	=	NOUN
ejpam-4863	52	31	a	a	DET
ejpam-4863	52	32	◦	◦	NOUN
ejpam-4863	52	33	e	e	NOUN
ejpam-4863	52	34	=	=	SYM
ejpam-4863	52	35	a	a	X
ejpam-4863	52	36	;	;	PUNCT
ejpam-4863	52	37	and	and	CCONJ
ejpam-4863	52	38	for	for	ADP
ejpam-4863	52	39	each	each	DET
ejpam-4863	52	40	element	element	NOUN
ejpam-4863	52	41	a	a	DET
ejpam-4863	52	42	∈	∈	PROPN
ejpam-4863	52	43	g	g	NOUN
ejpam-4863	52	44	,	,	PUNCT
ejpam-4863	52	45	there	there	PRON
ejpam-4863	52	46	exists	exist	VERB
ejpam-4863	52	47	an	an	DET
ejpam-4863	52	48	inverse	inverse	NOUN
ejpam-4863	52	49	element	element	NOUN
ejpam-4863	52	50	in	in	ADP
ejpam-4863	52	51	g	g	NOUN
ejpam-4863	52	52	,	,	PUNCT
ejpam-4863	52	53	denoted	denote	VERB
ejpam-4863	52	54	by	by	ADP
ejpam-4863	52	55	a−1	a−1	PROPN
ejpam-4863	52	56	,	,	PUNCT
ejpam-4863	52	57	such	such	ADJ
ejpam-4863	52	58	that	that	SCONJ
ejpam-4863	52	59	a	a	DET
ejpam-4863	52	60	◦	◦	NOUN
ejpam-4863	52	61	a−1	a−1	NOUN
ejpam-4863	52	62	=	=	SYM
ejpam-4863	52	63	a−1	a−1	PROPN
ejpam-4863	52	64	◦	◦	VERB
ejpam-4863	52	65	a	a	DET
ejpam-4863	52	66	=	=	X
ejpam-4863	52	67	e.	e.	PROPN
ejpam-4863	52	68	a	a	DET
ejpam-4863	52	69	group	group	NOUN
ejpam-4863	52	70	g	g	NOUN
ejpam-4863	52	71	with	with	ADP
ejpam-4863	52	72	the	the	DET
ejpam-4863	52	73	property	property	NOUN
ejpam-4863	52	74	that	that	PRON
ejpam-4863	52	75	a	a	DET
ejpam-4863	52	76	◦	◦	NOUN
ejpam-4863	52	77	b	b	NOUN
ejpam-4863	52	78	=	=	SYM
ejpam-4863	52	79	b	b	PROPN
ejpam-4863	52	80	◦	◦	NOUN
ejpam-4863	52	81	a	a	PRON
ejpam-4863	52	82	for	for	ADP
ejpam-4863	52	83	all	all	DET
ejpam-4863	52	84	a	a	PRON
ejpam-4863	52	85	,	,	PUNCT
ejpam-4863	52	86	b	b	X
ejpam-4863	52	87	∈	∈	PROPN
ejpam-4863	52	88	g	g	PROPN
ejpam-4863	52	89	is	be	AUX
ejpam-4863	52	90	called	call	VERB
ejpam-4863	52	91	abelian	abelian	ADJ
ejpam-4863	52	92	or	or	CCONJ
ejpam-4863	52	93	commutative	commutative	ADJ
ejpam-4863	52	94	.	.	PUNCT
ejpam-4863	53	1	groups	group	NOUN
ejpam-4863	53	2	not	not	PART
ejpam-4863	53	3	satisfying	satisfy	VERB
ejpam-4863	53	4	this	this	DET
ejpam-4863	53	5	property	property	NOUN
ejpam-4863	53	6	are	be	AUX
ejpam-4863	53	7	said	say	VERB
ejpam-4863	53	8	to	to	PART
ejpam-4863	53	9	be	be	AUX
ejpam-4863	53	10	non−abelian	non−abelian	ADJ
ejpam-4863	53	11	or	or	CCONJ
ejpam-4863	53	12	noncommutative	noncommutative	ADJ
ejpam-4863	53	13	.	.	PUNCT
ejpam-4863	54	1	a	a	DET
ejpam-4863	54	2	subgroup	subgroup	NOUN
ejpam-4863	54	3	h	h	NOUN
ejpam-4863	54	4	of	of	ADP
ejpam-4863	54	5	a	a	DET
ejpam-4863	54	6	group	group	NOUN
ejpam-4863	54	7	g	g	NOUN
ejpam-4863	54	8	is	be	AUX
ejpam-4863	54	9	a	a	DET
ejpam-4863	54	10	subset	subset	ADJ
ejpam-4863	54	11	h	h	NOUN
ejpam-4863	54	12	of	of	ADP
ejpam-4863	54	13	g	g	NOUN
ejpam-4863	54	14	such	such	ADJ
ejpam-4863	54	15	that	that	SCONJ
ejpam-4863	54	16	when	when	SCONJ
ejpam-4863	54	17	the	the	DET
ejpam-4863	54	18	group	group	NOUN
ejpam-4863	54	19	operation	operation	NOUN
ejpam-4863	54	20	of	of	ADP
ejpam-4863	54	21	g	g	PROPN
ejpam-4863	54	22	is	be	AUX
ejpam-4863	54	23	restricted	restrict	VERB
ejpam-4863	54	24	to	to	ADP
ejpam-4863	54	25	h	h	NOUN
ejpam-4863	54	26	,	,	PUNCT
ejpam-4863	54	27	h	h	PROPN
ejpam-4863	54	28	is	be	AUX
ejpam-4863	54	29	a	a	DET
ejpam-4863	54	30	group	group	NOUN
ejpam-4863	54	31	in	in	ADP
ejpam-4863	54	32	its	its	PRON
ejpam-4863	54	33	own	own	ADJ
ejpam-4863	54	34	right	right	NOUN
ejpam-4863	54	35	.	.	PUNCT
ejpam-4863	55	1	the	the	DET
ejpam-4863	55	2	subgroup	subgroup	NOUN
ejpam-4863	55	3	h	h	NOUN
ejpam-4863	55	4	=	=	SYM
ejpam-4863	55	5	e	e	PROPN
ejpam-4863	55	6	of	of	ADP
ejpam-4863	55	7	a	a	DET
ejpam-4863	55	8	group	group	NOUN
ejpam-4863	55	9	g	g	NOUN
ejpam-4863	55	10	is	be	AUX
ejpam-4863	55	11	called	call	VERB
ejpam-4863	55	12	the	the	DET
ejpam-4863	55	13	trivial	trivial	ADJ
ejpam-4863	55	14	subgroup	subgroup	NOUN
ejpam-4863	55	15	.	.	PUNCT
ejpam-4863	56	1	a	a	DET
ejpam-4863	56	2	subgroup	subgroup	NOUN
ejpam-4863	56	3	that	that	PRON
ejpam-4863	56	4	is	be	AUX
ejpam-4863	56	5	a	a	DET
ejpam-4863	56	6	proper	proper	ADJ
ejpam-4863	56	7	subset	subset	NOUN
ejpam-4863	56	8	of	of	ADP
ejpam-4863	56	9	g	g	PROPN
ejpam-4863	56	10	is	be	AUX
ejpam-4863	56	11	called	call	VERB
ejpam-4863	56	12	a	a	DET
ejpam-4863	56	13	proper	proper	ADJ
ejpam-4863	56	14	subgroup	subgroup	NOUN
ejpam-4863	56	15	.	.	PUNCT
ejpam-4863	57	1	let	let	VERB
ejpam-4863	57	2	g	g	PRON
ejpam-4863	57	3	be	be	AUX
ejpam-4863	57	4	a	a	DET
ejpam-4863	57	5	group	group	NOUN
ejpam-4863	57	6	,	,	PUNCT
ejpam-4863	57	7	and	and	CCONJ
ejpam-4863	57	8	let	let	VERB
ejpam-4863	57	9	a	a	DET
ejpam-4863	57	10	be	be	AUX
ejpam-4863	57	11	any	any	DET
ejpam-4863	57	12	element	element	NOUN
ejpam-4863	57	13	in	in	ADP
ejpam-4863	57	14	g.	g.	PROPN
ejpam-4863	57	15	then	then	ADV
ejpam-4863	57	16	the	the	DET
ejpam-4863	57	17	set	set	NOUN
ejpam-4863	57	18	(	(	PUNCT
ejpam-4863	57	19	a	a	X
ejpam-4863	57	20	)	)	PUNCT
ejpam-4863	57	21	=	=	SYM
ejpam-4863	57	22	{	{	PUNCT
ejpam-4863	57	23	ak	ak	PROPN
ejpam-4863	57	24	:	:	PUNCT
ejpam-4863	57	25	k	k	PROPN
ejpam-4863	57	26	is	be	AUX
ejpam-4863	57	27	an	an	DET
ejpam-4863	57	28	integer	integer	NOUN
ejpam-4863	57	29	}	}	PUNCT
ejpam-4863	57	30	is	be	AUX
ejpam-4863	57	31	a	a	DET
ejpam-4863	57	32	subgroup	subgroup	NOUN
ejpam-4863	57	33	of	of	ADP
ejpam-4863	57	34	g.	g.	PROPN
ejpam-4863	57	35	furthermore	furthermore	ADV
ejpam-4863	57	36	,	,	PUNCT
ejpam-4863	57	37	(	(	PUNCT
ejpam-4863	57	38	a	a	X
ejpam-4863	57	39	)	)	PUNCT
ejpam-4863	57	40	is	be	AUX
ejpam-4863	57	41	the	the	DET
ejpam-4863	57	42	smallest	small	ADJ
ejpam-4863	57	43	subgroup	subgroup	NOUN
ejpam-4863	57	44	of	of	ADP
ejpam-4863	57	45	g	g	PROPN
ejpam-4863	57	46	that	that	PRON
ejpam-4863	57	47	contains	contain	VERB
ejpam-4863	57	48	a.	a.	NOUN
ejpam-4863	57	49	for	for	ADP
ejpam-4863	57	50	a	a	DET
ejpam-4863	57	51	∈	∈	PROPN
ejpam-4863	57	52	g	g	NOUN
ejpam-4863	57	53	,	,	PUNCT
ejpam-4863	57	54	we	we	PRON
ejpam-4863	57	55	call	call	VERB
ejpam-4863	57	56	(	(	PUNCT
ejpam-4863	57	57	a	a	X
ejpam-4863	57	58	)	)	PUNCT
ejpam-4863	57	59	the	the	DET
ejpam-4863	57	60	cyclic	cyclic	PROPN
ejpam-4863	57	61	subgroup	subgroup	NOUN
ejpam-4863	57	62	generated	generate	VERB
ejpam-4863	57	63	by	by	ADP
ejpam-4863	57	64	a.	a.	NOUN
ejpam-4863	57	65	if	if	SCONJ
ejpam-4863	57	66	g	g	PROPN
ejpam-4863	57	67	contains	contain	VERB
ejpam-4863	57	68	some	some	DET
ejpam-4863	57	69	element	element	NOUN
ejpam-4863	57	70	a	a	DET
ejpam-4863	57	71	such	such	ADJ
ejpam-4863	57	72	that	that	DET
ejpam-4863	57	73	g	g	NOUN
ejpam-4863	57	74	=	=	PUNCT
ejpam-4863	57	75	(	(	PUNCT
ejpam-4863	57	76	a	a	NOUN
ejpam-4863	57	77	)	)	PUNCT
ejpam-4863	57	78	,	,	PUNCT
ejpam-4863	57	79	then	then	ADV
ejpam-4863	57	80	g	g	PROPN
ejpam-4863	57	81	is	be	AUX
ejpam-4863	57	82	a	a	DET
ejpam-4863	57	83	cyclic	cyclic	ADJ
ejpam-4863	57	84	group	group	NOUN
ejpam-4863	57	85	.	.	PUNCT
ejpam-4863	58	1	in	in	ADP
ejpam-4863	58	2	this	this	DET
ejpam-4863	58	3	case	case	NOUN
ejpam-4863	58	4	,	,	PUNCT
ejpam-4863	58	5	a	a	PRON
ejpam-4863	58	6	is	be	AUX
ejpam-4863	58	7	a	a	DET
ejpam-4863	58	8	generator	generator	NOUN
ejpam-4863	58	9	of	of	ADP
ejpam-4863	58	10	g.	g.	PROPN
ejpam-4863	58	11	the	the	DET
ejpam-4863	58	12	order	order	NOUN
ejpam-4863	58	13	of	of	ADP
ejpam-4863	58	14	a	a	PRON
ejpam-4863	58	15	is	be	AUX
ejpam-4863	58	16	the	the	DET
ejpam-4863	58	17	smallest	small	ADJ
ejpam-4863	58	18	positive	positive	ADJ
ejpam-4863	58	19	integer	integer	NOUN
ejpam-4863	58	20	n	n	CCONJ
ejpam-4863	58	21	such	such	ADJ
ejpam-4863	58	22	that	that	SCONJ
ejpam-4863	58	23	an	an	DET
ejpam-4863	58	24	=	=	SYM
ejpam-4863	58	25	e	e	NOUN
ejpam-4863	58	26	,	,	PUNCT
ejpam-4863	58	27	and	and	CCONJ
ejpam-4863	58	28	we	we	PRON
ejpam-4863	58	29	write	write	VERB
ejpam-4863	58	30	|a|	|a|	PROPN
ejpam-4863	58	31	=	=	PROPN
ejpam-4863	58	32	n.	n.	NOUN
ejpam-4863	58	33	if	if	SCONJ
ejpam-4863	58	34	there	there	PRON
ejpam-4863	58	35	is	be	VERB
ejpam-4863	58	36	no	no	DET
ejpam-4863	58	37	such	such	ADJ
ejpam-4863	58	38	integer	integer	NOUN
ejpam-4863	58	39	n	n	CCONJ
ejpam-4863	58	40	,	,	PUNCT
ejpam-4863	58	41	we	we	PRON
ejpam-4863	58	42	say	say	VERB
ejpam-4863	58	43	that	that	SCONJ
ejpam-4863	58	44	the	the	DET
ejpam-4863	58	45	order	order	NOUN
ejpam-4863	58	46	of	of	ADP
ejpam-4863	58	47	a	a	PRON
ejpam-4863	58	48	is	be	AUX
ejpam-4863	58	49	infinite	infinite	ADJ
ejpam-4863	58	50	and	and	CCONJ
ejpam-4863	58	51	write	write	VERB
ejpam-4863	58	52	|a|	|a|	PROPN
ejpam-4863	58	53	=	=	SYM
ejpam-4863	58	54	∞	∞	PROPN
ejpam-4863	58	55	to	to	PART
ejpam-4863	58	56	denote	denote	VERB
ejpam-4863	58	57	the	the	DET
ejpam-4863	58	58	order	order	NOUN
ejpam-4863	58	59	of	of	ADP
ejpam-4863	58	60	a.b	a.b	PROPN
ejpam-4863	58	61	note	note	VERB
ejpam-4863	58	62	that	that	SCONJ
ejpam-4863	58	63	a	a	DET
ejpam-4863	58	64	cyclic	cyclic	ADJ
ejpam-4863	58	65	group	group	NOUN
ejpam-4863	58	66	can	can	AUX
ejpam-4863	58	67	have	have	AUX
ejpam-4863	58	68	more	more	ADJ
ejpam-4863	58	69	than	than	ADP
ejpam-4863	58	70	a	a	DET
ejpam-4863	58	71	single	single	ADJ
ejpam-4863	58	72	generator	generator	NOUN
ejpam-4863	58	73	.	.	PUNCT
ejpam-4863	59	1	for	for	ADP
ejpam-4863	59	2	example	example	NOUN
ejpam-4863	59	3	,	,	PUNCT
ejpam-4863	59	4	from	from	ADP
ejpam-4863	59	5	the	the	DET
ejpam-4863	59	6	group	group	NOUN
ejpam-4863	59	7	of	of	ADP
ejpam-4863	59	8	integers	integer	NOUN
ejpam-4863	59	9	modulo	modulo	VERB
ejpam-4863	59	10	6	6	NUM
ejpam-4863	59	11	,	,	PUNCT
ejpam-4863	59	12	both	both	DET
ejpam-4863	59	13	1	1	NUM
ejpam-4863	59	14	and	and	CCONJ
ejpam-4863	59	15	5	5	NUM
ejpam-4863	59	16	generate	generate	NOUN
ejpam-4863	59	17	z6	z6	NOUN
ejpam-4863	59	18	;	;	PUNCT
ejpam-4863	59	19	hence	hence	ADV
ejpam-4863	59	20	,	,	PUNCT
ejpam-4863	59	21	z6	z6	PROPN
ejpam-4863	59	22	is	be	AUX
ejpam-4863	59	23	a	a	DET
ejpam-4863	59	24	cyclic	cyclic	ADJ
ejpam-4863	59	25	group	group	NOUN
ejpam-4863	59	26	.	.	PUNCT
ejpam-4863	60	1	not	not	PART
ejpam-4863	60	2	every	every	DET
ejpam-4863	60	3	element	element	NOUN
ejpam-4863	60	4	in	in	ADP
ejpam-4863	60	5	a	a	DET
ejpam-4863	60	6	cyclic	cyclic	ADJ
ejpam-4863	60	7	group	group	NOUN
ejpam-4863	60	8	is	be	AUX
ejpam-4863	60	9	necessarily	necessarily	ADV
ejpam-4863	60	10	a	a	DET
ejpam-4863	60	11	generator	generator	NOUN
ejpam-4863	60	12	of	of	ADP
ejpam-4863	60	13	the	the	DET
ejpam-4863	60	14	group	group	NOUN
ejpam-4863	60	15	.	.	PUNCT
ejpam-4863	61	1	the	the	DET
ejpam-4863	61	2	order	order	NOUN
ejpam-4863	61	3	of	of	ADP
ejpam-4863	61	4	2	2	NUM
ejpam-4863	61	5	∈	∈	NOUN
ejpam-4863	61	6	z6	z6	NOUN
ejpam-4863	61	7	is	be	AUX
ejpam-4863	61	8	3	3	NUM
ejpam-4863	61	9	.	.	PUNCT
ejpam-4863	62	1	the	the	DET
ejpam-4863	62	2	cyclic	cyclic	PROPN
ejpam-4863	62	3	subgroup	subgroup	NOUN
ejpam-4863	62	4	generated	generate	VERB
ejpam-4863	62	5	by	by	ADP
ejpam-4863	62	6	2	2	NUM
ejpam-4863	62	7	is	be	AUX
ejpam-4863	62	8	(	(	PUNCT
ejpam-4863	62	9	2	2	NUM
ejpam-4863	62	10	)	)	PUNCT
ejpam-4863	62	11	=	=	PRON
ejpam-4863	62	12	{	{	PUNCT
ejpam-4863	62	13	0	0	NUM
ejpam-4863	62	14	,	,	PUNCT
ejpam-4863	62	15	2	2	NUM
ejpam-4863	62	16	,	,	PUNCT
ejpam-4863	62	17	4	4	NUM
ejpam-4863	62	18	}	}	PUNCT
ejpam-4863	62	19	.	.	PUNCT
ejpam-4863	63	1	the	the	DET
ejpam-4863	63	2	klien	klien	PROPN
ejpam-4863	63	3	4	4	PROPN
ejpam-4863	63	4	-	-	PUNCT
ejpam-4863	63	5	group	group	NOUN
ejpam-4863	63	6	v	v	NOUN
ejpam-4863	63	7	is	be	AUX
ejpam-4863	63	8	an	an	DET
ejpam-4863	63	9	abelian	abelian	ADJ
ejpam-4863	63	10	noncyclic	noncyclic	NOUN
ejpam-4863	63	11	group	group	NOUN
ejpam-4863	63	12	consisting	consist	VERB
ejpam-4863	63	13	of	of	ADP
ejpam-4863	63	14	3	3	NUM
ejpam-4863	63	15	elements	element	NOUN
ejpam-4863	63	16	a	a	DET
ejpam-4863	63	17	,	,	PUNCT
ejpam-4863	63	18	b	b	NOUN
ejpam-4863	63	19	,	,	PUNCT
ejpam-4863	63	20	c	c	PROPN
ejpam-4863	63	21	and	and	CCONJ
ejpam-4863	63	22	an	an	DET
ejpam-4863	63	23	identity	identity	NOUN
ejpam-4863	63	24	element	element	NOUN
ejpam-4863	63	25	e	e	NOUN
ejpam-4863	63	26	,	,	PUNCT
ejpam-4863	63	27	with	with	ADP
ejpam-4863	63	28	the	the	DET
ejpam-4863	63	29	property	property	NOUN
ejpam-4863	63	30	that	that	PRON
ejpam-4863	63	31	a2	a2	PROPN
ejpam-4863	63	32	=	=	SYM
ejpam-4863	63	33	b2	b2	PROPN
ejpam-4863	63	34	=	=	PROPN
ejpam-4863	63	35	c2	c2	PROPN
ejpam-4863	63	36	=	=	PUNCT
ejpam-4863	63	37	e.	e.	PROPN
ejpam-4863	63	38	3	3	PROPN
ejpam-4863	63	39	.	.	PUNCT
ejpam-4863	63	40	generator	generator	NOUN
ejpam-4863	63	41	graph	graph	NOUN
ejpam-4863	63	42	of	of	ADP
ejpam-4863	63	43	group	group	NOUN
ejpam-4863	63	44	definition	definition	NOUN
ejpam-4863	63	45	1	1	NUM
ejpam-4863	63	46	.	.	PUNCT
ejpam-4863	64	1	the	the	DET
ejpam-4863	64	2	generator	generator	NOUN
ejpam-4863	64	3	graph	graph	NOUN
ejpam-4863	64	4	gg(g	gg(g	PROPN
ejpam-4863	64	5	)	)	PUNCT
ejpam-4863	64	6	of	of	ADP
ejpam-4863	64	7	a	a	DET
ejpam-4863	64	8	group	group	NOUN
ejpam-4863	64	9	g	g	NOUN
ejpam-4863	64	10	is	be	AUX
ejpam-4863	64	11	a	a	DET
ejpam-4863	64	12	graph	graph	NOUN
ejpam-4863	64	13	whose	whose	DET
ejpam-4863	64	14	vertices	vertex	NOUN
ejpam-4863	64	15	are	be	AUX
ejpam-4863	64	16	the	the	DET
ejpam-4863	64	17	elements	element	NOUN
ejpam-4863	64	18	of	of	ADP
ejpam-4863	64	19	g	g	NOUN
ejpam-4863	64	20	,	,	PUNCT
ejpam-4863	64	21	and	and	CCONJ
ejpam-4863	64	22	two	two	NUM
ejpam-4863	64	23	vertices	vertex	NOUN
ejpam-4863	64	24	x	x	PUNCT
ejpam-4863	64	25	and	and	CCONJ
ejpam-4863	64	26	y	y	PROPN
ejpam-4863	64	27	in	in	ADP
ejpam-4863	64	28	gg(g	gg(g	PROPN
ejpam-4863	64	29	)	)	PUNCT
ejpam-4863	64	30	are	be	AUX
ejpam-4863	64	31	joined	join	VERB
ejpam-4863	64	32	by	by	ADP
ejpam-4863	64	33	an	an	DET
ejpam-4863	64	34	edge	edge	NOUN
ejpam-4863	64	35	if	if	SCONJ
ejpam-4863	64	36	either	either	CCONJ
ejpam-4863	64	37	x	x	SYM
ejpam-4863	64	38	or	or	CCONJ
ejpam-4863	64	39	y	y	PROPN
ejpam-4863	64	40	is	be	AUX
ejpam-4863	64	41	a	a	DET
ejpam-4863	64	42	generator	generator	NOUN
ejpam-4863	64	43	of	of	ADP
ejpam-4863	64	44	g.	g.	PROPN
ejpam-4863	64	45	figure	figure	PROPN
ejpam-4863	64	46	1	1	NUM
ejpam-4863	64	47	illustrates	illustrate	VERB
ejpam-4863	64	48	the	the	DET
ejpam-4863	64	49	generator	generator	NOUN
ejpam-4863	64	50	graphs	graph	NOUN
ejpam-4863	64	51	gg(z6	gg(z6	NOUN
ejpam-4863	64	52	)	)	PUNCT
ejpam-4863	64	53	and	and	CCONJ
ejpam-4863	64	54	gg(z5	gg(z5	NOUN
ejpam-4863	64	55	)	)	PUNCT
ejpam-4863	64	56	of	of	ADP
ejpam-4863	64	57	groups	group	NOUN
ejpam-4863	64	58	z6	z6	PROPN
ejpam-4863	64	59	under	under	ADP
ejpam-4863	64	60	addition	addition	NOUN
ejpam-4863	64	61	modulo	modulo	NOUN
ejpam-4863	64	62	6	6	NUM
ejpam-4863	64	63	and	and	CCONJ
ejpam-4863	64	64	z5	z5	PROPN
ejpam-4863	64	65	under	under	ADP
ejpam-4863	64	66	addition	addition	NOUN
ejpam-4863	64	67	modulo	modulo	NOUN
ejpam-4863	64	68	5	5	NUM
ejpam-4863	64	69	,	,	PUNCT
ejpam-4863	64	70	respectively	respectively	ADV
ejpam-4863	64	71	.	.	PUNCT
ejpam-4863	65	1	the	the	DET
ejpam-4863	65	2	set	set	VERB
ejpam-4863	65	3	sz6	sz6	NOUN
ejpam-4863	65	4	=	=	SYM
ejpam-4863	65	5	{	{	PUNCT
ejpam-4863	65	6	1	1	NUM
ejpam-4863	65	7	,	,	PUNCT
ejpam-4863	65	8	5	5	NUM
ejpam-4863	65	9	}	}	PUNCT
ejpam-4863	65	10	is	be	AUX
ejpam-4863	65	11	the	the	DET
ejpam-4863	65	12	set	set	NOUN
ejpam-4863	65	13	of	of	ADP
ejpam-4863	65	14	all	all	DET
ejpam-4863	65	15	generators	generator	NOUN
ejpam-4863	65	16	of	of	ADP
ejpam-4863	65	17	z6	z6	PROPN
ejpam-4863	65	18	while	while	SCONJ
ejpam-4863	65	19	the	the	DET
ejpam-4863	65	20	set	set	NOUN
ejpam-4863	65	21	sz5	sz5	NOUN
ejpam-4863	65	22	=	=	PUNCT
ejpam-4863	65	23	{	{	PUNCT
ejpam-4863	65	24	1	1	NUM
ejpam-4863	65	25	,	,	PUNCT
ejpam-4863	65	26	2	2	NUM
ejpam-4863	65	27	,	,	PUNCT
ejpam-4863	65	28	3	3	NUM
ejpam-4863	65	29	,	,	PUNCT
ejpam-4863	65	30	4	4	NUM
ejpam-4863	65	31	}	}	PUNCT
ejpam-4863	65	32	is	be	AUX
ejpam-4863	65	33	the	the	DET
ejpam-4863	65	34	set	set	NOUN
ejpam-4863	65	35	of	of	ADP
ejpam-4863	65	36	all	all	DET
ejpam-4863	65	37	generators	generator	NOUN
ejpam-4863	65	38	of	of	ADP
ejpam-4863	65	39	z5	z5	PROPN
ejpam-4863	65	40	.	.	PUNCT
ejpam-4863	66	1	observe	observe	VERB
ejpam-4863	66	2	that	that	SCONJ
ejpam-4863	66	3	in	in	ADP
ejpam-4863	66	4	z6	z6	PROPN
ejpam-4863	66	5	,	,	PUNCT
ejpam-4863	66	6	degz6(1	degz6(1	NUM
ejpam-4863	66	7	)	)	PUNCT
ejpam-4863	66	8	=	=	SYM
ejpam-4863	66	9	degz6(5	degz6(5	X
ejpam-4863	66	10	)	)	PUNCT
ejpam-4863	66	11	=	=	SYM
ejpam-4863	66	12	5	5	NUM
ejpam-4863	66	13	=	=	SYM
ejpam-4863	66	14	|v	|v	X
ejpam-4863	66	15	(	(	PUNCT
ejpam-4863	66	16	gg(g))|−1	gg(g))|−1	PROPN
ejpam-4863	66	17	while	while	SCONJ
ejpam-4863	66	18	degz6(0	degz6(0	NUM
ejpam-4863	66	19	)	)	PUNCT
ejpam-4863	66	20	=	=	SYM
ejpam-4863	66	21	degz6(2	degz6(2	PROPN
ejpam-4863	66	22	)	)	PUNCT
ejpam-4863	66	23	=	=	PUNCT
ejpam-4863	66	24	degz6(3	degz6(3	PROPN
ejpam-4863	66	25	)	)	PUNCT
ejpam-4863	66	26	=	=	PUNCT
ejpam-4863	66	27	degz6(4	degz6(4	X
ejpam-4863	66	28	)	)	PUNCT
ejpam-4863	66	29	=	=	SYM
ejpam-4863	67	1	2	2	NUM
ejpam-4863	67	2	=	=	SYM
ejpam-4863	67	3	|sz6	|sz6	X
ejpam-4863	67	4	|	|	NOUN
ejpam-4863	67	5	.	.	PUNCT
ejpam-4863	68	1	theorem	theorem	NOUN
ejpam-4863	68	2	1	1	NUM
ejpam-4863	68	3	.	.	PUNCT
ejpam-4863	69	1	let	let	VERB
ejpam-4863	69	2	g	g	PRON
ejpam-4863	69	3	be	be	AUX
ejpam-4863	69	4	a	a	DET
ejpam-4863	69	5	group	group	NOUN
ejpam-4863	69	6	of	of	ADP
ejpam-4863	69	7	order	order	NOUN
ejpam-4863	69	8	n	n	CCONJ
ejpam-4863	69	9	>	>	X
ejpam-4863	69	10	1	1	NUM
ejpam-4863	70	1	and	and	CCONJ
ejpam-4863	70	2	,	,	PUNCT
ejpam-4863	70	3	sg	sg	PART
ejpam-4863	70	4	be	be	AUX
ejpam-4863	70	5	the	the	DET
ejpam-4863	70	6	set	set	NOUN
ejpam-4863	70	7	of	of	ADP
ejpam-4863	70	8	all	all	DET
ejpam-4863	70	9	generators	generator	NOUN
ejpam-4863	70	10	of	of	ADP
ejpam-4863	70	11	g.	g.	PROPN
ejpam-4863	70	12	let	let	VERB
ejpam-4863	70	13	x	x	SYM
ejpam-4863	70	14	∈	∈	PROPN
ejpam-4863	70	15	v	v	X
ejpam-4863	70	16	(	(	PUNCT
ejpam-4863	70	17	gg(g	gg(g	PROPN
ejpam-4863	70	18	)	)	PUNCT
ejpam-4863	70	19	)	)	PUNCT
ejpam-4863	70	20	.	.	PUNCT
ejpam-4863	71	1	then	then	ADV
ejpam-4863	71	2	(	(	PUNCT
ejpam-4863	71	3	i	i	NOUN
ejpam-4863	71	4	)	)	PUNCT
ejpam-4863	71	5	degg(x	degg(x	NOUN
ejpam-4863	71	6	)	)	PUNCT
ejpam-4863	71	7	=	=	PUNCT
ejpam-4863	71	8	n−	n−	NOUN
ejpam-4863	71	9	1	1	NUM
ejpam-4863	71	10	if	if	SCONJ
ejpam-4863	71	11	x	x	PROPN
ejpam-4863	71	12	∈	∈	NOUN
ejpam-4863	71	13	sg	sg	NOUN
ejpam-4863	71	14	and	and	CCONJ
ejpam-4863	71	15	degg(x	degg(x	NOUN
ejpam-4863	71	16	)	)	PUNCT
ejpam-4863	72	1	=	=	NOUN
ejpam-4863	72	2	|sg|	|sg|	NOUN
ejpam-4863	72	3	if	if	SCONJ
ejpam-4863	72	4	x	x	PROPN
ejpam-4863	72	5	/∈	/∈	PUNCT
ejpam-4863	72	6	sg	sg	PROPN
ejpam-4863	72	7	;	;	PUNCT
ejpam-4863	72	8	and	and	CCONJ
ejpam-4863	72	9	(	(	PUNCT
ejpam-4863	72	10	ii	ii	NOUN
ejpam-4863	72	11	)	)	PUNCT
ejpam-4863	72	12	the	the	DET
ejpam-4863	72	13	size	size	NOUN
ejpam-4863	72	14	of	of	ADP
ejpam-4863	72	15	gg(g	gg(g	PROPN
ejpam-4863	72	16	)	)	PUNCT
ejpam-4863	72	17	is	be	AUX
ejpam-4863	72	18	given	give	VERB
ejpam-4863	72	19	by	by	ADP
ejpam-4863	72	20	|e(gg(g))|	|e(gg(g))|	NOUN
ejpam-4863	72	21	=	=	SYM
ejpam-4863	72	22	|sg|	|sg|	NOUN
ejpam-4863	72	23	2	2	NUM
ejpam-4863	72	24	(	(	PUNCT
ejpam-4863	72	25	2n−	2n−	PROPN
ejpam-4863	72	26	|sg|	|sg|	PROPN
ejpam-4863	72	27	−	−	NOUN
ejpam-4863	72	28	1	1	NUM
ejpam-4863	72	29	)	)	PUNCT
ejpam-4863	72	30	.	.	PUNCT
ejpam-4863	72	31	.	.	PUNCT
ejpam-4863	73	1	t.	t.	PROPN
ejpam-4863	73	2	l.	l.	PROPN
ejpam-4863	73	3	tacbobo	tacbobo	PROPN
ejpam-4863	73	4	/	/	SYM
ejpam-4863	73	5	eur	eur	PROPN
ejpam-4863	73	6	.	.	PUNCT
ejpam-4863	74	1	j.	j.	PROPN
ejpam-4863	74	2	pure	pure	PROPN
ejpam-4863	74	3	appl	appl	PROPN
ejpam-4863	74	4	.	.	PROPN
ejpam-4863	74	5	math	math	PROPN
ejpam-4863	74	6	,	,	PUNCT
ejpam-4863	74	7	16	16	NUM
ejpam-4863	74	8	(	(	PUNCT
ejpam-4863	74	9	3	3	NUM
ejpam-4863	74	10	)	)	PUNCT
ejpam-4863	74	11	(	(	PUNCT
ejpam-4863	74	12	2023	2023	NUM
ejpam-4863	74	13	)	)	PUNCT
ejpam-4863	74	14	,	,	PUNCT
ejpam-4863	74	15	1894	1894	NUM
ejpam-4863	74	16	-	-	SYM
ejpam-4863	74	17	1901	1901	NUM
ejpam-4863	74	18	1897	1897	NUM
ejpam-4863	74	19	....................................	....................................	PUNCT
ejpam-4863	75	1	....................................	....................................	PUNCT
ejpam-4863	75	2	....................................	....................................	PUNCT
ejpam-4863	76	1	....................................	....................................	PUNCT
ejpam-4863	76	2	....................................	....................................	PUNCT
ejpam-4863	77	1	....................................	....................................	PUNCT
ejpam-4863	77	2	...................	...................	PUNCT
ejpam-4863	78	1	..................	..................	PUNCT
ejpam-4863	78	2	..................	..................	PUNCT
ejpam-4863	79	1	..................	..................	PUNCT
ejpam-4863	79	2	..................	..................	PUNCT
ejpam-4863	80	1	..................	..................	PUNCT
ejpam-4863	80	2	..................	..................	PUNCT
ejpam-4863	81	1	..................	..................	PUNCT
ejpam-4863	81	2	..................	..................	PUNCT
ejpam-4863	82	1	..................	..................	PUNCT
ejpam-4863	82	2	..................	..................	PUNCT
ejpam-4863	83	1	..................	..................	PUNCT
ejpam-4863	83	2	..................	..................	PUNCT
ejpam-4863	84	1	...........	...........	PUNCT
ejpam-4863	84	2	..........	..........	PUNCT
ejpam-4863	85	1	.........	.........	PUNCT
ejpam-4863	85	2	.........	.........	PUNCT
ejpam-4863	86	1	.........	.........	PUNCT
ejpam-4863	86	2	.........	.........	PUNCT
ejpam-4863	87	1	.........	.........	PUNCT
ejpam-4863	87	2	.........	.........	PUNCT
ejpam-4863	88	1	.........	.........	PUNCT
ejpam-4863	88	2	.........	.........	PUNCT
ejpam-4863	89	1	.........	.........	PUNCT
ejpam-4863	89	2	.........	.........	PUNCT
ejpam-4863	90	1	.........	.........	PUNCT
ejpam-4863	90	2	.........	.........	PUNCT
ejpam-4863	91	1	.........	.........	PUNCT
ejpam-4863	91	2	.........	.........	PUNCT
ejpam-4863	92	1	.........	.........	PUNCT
ejpam-4863	92	2	.........	.........	PUNCT
ejpam-4863	93	1	.........	.........	PUNCT
ejpam-4863	93	2	.........	.........	PUNCT
ejpam-4863	94	1	.........	.........	PUNCT
ejpam-4863	94	2	.........	.........	PUNCT
ejpam-4863	95	1	.........	.........	PUNCT
ejpam-4863	95	2	.........	.........	PUNCT
ejpam-4863	96	1	.........	.........	PUNCT
ejpam-4863	96	2	.........	.........	PUNCT
ejpam-4863	97	1	.........	.........	PUNCT
ejpam-4863	97	2	.........	.........	PUNCT
ejpam-4863	97	3	..	..	PUNCT
ejpam-4863	97	4	.........	.........	PUNCT
ejpam-4863	97	5	........	........	PUNCT
ejpam-4863	97	6	........	........	PUNCT
ejpam-4863	97	7	........	........	PUNCT
ejpam-4863	97	8	........	........	PUNCT
ejpam-4863	97	9	........	........	PUNCT
ejpam-4863	97	10	........	........	PUNCT
ejpam-4863	97	11	........	........	PUNCT
ejpam-4863	97	12	........	........	PUNCT
ejpam-4863	97	13	........	........	PUNCT
ejpam-4863	97	14	........	........	PUNCT
ejpam-4863	97	15	........	........	PUNCT
ejpam-4863	97	16	........	........	PUNCT
ejpam-4863	97	17	........	........	PUNCT
ejpam-4863	97	18	........	........	PUNCT
ejpam-4863	97	19	........	........	PUNCT
ejpam-4863	97	20	........	........	PUNCT
ejpam-4863	97	21	........	........	PUNCT
ejpam-4863	97	22	........	........	PUNCT
ejpam-4863	97	23	........	........	PUNCT
ejpam-4863	97	24	........	........	PUNCT
ejpam-4863	97	25	........	........	PUNCT
ejpam-4863	97	26	........	........	PUNCT
ejpam-4863	97	27	........	........	PUNCT
ejpam-4863	97	28	........	........	PUNCT
ejpam-4863	97	29	........	........	PUNCT
ejpam-4863	98	1	........	........	PUNCT
ejpam-4863	98	2	.......................................................................................................................................................................	.......................................................................................................................................................................	PUNCT
ejpam-4863	98	3	...........	...........	PUNCT
ejpam-4863	98	4	...........	...........	PUNCT
ejpam-4863	98	5	...........	...........	PUNCT
ejpam-4863	98	6	...........	...........	PUNCT
ejpam-4863	98	7	...........	...........	PUNCT
ejpam-4863	98	8	...........	...........	PUNCT
ejpam-4863	98	9	...........	...........	PUNCT
ejpam-4863	98	10	...........	...........	PUNCT
ejpam-4863	98	11	...........	...........	PUNCT
ejpam-4863	98	12	...........	...........	PUNCT
ejpam-4863	98	13	...........	...........	PUNCT
ejpam-4863	98	14	...........	...........	PUNCT
ejpam-4863	98	15	........	........	PUNCT
ejpam-4863	98	16	.........	.........	PUNCT
ejpam-4863	98	17	........	........	PUNCT
ejpam-4863	98	18	........	........	PUNCT
ejpam-4863	98	19	........	........	PUNCT
ejpam-4863	98	20	........	........	PUNCT
ejpam-4863	98	21	........	........	PUNCT
ejpam-4863	98	22	........	........	PUNCT
ejpam-4863	98	23	........	........	PUNCT
ejpam-4863	98	24	........	........	PUNCT
ejpam-4863	98	25	........	........	PUNCT
ejpam-4863	98	26	........	........	PUNCT
ejpam-4863	98	27	........	........	PUNCT
ejpam-4863	98	28	........	........	PUNCT
ejpam-4863	98	29	........	........	PUNCT
ejpam-4863	98	30	........	........	PUNCT
ejpam-4863	98	31	........	........	PUNCT
ejpam-4863	98	32	........	........	PUNCT
ejpam-4863	98	33	........	........	PUNCT
ejpam-4863	98	34	........	........	PUNCT
ejpam-4863	98	35	........	........	PUNCT
ejpam-4863	98	36	........	........	PUNCT
ejpam-4863	98	37	........	........	PUNCT
ejpam-4863	98	38	........	........	PUNCT
ejpam-4863	98	39	........	........	PUNCT
ejpam-4863	98	40	........	........	PUNCT
ejpam-4863	98	41	........	........	PUNCT
ejpam-4863	98	42	........	........	PUNCT
ejpam-4863	99	1	.........................................................................................................................................................................................................................................................	.........................................................................................................................................................................................................................................................	PUNCT
ejpam-4863	99	2	......................................................................................................................................................................................................................................................	......................................................................................................................................................................................................................................................	PUNCT
ejpam-4863	100	1	........................................................................................................	........................................................................................................	NUM
ejpam-4863	101	1	•	•	NUM
ejpam-4863	102	1	•	•	NOUN
ejpam-4863	102	2	1	1	NUM
ejpam-4863	102	3	5	5	NUM
ejpam-4863	102	4	0	0	NUM
ejpam-4863	102	5	2	2	NUM
ejpam-4863	102	6	3	3	NUM
ejpam-4863	102	7	4	4	NUM
ejpam-4863	102	8	gg(z6	gg(z6	NOUN
ejpam-4863	102	9	)	)	PUNCT
ejpam-4863	102	10	....................................	....................................	PUNCT
ejpam-4863	103	1	....................................	....................................	PUNCT
ejpam-4863	103	2	....................................	....................................	PUNCT
ejpam-4863	104	1	....................................	....................................	PUNCT
ejpam-4863	104	2	....................................	....................................	PUNCT
ejpam-4863	105	1	.....................................................................................................................................	.....................................................................................................................................	PUNCT
ejpam-4863	105	2	................................................................................................................................................................................................................................................................................	................................................................................................................................................................................................................................................................................	PUNCT
ejpam-4863	106	1	...............................................................................................................................................................................................................................................................................................................................................................	...............................................................................................................................................................................................................................................................................................................................................................	PUNCT
ejpam-4863	106	2	..............	..............	PUNCT
ejpam-4863	107	1	..............	..............	PUNCT
ejpam-4863	107	2	..............	..............	PUNCT
ejpam-4863	108	1	..............	..............	PUNCT
ejpam-4863	108	2	..............	..............	PUNCT
ejpam-4863	109	1	..............	..............	PUNCT
ejpam-4863	109	2	..............	..............	PUNCT
ejpam-4863	110	1	..............	..............	PUNCT
ejpam-4863	110	2	..............	..............	PUNCT
ejpam-4863	111	1	..............	..............	PUNCT
ejpam-4863	111	2	..............	..............	PUNCT
ejpam-4863	112	1	..............	..............	PUNCT
ejpam-4863	112	2	..............	..............	PUNCT
ejpam-4863	113	1	.......................................................................................................................................................................................	.......................................................................................................................................................................................	PUNCT
ejpam-4863	113	2	....................	....................	PUNCT
ejpam-4863	113	3	....................	....................	PUNCT
ejpam-4863	113	4	....................	....................	PUNCT
ejpam-4863	113	5	....................	....................	PUNCT
ejpam-4863	113	6	....................	....................	PUNCT
ejpam-4863	113	7	....................	....................	PUNCT
ejpam-4863	113	8	....................	....................	PUNCT
ejpam-4863	113	9	....................	....................	PUNCT
ejpam-4863	113	10	....................	....................	PUNCT
ejpam-4863	113	11	....................	....................	PUNCT
ejpam-4863	113	12	....................	....................	PUNCT
ejpam-4863	113	13	....................	....................	PUNCT
ejpam-4863	113	14	...........	...........	PUNCT
ejpam-4863	114	1	..........	..........	PUNCT
ejpam-4863	114	2	.........	.........	PUNCT
ejpam-4863	115	1	.........	.........	PUNCT
ejpam-4863	115	2	.........	.........	PUNCT
ejpam-4863	116	1	.........	.........	PUNCT
ejpam-4863	116	2	.........	.........	PUNCT
ejpam-4863	117	1	.........	.........	PUNCT
ejpam-4863	117	2	.........	.........	PUNCT
ejpam-4863	118	1	.........	.........	PUNCT
ejpam-4863	118	2	.........	.........	PUNCT
ejpam-4863	119	1	.........	.........	PUNCT
ejpam-4863	119	2	.........	.........	PUNCT
ejpam-4863	120	1	.........	.........	PUNCT
ejpam-4863	120	2	.........	.........	PUNCT
ejpam-4863	121	1	.........	.........	PUNCT
ejpam-4863	121	2	.........	.........	PUNCT
ejpam-4863	122	1	.........	.........	PUNCT
ejpam-4863	122	2	.........	.........	PUNCT
ejpam-4863	123	1	.........	.........	PUNCT
ejpam-4863	123	2	.........	.........	PUNCT
ejpam-4863	124	1	.........	.........	PUNCT
ejpam-4863	124	2	.........	.........	PUNCT
ejpam-4863	125	1	.........	.........	PUNCT
ejpam-4863	125	2	.........	.........	PUNCT
ejpam-4863	126	1	.........	.........	PUNCT
ejpam-4863	126	2	.........	.........	PUNCT
ejpam-4863	126	3	.	.	PUNCT
ejpam-4863	127	1	...........	...........	PUNCT
ejpam-4863	127	2	..........	..........	PUNCT
ejpam-4863	128	1	..........	..........	PUNCT
ejpam-4863	128	2	..........	..........	PUNCT
ejpam-4863	129	1	..........	..........	PUNCT
ejpam-4863	129	2	..........	..........	PUNCT
ejpam-4863	130	1	..........	..........	PUNCT
ejpam-4863	130	2	..........	..........	PUNCT
ejpam-4863	131	1	..........	..........	PUNCT
ejpam-4863	131	2	..........	..........	PUNCT
ejpam-4863	132	1	..........	..........	PUNCT
ejpam-4863	132	2	..........	..........	PUNCT
ejpam-4863	133	1	..........	..........	PUNCT
ejpam-4863	133	2	..	..	PUNCT
ejpam-4863	133	3	............................................................................................................................................................................................................................................	............................................................................................................................................................................................................................................	PUNCT
ejpam-4863	134	1	.....................................................................................................................................................................................................	.....................................................................................................................................................................................................	PUNCT
ejpam-4863	135	1	•	•	NUM
ejpam-4863	135	2	•	•	NUM
ejpam-4863	135	3	••	••	NOUN
ejpam-4863	135	4	0	0	NUM
ejpam-4863	135	5	1	1	NUM
ejpam-4863	135	6	2	2	NUM
ejpam-4863	135	7	34	34	NUM
ejpam-4863	135	8	gg(z5	gg(z5	NOUN
ejpam-4863	135	9	)	)	PUNCT
ejpam-4863	135	10	figure	figure	NOUN
ejpam-4863	135	11	1	1	NUM
ejpam-4863	135	12	:	:	PUNCT
ejpam-4863	135	13	the	the	DET
ejpam-4863	135	14	generator	generator	NOUN
ejpam-4863	135	15	graphs	graph	VERB
ejpam-4863	135	16	gg(z6	gg(z6	NOUN
ejpam-4863	135	17	)	)	PUNCT
ejpam-4863	135	18	and	and	CCONJ
ejpam-4863	135	19	gg(z5	gg(z5	NOUN
ejpam-4863	135	20	)	)	PUNCT
ejpam-4863	135	21	.	.	PUNCT
ejpam-4863	136	1	proof	proof	NOUN
ejpam-4863	136	2	.	.	PUNCT
ejpam-4863	137	1	(	(	PUNCT
ejpam-4863	137	2	i	i	NOUN
ejpam-4863	137	3	)	)	PUNCT
ejpam-4863	137	4	if	if	SCONJ
ejpam-4863	137	5	x	x	PROPN
ejpam-4863	137	6	∈	∈	PROPN
ejpam-4863	137	7	sg	sg	PROPN
ejpam-4863	137	8	,	,	PUNCT
ejpam-4863	137	9	then	then	ADV
ejpam-4863	137	10	x	x	PUNCT
ejpam-4863	137	11	is	be	AUX
ejpam-4863	137	12	adjacent	adjacent	ADJ
ejpam-4863	137	13	to	to	ADP
ejpam-4863	137	14	the	the	DET
ejpam-4863	137	15	other	other	ADJ
ejpam-4863	137	16	n	n	CCONJ
ejpam-4863	137	17	−	−	NUM
ejpam-4863	137	18	1	1	NUM
ejpam-4863	137	19	vertices	vertex	NOUN
ejpam-4863	137	20	of	of	ADP
ejpam-4863	137	21	gg(g	gg(g	NOUN
ejpam-4863	137	22	)	)	PUNCT
ejpam-4863	137	23	.	.	PUNCT
ejpam-4863	138	1	in	in	ADP
ejpam-4863	138	2	this	this	DET
ejpam-4863	138	3	case	case	NOUN
ejpam-4863	138	4	,	,	PUNCT
ejpam-4863	138	5	degg(x	degg(x	NOUN
ejpam-4863	138	6	)	)	PUNCT
ejpam-4863	138	7	=	=	SYM
ejpam-4863	139	1	n	n	CCONJ
ejpam-4863	139	2	−	−	NOUN
ejpam-4863	140	1	1	1	X
ejpam-4863	140	2	.	.	PUNCT
ejpam-4863	141	1	if	if	SCONJ
ejpam-4863	141	2	x	x	PROPN
ejpam-4863	141	3	/∈	/∈	VERB
ejpam-4863	141	4	sg	sg	INTJ
ejpam-4863	141	5	,	,	PUNCT
ejpam-4863	141	6	then	then	ADV
ejpam-4863	141	7	x	x	PUNCT
ejpam-4863	141	8	is	be	AUX
ejpam-4863	141	9	adjacent	adjacent	ADJ
ejpam-4863	141	10	only	only	ADV
ejpam-4863	141	11	to	to	ADP
ejpam-4863	141	12	the	the	DET
ejpam-4863	141	13	|sg|	|sg|	PROPN
ejpam-4863	141	14	vertices	vertex	NOUN
ejpam-4863	141	15	in	in	ADP
ejpam-4863	141	16	gg(g	gg(g	PROPN
ejpam-4863	141	17	)	)	PUNCT
ejpam-4863	141	18	.	.	PUNCT
ejpam-4863	142	1	in	in	ADP
ejpam-4863	142	2	this	this	DET
ejpam-4863	142	3	case	case	NOUN
ejpam-4863	142	4	,	,	PUNCT
ejpam-4863	142	5	degg(x	degg(x	NOUN
ejpam-4863	142	6	)	)	PUNCT
ejpam-4863	142	7	=	=	SYM
ejpam-4863	142	8	|sg|	|sg|	NOUN
ejpam-4863	142	9	.	.	PUNCT
ejpam-4863	143	1	(	(	PUNCT
ejpam-4863	143	2	ii	ii	NOUN
ejpam-4863	143	3	)	)	PUNCT
ejpam-4863	143	4	the	the	DET
ejpam-4863	143	5	size	size	NOUN
ejpam-4863	143	6	of	of	ADP
ejpam-4863	143	7	gg(g	gg(g	PROPN
ejpam-4863	143	8	)	)	PUNCT
ejpam-4863	143	9	is	be	AUX
ejpam-4863	143	10	|e(gg(g))|	|e(gg(g))|	NOUN
ejpam-4863	143	11	=	=	SYM
ejpam-4863	143	12	1	1	NUM
ejpam-4863	143	13	2	2	NUM
ejpam-4863	143	14	∑	∑	PROPN
ejpam-4863	143	15	x∈v	x∈v	PROPN
ejpam-4863	143	16	(	(	PUNCT
ejpam-4863	143	17	gg(g	gg(g	PROPN
ejpam-4863	143	18	)	)	PUNCT
ejpam-4863	143	19	)	)	PUNCT
ejpam-4863	143	20	(	(	PUNCT
ejpam-4863	143	21	degg(x	degg(x	NOUN
ejpam-4863	143	22	)	)	PUNCT
ejpam-4863	143	23	)	)	PUNCT
ejpam-4863	143	24	=	=	SYM
ejpam-4863	144	1	1	1	NUM
ejpam-4863	144	2	2	2	NUM
ejpam-4863	145	1	[	[	X
ejpam-4863	145	2	|sg|(n−	|sg|(n−	PROPN
ejpam-4863	145	3	1	1	NUM
ejpam-4863	145	4	)	)	PUNCT
ejpam-4863	145	5	+	+	CCONJ
ejpam-4863	145	6	(	(	PUNCT
ejpam-4863	145	7	n−	n−	NOUN
ejpam-4863	145	8	|sg|)|sg|	|sg|)|sg|	NOUN
ejpam-4863	145	9	]	]	X
ejpam-4863	145	10	=	=	SYM
ejpam-4863	145	11	|sg|	|sg|	NOUN
ejpam-4863	145	12	2	2	NUM
ejpam-4863	146	1	[	[	X
ejpam-4863	146	2	(	(	PUNCT
ejpam-4863	146	3	n−	n−	NOUN
ejpam-4863	146	4	1	1	NUM
ejpam-4863	146	5	)	)	PUNCT
ejpam-4863	146	6	+	+	CCONJ
ejpam-4863	146	7	(	(	PUNCT
ejpam-4863	146	8	n−	n−	NOUN
ejpam-4863	146	9	|sg|	|sg|	NOUN
ejpam-4863	146	10	)	)	PUNCT
ejpam-4863	146	11	]	]	PUNCT
ejpam-4863	147	1	=	=	PUNCT
ejpam-4863	147	2	|sg|	|sg|	NOUN
ejpam-4863	147	3	2	2	NUM
ejpam-4863	147	4	(	(	PUNCT
ejpam-4863	147	5	2n−	2n−	PROPN
ejpam-4863	147	6	|sg|	|sg|	PROPN
ejpam-4863	147	7	−	−	NOUN
ejpam-4863	147	8	1	1	NUM
ejpam-4863	147	9	)	)	PUNCT
ejpam-4863	147	10	.	.	PUNCT
ejpam-4863	148	1	theorem	theorem	NOUN
ejpam-4863	148	2	2	2	NUM
ejpam-4863	148	3	.	.	PUNCT
ejpam-4863	149	1	let	let	VERB
ejpam-4863	149	2	g	g	PRON
ejpam-4863	149	3	be	be	AUX
ejpam-4863	149	4	a	a	DET
ejpam-4863	149	5	group	group	NOUN
ejpam-4863	149	6	of	of	ADP
ejpam-4863	149	7	order	order	NOUN
ejpam-4863	149	8	n	n	CCONJ
ejpam-4863	149	9	>	>	X
ejpam-4863	149	10	1	1	X
ejpam-4863	149	11	.	.	PUNCT
ejpam-4863	150	1	the	the	DET
ejpam-4863	150	2	generator	generator	NOUN
ejpam-4863	150	3	graph	graph	NOUN
ejpam-4863	150	4	gg(g	gg(g	PROPN
ejpam-4863	150	5	)	)	PUNCT
ejpam-4863	150	6	of	of	ADP
ejpam-4863	150	7	g	g	PROPN
ejpam-4863	150	8	is	be	AUX
ejpam-4863	150	9	complete	complete	ADJ
ejpam-4863	150	10	if	if	SCONJ
ejpam-4863	150	11	and	and	CCONJ
ejpam-4863	150	12	only	only	ADV
ejpam-4863	150	13	if	if	SCONJ
ejpam-4863	150	14	n	n	NOUN
ejpam-4863	150	15	is	be	AUX
ejpam-4863	150	16	prime	prime	ADJ
ejpam-4863	150	17	.	.	PUNCT
ejpam-4863	151	1	proof	proof	NOUN
ejpam-4863	151	2	.	.	PUNCT
ejpam-4863	152	1	assume	assume	VERB
ejpam-4863	152	2	that	that	SCONJ
ejpam-4863	152	3	gg(g	gg(g	PROPN
ejpam-4863	152	4	)	)	PUNCT
ejpam-4863	152	5	is	be	AUX
ejpam-4863	152	6	complete	complete	ADJ
ejpam-4863	152	7	,	,	PUNCT
ejpam-4863	152	8	and	and	CCONJ
ejpam-4863	152	9	suppose	suppose	VERB
ejpam-4863	152	10	the	the	DET
ejpam-4863	152	11	order	order	NOUN
ejpam-4863	152	12	n	n	CCONJ
ejpam-4863	152	13	>	>	X
ejpam-4863	152	14	1	1	NUM
ejpam-4863	152	15	of	of	ADP
ejpam-4863	152	16	g	g	PROPN
ejpam-4863	152	17	is	be	AUX
ejpam-4863	152	18	not	not	PART
ejpam-4863	152	19	prime	prime	ADJ
ejpam-4863	152	20	.	.	PUNCT
ejpam-4863	153	1	this	this	PRON
ejpam-4863	153	2	implies	imply	VERB
ejpam-4863	153	3	that	that	SCONJ
ejpam-4863	153	4	for	for	ADP
ejpam-4863	153	5	some	some	DET
ejpam-4863	153	6	integer	integer	NOUN
ejpam-4863	153	7	k	k	PROPN
ejpam-4863	153	8	̸=	̸=	PROPN
ejpam-4863	153	9	n	n	CCONJ
ejpam-4863	153	10	there	there	ADV
ejpam-4863	153	11	exists	exist	VERB
ejpam-4863	153	12	an	an	DET
ejpam-4863	153	13	integers	integer	NOUN
ejpam-4863	153	14	m	m	VERB
ejpam-4863	153	15	̸=	̸=	PROPN
ejpam-4863	153	16	n	n	NOUN
ejpam-4863	153	17	such	such	ADJ
ejpam-4863	153	18	that	that	DET
ejpam-4863	153	19	km	km	NOUN
ejpam-4863	153	20	=	=	SYM
ejpam-4863	153	21	n	n	CCONJ
ejpam-4863	153	22	,	,	PUNCT
ejpam-4863	153	23	and	and	CCONJ
ejpam-4863	153	24	k	k	PROPN
ejpam-4863	153	25	is	be	AUX
ejpam-4863	153	26	the	the	DET
ejpam-4863	153	27	order	order	NOUN
ejpam-4863	153	28	of	of	ADP
ejpam-4863	153	29	some	some	DET
ejpam-4863	153	30	vertex	vertex	NOUN
ejpam-4863	153	31	a	a	DET
ejpam-4863	153	32	∈	∈	PROPN
ejpam-4863	153	33	v	v	NOUN
ejpam-4863	153	34	(	(	PUNCT
ejpam-4863	153	35	gg(g	gg(g	PROPN
ejpam-4863	153	36	)	)	PUNCT
ejpam-4863	153	37	)	)	PUNCT
ejpam-4863	153	38	,	,	PUNCT
ejpam-4863	153	39	i.e.	i.e.	X
ejpam-4863	153	40	,	,	PUNCT
ejpam-4863	153	41	(	(	PUNCT
ejpam-4863	153	42	a	a	X
ejpam-4863	153	43	)	)	PUNCT
ejpam-4863	153	44	̸=	̸=	PROPN
ejpam-4863	153	45	g.	g.	NOUN
ejpam-4863	153	46	this	this	PRON
ejpam-4863	153	47	means	mean	VERB
ejpam-4863	153	48	that	that	SCONJ
ejpam-4863	153	49	a	a	PRON
ejpam-4863	153	50	is	be	AUX
ejpam-4863	153	51	not	not	PART
ejpam-4863	153	52	a	a	DET
ejpam-4863	153	53	generator	generator	NOUN
ejpam-4863	153	54	of	of	ADP
ejpam-4863	153	55	g.	g.	PROPN
ejpam-4863	153	56	consequently	consequently	ADV
ejpam-4863	153	57	,	,	PUNCT
ejpam-4863	153	58	vertex	vertex	NOUN
ejpam-4863	153	59	a	a	PRON
ejpam-4863	153	60	is	be	AUX
ejpam-4863	153	61	not	not	PART
ejpam-4863	153	62	adjacent	adjacent	ADJ
ejpam-4863	153	63	to	to	ADP
ejpam-4863	153	64	the	the	DET
ejpam-4863	153	65	identity	identity	NOUN
ejpam-4863	153	66	element	element	NOUN
ejpam-4863	153	67	of	of	ADP
ejpam-4863	153	68	g	g	PROPN
ejpam-4863	153	69	in	in	ADP
ejpam-4863	153	70	gg(g	gg(g	PROPN
ejpam-4863	153	71	)	)	PUNCT
ejpam-4863	153	72	.	.	PUNCT
ejpam-4863	154	1	thus	thus	ADV
ejpam-4863	154	2	,	,	PUNCT
ejpam-4863	154	3	degg(a	degg(a	PROPN
ejpam-4863	154	4	)	)	PUNCT
ejpam-4863	154	5	≤	≤	NUM
ejpam-4863	154	6	n−	n−	NOUN
ejpam-4863	154	7	2	2	NUM
ejpam-4863	154	8	in	in	ADP
ejpam-4863	154	9	gg(g	gg(g	PROPN
ejpam-4863	154	10	)	)	PUNCT
ejpam-4863	154	11	.	.	PUNCT
ejpam-4863	155	1	this	this	PRON
ejpam-4863	155	2	is	be	AUX
ejpam-4863	155	3	a	a	DET
ejpam-4863	155	4	contradiction	contradiction	NOUN
ejpam-4863	155	5	to	to	ADP
ejpam-4863	155	6	the	the	DET
ejpam-4863	155	7	assumption	assumption	NOUN
ejpam-4863	155	8	that	that	SCONJ
ejpam-4863	155	9	gg(g	gg(g	PROPN
ejpam-4863	155	10	)	)	PUNCT
ejpam-4863	155	11	is	be	AUX
ejpam-4863	155	12	complete	complete	ADJ
ejpam-4863	155	13	.	.	PUNCT
ejpam-4863	156	1	therefore	therefore	ADV
ejpam-4863	156	2	,	,	PUNCT
ejpam-4863	156	3	the	the	DET
ejpam-4863	156	4	order	order	NOUN
ejpam-4863	156	5	n	n	NOUN
ejpam-4863	156	6	of	of	ADP
ejpam-4863	156	7	g	g	NOUN
ejpam-4863	156	8	must	must	AUX
ejpam-4863	156	9	be	be	AUX
ejpam-4863	156	10	prime	prime	ADJ
ejpam-4863	156	11	.	.	PUNCT
ejpam-4863	157	1	suppose	suppose	VERB
ejpam-4863	157	2	that	that	SCONJ
ejpam-4863	157	3	the	the	DET
ejpam-4863	157	4	order	order	NOUN
ejpam-4863	157	5	of	of	ADP
ejpam-4863	157	6	g	g	PROPN
ejpam-4863	157	7	is	be	AUX
ejpam-4863	157	8	prime	prime	ADJ
ejpam-4863	157	9	,	,	PUNCT
ejpam-4863	157	10	and	and	CCONJ
ejpam-4863	157	11	let	let	VERB
ejpam-4863	157	12	e	e	PRON
ejpam-4863	157	13	be	be	AUX
ejpam-4863	157	14	the	the	DET
ejpam-4863	157	15	identity	identity	NOUN
ejpam-4863	157	16	element	element	NOUN
ejpam-4863	157	17	of	of	ADP
ejpam-4863	157	18	g.	g.	PROPN
ejpam-4863	157	19	then	then	ADV
ejpam-4863	157	20	for	for	ADP
ejpam-4863	157	21	all	all	DET
ejpam-4863	157	22	x	x	SYM
ejpam-4863	157	23	∈	∈	PROPN
ejpam-4863	157	24	g\{e	g\{e	NOUN
ejpam-4863	157	25	}	}	PUNCT
ejpam-4863	157	26	,	,	PUNCT
ejpam-4863	157	27	(	(	PUNCT
ejpam-4863	157	28	x	x	X
ejpam-4863	157	29	)	)	PUNCT
ejpam-4863	157	30	=	=	PUNCT
ejpam-4863	158	1	g.	g.	NOUN
ejpam-4863	159	1	this	this	PRON
ejpam-4863	159	2	means	mean	VERB
ejpam-4863	159	3	that	that	SCONJ
ejpam-4863	159	4	x	x	PRON
ejpam-4863	159	5	is	be	AUX
ejpam-4863	159	6	a	a	DET
ejpam-4863	159	7	generator	generator	NOUN
ejpam-4863	159	8	of	of	ADP
ejpam-4863	159	9	g	g	NOUN
ejpam-4863	159	10	,	,	PUNCT
ejpam-4863	159	11	and	and	CCONJ
ejpam-4863	159	12	x	x	X
ejpam-4863	159	13	is	be	AUX
ejpam-4863	159	14	adjacent	adjacent	ADJ
ejpam-4863	159	15	to	to	ADP
ejpam-4863	159	16	all	all	DET
ejpam-4863	159	17	other	other	ADJ
ejpam-4863	159	18	n	n	CCONJ
ejpam-4863	159	19	−	−	NUM
ejpam-4863	159	20	1	1	NUM
ejpam-4863	159	21	vertices	vertex	NOUN
ejpam-4863	159	22	of	of	ADP
ejpam-4863	159	23	gg(g	gg(g	NOUN
ejpam-4863	159	24	)	)	PUNCT
ejpam-4863	159	25	.	.	PUNCT
ejpam-4863	160	1	thus	thus	ADV
ejpam-4863	160	2	,	,	PUNCT
ejpam-4863	160	3	deggg(g)(x	deggg(g)(x	NOUN
ejpam-4863	160	4	)	)	PUNCT
ejpam-4863	160	5	=	=	SYM
ejpam-4863	160	6	n	n	CCONJ
ejpam-4863	160	7	−	−	NOUN
ejpam-4863	160	8	1	1	NUM
ejpam-4863	160	9	for	for	ADP
ejpam-4863	160	10	all	all	DET
ejpam-4863	160	11	x	x	SYM
ejpam-4863	160	12	∈	∈	PROPN
ejpam-4863	160	13	g\{e	g\{e	NOUN
ejpam-4863	160	14	}	}	PUNCT
ejpam-4863	160	15	.	.	PUNCT
ejpam-4863	161	1	since	since	SCONJ
ejpam-4863	161	2	t.	t.	PROPN
ejpam-4863	161	3	l.	l.	PROPN
ejpam-4863	161	4	tacbobo	tacbobo	PROPN
ejpam-4863	161	5	/	/	SYM
ejpam-4863	161	6	eur	eur	PROPN
ejpam-4863	161	7	.	.	PUNCT
ejpam-4863	162	1	j.	j.	PROPN
ejpam-4863	162	2	pure	pure	PROPN
ejpam-4863	162	3	appl	appl	PROPN
ejpam-4863	162	4	.	.	PROPN
ejpam-4863	162	5	math	math	PROPN
ejpam-4863	162	6	,	,	PUNCT
ejpam-4863	162	7	16	16	NUM
ejpam-4863	162	8	(	(	PUNCT
ejpam-4863	162	9	3	3	NUM
ejpam-4863	162	10	)	)	PUNCT
ejpam-4863	162	11	(	(	PUNCT
ejpam-4863	162	12	2023	2023	NUM
ejpam-4863	162	13	)	)	PUNCT
ejpam-4863	162	14	,	,	PUNCT
ejpam-4863	162	15	1894	1894	NUM
ejpam-4863	162	16	-	-	SYM
ejpam-4863	162	17	1901	1901	NUM
ejpam-4863	162	18	1898	1898	NUM
ejpam-4863	162	19	all	all	DET
ejpam-4863	162	20	elements	element	NOUN
ejpam-4863	162	21	of	of	ADP
ejpam-4863	162	22	x	x	PUNCT
ejpam-4863	162	23	∈	∈	PROPN
ejpam-4863	162	24	g\{e	g\{e	PROPN
ejpam-4863	162	25	}	}	PUNCT
ejpam-4863	162	26	are	be	AUX
ejpam-4863	162	27	generators	generator	NOUN
ejpam-4863	162	28	,	,	PUNCT
ejpam-4863	162	29	all	all	DET
ejpam-4863	162	30	|x	|x	NOUN
ejpam-4863	162	31	∈	∈	PROPN
ejpam-4863	162	32	g\{e}|	g\{e}|	NOUN
ejpam-4863	162	33	=	=	SYM
ejpam-4863	162	34	n	n	CCONJ
ejpam-4863	162	35	−	−	NOUN
ejpam-4863	162	36	1	1	NUM
ejpam-4863	162	37	vertices	vertex	NOUN
ejpam-4863	162	38	of	of	ADP
ejpam-4863	162	39	gg(g	gg(g	PROPN
ejpam-4863	162	40	)	)	PUNCT
ejpam-4863	162	41	are	be	AUX
ejpam-4863	162	42	adjacent	adjacent	ADJ
ejpam-4863	162	43	to	to	ADP
ejpam-4863	162	44	the	the	DET
ejpam-4863	162	45	identity	identity	NOUN
ejpam-4863	162	46	element	element	NOUN
ejpam-4863	162	47	e	e	NOUN
ejpam-4863	162	48	of	of	ADP
ejpam-4863	162	49	g	g	PROPN
ejpam-4863	162	50	in	in	ADP
ejpam-4863	162	51	gg(g	gg(g	PROPN
ejpam-4863	162	52	)	)	PUNCT
ejpam-4863	162	53	.	.	PUNCT
ejpam-4863	163	1	so	so	ADV
ejpam-4863	163	2	,	,	PUNCT
ejpam-4863	163	3	deg(e	deg(e	NOUN
ejpam-4863	163	4	)	)	PUNCT
ejpam-4863	163	5	=	=	SYM
ejpam-4863	163	6	n−	n−	NOUN
ejpam-4863	163	7	1	1	NUM
ejpam-4863	163	8	.	.	PUNCT
ejpam-4863	164	1	this	this	PRON
ejpam-4863	164	2	proves	prove	VERB
ejpam-4863	164	3	that	that	SCONJ
ejpam-4863	164	4	for	for	ADP
ejpam-4863	164	5	all	all	PRON
ejpam-4863	164	6	x	x	SYM
ejpam-4863	164	7	∈	∈	PROPN
ejpam-4863	164	8	v	v	NOUN
ejpam-4863	164	9	(	(	PUNCT
ejpam-4863	164	10	gg(g	gg(g	PROPN
ejpam-4863	164	11	)	)	PUNCT
ejpam-4863	164	12	)	)	PUNCT
ejpam-4863	164	13	,	,	PUNCT
ejpam-4863	164	14	deggg(g)(x	deggg(g)(x	NOUN
ejpam-4863	164	15	)	)	PUNCT
ejpam-4863	164	16	=	=	PUNCT
ejpam-4863	164	17	n−	n−	NOUN
ejpam-4863	164	18	1	1	NUM
ejpam-4863	164	19	.	.	PUNCT
ejpam-4863	164	20	therefore	therefore	ADV
ejpam-4863	164	21	,	,	PUNCT
ejpam-4863	164	22	gg(g	gg(g	PROPN
ejpam-4863	164	23	)	)	PUNCT
ejpam-4863	164	24	is	be	AUX
ejpam-4863	164	25	a	a	DET
ejpam-4863	164	26	complete	complete	ADJ
ejpam-4863	164	27	graph	graph	NOUN
ejpam-4863	164	28	.	.	PUNCT
ejpam-4863	164	29	example	example	NOUN
ejpam-4863	165	1	1	1	NUM
ejpam-4863	165	2	.	.	PUNCT
ejpam-4863	165	3	let	let	VERB
ejpam-4863	165	4	zp	zp	PROPN
ejpam-4863	165	5	be	be	AUX
ejpam-4863	165	6	the	the	DET
ejpam-4863	165	7	group	group	NOUN
ejpam-4863	165	8	of	of	ADP
ejpam-4863	165	9	integers	integer	NOUN
ejpam-4863	165	10	under	under	ADP
ejpam-4863	165	11	addition	addition	NOUN
ejpam-4863	165	12	modulo	modulo	VERB
ejpam-4863	165	13	p	p	X
ejpam-4863	165	14	,	,	PUNCT
ejpam-4863	165	15	where	where	SCONJ
ejpam-4863	165	16	p	p	NOUN
ejpam-4863	165	17	is	be	AUX
ejpam-4863	165	18	prime	prime	ADJ
ejpam-4863	165	19	.	.	PUNCT
ejpam-4863	166	1	then	then	ADV
ejpam-4863	166	2	gg(zp	gg(zp	PROPN
ejpam-4863	166	3	)	)	PUNCT
ejpam-4863	167	1	=	=	SYM
ejpam-4863	167	2	kp.the	kp.the	NOUN
ejpam-4863	167	3	graph	graph	NOUN
ejpam-4863	167	4	gg(z5	gg(z5	NOUN
ejpam-4863	167	5	)	)	PUNCT
ejpam-4863	167	6	of	of	ADP
ejpam-4863	167	7	z5	z5	PROPN
ejpam-4863	167	8	in	in	ADP
ejpam-4863	167	9	figure	figure	NOUN
ejpam-4863	167	10	1	1	NUM
ejpam-4863	167	11	is	be	AUX
ejpam-4863	167	12	a	a	DET
ejpam-4863	167	13	complete	complete	ADJ
ejpam-4863	167	14	graph	graph	NOUN
ejpam-4863	167	15	k5	k5	PROPN
ejpam-4863	167	16	.	.	PUNCT
ejpam-4863	168	1	remark	remark	PROPN
ejpam-4863	168	2	1	1	NUM
ejpam-4863	168	3	.	.	PUNCT
ejpam-4863	169	1	let	let	VERB
ejpam-4863	169	2	g	g	PRON
ejpam-4863	169	3	be	be	AUX
ejpam-4863	169	4	a	a	DET
ejpam-4863	169	5	nontrivial	nontrivial	ADJ
ejpam-4863	169	6	group	group	NOUN
ejpam-4863	169	7	.	.	PUNCT
ejpam-4863	170	1	the	the	DET
ejpam-4863	170	2	generator	generator	NOUN
ejpam-4863	170	3	graph	graph	NOUN
ejpam-4863	170	4	of	of	ADP
ejpam-4863	170	5	g	g	PROPN
ejpam-4863	170	6	is	be	AUX
ejpam-4863	170	7	connected	connect	VERB
ejpam-4863	170	8	if	if	SCONJ
ejpam-4863	170	9	and	and	CCONJ
ejpam-4863	170	10	only	only	ADV
ejpam-4863	170	11	if	if	SCONJ
ejpam-4863	170	12	g	g	PROPN
ejpam-4863	170	13	is	be	AUX
ejpam-4863	170	14	cyclic	cyclic	ADJ
ejpam-4863	170	15	.	.	PUNCT
ejpam-4863	171	1	example	example	NOUN
ejpam-4863	172	1	2	2	NUM
ejpam-4863	172	2	.	.	X
ejpam-4863	172	3	in	in	ADP
ejpam-4863	172	4	figure	figure	NOUN
ejpam-4863	172	5	1	1	NUM
ejpam-4863	172	6	,	,	PUNCT
ejpam-4863	172	7	the	the	DET
ejpam-4863	172	8	generator	generator	NOUN
ejpam-4863	172	9	graphs	graph	VERB
ejpam-4863	172	10	gg(z6	gg(z6	NOUN
ejpam-4863	172	11	)	)	PUNCT
ejpam-4863	172	12	of	of	ADP
ejpam-4863	172	13	z6	z6	PROPN
ejpam-4863	172	14	under	under	ADP
ejpam-4863	172	15	addition	addition	NOUN
ejpam-4863	172	16	modulo	modulo	NOUN
ejpam-4863	172	17	6	6	NUM
ejpam-4863	172	18	and	and	CCONJ
ejpam-4863	172	19	gg(z5	gg(z5	NOUN
ejpam-4863	172	20	)	)	PUNCT
ejpam-4863	172	21	of	of	ADP
ejpam-4863	172	22	z5	z5	PROPN
ejpam-4863	172	23	under	under	ADP
ejpam-4863	172	24	addition	addition	NOUN
ejpam-4863	172	25	modulo	modulo	NOUN
ejpam-4863	172	26	5	5	NUM
ejpam-4863	172	27	are	be	AUX
ejpam-4863	172	28	connected	connect	VERB
ejpam-4863	172	29	.	.	PUNCT
ejpam-4863	173	1	it	it	PRON
ejpam-4863	173	2	is	be	AUX
ejpam-4863	173	3	easy	easy	ADJ
ejpam-4863	173	4	to	to	PART
ejpam-4863	173	5	verify	verify	VERB
ejpam-4863	173	6	that	that	SCONJ
ejpam-4863	173	7	the	the	DET
ejpam-4863	173	8	generator	generator	NOUN
ejpam-4863	173	9	graph	graph	NOUN
ejpam-4863	173	10	gg(v	gg(v	PUNCT
ejpam-4863	173	11	)	)	PUNCT
ejpam-4863	173	12	of	of	ADP
ejpam-4863	173	13	klien	klien	PROPN
ejpam-4863	173	14	4	4	PROPN
ejpam-4863	173	15	-	-	PUNCT
ejpam-4863	173	16	group	group	NOUN
ejpam-4863	173	17	v	v	NOUN
ejpam-4863	173	18	is	be	AUX
ejpam-4863	173	19	a	a	DET
ejpam-4863	173	20	null	null	ADJ
ejpam-4863	173	21	graph	graph	NOUN
ejpam-4863	173	22	of	of	ADP
ejpam-4863	173	23	order	order	NOUN
ejpam-4863	173	24	4	4	NUM
ejpam-4863	173	25	which	which	PRON
ejpam-4863	173	26	is	be	AUX
ejpam-4863	173	27	disconnected	disconnect	VERB
ejpam-4863	173	28	.	.	PUNCT
ejpam-4863	174	1	theorem	theorem	NOUN
ejpam-4863	174	2	3	3	X
ejpam-4863	174	3	.	.	PUNCT
ejpam-4863	175	1	let	let	VERB
ejpam-4863	175	2	g	g	PRON
ejpam-4863	175	3	be	be	AUX
ejpam-4863	175	4	a	a	DET
ejpam-4863	175	5	cyclic	cyclic	ADJ
ejpam-4863	175	6	group	group	NOUN
ejpam-4863	175	7	of	of	ADP
ejpam-4863	175	8	order	order	NOUN
ejpam-4863	175	9	n	n	CCONJ
ejpam-4863	175	10	>	>	X
ejpam-4863	175	11	1	1	NUM
ejpam-4863	175	12	,	,	PUNCT
ejpam-4863	175	13	and	and	CCONJ
ejpam-4863	175	14	sg	sg	PART
ejpam-4863	175	15	be	be	AUX
ejpam-4863	175	16	the	the	DET
ejpam-4863	175	17	set	set	NOUN
ejpam-4863	175	18	of	of	ADP
ejpam-4863	175	19	all	all	DET
ejpam-4863	175	20	generators	generator	NOUN
ejpam-4863	175	21	of	of	ADP
ejpam-4863	175	22	g.	g.	PROPN
ejpam-4863	175	23	then	then	ADV
ejpam-4863	175	24	each	each	PRON
ejpam-4863	175	25	of	of	ADP
ejpam-4863	175	26	the	the	DET
ejpam-4863	175	27	following	follow	VERB
ejpam-4863	175	28	is	be	AUX
ejpam-4863	175	29	true	true	ADJ
ejpam-4863	175	30	:	:	PUNCT
ejpam-4863	175	31	(	(	PUNCT
ejpam-4863	175	32	i	i	NOUN
ejpam-4863	175	33	)	)	PUNCT
ejpam-4863	175	34	the	the	DET
ejpam-4863	175	35	induced	induced	ADJ
ejpam-4863	175	36	subgraph	subgraph	NOUN
ejpam-4863	175	37	<	<	X
ejpam-4863	175	38	sg	sg	X
ejpam-4863	175	39	>	>	X
ejpam-4863	175	40	generated	generate	VERB
ejpam-4863	175	41	by	by	ADP
ejpam-4863	175	42	sg	sg	PROPN
ejpam-4863	175	43	of	of	ADP
ejpam-4863	175	44	gg(g	gg(g	PROPN
ejpam-4863	175	45	)	)	PUNCT
ejpam-4863	175	46	is	be	AUX
ejpam-4863	175	47	the	the	DET
ejpam-4863	175	48	complete	complete	ADJ
ejpam-4863	175	49	graph	graph	NOUN
ejpam-4863	175	50	k|sg|	k|sg|	PROPN
ejpam-4863	175	51	;	;	PUNCT
ejpam-4863	175	52	and	and	CCONJ
ejpam-4863	175	53	(	(	PUNCT
ejpam-4863	175	54	ii	ii	NOUN
ejpam-4863	175	55	)	)	PUNCT
ejpam-4863	175	56	the	the	DET
ejpam-4863	175	57	induced	induced	ADJ
ejpam-4863	175	58	subgraph	subgraph	NOUN
ejpam-4863	175	59	<	<	X
ejpam-4863	175	60	g\sg	g\sg	PROPN
ejpam-4863	175	61	>	>	X
ejpam-4863	175	62	generated	generate	VERB
ejpam-4863	175	63	by	by	ADP
ejpam-4863	175	64	g\sg	g\sg	NOUN
ejpam-4863	175	65	of	of	ADP
ejpam-4863	175	66	gg(g	gg(g	PROPN
ejpam-4863	175	67	)	)	PUNCT
ejpam-4863	175	68	is	be	AUX
ejpam-4863	175	69	the	the	DET
ejpam-4863	175	70	empty	empty	ADJ
ejpam-4863	175	71	graph	graph	NOUN
ejpam-4863	175	72	kn−|sg|	kn−|sg|	NOUN
ejpam-4863	175	73	.	.	PUNCT
ejpam-4863	176	1	proof	proof	NOUN
ejpam-4863	176	2	.	.	PUNCT
ejpam-4863	177	1	(	(	PUNCT
ejpam-4863	177	2	i	i	NOUN
ejpam-4863	177	3	)	)	PUNCT
ejpam-4863	177	4	since	since	SCONJ
ejpam-4863	177	5	g	g	PROPN
ejpam-4863	177	6	is	be	AUX
ejpam-4863	177	7	cyclic	cyclic	ADJ
ejpam-4863	177	8	and	and	CCONJ
ejpam-4863	177	9	n	n	CCONJ
ejpam-4863	177	10	>	>	ADP
ejpam-4863	177	11	1	1	NUM
ejpam-4863	177	12	,	,	PUNCT
ejpam-4863	177	13	there	there	PRON
ejpam-4863	177	14	exist	exist	VERB
ejpam-4863	177	15	a	a	DET
ejpam-4863	177	16	∈	∈	NOUN
ejpam-4863	177	17	sg	sg	ADP
ejpam-4863	177	18	such	such	ADJ
ejpam-4863	177	19	that	that	SCONJ
ejpam-4863	177	20	(	(	PUNCT
ejpam-4863	177	21	a	a	X
ejpam-4863	177	22	)	)	PUNCT
ejpam-4863	177	23	=	=	SYM
ejpam-4863	177	24	g	g	NOUN
ejpam-4863	177	25	,	,	PUNCT
ejpam-4863	177	26	i.e.	i.e.	X
ejpam-4863	177	27	,	,	PUNCT
ejpam-4863	177	28	sg	sg	AUX
ejpam-4863	177	29	̸=	̸=	PROPN
ejpam-4863	177	30	∅.	∅.	VERB
ejpam-4863	177	31	then	then	ADV
ejpam-4863	177	32	for	for	ADP
ejpam-4863	177	33	every	every	DET
ejpam-4863	177	34	pair	pair	NOUN
ejpam-4863	177	35	x	x	PUNCT
ejpam-4863	177	36	and	and	CCONJ
ejpam-4863	177	37	y	y	PROPN
ejpam-4863	177	38	in	in	ADP
ejpam-4863	177	39	sg	sg	PROPN
ejpam-4863	177	40	,	,	PUNCT
ejpam-4863	177	41	x	x	X
ejpam-4863	177	42	and	and	CCONJ
ejpam-4863	177	43	y	y	PROPN
ejpam-4863	177	44	generate	generate	VERB
ejpam-4863	177	45	each	each	DET
ejpam-4863	177	46	other	other	ADJ
ejpam-4863	177	47	,	,	PUNCT
ejpam-4863	177	48	i.e.	i.e.	X
ejpam-4863	177	49	,	,	PUNCT
ejpam-4863	177	50	x	x	SYM
ejpam-4863	177	51	∈	∈	PROPN
ejpam-4863	177	52	(	(	PUNCT
ejpam-4863	177	53	y	y	NOUN
ejpam-4863	177	54	)	)	PUNCT
ejpam-4863	177	55	and	and	CCONJ
ejpam-4863	177	56	y	y	PROPN
ejpam-4863	177	57	∈	∈	PROPN
ejpam-4863	177	58	(	(	PUNCT
ejpam-4863	177	59	x	x	NOUN
ejpam-4863	177	60	)	)	PUNCT
ejpam-4863	177	61	.	.	PUNCT
ejpam-4863	178	1	hence	hence	ADV
ejpam-4863	178	2	,	,	PUNCT
ejpam-4863	178	3	x	x	PUNCT
ejpam-4863	178	4	and	and	CCONJ
ejpam-4863	178	5	y	y	PROPN
ejpam-4863	178	6	are	be	AUX
ejpam-4863	178	7	adjacent	adjacent	ADJ
ejpam-4863	178	8	in	in	ADP
ejpam-4863	178	9	gg(g	gg(g	PROPN
ejpam-4863	178	10	)	)	PUNCT
ejpam-4863	178	11	for	for	ADP
ejpam-4863	178	12	all	all	DET
ejpam-4863	178	13	x	x	SYM
ejpam-4863	178	14	and	and	CCONJ
ejpam-4863	178	15	y	y	PROPN
ejpam-4863	178	16	in	in	ADP
ejpam-4863	178	17	sg	sg	PROPN
ejpam-4863	178	18	.	.	PUNCT
ejpam-4863	179	1	this	this	PRON
ejpam-4863	179	2	means	mean	VERB
ejpam-4863	179	3	also	also	ADV
ejpam-4863	179	4	that	that	SCONJ
ejpam-4863	179	5	x	x	PRON
ejpam-4863	179	6	and	and	CCONJ
ejpam-4863	179	7	y	y	PROPN
ejpam-4863	179	8	are	be	AUX
ejpam-4863	179	9	adjacent	adjacent	ADJ
ejpam-4863	179	10	in	in	ADP
ejpam-4863	179	11	<	<	X
ejpam-4863	179	12	sg	sg	X
ejpam-4863	179	13	>	>	X
ejpam-4863	179	14	for	for	ADP
ejpam-4863	179	15	all	all	DET
ejpam-4863	179	16	x	x	PUNCT
ejpam-4863	179	17	and	and	CCONJ
ejpam-4863	179	18	y	y	PROPN
ejpam-4863	179	19	in	in	ADP
ejpam-4863	179	20	sg	sg	PROPN
ejpam-4863	179	21	.	.	PUNCT
ejpam-4863	180	1	therefore	therefore	ADV
ejpam-4863	180	2	,	,	PUNCT
ejpam-4863	180	3	<	<	X
ejpam-4863	180	4	sg	sg	X
ejpam-4863	180	5	>	>	X
ejpam-4863	180	6	is	be	AUX
ejpam-4863	180	7	a	a	DET
ejpam-4863	180	8	complete	complete	ADJ
ejpam-4863	180	9	graph	graph	NOUN
ejpam-4863	180	10	,	,	PUNCT
ejpam-4863	180	11	i.e.	i.e.	X
ejpam-4863	180	12	,	,	PUNCT
ejpam-4863	180	13	<	<	X
ejpam-4863	180	14	sg	sg	X
ejpam-4863	180	15	>	>	X
ejpam-4863	180	16	=	=	PUNCT
ejpam-4863	180	17	k|sg|	k|sg|	PROPN
ejpam-4863	180	18	.	.	PROPN
ejpam-4863	180	19	(	(	PUNCT
ejpam-4863	180	20	ii	ii	NOUN
ejpam-4863	180	21	)	)	PUNCT
ejpam-4863	180	22	for	for	ADP
ejpam-4863	180	23	every	every	DET
ejpam-4863	180	24	x	x	PROPN
ejpam-4863	180	25	,	,	PUNCT
ejpam-4863	180	26	y	y	PROPN
ejpam-4863	180	27	∈	∈	PROPN
ejpam-4863	180	28	g\sg	g\sg	PROPN
ejpam-4863	180	29	,	,	PUNCT
ejpam-4863	180	30	x	x	X
ejpam-4863	180	31	and	and	CCONJ
ejpam-4863	180	32	y	y	PROPN
ejpam-4863	180	33	are	be	AUX
ejpam-4863	180	34	not	not	PART
ejpam-4863	180	35	adjacent	adjacent	ADJ
ejpam-4863	180	36	in	in	ADP
ejpam-4863	180	37	gg(g	gg(g	PROPN
ejpam-4863	180	38	)	)	PUNCT
ejpam-4863	180	39	.	.	PUNCT
ejpam-4863	181	1	thus	thus	ADV
ejpam-4863	181	2	,	,	PUNCT
ejpam-4863	181	3	x	x	PUNCT
ejpam-4863	181	4	and	and	CCONJ
ejpam-4863	181	5	y	y	PROPN
ejpam-4863	181	6	are	be	AUX
ejpam-4863	181	7	also	also	ADV
ejpam-4863	181	8	not	not	PART
ejpam-4863	181	9	adjacent	adjacent	ADJ
ejpam-4863	181	10	in	in	ADP
ejpam-4863	181	11	<	<	X
ejpam-4863	181	12	g\sg	g\sg	PROPN
ejpam-4863	181	13	>	>	PUNCT
ejpam-4863	181	14	.	.	PUNCT
ejpam-4863	182	1	therefore	therefore	ADV
ejpam-4863	182	2	,	,	PUNCT
ejpam-4863	182	3	e	e	X
ejpam-4863	182	4	(	(	PUNCT
ejpam-4863	182	5	<	<	X
ejpam-4863	182	6	g\sg	g\sg	PROPN
ejpam-4863	182	7	>	>	PUNCT
ejpam-4863	182	8	)	)	PUNCT
ejpam-4863	182	9	=	=	NOUN
ejpam-4863	182	10	∅	∅	NOUN
ejpam-4863	182	11	and	and	CCONJ
ejpam-4863	182	12	<	<	X
ejpam-4863	182	13	g\sg	g\sg	NOUN
ejpam-4863	182	14	>	>	X
ejpam-4863	182	15	is	be	AUX
ejpam-4863	182	16	an	an	DET
ejpam-4863	182	17	empty	empty	ADJ
ejpam-4863	182	18	graph	graph	NOUN
ejpam-4863	182	19	.	.	PUNCT
ejpam-4863	182	20	example	example	NOUN
ejpam-4863	183	1	3	3	NUM
ejpam-4863	183	2	.	.	PUNCT
ejpam-4863	183	3	in	in	ADP
ejpam-4863	183	4	z6	z6	PROPN
ejpam-4863	183	5	,	,	PUNCT
ejpam-4863	183	6	⟨sz6⟩	⟨sz6⟩	NOUN
ejpam-4863	183	7	=	=	PUNCT
ejpam-4863	183	8	⟨{1	⟨{1	PROPN
ejpam-4863	183	9	,	,	PUNCT
ejpam-4863	183	10	5}⟩	5}⟩	NUM
ejpam-4863	183	11	is	be	AUX
ejpam-4863	183	12	a	a	DET
ejpam-4863	183	13	complete	complete	ADJ
ejpam-4863	183	14	subgraph	subgraph	NOUN
ejpam-4863	183	15	while	while	SCONJ
ejpam-4863	183	16	⟨z6\sz6⟩	⟨z6\sz6⟩	PROPN
ejpam-4863	183	17	=	=	SYM
ejpam-4863	183	18	⟨{0	⟨{0	PROPN
ejpam-4863	183	19	,	,	PUNCT
ejpam-4863	183	20	2	2	NUM
ejpam-4863	183	21	,	,	PUNCT
ejpam-4863	183	22	3	3	NUM
ejpam-4863	183	23	,	,	PUNCT
ejpam-4863	183	24	4}⟩	4}⟩	PROPN
ejpam-4863	183	25	is	be	AUX
ejpam-4863	183	26	a	a	DET
ejpam-4863	183	27	null	null	ADJ
ejpam-4863	183	28	subgraph	subgraph	NOUN
ejpam-4863	183	29	of	of	ADP
ejpam-4863	183	30	z6	z6	PROPN
ejpam-4863	183	31	.	.	PUNCT
ejpam-4863	184	1	these	these	PRON
ejpam-4863	184	2	are	be	AUX
ejpam-4863	184	3	illustrated	illustrate	VERB
ejpam-4863	184	4	in	in	ADP
ejpam-4863	184	5	figure	figure	NOUN
ejpam-4863	184	6	2	2	NUM
ejpam-4863	184	7	and	and	CCONJ
ejpam-4863	184	8	figure	figure	VERB
ejpam-4863	184	9	3	3	NUM
ejpam-4863	184	10	,	,	PUNCT
ejpam-4863	184	11	respectively	respectively	ADV
ejpam-4863	184	12	.	.	PUNCT
ejpam-4863	184	13	....................................	....................................	PUNCT
ejpam-4863	185	1	...................................................................................................................................................................................................................................	...................................................................................................................................................................................................................................	PUNCT
ejpam-4863	186	1	•	•	NUM
ejpam-4863	187	1	•	•	NOUN
ejpam-4863	187	2	1	1	NUM
ejpam-4863	187	3	5	5	NUM
ejpam-4863	187	4	<	<	X
ejpam-4863	187	5	sz6	sz6	PROPN
ejpam-4863	187	6	)	)	PUNCT
ejpam-4863	187	7	>	>	X
ejpam-4863	187	8	figure	figure	NOUN
ejpam-4863	187	9	2	2	NUM
ejpam-4863	187	10	:	:	PUNCT
ejpam-4863	187	11	the	the	DET
ejpam-4863	187	12	induced	induced	ADJ
ejpam-4863	187	13	subgraph	subgraph	NOUN
ejpam-4863	187	14	of	of	ADP
ejpam-4863	187	15	sz6	sz6	NOUN
ejpam-4863	187	16	=	=	SYM
ejpam-4863	187	17	{	{	PUNCT
ejpam-4863	187	18	1	1	NUM
ejpam-4863	187	19	,	,	PUNCT
ejpam-4863	187	20	5	5	NUM
ejpam-4863	187	21	}	}	PUNCT
ejpam-4863	187	22	of	of	ADP
ejpam-4863	187	23	z6	z6	PROPN
ejpam-4863	187	24	under	under	ADP
ejpam-4863	187	25	addition	addition	NOUN
ejpam-4863	187	26	modulo	modulo	NOUN
ejpam-4863	187	27	6	6	NUM
ejpam-4863	187	28	.	.	PUNCT
ejpam-4863	187	29	t.	t.	PROPN
ejpam-4863	187	30	l.	l.	PROPN
ejpam-4863	187	31	tacbobo	tacbobo	PROPN
ejpam-4863	187	32	/	/	SYM
ejpam-4863	187	33	eur	eur	PROPN
ejpam-4863	187	34	.	.	PUNCT
ejpam-4863	188	1	j.	j.	PROPN
ejpam-4863	188	2	pure	pure	PROPN
ejpam-4863	188	3	appl	appl	PROPN
ejpam-4863	188	4	.	.	PROPN
ejpam-4863	188	5	math	math	PROPN
ejpam-4863	188	6	,	,	PUNCT
ejpam-4863	188	7	16	16	NUM
ejpam-4863	188	8	(	(	PUNCT
ejpam-4863	188	9	3	3	NUM
ejpam-4863	188	10	)	)	PUNCT
ejpam-4863	188	11	(	(	PUNCT
ejpam-4863	188	12	2023	2023	NUM
ejpam-4863	188	13	)	)	PUNCT
ejpam-4863	188	14	,	,	PUNCT
ejpam-4863	188	15	1894	1894	NUM
ejpam-4863	188	16	-	-	SYM
ejpam-4863	188	17	1901	1901	NUM
ejpam-4863	188	18	1899	1899	NUM
ejpam-4863	188	19	....................................	....................................	PUNCT
ejpam-4863	188	20	....................................	....................................	PUNCT
ejpam-4863	188	21	....................................	....................................	PUNCT
ejpam-4863	189	1	....................................	....................................	PUNCT
ejpam-4863	189	2	0	0	NUM
ejpam-4863	189	3	2	2	NUM
ejpam-4863	189	4	3	3	NUM
ejpam-4863	189	5	4	4	NUM
ejpam-4863	189	6	<	<	X
ejpam-4863	189	7	z6\(sz6	z6\(sz6	X
ejpam-4863	189	8	)	)	PUNCT
ejpam-4863	189	9	>	>	X
ejpam-4863	189	10	figure	figure	NOUN
ejpam-4863	189	11	3	3	NUM
ejpam-4863	189	12	:	:	PUNCT
ejpam-4863	189	13	the	the	DET
ejpam-4863	189	14	induced	induced	ADJ
ejpam-4863	189	15	subgraph	subgraph	NOUN
ejpam-4863	189	16	of	of	ADP
ejpam-4863	189	17	z6\sz6under	z6\sz6under	PROPN
ejpam-4863	189	18	addition	addition	NOUN
ejpam-4863	189	19	modulo	modulo	VERB
ejpam-4863	189	20	6	6	NUM
ejpam-4863	189	21	.	.	PUNCT
ejpam-4863	189	22	theorem	theorem	NOUN
ejpam-4863	189	23	4	4	NUM
ejpam-4863	189	24	.	.	PUNCT
ejpam-4863	190	1	let	let	VERB
ejpam-4863	190	2	g	g	PRON
ejpam-4863	190	3	be	be	AUX
ejpam-4863	190	4	a	a	DET
ejpam-4863	190	5	cyclic	cyclic	ADJ
ejpam-4863	190	6	group	group	NOUN
ejpam-4863	190	7	of	of	ADP
ejpam-4863	190	8	order	order	NOUN
ejpam-4863	190	9	n	n	CCONJ
ejpam-4863	190	10	>	>	X
ejpam-4863	190	11	1	1	NUM
ejpam-4863	190	12	,	,	PUNCT
ejpam-4863	190	13	and	and	CCONJ
ejpam-4863	190	14	sg	sg	PART
ejpam-4863	190	15	be	be	AUX
ejpam-4863	190	16	the	the	DET
ejpam-4863	190	17	set	set	NOUN
ejpam-4863	190	18	of	of	ADP
ejpam-4863	190	19	all	all	DET
ejpam-4863	190	20	generators	generator	NOUN
ejpam-4863	190	21	of	of	ADP
ejpam-4863	190	22	g.	g.	PROPN
ejpam-4863	190	23	then	then	ADV
ejpam-4863	190	24	g	g	PROPN
ejpam-4863	190	25	=	=	SYM
ejpam-4863	190	26	k|sg|	k|sg|	PROPN
ejpam-4863	190	27	+	+	NOUN
ejpam-4863	190	28	kn−|sg|	kn−|sg|	NOUN
ejpam-4863	190	29	.	.	PUNCT
ejpam-4863	191	1	proof	proof	NOUN
ejpam-4863	191	2	.	.	PUNCT
ejpam-4863	192	1	let	let	VERB
ejpam-4863	192	2	g	g	PRON
ejpam-4863	192	3	be	be	AUX
ejpam-4863	192	4	a	a	DET
ejpam-4863	192	5	cyclic	cyclic	ADJ
ejpam-4863	192	6	group	group	NOUN
ejpam-4863	192	7	of	of	ADP
ejpam-4863	192	8	order	order	NOUN
ejpam-4863	192	9	n	n	CCONJ
ejpam-4863	192	10	>	>	X
ejpam-4863	192	11	1,and	1,and	NUM
ejpam-4863	192	12	let	let	VERB
ejpam-4863	192	13	sg	sg	PART
ejpam-4863	192	14	be	be	AUX
ejpam-4863	192	15	the	the	DET
ejpam-4863	192	16	set	set	NOUN
ejpam-4863	192	17	of	of	ADP
ejpam-4863	192	18	all	all	DET
ejpam-4863	192	19	generators	generator	NOUN
ejpam-4863	192	20	of	of	ADP
ejpam-4863	192	21	g.	g.	PROPN
ejpam-4863	192	22	for	for	ADP
ejpam-4863	192	23	x	x	PROPN
ejpam-4863	192	24	,	,	PUNCT
ejpam-4863	192	25	y	y	PROPN
ejpam-4863	192	26	∈	∈	PROPN
ejpam-4863	192	27	v	v	PROPN
ejpam-4863	192	28	(	(	PUNCT
ejpam-4863	192	29	ggg	ggg	NOUN
ejpam-4863	192	30	)	)	PUNCT
ejpam-4863	192	31	,	,	PUNCT
ejpam-4863	192	32	if	if	SCONJ
ejpam-4863	192	33	x	x	X
ejpam-4863	192	34	,	,	PUNCT
ejpam-4863	192	35	y	y	PROPN
ejpam-4863	192	36	∈	∈	PROPN
ejpam-4863	192	37	g\sg	g\sg	PROPN
ejpam-4863	192	38	,	,	PUNCT
ejpam-4863	192	39	then	then	ADV
ejpam-4863	192	40	xy	xy	PROPN
ejpam-4863	192	41	/∈	/∈	PUNCT
ejpam-4863	192	42	e(ggg	e(ggg	PROPN
ejpam-4863	192	43	)	)	PUNCT
ejpam-4863	192	44	.	.	PUNCT
ejpam-4863	193	1	this	this	DET
ejpam-4863	193	2	case	case	NOUN
ejpam-4863	193	3	is	be	AUX
ejpam-4863	193	4	the	the	DET
ejpam-4863	193	5	same	same	ADJ
ejpam-4863	193	6	as	as	ADP
ejpam-4863	193	7	connecting	connect	VERB
ejpam-4863	193	8	the	the	DET
ejpam-4863	193	9	generator	generator	NOUN
ejpam-4863	193	10	element	element	NOUN
ejpam-4863	193	11	of	of	ADP
ejpam-4863	193	12	the	the	DET
ejpam-4863	193	13	group	group	NOUN
ejpam-4863	193	14	to	to	ADP
ejpam-4863	193	15	all	all	DET
ejpam-4863	193	16	other	other	ADJ
ejpam-4863	193	17	elements	element	NOUN
ejpam-4863	193	18	of	of	ADP
ejpam-4863	193	19	the	the	DET
ejpam-4863	193	20	group	group	NOUN
ejpam-4863	193	21	whether	whether	SCONJ
ejpam-4863	193	22	they	they	PRON
ejpam-4863	193	23	are	be	AUX
ejpam-4863	193	24	another	another	DET
ejpam-4863	193	25	generator	generator	NOUN
ejpam-4863	193	26	or	or	CCONJ
ejpam-4863	193	27	non	non	NOUN
ejpam-4863	193	28	-	-	NOUN
ejpam-4863	193	29	generators	generator	NOUN
ejpam-4863	193	30	.	.	PUNCT
ejpam-4863	194	1	in	in	ADP
ejpam-4863	194	2	other	other	ADJ
ejpam-4863	194	3	words	word	NOUN
ejpam-4863	194	4	,	,	PUNCT
ejpam-4863	194	5	all	all	DET
ejpam-4863	194	6	gerators	gerator	NOUN
ejpam-4863	194	7	of	of	ADP
ejpam-4863	194	8	g	g	PROPN
ejpam-4863	194	9	are	be	AUX
ejpam-4863	194	10	adjacent	adjacent	ADJ
ejpam-4863	194	11	in	in	ADP
ejpam-4863	194	12	gg(g	gg(g	PROPN
ejpam-4863	194	13	)	)	PUNCT
ejpam-4863	194	14	,	,	PUNCT
ejpam-4863	194	15	forming	form	VERB
ejpam-4863	194	16	a	a	DET
ejpam-4863	194	17	complete	complete	ADJ
ejpam-4863	194	18	subgroup	subgroup	NOUN
ejpam-4863	194	19	.	.	PUNCT
ejpam-4863	195	1	the	the	DET
ejpam-4863	195	2	other	other	ADJ
ejpam-4863	195	3	edges	edge	NOUN
ejpam-4863	195	4	are	be	AUX
ejpam-4863	195	5	formed	form	VERB
ejpam-4863	195	6	by	by	ADP
ejpam-4863	195	7	connecting	connect	VERB
ejpam-4863	195	8	each	each	DET
ejpam-4863	195	9	genrator	genrator	NOUN
ejpam-4863	195	10	by	by	ADP
ejpam-4863	195	11	an	an	DET
ejpam-4863	195	12	edge	edge	NOUN
ejpam-4863	195	13	to	to	ADP
ejpam-4863	195	14	each	each	PRON
ejpam-4863	195	15	of	of	ADP
ejpam-4863	195	16	the	the	DET
ejpam-4863	195	17	non	non	NOUN
ejpam-4863	195	18	-	-	NOUN
ejpam-4863	195	19	generators	generator	NOUN
ejpam-4863	195	20	.	.	PUNCT
ejpam-4863	196	1	therefore	therefore	ADV
ejpam-4863	196	2	,	,	PUNCT
ejpam-4863	196	3	the	the	DET
ejpam-4863	196	4	generator	generator	NOUN
ejpam-4863	196	5	graph	graph	NOUN
ejpam-4863	196	6	ggg	ggg	NOUN
ejpam-4863	196	7	can	can	AUX
ejpam-4863	196	8	be	be	AUX
ejpam-4863	196	9	described	describe	VERB
ejpam-4863	196	10	as	as	ADP
ejpam-4863	196	11	the	the	DET
ejpam-4863	196	12	join	join	NOUN
ejpam-4863	196	13	of	of	ADP
ejpam-4863	196	14	complete	complete	ADJ
ejpam-4863	196	15	graph	graph	NOUN
ejpam-4863	196	16	of	of	ADP
ejpam-4863	196	17	order	order	NOUN
ejpam-4863	196	18	|sg|	|sg|	NOUN
ejpam-4863	196	19	and	and	CCONJ
ejpam-4863	196	20	null	null	ADJ
ejpam-4863	196	21	graph	graph	NOUN
ejpam-4863	196	22	of	of	ADP
ejpam-4863	196	23	order	order	NOUN
ejpam-4863	196	24	n−	n−	PROPN
ejpam-4863	196	25	|sg|	|sg|	NOUN
ejpam-4863	196	26	.	.	PUNCT
ejpam-4863	197	1	4	4	X
ejpam-4863	197	2	.	.	X
ejpam-4863	197	3	relationship	relationship	NOUN
ejpam-4863	197	4	between	between	ADP
ejpam-4863	197	5	generating	generate	VERB
ejpam-4863	197	6	graph	graph	NOUN
ejpam-4863	197	7	and	and	CCONJ
ejpam-4863	197	8	generator	generator	NOUN
ejpam-4863	197	9	graph	graph	NOUN
ejpam-4863	197	10	of	of	ADP
ejpam-4863	197	11	group	group	NOUN
ejpam-4863	197	12	the	the	DET
ejpam-4863	197	13	concept	concept	NOUN
ejpam-4863	197	14	of	of	ADP
ejpam-4863	197	15	the	the	DET
ejpam-4863	197	16	generating	generate	VERB
ejpam-4863	197	17	graph	graph	NOUN
ejpam-4863	197	18	of	of	ADP
ejpam-4863	197	19	a	a	DET
ejpam-4863	197	20	group	group	NOUN
ejpam-4863	197	21	was	be	AUX
ejpam-4863	197	22	introduced	introduce	VERB
ejpam-4863	197	23	by	by	ADP
ejpam-4863	197	24	luchini	luchini	PROPN
ejpam-4863	197	25	et	et	PROPN
ejpam-4863	197	26	al	al	PROPN
ejpam-4863	197	27	in	in	ADP
ejpam-4863	197	28	[	[	X
ejpam-4863	197	29	7	7	NUM
ejpam-4863	197	30	]	]	PUNCT
ejpam-4863	197	31	.	.	PUNCT
ejpam-4863	198	1	in	in	ADP
ejpam-4863	198	2	their	their	PRON
ejpam-4863	198	3	study	study	NOUN
ejpam-4863	198	4	,	,	PUNCT
ejpam-4863	198	5	two	two	NUM
ejpam-4863	198	6	non	non	ADJ
ejpam-4863	198	7	-	-	ADJ
ejpam-4863	198	8	generator	generator	ADJ
ejpam-4863	198	9	elements	element	NOUN
ejpam-4863	198	10	of	of	ADP
ejpam-4863	198	11	a	a	DET
ejpam-4863	198	12	group	group	NOUN
ejpam-4863	198	13	g	g	NOUN
ejpam-4863	198	14	are	be	AUX
ejpam-4863	198	15	adjacent	adjacent	ADJ
ejpam-4863	198	16	in	in	ADP
ejpam-4863	198	17	the	the	DET
ejpam-4863	198	18	generating	generate	VERB
ejpam-4863	198	19	graph	graph	NOUN
ejpam-4863	198	20	of	of	ADP
ejpam-4863	198	21	g	g	PROPN
ejpam-4863	198	22	if	if	SCONJ
ejpam-4863	198	23	they	they	PRON
ejpam-4863	198	24	generate	generate	VERB
ejpam-4863	198	25	g	g	NOUN
ejpam-4863	198	26	,	,	PUNCT
ejpam-4863	198	27	while	while	SCONJ
ejpam-4863	198	28	they	they	PRON
ejpam-4863	198	29	are	be	AUX
ejpam-4863	198	30	not	not	PART
ejpam-4863	198	31	adjacent	adjacent	ADJ
ejpam-4863	198	32	in	in	ADP
ejpam-4863	198	33	the	the	DET
ejpam-4863	198	34	generator	generator	NOUN
ejpam-4863	198	35	graph	graph	NOUN
ejpam-4863	198	36	of	of	ADP
ejpam-4863	198	37	g.	g.	PROPN
ejpam-4863	198	38	definition	definition	NOUN
ejpam-4863	198	39	2	2	NUM
ejpam-4863	198	40	.	.	PUNCT
ejpam-4863	199	1	[	[	X
ejpam-4863	199	2	7	7	X
ejpam-4863	199	3	]	]	X
ejpam-4863	199	4	the	the	DET
ejpam-4863	199	5	generating	generate	VERB
ejpam-4863	199	6	graph	graph	NOUN
ejpam-4863	199	7	γ(g	γ(g	PROPN
ejpam-4863	199	8	)	)	PUNCT
ejpam-4863	199	9	of	of	ADP
ejpam-4863	199	10	a	a	DET
ejpam-4863	199	11	group	group	NOUN
ejpam-4863	199	12	g	g	NOUN
ejpam-4863	199	13	is	be	AUX
ejpam-4863	199	14	the	the	DET
ejpam-4863	199	15	graph	graph	NOUN
ejpam-4863	199	16	defined	define	VERB
ejpam-4863	199	17	on	on	ADP
ejpam-4863	199	18	the	the	DET
ejpam-4863	199	19	elements	element	NOUN
ejpam-4863	199	20	of	of	ADP
ejpam-4863	199	21	g	g	NOUN
ejpam-4863	199	22	,	,	PUNCT
ejpam-4863	199	23	with	with	ADP
ejpam-4863	199	24	edge	edge	NOUN
ejpam-4863	199	25	between	between	ADP
ejpam-4863	199	26	two	two	NUM
ejpam-4863	199	27	vertices	vertex	NOUN
ejpam-4863	199	28	if	if	SCONJ
ejpam-4863	199	29	and	and	CCONJ
ejpam-4863	199	30	only	only	ADV
ejpam-4863	199	31	if	if	SCONJ
ejpam-4863	199	32	they	they	PRON
ejpam-4863	199	33	generate	generate	VERB
ejpam-4863	199	34	g.	g.	NOUN
ejpam-4863	199	35	figure	figure	NOUN
ejpam-4863	199	36	4	4	NUM
ejpam-4863	199	37	illustrates	illustrate	VERB
ejpam-4863	199	38	the	the	DET
ejpam-4863	199	39	generating	generate	VERB
ejpam-4863	199	40	graph	graph	NOUN
ejpam-4863	199	41	of	of	ADP
ejpam-4863	199	42	the	the	DET
ejpam-4863	199	43	group	group	NOUN
ejpam-4863	199	44	of	of	ADP
ejpam-4863	199	45	integers	integer	NOUN
ejpam-4863	199	46	modulo	modulo	VERB
ejpam-4863	199	47	6	6	NUM
ejpam-4863	199	48	,	,	PUNCT
ejpam-4863	199	49	z6	z6	PROPN
ejpam-4863	199	50	.	.	PUNCT
ejpam-4863	200	1	both	both	DET
ejpam-4863	200	2	sets	set	VERB
ejpam-4863	200	3	{	{	PUNCT
ejpam-4863	200	4	2	2	NUM
ejpam-4863	200	5	,	,	PUNCT
ejpam-4863	200	6	3	3	NUM
ejpam-4863	200	7	}	}	PUNCT
ejpam-4863	200	8	)	)	PUNCT
ejpam-4863	200	9	and	and	CCONJ
ejpam-4863	200	10	{	{	PUNCT
ejpam-4863	200	11	3	3	NUM
ejpam-4863	200	12	,	,	PUNCT
ejpam-4863	200	13	4	4	NUM
ejpam-4863	200	14	}	}	PUNCT
ejpam-4863	200	15	generate	generate	VERB
ejpam-4863	200	16	the	the	DET
ejpam-4863	200	17	group	group	NOUN
ejpam-4863	200	18	z6	z6	PROPN
ejpam-4863	200	19	,	,	PUNCT
ejpam-4863	200	20	that	that	ADV
ejpam-4863	200	21	is	is	ADV
ejpam-4863	200	22	,	,	PUNCT
ejpam-4863	200	23	(	(	PUNCT
ejpam-4863	200	24	{	{	PUNCT
ejpam-4863	200	25	2	2	NUM
ejpam-4863	200	26	,	,	PUNCT
ejpam-4863	200	27	3	3	NUM
ejpam-4863	200	28	}	}	PUNCT
ejpam-4863	200	29	)	)	PUNCT
ejpam-4863	200	30	=	=	SYM
ejpam-4863	200	31	z6	z6	PROPN
ejpam-4863	200	32	and	and	CCONJ
ejpam-4863	200	33	(	(	PUNCT
ejpam-4863	200	34	{	{	PUNCT
ejpam-4863	200	35	3	3	NUM
ejpam-4863	200	36	,	,	PUNCT
ejpam-4863	200	37	4	4	NUM
ejpam-4863	200	38	}	}	PUNCT
ejpam-4863	200	39	)	)	PUNCT
ejpam-4863	200	40	=	=	SYM
ejpam-4863	200	41	z6	z6	PROPN
ejpam-4863	200	42	.	.	PUNCT
ejpam-4863	201	1	thus	thus	ADV
ejpam-4863	201	2	,	,	PUNCT
ejpam-4863	201	3	(	(	PUNCT
ejpam-4863	201	4	2	2	NUM
ejpam-4863	201	5	,	,	PUNCT
ejpam-4863	201	6	3	3	NUM
ejpam-4863	201	7	)	)	PUNCT
ejpam-4863	202	1	,	,	PUNCT
ejpam-4863	202	2	(	(	PUNCT
ejpam-4863	202	3	3	3	NUM
ejpam-4863	202	4	,	,	PUNCT
ejpam-4863	202	5	4	4	NUM
ejpam-4863	202	6	)	)	PUNCT
ejpam-4863	202	7	∈	∈	PROPN
ejpam-4863	202	8	e(z6	e(z6	NOUN
ejpam-4863	202	9	)	)	PUNCT
ejpam-4863	202	10	.	.	PUNCT
ejpam-4863	203	1	note	note	VERB
ejpam-4863	203	2	that	that	SCONJ
ejpam-4863	203	3	2	2	NUM
ejpam-4863	203	4	,	,	PUNCT
ejpam-4863	203	5	3	3	NUM
ejpam-4863	203	6	and	and	CCONJ
ejpam-4863	203	7	4	4	NUM
ejpam-4863	203	8	are	be	AUX
ejpam-4863	203	9	not	not	PART
ejpam-4863	203	10	generators	generator	NOUN
ejpam-4863	203	11	of	of	ADP
ejpam-4863	203	12	g	g	NOUN
ejpam-4863	203	13	,	,	PUNCT
ejpam-4863	203	14	hence	hence	ADV
ejpam-4863	203	15	none	none	NOUN
ejpam-4863	203	16	of	of	ADP
ejpam-4863	203	17	these	these	DET
ejpam-4863	203	18	vertices	vertex	NOUN
ejpam-4863	203	19	are	be	AUX
ejpam-4863	203	20	adjacent	adjacent	ADJ
ejpam-4863	203	21	in	in	ADP
ejpam-4863	203	22	the	the	DET
ejpam-4863	203	23	generator	generator	NOUN
ejpam-4863	203	24	graph	graph	NOUN
ejpam-4863	203	25	of	of	ADP
ejpam-4863	203	26	g.	g.	PROPN
ejpam-4863	204	1	this	this	PRON
ejpam-4863	204	2	can	can	AUX
ejpam-4863	204	3	be	be	AUX
ejpam-4863	204	4	verified	verify	VERB
ejpam-4863	204	5	in	in	ADP
ejpam-4863	204	6	figure	figure	NOUN
ejpam-4863	204	7	1	1	NUM
ejpam-4863	204	8	.	.	PUNCT
ejpam-4863	205	1	this	this	DET
ejpam-4863	205	2	observation	observation	NOUN
ejpam-4863	205	3	is	be	AUX
ejpam-4863	205	4	generalized	generalize	VERB
ejpam-4863	205	5	in	in	ADP
ejpam-4863	205	6	the	the	DET
ejpam-4863	205	7	next	next	ADJ
ejpam-4863	205	8	result	result	NOUN
ejpam-4863	205	9	.	.	PUNCT
ejpam-4863	206	1	....................................	....................................	PUNCT
ejpam-4863	206	2	....................................	....................................	PUNCT
ejpam-4863	207	1	....................................	....................................	PUNCT
ejpam-4863	207	2	....................................	....................................	PUNCT
ejpam-4863	208	1	....................................	....................................	PUNCT
ejpam-4863	208	2	....................................	....................................	PUNCT
ejpam-4863	209	1	...................	...................	PUNCT
ejpam-4863	209	2	..................	..................	PUNCT
ejpam-4863	210	1	..................	..................	PUNCT
ejpam-4863	210	2	..................	..................	PUNCT
ejpam-4863	211	1	..................	..................	PUNCT
ejpam-4863	211	2	..................	..................	PUNCT
ejpam-4863	212	1	..................	..................	PUNCT
ejpam-4863	212	2	..................	..................	PUNCT
ejpam-4863	213	1	.....	.....	PUNCT
ejpam-4863	213	2	..........	..........	PUNCT
ejpam-4863	214	1	.........	.........	PUNCT
ejpam-4863	214	2	.........	.........	PUNCT
ejpam-4863	215	1	.........	.........	PUNCT
ejpam-4863	215	2	.........	.........	PUNCT
ejpam-4863	216	1	.........	.........	PUNCT
ejpam-4863	216	2	.........	.........	PUNCT
ejpam-4863	217	1	.........	.........	PUNCT
ejpam-4863	217	2	.........	.........	PUNCT
ejpam-4863	218	1	.........	.........	PUNCT
ejpam-4863	218	2	.........	.........	PUNCT
ejpam-4863	219	1	.........	.........	PUNCT
ejpam-4863	219	2	.........	.........	PUNCT
ejpam-4863	220	1	.........	.........	PUNCT
ejpam-4863	220	2	.........	.........	PUNCT
ejpam-4863	221	1	.........	.........	PUNCT
ejpam-4863	221	2	.....	.....	PUNCT
ejpam-4863	221	3	.........	.........	PUNCT
ejpam-4863	221	4	........	........	PUNCT
ejpam-4863	221	5	........	........	PUNCT
ejpam-4863	221	6	........	........	PUNCT
ejpam-4863	221	7	........	........	PUNCT
ejpam-4863	221	8	........	........	PUNCT
ejpam-4863	221	9	........	........	PUNCT
ejpam-4863	221	10	........	........	PUNCT
ejpam-4863	221	11	........	........	PUNCT
ejpam-4863	221	12	........	........	PUNCT
ejpam-4863	221	13	........	........	PUNCT
ejpam-4863	221	14	........	........	PUNCT
ejpam-4863	221	15	........	........	PUNCT
ejpam-4863	221	16	........	........	PUNCT
ejpam-4863	221	17	........	........	PUNCT
ejpam-4863	221	18	........	........	PUNCT
ejpam-4863	222	1	...........................................................................................................	...........................................................................................................	PUNCT
ejpam-4863	222	2	...........	...........	PUNCT
ejpam-4863	222	3	...........	...........	PUNCT
ejpam-4863	222	4	...........	...........	PUNCT
ejpam-4863	222	5	...........	...........	PUNCT
ejpam-4863	222	6	...........	...........	PUNCT
ejpam-4863	222	7	...........	...........	PUNCT
ejpam-4863	222	8	...........	...........	PUNCT
ejpam-4863	222	9	..	..	PUNCT
ejpam-4863	222	10	.........	.........	PUNCT
ejpam-4863	222	11	........	........	PUNCT
ejpam-4863	222	12	........	........	PUNCT
ejpam-4863	222	13	........	........	PUNCT
ejpam-4863	222	14	........	........	PUNCT
ejpam-4863	222	15	........	........	PUNCT
ejpam-4863	222	16	........	........	PUNCT
ejpam-4863	222	17	........	........	PUNCT
ejpam-4863	222	18	........	........	PUNCT
ejpam-4863	222	19	........	........	PUNCT
ejpam-4863	222	20	........	........	PUNCT
ejpam-4863	222	21	........	........	PUNCT
ejpam-4863	222	22	........	........	PUNCT
ejpam-4863	222	23	........	........	PUNCT
ejpam-4863	222	24	........	........	PUNCT
ejpam-4863	223	1	........	........	PUNCT
ejpam-4863	223	2	..........................................................................................................................................................	..........................................................................................................................................................	PUNCT
ejpam-4863	224	1	......................................................................................................................................................	......................................................................................................................................................	NUM
ejpam-4863	224	2	..............................................................	..............................................................	PUNCT
ejpam-4863	224	3	............	............	PUNCT
ejpam-4863	224	4	...........	...........	PUNCT
ejpam-4863	224	5	...........	...........	PUNCT
ejpam-4863	224	6	...........	...........	PUNCT
ejpam-4863	224	7	...........	...........	PUNCT
ejpam-4863	224	8	...........	...........	PUNCT
ejpam-4863	224	9	...........	...........	PUNCT
ejpam-4863	224	10	...........	...........	PUNCT
ejpam-4863	224	11	..	..	PUNCT
ejpam-4863	225	1	..............................................................	..............................................................	PUNCT
ejpam-4863	226	1	•	•	NUM
ejpam-4863	226	2	•	•	NUM
ejpam-4863	226	3	•	•	NUM
ejpam-4863	226	4	•	•	NOUN
ejpam-4863	226	5	•	•	NOUN
ejpam-4863	226	6	•1	•1	PRON
ejpam-4863	226	7	5	5	NUM
ejpam-4863	226	8	0	0	NUM
ejpam-4863	226	9	2	2	NUM
ejpam-4863	226	10	3	3	NUM
ejpam-4863	226	11	4	4	NUM
ejpam-4863	226	12	γ(z6	γ(z6	NOUN
ejpam-4863	226	13	)	)	PUNCT
ejpam-4863	226	14	figure	figure	NOUN
ejpam-4863	226	15	4	4	NUM
ejpam-4863	226	16	:	:	PUNCT
ejpam-4863	226	17	the	the	DET
ejpam-4863	226	18	generating	generate	VERB
ejpam-4863	226	19	graph	graph	NOUN
ejpam-4863	226	20	of	of	ADP
ejpam-4863	226	21	γ(z6	γ(z6	NOUN
ejpam-4863	226	22	)	)	PUNCT
ejpam-4863	226	23	references	reference	NOUN
ejpam-4863	226	24	1900	1900	NUM
ejpam-4863	226	25	theorem	theorem	VERB
ejpam-4863	226	26	5	5	NUM
ejpam-4863	226	27	.	.	PUNCT
ejpam-4863	227	1	let	let	VERB
ejpam-4863	227	2	g	g	PRON
ejpam-4863	227	3	be	be	AUX
ejpam-4863	227	4	a	a	DET
ejpam-4863	227	5	group	group	NOUN
ejpam-4863	227	6	.	.	PUNCT
ejpam-4863	228	1	then	then	ADV
ejpam-4863	228	2	the	the	DET
ejpam-4863	228	3	generator	generator	NOUN
ejpam-4863	228	4	graph	graph	NOUN
ejpam-4863	228	5	of	of	ADP
ejpam-4863	228	6	g	g	PROPN
ejpam-4863	228	7	is	be	AUX
ejpam-4863	228	8	a	a	DET
ejpam-4863	228	9	spanning	span	VERB
ejpam-4863	228	10	subgraph	subgraph	NOUN
ejpam-4863	228	11	of	of	ADP
ejpam-4863	228	12	the	the	DET
ejpam-4863	228	13	generating	generate	VERB
ejpam-4863	228	14	graph	graph	NOUN
ejpam-4863	228	15	of	of	ADP
ejpam-4863	228	16	g.	g.	PROPN
ejpam-4863	228	17	proof	proof	NOUN
ejpam-4863	228	18	.	.	PUNCT
ejpam-4863	229	1	let	let	VERB
ejpam-4863	229	2	g	g	PRON
ejpam-4863	229	3	be	be	AUX
ejpam-4863	229	4	a	a	DET
ejpam-4863	229	5	group	group	NOUN
ejpam-4863	229	6	.	.	PUNCT
ejpam-4863	230	1	by	by	ADP
ejpam-4863	230	2	definition	definition	NOUN
ejpam-4863	230	3	of	of	ADP
ejpam-4863	230	4	the	the	DET
ejpam-4863	230	5	generator	generator	NOUN
ejpam-4863	230	6	graph	graph	NOUN
ejpam-4863	230	7	and	and	CCONJ
ejpam-4863	230	8	the	the	DET
ejpam-4863	230	9	generating	generating	NOUN
ejpam-4863	230	10	graph	graph	NOUN
ejpam-4863	230	11	,	,	PUNCT
ejpam-4863	230	12	v	v	NOUN
ejpam-4863	230	13	(	(	PUNCT
ejpam-4863	230	14	ggg	ggg	NOUN
ejpam-4863	230	15	)	)	PUNCT
ejpam-4863	230	16	=	=	SYM
ejpam-4863	230	17	v	v	X
ejpam-4863	230	18	(	(	PUNCT
ejpam-4863	230	19	γ(g	γ(g	PROPN
ejpam-4863	230	20	)	)	PUNCT
ejpam-4863	230	21	)	)	PUNCT
ejpam-4863	230	22	.	.	PUNCT
ejpam-4863	231	1	let	let	VERB
ejpam-4863	231	2	x	x	PRON
ejpam-4863	231	3	,	,	PUNCT
ejpam-4863	231	4	y	y	PROPN
ejpam-4863	231	5	∈	∈	PROPN
ejpam-4863	231	6	v	v	PROPN
ejpam-4863	231	7	(	(	PUNCT
ejpam-4863	231	8	ggg	ggg	NOUN
ejpam-4863	231	9	)	)	PUNCT
ejpam-4863	231	10	.	.	PUNCT
ejpam-4863	232	1	if	if	SCONJ
ejpam-4863	232	2	both	both	PRON
ejpam-4863	232	3	or	or	CCONJ
ejpam-4863	232	4	one	one	NUM
ejpam-4863	232	5	of	of	ADP
ejpam-4863	232	6	x	x	PUNCT
ejpam-4863	232	7	and	and	CCONJ
ejpam-4863	232	8	y	y	PROPN
ejpam-4863	232	9	are	be	AUX
ejpam-4863	232	10	generators	generator	NOUN
ejpam-4863	232	11	,	,	PUNCT
ejpam-4863	232	12	then	then	ADV
ejpam-4863	232	13	the	the	DET
ejpam-4863	232	14	set	set	NOUN
ejpam-4863	232	15	{	{	PUNCT
ejpam-4863	232	16	x	x	NOUN
ejpam-4863	232	17	,	,	PUNCT
ejpam-4863	232	18	y	y	NOUN
ejpam-4863	232	19	}	}	PUNCT
ejpam-4863	232	20	clearly	clearly	ADV
ejpam-4863	232	21	generates	generate	VERB
ejpam-4863	232	22	g.	g.	NOUN
ejpam-4863	232	23	in	in	ADP
ejpam-4863	232	24	this	this	DET
ejpam-4863	232	25	case	case	NOUN
ejpam-4863	232	26	,	,	PUNCT
ejpam-4863	232	27	xy	xy	PROPN
ejpam-4863	232	28	∈	∈	PROPN
ejpam-4863	232	29	e(ggg	e(ggg	NOUN
ejpam-4863	232	30	)	)	PUNCT
ejpam-4863	232	31	and	and	CCONJ
ejpam-4863	232	32	xy	xy	PROPN
ejpam-4863	232	33	∈	∈	PROPN
ejpam-4863	232	34	e(γ(g	e(γ(g	PROPN
ejpam-4863	232	35	)	)	PUNCT
ejpam-4863	232	36	)	)	PUNCT
ejpam-4863	232	37	.	.	PUNCT
ejpam-4863	233	1	if	if	SCONJ
ejpam-4863	233	2	both	both	DET
ejpam-4863	233	3	x	x	X
ejpam-4863	233	4	and	and	CCONJ
ejpam-4863	233	5	y	y	PROPN
ejpam-4863	233	6	are	be	AUX
ejpam-4863	233	7	non	non	NOUN
ejpam-4863	233	8	-	-	NOUN
ejpam-4863	233	9	generators	generator	NOUN
ejpam-4863	233	10	,	,	PUNCT
ejpam-4863	233	11	then	then	ADV
ejpam-4863	233	12	the	the	DET
ejpam-4863	233	13	set	set	NOUN
ejpam-4863	233	14	{	{	PUNCT
ejpam-4863	233	15	x	x	NOUN
ejpam-4863	233	16	,	,	PUNCT
ejpam-4863	233	17	y	y	NOUN
ejpam-4863	233	18	}	}	PUNCT
ejpam-4863	233	19	either	either	CCONJ
ejpam-4863	233	20	generates	generate	VERB
ejpam-4863	233	21	g	g	NOUN
ejpam-4863	233	22	or	or	CCONJ
ejpam-4863	233	23	does	do	AUX
ejpam-4863	233	24	not	not	PART
ejpam-4863	233	25	generate	generate	VERB
ejpam-4863	233	26	g.	g.	NOUN
ejpam-4863	233	27	in	in	ADP
ejpam-4863	233	28	this	this	DET
ejpam-4863	233	29	case	case	NOUN
ejpam-4863	233	30	,	,	PUNCT
ejpam-4863	233	31	xy	xy	PROPN
ejpam-4863	233	32	/∈	/∈	PUNCT
ejpam-4863	233	33	e(ggg	e(ggg	NOUN
ejpam-4863	233	34	)	)	PUNCT
ejpam-4863	233	35	but	but	CCONJ
ejpam-4863	233	36	either	either	CCONJ
ejpam-4863	233	37	xy	xy	PROPN
ejpam-4863	233	38	∈	∈	PROPN
ejpam-4863	233	39	e(γ(g	e(γ(g	PROPN
ejpam-4863	233	40	)	)	PUNCT
ejpam-4863	233	41	)	)	PUNCT
ejpam-4863	233	42	or	or	CCONJ
ejpam-4863	233	43	xy	xy	INTJ
ejpam-4863	233	44	/∈	/∈	PUNCT
ejpam-4863	234	1	e(γ(g	e(γ(g	PROPN
ejpam-4863	234	2	)	)	PUNCT
ejpam-4863	234	3	)	)	PUNCT
ejpam-4863	234	4	.	.	PUNCT
ejpam-4863	235	1	it	it	PRON
ejpam-4863	235	2	follows	follow	VERB
ejpam-4863	235	3	that	that	SCONJ
ejpam-4863	235	4	e(ggg	e(ggg	NOUN
ejpam-4863	235	5	)	)	PUNCT
ejpam-4863	235	6	⊆	⊆	NUM
ejpam-4863	235	7	e(γg	e(γg	NOUN
ejpam-4863	235	8	)	)	PUNCT
ejpam-4863	235	9	.	.	PUNCT
ejpam-4863	236	1	therefore	therefore	ADV
ejpam-4863	236	2	,	,	PUNCT
ejpam-4863	236	3	gg(g	gg(g	PROPN
ejpam-4863	236	4	)	)	PUNCT
ejpam-4863	236	5	is	be	AUX
ejpam-4863	236	6	a	a	DET
ejpam-4863	236	7	spanning	span	VERB
ejpam-4863	236	8	subgraph	subgraph	NOUN
ejpam-4863	236	9	of	of	ADP
ejpam-4863	236	10	γ(g	γ(g	PROPN
ejpam-4863	236	11	)	)	PUNCT
ejpam-4863	236	12	.	.	PUNCT
ejpam-4863	237	1	example	example	NOUN
ejpam-4863	238	1	4	4	NUM
ejpam-4863	238	2	.	.	PUNCT
ejpam-4863	238	3	the	the	DET
ejpam-4863	238	4	dihedral	dihedral	ADJ
ejpam-4863	238	5	group	group	NOUN
ejpam-4863	238	6	dn	dn	PROPN
ejpam-4863	238	7	is	be	AUX
ejpam-4863	238	8	the	the	DET
ejpam-4863	238	9	symmetry	symmetry	NOUN
ejpam-4863	238	10	group	group	NOUN
ejpam-4863	238	11	,	,	PUNCT
ejpam-4863	238	12	which	which	PRON
ejpam-4863	238	13	includes	include	VERB
ejpam-4863	238	14	rotations	rotation	NOUN
ejpam-4863	238	15	and	and	CCONJ
ejpam-4863	238	16	reflections	reflection	NOUN
ejpam-4863	238	17	,	,	PUNCT
ejpam-4863	238	18	of	of	ADP
ejpam-4863	238	19	an	an	DET
ejpam-4863	238	20	n	n	ADV
ejpam-4863	238	21	-	-	PUNCT
ejpam-4863	238	22	sided	sided	ADJ
ejpam-4863	238	23	regular	regular	ADJ
ejpam-4863	238	24	polygon	polygon	NOUN
ejpam-4863	238	25	for	for	ADP
ejpam-4863	238	26	n	n	PROPN
ejpam-4863	238	27	>	>	X
ejpam-4863	238	28	1	1	X
ejpam-4863	238	29	.	.	PUNCT
ejpam-4863	238	30	dihedral	dihedral	ADJ
ejpam-4863	238	31	groups	group	NOUN
ejpam-4863	238	32	dn	dn	X
ejpam-4863	238	33	are	be	AUX
ejpam-4863	238	34	non	non	ADJ
ejpam-4863	238	35	-	-	ADJ
ejpam-4863	238	36	abelian	abelian	ADJ
ejpam-4863	238	37	permutation	permutation	NOUN
ejpam-4863	238	38	groups	group	NOUN
ejpam-4863	238	39	for	for	ADP
ejpam-4863	238	40	n	n	X
ejpam-4863	238	41	>	>	X
ejpam-4863	238	42	2	2	NUM
ejpam-4863	238	43	.	.	PUNCT
ejpam-4863	239	1	the	the	DET
ejpam-4863	239	2	group	group	NOUN
ejpam-4863	239	3	dn	dn	PROPN
ejpam-4863	239	4	has	have	VERB
ejpam-4863	239	5	elements	element	NOUN
ejpam-4863	239	6	r0	r0	NOUN
ejpam-4863	239	7	,	,	PUNCT
ejpam-4863	239	8	...	...	PUNCT
ejpam-4863	239	9	,	,	PUNCT
ejpam-4863	239	10	rn−1	rn−1	NOUN
ejpam-4863	239	11	that	that	PRON
ejpam-4863	239	12	represents	represent	VERB
ejpam-4863	239	13	rotations	rotation	NOUN
ejpam-4863	239	14	and	and	CCONJ
ejpam-4863	239	15	s0	s0	NOUN
ejpam-4863	239	16	,	,	PUNCT
ejpam-4863	239	17	...	...	PUNCT
ejpam-4863	239	18	,	,	PUNCT
ejpam-4863	239	19	sn−1	sn−1	PROPN
ejpam-4863	239	20	that	that	PRON
ejpam-4863	239	21	represents	represent	VERB
ejpam-4863	239	22	reflections	reflection	NOUN
ejpam-4863	239	23	.	.	PUNCT
ejpam-4863	240	1	their	their	PRON
ejpam-4863	240	2	compositions	composition	NOUN
ejpam-4863	240	3	are	be	AUX
ejpam-4863	240	4	given	give	VERB
ejpam-4863	240	5	by	by	ADP
ejpam-4863	240	6	:	:	PUNCT
ejpam-4863	240	7	rirj	rirj	ADJ
ejpam-4863	240	8	=	=	PUNCT
ejpam-4863	240	9	r(i+j)(mod	r(i+j)(mod	PROPN
ejpam-4863	240	10	n	n	CCONJ
ejpam-4863	240	11	)	)	PUNCT
ejpam-4863	240	12	,	,	PUNCT
ejpam-4863	240	13	risj	risj	NOUN
ejpam-4863	240	14	=	=	SYM
ejpam-4863	240	15	s(i+j)(mod	s(i+j)(mod	PROPN
ejpam-4863	240	16	n	n	CCONJ
ejpam-4863	240	17	)	)	PUNCT
ejpam-4863	240	18	,	,	PUNCT
ejpam-4863	240	19	sirj	sirj	NOUN
ejpam-4863	240	20	=	=	SYM
ejpam-4863	240	21	r(i−j)(mod	r(i−j)(mod	PROPN
ejpam-4863	240	22	n	n	CCONJ
ejpam-4863	240	23	)	)	PUNCT
ejpam-4863	240	24	,	,	PUNCT
ejpam-4863	240	25	and	and	CCONJ
ejpam-4863	240	26	sisj	sisj	NOUN
ejpam-4863	240	27	=	=	SYM
ejpam-4863	240	28	r(i−j)(mod	r(i−j)(mod	PROPN
ejpam-4863	240	29	n	n	CCONJ
ejpam-4863	240	30	)	)	PUNCT
ejpam-4863	240	31	where	where	SCONJ
ejpam-4863	240	32	i	i	PRON
ejpam-4863	240	33	,	,	PUNCT
ejpam-4863	240	34	j	j	PROPN
ejpam-4863	240	35	∈	∈	PROPN
ejpam-4863	240	36	{	{	PUNCT
ejpam-4863	240	37	0	0	NUM
ejpam-4863	240	38	,	,	PUNCT
ejpam-4863	240	39	1	1	NUM
ejpam-4863	240	40	,	,	PUNCT
ejpam-4863	240	41	2	2	NUM
ejpam-4863	240	42	}	}	PUNCT
ejpam-4863	240	43	.	.	PUNCT
ejpam-4863	241	1	for	for	ADP
ejpam-4863	241	2	n3	n3	NOUN
ejpam-4863	241	3	,	,	PUNCT
ejpam-4863	241	4	d3	d3	PROPN
ejpam-4863	241	5	=	=	SYM
ejpam-4863	241	6	{	{	PUNCT
ejpam-4863	241	7	r0	r0	NOUN
ejpam-4863	241	8	,	,	PUNCT
ejpam-4863	241	9	r1	r1	NOUN
ejpam-4863	241	10	,	,	PUNCT
ejpam-4863	241	11	r2	r2	PROPN
ejpam-4863	241	12	,	,	PUNCT
ejpam-4863	241	13	s0	s0	PROPN
ejpam-4863	241	14	,	,	PUNCT
ejpam-4863	241	15	s1	s1	NOUN
ejpam-4863	241	16	,	,	PUNCT
ejpam-4863	241	17	s2	s2	PROPN
ejpam-4863	241	18	}	}	PUNCT
ejpam-4863	241	19	,	,	PUNCT
ejpam-4863	241	20	representing	represent	VERB
ejpam-4863	241	21	the	the	DET
ejpam-4863	241	22	symmetric	symmetric	ADJ
ejpam-4863	241	23	group	group	NOUN
ejpam-4863	241	24	of	of	ADP
ejpam-4863	241	25	triangle	triangle	NOUN
ejpam-4863	241	26	with	with	ADP
ejpam-4863	241	27	the	the	DET
ejpam-4863	241	28	identity	identity	NOUN
ejpam-4863	241	29	r0	r0	NOUN
ejpam-4863	241	30	.	.	PUNCT
ejpam-4863	242	1	note	note	VERB
ejpam-4863	242	2	that	that	SCONJ
ejpam-4863	242	3	the	the	DET
ejpam-4863	242	4	generator	generator	NOUN
ejpam-4863	242	5	graph	graph	NOUN
ejpam-4863	242	6	of	of	ADP
ejpam-4863	242	7	d3	d3	PROPN
ejpam-4863	242	8	is	be	AUX
ejpam-4863	242	9	the	the	DET
ejpam-4863	242	10	empty	empty	ADJ
ejpam-4863	242	11	graph	graph	NOUN
ejpam-4863	242	12	of	of	ADP
ejpam-4863	242	13	order	order	NOUN
ejpam-4863	242	14	6	6	NUM
ejpam-4863	242	15	,	,	PUNCT
ejpam-4863	242	16	i.e.	i.e.	X
ejpam-4863	242	17	,	,	PUNCT
ejpam-4863	242	18	gg(d3	gg(d3	NOUN
ejpam-4863	242	19	)	)	PUNCT
ejpam-4863	242	20	=	=	SYM
ejpam-4863	242	21	k6	k6	NOUN
ejpam-4863	242	22	,	,	PUNCT
ejpam-4863	242	23	since	since	SCONJ
ejpam-4863	242	24	d3	d3	PROPN
ejpam-4863	242	25	has	have	VERB
ejpam-4863	242	26	no	no	DET
ejpam-4863	242	27	generator	generator	NOUN
ejpam-4863	242	28	.	.	PUNCT
ejpam-4863	243	1	it	it	PRON
ejpam-4863	243	2	is	be	AUX
ejpam-4863	243	3	easy	easy	ADJ
ejpam-4863	243	4	to	to	PART
ejpam-4863	243	5	verify	verify	VERB
ejpam-4863	243	6	that	that	DET
ejpam-4863	243	7	γ(d3	γ(d3	NOUN
ejpam-4863	243	8	)	)	PUNCT
ejpam-4863	244	1	=	=	PUNCT
ejpam-4863	244	2	(	(	PUNCT
ejpam-4863	244	3	k2	k2	PROPN
ejpam-4863	244	4	+	+	PROPN
ejpam-4863	244	5	k3	k3	ADJ
ejpam-4863	244	6	)	)	PUNCT
ejpam-4863	244	7	∪k1	∪k1	ADV
ejpam-4863	244	8	.	.	PUNCT
ejpam-4863	245	1	clearly	clearly	ADV
ejpam-4863	245	2	,	,	PUNCT
ejpam-4863	245	3	v	v	PROPN
ejpam-4863	245	4	(	(	PUNCT
ejpam-4863	245	5	gg(d3	gg(d3	PROPN
ejpam-4863	245	6	)	)	PUNCT
ejpam-4863	245	7	)	)	PUNCT
ejpam-4863	246	1	⊂	⊂	PROPN
ejpam-4863	246	2	v	v	X
ejpam-4863	246	3	(	(	PUNCT
ejpam-4863	246	4	k2	k2	PROPN
ejpam-4863	246	5	+	+	PROPN
ejpam-4863	246	6	k3	k3	ADJ
ejpam-4863	246	7	)	)	PUNCT
ejpam-4863	246	8	∪k1	∪k1	ADV
ejpam-4863	246	9	)	)	PUNCT
ejpam-4863	246	10	=	=	SYM
ejpam-4863	246	11	γ(d3	γ(d3	NOUN
ejpam-4863	246	12	)	)	PUNCT
ejpam-4863	246	13	.	.	PUNCT
ejpam-4863	247	1	therefore	therefore	ADV
ejpam-4863	247	2	,	,	PUNCT
ejpam-4863	247	3	gg(d3	gg(d3	PROPN
ejpam-4863	247	4	)	)	PUNCT
ejpam-4863	247	5	is	be	AUX
ejpam-4863	247	6	a	a	DET
ejpam-4863	247	7	spanning	span	VERB
ejpam-4863	247	8	subgraph	subgraph	NOUN
ejpam-4863	247	9	of	of	ADP
ejpam-4863	247	10	γ(d3	γ(d3	NOUN
ejpam-4863	247	11	)	)	PUNCT
ejpam-4863	247	12	.	.	PUNCT
ejpam-4863	248	1	5	5	X
ejpam-4863	248	2	.	.	X
ejpam-4863	248	3	conclusion	conclusion	NOUN
ejpam-4863	248	4	this	this	DET
ejpam-4863	248	5	paper	paper	NOUN
ejpam-4863	248	6	introduces	introduce	VERB
ejpam-4863	248	7	the	the	DET
ejpam-4863	248	8	concept	concept	NOUN
ejpam-4863	248	9	of	of	ADP
ejpam-4863	248	10	the	the	DET
ejpam-4863	248	11	generator	generator	NOUN
ejpam-4863	248	12	graph	graph	NOUN
ejpam-4863	248	13	of	of	ADP
ejpam-4863	248	14	a	a	DET
ejpam-4863	248	15	group	group	NOUN
ejpam-4863	248	16	.	.	PUNCT
ejpam-4863	249	1	the	the	DET
ejpam-4863	249	2	properties	property	NOUN
ejpam-4863	249	3	of	of	ADP
ejpam-4863	249	4	the	the	DET
ejpam-4863	249	5	generator	generator	NOUN
ejpam-4863	249	6	graph	graph	NOUN
ejpam-4863	249	7	are	be	AUX
ejpam-4863	249	8	presented	present	VERB
ejpam-4863	249	9	in	in	ADP
ejpam-4863	249	10	terms	term	NOUN
ejpam-4863	249	11	its	its	PRON
ejpam-4863	249	12	structure	structure	NOUN
ejpam-4863	249	13	,	,	PUNCT
ejpam-4863	249	14	the	the	DET
ejpam-4863	249	15	degree	degree	NOUN
ejpam-4863	249	16	of	of	ADP
ejpam-4863	249	17	a	a	DET
ejpam-4863	249	18	vertex	vertex	NOUN
ejpam-4863	249	19	,	,	PUNCT
ejpam-4863	249	20	and	and	CCONJ
ejpam-4863	249	21	size	size	NOUN
ejpam-4863	249	22	of	of	ADP
ejpam-4863	249	23	the	the	DET
ejpam-4863	249	24	induced	induced	ADJ
ejpam-4863	249	25	subgraph	subgraph	NOUN
ejpam-4863	249	26	of	of	ADP
ejpam-4863	249	27	the	the	DET
ejpam-4863	249	28	set	set	NOUN
ejpam-4863	249	29	of	of	ADP
ejpam-4863	249	30	generators	generator	NOUN
ejpam-4863	249	31	or	or	CCONJ
ejpam-4863	249	32	non	non	NOUN
ejpam-4863	249	33	-	-	NOUN
ejpam-4863	249	34	generators	generator	NOUN
ejpam-4863	249	35	.	.	PUNCT
ejpam-4863	250	1	additionally	additionally	ADV
ejpam-4863	250	2	,	,	PUNCT
ejpam-4863	250	3	the	the	DET
ejpam-4863	250	4	generator	generator	NOUN
ejpam-4863	250	5	graphs	graph	NOUN
ejpam-4863	250	6	of	of	ADP
ejpam-4863	250	7	some	some	DET
ejpam-4863	250	8	special	special	ADJ
ejpam-4863	250	9	graphs	graph	NOUN
ejpam-4863	250	10	are	be	AUX
ejpam-4863	250	11	also	also	ADV
ejpam-4863	250	12	presented	present	VERB
ejpam-4863	250	13	.	.	PUNCT
ejpam-4863	251	1	it	it	PRON
ejpam-4863	251	2	has	have	AUX
ejpam-4863	251	3	been	be	AUX
ejpam-4863	251	4	shown	show	VERB
ejpam-4863	251	5	that	that	SCONJ
ejpam-4863	251	6	the	the	DET
ejpam-4863	251	7	generator	generator	NOUN
ejpam-4863	251	8	graph	graph	NOUN
ejpam-4863	251	9	of	of	ADP
ejpam-4863	251	10	a	a	DET
ejpam-4863	251	11	group	group	NOUN
ejpam-4863	251	12	forms	form	VERB
ejpam-4863	251	13	a	a	DET
ejpam-4863	251	14	spanning	span	VERB
ejpam-4863	251	15	subgraph	subgraph	NOUN
ejpam-4863	251	16	of	of	ADP
ejpam-4863	251	17	the	the	DET
ejpam-4863	251	18	generating	generate	VERB
ejpam-4863	251	19	graph	graph	NOUN
ejpam-4863	251	20	.	.	PUNCT
ejpam-4863	252	1	acknowledgements	acknowledgement	NOUN
ejpam-4863	252	2	the	the	DET
ejpam-4863	252	3	author	author	NOUN
ejpam-4863	252	4	is	be	AUX
ejpam-4863	252	5	very	very	ADV
ejpam-4863	252	6	grateful	grateful	ADJ
ejpam-4863	252	7	to	to	ADP
ejpam-4863	252	8	the	the	DET
ejpam-4863	252	9	referees	referee	NOUN
ejpam-4863	252	10	for	for	ADP
ejpam-4863	252	11	the	the	DET
ejpam-4863	252	12	corrections	correction	NOUN
ejpam-4863	252	13	and	and	CCONJ
ejpam-4863	252	14	suggestions	suggestion	NOUN
ejpam-4863	252	15	they	they	PRON
ejpam-4863	252	16	made	make	VERB
ejpam-4863	252	17	in	in	ADP
ejpam-4863	252	18	the	the	DET
ejpam-4863	252	19	initial	initial	ADJ
ejpam-4863	252	20	manuscript	manuscript	NOUN
ejpam-4863	252	21	.	.	PUNCT
ejpam-4863	253	1	the	the	DET
ejpam-4863	253	2	author	author	NOUN
ejpam-4863	253	3	would	would	AUX
ejpam-4863	253	4	also	also	ADV
ejpam-4863	253	5	like	like	VERB
ejpam-4863	253	6	to	to	PART
ejpam-4863	253	7	thank	thank	VERB
ejpam-4863	253	8	the	the	DET
ejpam-4863	253	9	center	center	NOUN
ejpam-4863	253	10	of	of	ADP
ejpam-4863	253	11	mathematical	mathematical	ADJ
ejpam-4863	253	12	innovations	innovation	NOUN
ejpam-4863	253	13	,	,	PUNCT
ejpam-4863	253	14	bukidnon	bukidnon	NOUN
ejpam-4863	253	15	state	state	PROPN
ejpam-4863	253	16	university	university	PROPN
ejpam-4863	253	17	,	,	PUNCT
ejpam-4863	253	18	for	for	ADP
ejpam-4863	253	19	funding	fund	VERB
ejpam-4863	253	20	this	this	DET
ejpam-4863	253	21	research	research	NOUN
ejpam-4863	253	22	.	.	PUNCT
ejpam-4863	254	1	references	reference	NOUN
ejpam-4863	254	2	[	[	X
ejpam-4863	254	3	1	1	NUM
ejpam-4863	254	4	]	]	X
ejpam-4863	254	5	f	f	PROPN
ejpam-4863	254	6	buckley	buckley	PROPN
ejpam-4863	254	7	and	and	CCONJ
ejpam-4863	254	8	f	f	PROPN
ejpam-4863	254	9	harary	harary	NOUN
ejpam-4863	254	10	.	.	PUNCT
ejpam-4863	255	1	distance	distance	NOUN
ejpam-4863	255	2	in	in	ADP
ejpam-4863	255	3	graphs	graph	NOUN
ejpam-4863	255	4	.	.	PUNCT
ejpam-4863	256	1	addison	addison	PROPN
ejpam-4863	256	2	-	-	PUNCT
ejpam-4863	256	3	wesley	wesley	PROPN
ejpam-4863	256	4	,	,	PUNCT
ejpam-4863	256	5	redwood	redwood	NOUN
ejpam-4863	256	6	city	city	NOUN
ejpam-4863	256	7	,	,	PUNCT
ejpam-4863	256	8	1990	1990	NUM
ejpam-4863	256	9	.	.	PUNCT
ejpam-4863	257	1	[	[	X
ejpam-4863	257	2	2	2	NUM
ejpam-4863	257	3	]	]	X
ejpam-4863	257	4	f	f	PROPN
ejpam-4863	257	5	erdem	erdem	PROPN
ejpam-4863	257	6	.	.	PUNCT
ejpam-4863	258	1	on	on	ADP
ejpam-4863	258	2	the	the	DET
ejpam-4863	258	3	generating	generate	VERB
ejpam-4863	258	4	graphs	graph	NOUN
ejpam-4863	258	5	of	of	ADP
ejpam-4863	258	6	symmetric	symmetric	ADJ
ejpam-4863	258	7	groups	group	NOUN
ejpam-4863	258	8	.	.	PUNCT
ejpam-4863	259	1	journal	journal	PROPN
ejpam-4863	259	2	of	of	ADP
ejpam-4863	259	3	group	group	NOUN
ejpam-4863	259	4	theory	theory	NOUN
ejpam-4863	259	5	(	(	PUNCT
ejpam-4863	259	6	2018	2018	NUM
ejpam-4863	259	7	)	)	PUNCT
ejpam-4863	259	8	,	,	PUNCT
ejpam-4863	259	9	21(4	21(4	NUM
ejpam-4863	259	10	)	)	PUNCT
ejpam-4863	259	11	,	,	PUNCT
ejpam-4863	259	12	pp	pp	ADP
ejpam-4863	259	13	.	.	PUNCT
ejpam-4863	260	1	629	629	NUM
ejpam-4863	260	2	-	-	SYM
ejpam-4863	260	3	649	649	NUM
ejpam-4863	260	4	.	.	PUNCT
ejpam-4863	261	1	[	[	X
ejpam-4863	261	2	3	3	X
ejpam-4863	261	3	]	]	X
ejpam-4863	261	4	j	j	PROPN
ejpam-4863	261	5	fraleigh	fraleigh	PROPN
ejpam-4863	261	6	.	.	PUNCT
ejpam-4863	262	1	a	a	DET
ejpam-4863	262	2	first	first	ADJ
ejpam-4863	262	3	course	course	NOUN
ejpam-4863	262	4	in	in	ADP
ejpam-4863	262	5	abstract	abstract	ADJ
ejpam-4863	262	6	algebra	algebra	NOUN
ejpam-4863	262	7	(	(	PUNCT
ejpam-4863	262	8	5th	5th	ADJ
ejpam-4863	262	9	ed	ed	NOUN
ejpam-4863	262	10	.	.	PUNCT
ejpam-4863	262	11	)	)	PUNCT
ejpam-4863	262	12	,	,	PUNCT
ejpam-4863	262	13	addison	addison	PROPN
ejpam-4863	262	14	-	-	PUNCT
ejpam-4863	262	15	wesley	wesley	PROPN
ejpam-4863	262	16	,	,	PUNCT
ejpam-4863	262	17	2000	2000	NUM
ejpam-4863	262	18	.	.	PUNCT
ejpam-4863	263	1	references	reference	NOUN
ejpam-4863	263	2	1901	1901	NUM
ejpam-4863	264	1	[	[	X
ejpam-4863	264	2	4	4	NUM
ejpam-4863	264	3	]	]	X
ejpam-4863	264	4	f	f	PROPN
ejpam-4863	264	5	harary.graph	harary.graph	PROPN
ejpam-4863	264	6	theory.addison	theory.addison	PROPN
ejpam-4863	264	7	-	-	PUNCT
ejpam-4863	264	8	wesley	wesley	PROPN
ejpam-4863	264	9	publication	publication	NOUN
ejpam-4863	264	10	company	company	PROPN
ejpam-4863	264	11	,	,	PUNCT
ejpam-4863	264	12	inc	inc	PROPN
ejpam-4863	264	13	.	.	PROPN
ejpam-4863	264	14	,	,	PUNCT
ejpam-4863	264	15	massachusetts	massachusetts	PROPN
ejpam-4863	264	16	,	,	PUNCT
ejpam-4863	264	17	1972	1972	NUM
ejpam-4863	264	18	.	.	PUNCT
ejpam-4863	265	1	[	[	X
ejpam-4863	265	2	5	5	NUM
ejpam-4863	265	3	]	]	PUNCT
ejpam-4863	265	4	t	t	PROPN
ejpam-4863	265	5	hungerford	hungerford	PROPN
ejpam-4863	265	6	.	.	PUNCT
ejpam-4863	266	1	abstract	abstract	ADJ
ejpam-4863	266	2	algebra	algebra	PROPN
ejpam-4863	266	3	:	:	PUNCT
ejpam-4863	266	4	an	an	DET
ejpam-4863	266	5	introduction	introduction	NOUN
ejpam-4863	266	6	(	(	PUNCT
ejpam-4863	266	7	2nd	2nd	ADJ
ejpam-4863	266	8	ed	ed	NOUN
ejpam-4863	266	9	.	.	PUNCT
ejpam-4863	266	10	)	)	PUNCT
ejpam-4863	266	11	,	,	PUNCT
ejpam-4863	266	12	sunders	sunder	NOUN
ejpam-4863	266	13	college	college	PROPN
ejpam-4863	266	14	,	,	PUNCT
ejpam-4863	266	15	1991	1991	NUM
ejpam-4863	266	16	.	.	PUNCT
ejpam-4863	267	1	[	[	X
ejpam-4863	267	2	6	6	NUM
ejpam-4863	267	3	]	]	PUNCT
ejpam-4863	267	4	wb	wb	X
ejpam-4863	267	5	kandasamy	kandasamy	NOUN
ejpam-4863	267	6	and	and	CCONJ
ejpam-4863	267	7	f	f	PROPN
ejpam-4863	267	8	smarandache	smarandache	PROPN
ejpam-4863	267	9	.	.	PUNCT
ejpam-4863	267	10	group	group	NOUN
ejpam-4863	267	11	as	as	ADP
ejpam-4863	267	12	graphs	graph	NOUN
ejpam-4863	267	13	.	.	PUNCT
ejpam-4863	268	1	romania	romania	PROPN
ejpam-4863	268	2	:	:	PUNCT
ejpam-4863	268	3	editura	editura	NOUN
ejpam-4863	268	4	cuart	cuart	NOUN
ejpam-4863	268	5	,	,	PUNCT
ejpam-4863	268	6	2009	2009	NUM
ejpam-4863	268	7	.	.	PUNCT
ejpam-4863	269	1	[	[	X
ejpam-4863	269	2	7	7	X
ejpam-4863	269	3	]	]	X
ejpam-4863	269	4	a	a	DET
ejpam-4863	269	5	lucchini	lucchini	NOUN
ejpam-4863	269	6	,	,	PUNCT
ejpam-4863	269	7	a	a	DET
ejpam-4863	269	8	maroti	maroti	NOUN
ejpam-4863	269	9	and	and	CCONJ
ejpam-4863	269	10	c.	c.	PROPN
ejpam-4863	269	11	roney	roney	PROPN
ejpam-4863	269	12	-	-	PUNCT
ejpam-4863	269	13	dougal	dougal	PROPN
ejpam-4863	269	14	.	.	PUNCT
ejpam-4863	270	1	on	on	ADP
ejpam-4863	270	2	the	the	DET
ejpam-4863	270	3	generating	generate	VERB
ejpam-4863	270	4	graph	graph	NOUN
ejpam-4863	270	5	of	of	ADP
ejpam-4863	270	6	a	a	DET
ejpam-4863	270	7	simple	simple	ADJ
ejpam-4863	270	8	group	group	NOUN
ejpam-4863	270	9	.	.	PUNCT
ejpam-4863	271	1	journal	journal	PROPN
ejpam-4863	271	2	of	of	ADP
ejpam-4863	271	3	the	the	DET
ejpam-4863	271	4	australian	australian	ADJ
ejpam-4863	271	5	mathematical	mathematical	ADJ
ejpam-4863	271	6	society	society	NOUN
ejpam-4863	271	7	(	(	PUNCT
ejpam-4863	271	8	2018	2018	NUM
ejpam-4863	271	9	)	)	PUNCT
ejpam-4863	271	10	103(1	103(1	NUM
ejpam-4863	271	11	)	)	PUNCT
ejpam-4863	271	12	,	,	PUNCT
ejpam-4863	271	13	91	91	NUM
ejpam-4863	271	14	-	-	SYM
ejpam-4863	271	15	103	103	NUM
ejpam-4863	271	16	.	.	PUNCT
ejpam-4863	272	1	[	[	X
ejpam-4863	272	2	8	8	NUM
ejpam-4863	272	3	]	]	X
ejpam-4863	272	4	y	y	PROPN
ejpam-4863	272	5	zakaraya	zakaraya	PROPN
ejpam-4863	272	6	.	.	PUNCT
ejpam-4863	273	1	graphs	graph	NOUN
ejpam-4863	273	2	from	from	ADP
ejpam-4863	273	3	finite	finite	ADJ
ejpam-4863	273	4	groups	group	NOUN
ejpam-4863	273	5	:	:	PUNCT
ejpam-4863	273	6	an	an	DET
ejpam-4863	273	7	overview	overview	NOUN
ejpam-4863	273	8	.	.	PUNCT
ejpam-4863	274	1	proceedings	proceeding	NOUN
ejpam-4863	274	2	of	of	ADP
ejpam-4863	274	3	the	the	DET
ejpam-4863	274	4	53rd	53rd	PROPN
ejpam-4863	274	5	mathematical	mathematical	ADJ
ejpam-4863	274	6	association	association	PROPN
ejpam-4863	274	7	of	of	ADP
ejpam-4863	274	8	nigeria	nigeria	PROPN
ejpam-4863	274	9	annual	annual	ADJ
ejpam-4863	274	10	conference	conference	NOUN
ejpam-4863	274	11	,	,	PUNCT
ejpam-4863	274	12	september	september	PROPN
ejpam-4863	274	13	2016	2016	NUM
ejpam-4863	274	14	.	.	PUNCT