id	sid	tid	token	lemma	pos
ejpam-5812	1	1	european	european	PROPN
ejpam-5812	1	2	journal	journal	PROPN
ejpam-5812	1	3	of	of	ADP
ejpam-5812	1	4	pure	pure	ADJ
ejpam-5812	1	5	and	and	CCONJ
ejpam-5812	1	6	applied	applied	ADJ
ejpam-5812	1	7	mathematics	mathematic	NOUN
ejpam-5812	1	8	2025	2025	NUM
ejpam-5812	1	9	,	,	PUNCT
ejpam-5812	1	10	vol	vol	NOUN
ejpam-5812	1	11	.	.	PROPN
ejpam-5812	1	12	18	18	NUM
ejpam-5812	1	13	,	,	PUNCT
ejpam-5812	1	14	issue	issue	NOUN
ejpam-5812	1	15	1	1	NUM
ejpam-5812	1	16	,	,	PUNCT
ejpam-5812	1	17	article	article	NOUN
ejpam-5812	1	18	number	number	NOUN
ejpam-5812	1	19	5812	5812	NUM
ejpam-5812	1	20	issn	issn	PROPN
ejpam-5812	1	21	1307	1307	NUM
ejpam-5812	1	22	-	-	SYM
ejpam-5812	1	23	5543	5543	NUM
ejpam-5812	1	24	–	–	PUNCT
ejpam-5812	1	25	ejpam.com	ejpam.com	X
ejpam-5812	1	26	published	publish	VERB
ejpam-5812	1	27	by	by	ADP
ejpam-5812	1	28	new	new	PROPN
ejpam-5812	1	29	york	york	PROPN
ejpam-5812	1	30	business	business	PROPN
ejpam-5812	1	31	global	global	PROPN
ejpam-5812	1	32	a	a	DET
ejpam-5812	1	33	novel	novel	ADJ
ejpam-5812	1	34	problem	problem	NOUN
ejpam-5812	1	35	and	and	CCONJ
ejpam-5812	1	36	algorithm	algorithm	NOUN
ejpam-5812	1	37	for	for	ADP
ejpam-5812	1	38	solving	solve	VERB
ejpam-5812	1	39	cordial	cordial	ADJ
ejpam-5812	1	40	labeling	labeling	NOUN
ejpam-5812	1	41	of	of	ADP
ejpam-5812	1	42	some	some	DET
ejpam-5812	1	43	fifth	fifth	ADJ
ejpam-5812	1	44	powers	power	NOUN
ejpam-5812	1	45	of	of	ADP
ejpam-5812	1	46	graphs	graph	NOUN
ejpam-5812	1	47	atef	atef	PROPN
ejpam-5812	1	48	abd	abd	PROPN
ejpam-5812	1	49	el	el	PROPN
ejpam-5812	1	50	-	-	PROPN
ejpam-5812	1	51	hay1,∗	hay1,∗	PROPN
ejpam-5812	1	52	,	,	PUNCT
ejpam-5812	1	53	khalid	khalid	PROPN
ejpam-5812	1	54	a.	a.	PROPN
ejpam-5812	1	55	alsatami2	alsatami2	PROPN
ejpam-5812	1	56	,	,	PUNCT
ejpam-5812	1	57	ashraf	ashraf	VERB
ejpam-5812	1	58	elrokh1	elrokh1	NOUN
ejpam-5812	1	59	1	1	NUM
ejpam-5812	1	60	mathematics	mathematic	NOUN
ejpam-5812	1	61	and	and	CCONJ
ejpam-5812	1	62	computer	computer	NOUN
ejpam-5812	1	63	science	science	PROPN
ejpam-5812	1	64	department	department	PROPN
ejpam-5812	1	65	,	,	PUNCT
ejpam-5812	1	66	faculty	faculty	NOUN
ejpam-5812	1	67	of	of	ADP
ejpam-5812	1	68	science	science	PROPN
ejpam-5812	1	69	menoufia	menoufia	PROPN
ejpam-5812	1	70	university	university	PROPN
ejpam-5812	1	71	,	,	PUNCT
ejpam-5812	1	72	menoufia	menoufia	PROPN
ejpam-5812	1	73	,	,	PUNCT
ejpam-5812	1	74	egypt	egypt	PROPN
ejpam-5812	1	75	.	.	PROPN
ejpam-5812	2	1	2	2	NUM
ejpam-5812	2	2	department	department	NOUN
ejpam-5812	2	3	of	of	ADP
ejpam-5812	2	4	mathematics	mathematic	NOUN
ejpam-5812	2	5	,	,	PUNCT
ejpam-5812	2	6	college	college	NOUN
ejpam-5812	2	7	of	of	ADP
ejpam-5812	2	8	science	science	NOUN
ejpam-5812	2	9	,	,	PUNCT
ejpam-5812	2	10	qassim	qassim	PROPN
ejpam-5812	2	11	university	university	PROPN
ejpam-5812	2	12	,	,	PUNCT
ejpam-5812	2	13	buraydah	buraydah	PROPN
ejpam-5812	2	14	,	,	PUNCT
ejpam-5812	2	15	ksa	ksa	PROPN
ejpam-5812	2	16	.	.	PROPN
ejpam-5812	2	17	abstract	abstract	PROPN
ejpam-5812	2	18	.	.	PUNCT
ejpam-5812	3	1	in	in	ADP
ejpam-5812	3	2	this	this	DET
ejpam-5812	3	3	paper	paper	NOUN
ejpam-5812	3	4	we	we	PRON
ejpam-5812	3	5	introduce	introduce	VERB
ejpam-5812	3	6	a	a	DET
ejpam-5812	3	7	novel	novel	ADJ
ejpam-5812	3	8	application	application	NOUN
ejpam-5812	3	9	of	of	ADP
ejpam-5812	3	10	cordial	cordial	ADJ
ejpam-5812	3	11	labeling	labeling	NOUN
ejpam-5812	3	12	using	use	VERB
ejpam-5812	3	13	the	the	DET
ejpam-5812	3	14	fifth	fifth	ADJ
ejpam-5812	3	15	power	power	NOUN
ejpam-5812	3	16	of	of	ADP
ejpam-5812	3	17	graphs	graph	NOUN
ejpam-5812	3	18	,	,	PUNCT
ejpam-5812	3	19	demonstrating	demonstrate	VERB
ejpam-5812	3	20	its	its	PRON
ejpam-5812	3	21	potential	potential	NOUN
ejpam-5812	3	22	for	for	ADP
ejpam-5812	3	23	understanding	understanding	NOUN
ejpam-5812	3	24	and	and	CCONJ
ejpam-5812	3	25	studying	study	VERB
ejpam-5812	3	26	specific	specific	ADJ
ejpam-5812	3	27	graph	graph	NOUN
ejpam-5812	3	28	structures	structure	NOUN
ejpam-5812	3	29	.	.	PUNCT
ejpam-5812	4	1	the	the	DET
ejpam-5812	4	2	resulting	result	VERB
ejpam-5812	4	3	cordial	cordial	ADJ
ejpam-5812	4	4	labeling	labeling	NOUN
ejpam-5812	4	5	scheme	scheme	NOUN
ejpam-5812	4	6	for	for	ADP
ejpam-5812	4	7	the	the	DET
ejpam-5812	4	8	fifth	fifth	ADJ
ejpam-5812	4	9	power	power	NOUN
ejpam-5812	4	10	of	of	ADP
ejpam-5812	4	11	paths	path	NOUN
ejpam-5812	4	12	,	,	PUNCT
ejpam-5812	4	13	cycles	cycle	NOUN
ejpam-5812	4	14	,	,	PUNCT
ejpam-5812	4	15	fans	fan	NOUN
ejpam-5812	4	16	,	,	PUNCT
ejpam-5812	4	17	wheels	wheel	NOUN
ejpam-5812	4	18	,	,	PUNCT
ejpam-5812	4	19	lemniscate	lemniscate	PROPN
ejpam-5812	4	20	and	and	CCONJ
ejpam-5812	4	21	the	the	DET
ejpam-5812	4	22	union	union	NOUN
ejpam-5812	4	23	of	of	ADP
ejpam-5812	4	24	fifth	fifth	ADJ
ejpam-5812	4	25	power	power	NOUN
ejpam-5812	4	26	of	of	ADP
ejpam-5812	4	27	paths	path	NOUN
ejpam-5812	4	28	and	and	CCONJ
ejpam-5812	4	29	cycles	cycle	NOUN
ejpam-5812	4	30	graphs	graph	NOUN
ejpam-5812	4	31	can	can	AUX
ejpam-5812	4	32	provide	provide	VERB
ejpam-5812	4	33	insights	insight	NOUN
ejpam-5812	4	34	into	into	ADP
ejpam-5812	4	35	the	the	DET
ejpam-5812	4	36	properties	property	NOUN
ejpam-5812	4	37	and	and	CCONJ
ejpam-5812	4	38	structures	structure	NOUN
ejpam-5812	4	39	of	of	ADP
ejpam-5812	4	40	these	these	DET
ejpam-5812	4	41	graphs	graph	NOUN
ejpam-5812	4	42	.	.	PUNCT
ejpam-5812	5	1	it	it	PRON
ejpam-5812	5	2	can	can	AUX
ejpam-5812	5	3	be	be	AUX
ejpam-5812	5	4	used	use	VERB
ejpam-5812	5	5	to	to	PART
ejpam-5812	5	6	analyze	analyze	VERB
ejpam-5812	5	7	its	its	PRON
ejpam-5812	5	8	connectivity	connectivity	NOUN
ejpam-5812	5	9	,	,	PUNCT
ejpam-5812	5	10	symmetry	symmetry	NOUN
ejpam-5812	5	11	,	,	PUNCT
ejpam-5812	5	12	and	and	CCONJ
ejpam-5812	5	13	other	other	ADJ
ejpam-5812	5	14	graph	graph	NOUN
ejpam-5812	5	15	-	-	PUNCT
ejpam-5812	5	16	theoretical	theoretical	ADJ
ejpam-5812	5	17	characteristics	characteristic	NOUN
ejpam-5812	5	18	.	.	PUNCT
ejpam-5812	6	1	2020	2020	NUM
ejpam-5812	6	2	mathematics	mathematic	NOUN
ejpam-5812	6	3	subject	subject	NOUN
ejpam-5812	6	4	classifications	classification	NOUN
ejpam-5812	6	5	:	:	PUNCT
ejpam-5812	6	6	05c78,05c15	05c78,05c15	NUM
ejpam-5812	6	7	key	key	ADJ
ejpam-5812	6	8	words	word	NOUN
ejpam-5812	6	9	and	and	CCONJ
ejpam-5812	6	10	phrases	phrase	NOUN
ejpam-5812	6	11	:	:	PUNCT
ejpam-5812	6	12	cordial	cordial	ADJ
ejpam-5812	6	13	labeling	labeling	NOUN
ejpam-5812	6	14	,	,	PUNCT
ejpam-5812	6	15	fifth	fifth	ADJ
ejpam-5812	6	16	power	power	NOUN
ejpam-5812	6	17	,	,	PUNCT
ejpam-5812	6	18	lemniscate	lemniscate	PROPN
ejpam-5812	6	19	,	,	PUNCT
ejpam-5812	6	20	social	social	ADJ
ejpam-5812	6	21	networking	networking	NOUN
ejpam-5812	6	22	,	,	PUNCT
ejpam-5812	6	23	network	network	NOUN
ejpam-5812	6	24	security	security	NOUN
ejpam-5812	6	25	,	,	PUNCT
ejpam-5812	6	26	edge	edge	NOUN
ejpam-5812	6	27	computing	compute	VERB
ejpam-5812	6	28	1	1	NUM
ejpam-5812	6	29	.	.	PUNCT
ejpam-5812	6	30	introduction	introduction	NOUN
ejpam-5812	6	31	a	a	DET
ejpam-5812	6	32	graph	graph	NOUN
ejpam-5812	6	33	labeling	labeling	NOUN
ejpam-5812	6	34	is	be	AUX
ejpam-5812	6	35	a	a	DET
ejpam-5812	6	36	way	way	NOUN
ejpam-5812	6	37	of	of	ADP
ejpam-5812	6	38	assigning	assign	VERB
ejpam-5812	6	39	numbers	number	NOUN
ejpam-5812	6	40	to	to	ADP
ejpam-5812	6	41	the	the	DET
ejpam-5812	6	42	vertices	vertex	NOUN
ejpam-5812	6	43	or	or	CCONJ
ejpam-5812	6	44	edges	edge	NOUN
ejpam-5812	6	45	of	of	ADP
ejpam-5812	6	46	a	a	DET
ejpam-5812	6	47	graph	graph	NOUN
ejpam-5812	6	48	,	,	PUNCT
ejpam-5812	6	49	or	or	CCONJ
ejpam-5812	6	50	both	both	PRON
ejpam-5812	6	51	,	,	PUNCT
ejpam-5812	6	52	according	accord	VERB
ejpam-5812	6	53	to	to	ADP
ejpam-5812	6	54	some	some	DET
ejpam-5812	6	55	rules	rule	NOUN
ejpam-5812	6	56	.	.	PUNCT
ejpam-5812	7	1	graph	graph	NOUN
ejpam-5812	7	2	labeling	labeling	NOUN
ejpam-5812	7	3	is	be	AUX
ejpam-5812	7	4	useful	useful	ADJ
ejpam-5812	7	5	for	for	ADP
ejpam-5812	7	6	studying	study	VERB
ejpam-5812	7	7	various	various	ADJ
ejpam-5812	7	8	properties	property	NOUN
ejpam-5812	7	9	and	and	CCONJ
ejpam-5812	7	10	applications	application	NOUN
ejpam-5812	7	11	of	of	ADP
ejpam-5812	7	12	graphs	graph	NOUN
ejpam-5812	7	13	,	,	PUNCT
ejpam-5812	7	14	such	such	ADJ
ejpam-5812	7	15	as	as	ADP
ejpam-5812	7	16	symmetry	symmetry	NOUN
ejpam-5812	7	17	,	,	PUNCT
ejpam-5812	7	18	coloring	coloring	NOUN
ejpam-5812	7	19	,	,	PUNCT
ejpam-5812	7	20	coding	coding	NOUN
ejpam-5812	7	21	,	,	PUNCT
ejpam-5812	7	22	and	and	CCONJ
ejpam-5812	7	23	communication	communication	NOUN
ejpam-5812	7	24	.	.	PUNCT
ejpam-5812	8	1	it	it	PRON
ejpam-5812	8	2	is	be	AUX
ejpam-5812	8	3	universally	universally	ADV
ejpam-5812	8	4	recognizable	recognizable	ADJ
ejpam-5812	8	5	that	that	SCONJ
ejpam-5812	8	6	graph	graph	NOUN
ejpam-5812	8	7	theory	theory	NOUN
ejpam-5812	8	8	has	have	VERB
ejpam-5812	8	9	applications	application	NOUN
ejpam-5812	8	10	in	in	ADP
ejpam-5812	8	11	many	many	ADJ
ejpam-5812	8	12	other	other	ADJ
ejpam-5812	8	13	academic	academic	ADJ
ejpam-5812	8	14	disciplines	discipline	NOUN
ejpam-5812	8	15	,	,	PUNCT
ejpam-5812	8	16	particularly	particularly	ADV
ejpam-5812	8	17	computer	computer	NOUN
ejpam-5812	8	18	science	science	NOUN
ejpam-5812	8	19	[	[	X
ejpam-5812	8	20	5	5	NUM
ejpam-5812	8	21	,	,	PUNCT
ejpam-5812	8	22	21	21	NUM
ejpam-5812	8	23	]	]	PUNCT
ejpam-5812	8	24	,	,	PUNCT
ejpam-5812	8	25	and	and	CCONJ
ejpam-5812	8	26	also	also	ADV
ejpam-5812	8	27	in	in	ADP
ejpam-5812	8	28	physics	physics	NOUN
ejpam-5812	8	29	,	,	PUNCT
ejpam-5812	8	30	chemistry	chemistry	NOUN
ejpam-5812	8	31	,	,	PUNCT
ejpam-5812	8	32	biology	biology	NOUN
ejpam-5812	8	33	,	,	PUNCT
ejpam-5812	8	34	communication	communication	NOUN
ejpam-5812	8	35	,	,	PUNCT
ejpam-5812	8	36	psychology	psychology	NOUN
ejpam-5812	8	37	,	,	PUNCT
ejpam-5812	8	38	sociology	sociology	NOUN
ejpam-5812	8	39	,	,	PUNCT
ejpam-5812	8	40	and	and	CCONJ
ejpam-5812	8	41	economics	economic	NOUN
ejpam-5812	8	42	.	.	PUNCT
ejpam-5812	9	1	graph	graph	NOUN
ejpam-5812	9	2	labelling	labelling	NOUN
ejpam-5812	9	3	is	be	AUX
ejpam-5812	9	4	one	one	NUM
ejpam-5812	9	5	area	area	NOUN
ejpam-5812	9	6	of	of	ADP
ejpam-5812	9	7	graph	graph	NOUN
ejpam-5812	9	8	theory	theory	NOUN
ejpam-5812	9	9	that	that	PRON
ejpam-5812	9	10	has	have	AUX
ejpam-5812	9	11	seen	see	VERB
ejpam-5812	9	12	a	a	DET
ejpam-5812	9	13	great	great	ADJ
ejpam-5812	9	14	deal	deal	NOUN
ejpam-5812	9	15	of	of	ADP
ejpam-5812	9	16	ongoing	ongoing	ADJ
ejpam-5812	9	17	research	research	NOUN
ejpam-5812	9	18	.	.	PUNCT
ejpam-5812	10	1	labeled	label	VERB
ejpam-5812	10	2	graphs	graph	NOUN
ejpam-5812	10	3	are	be	AUX
ejpam-5812	10	4	effective	effective	ADJ
ejpam-5812	10	5	models	model	NOUN
ejpam-5812	10	6	for	for	ADP
ejpam-5812	10	7	a	a	DET
ejpam-5812	10	8	variety	variety	NOUN
ejpam-5812	10	9	of	of	ADP
ejpam-5812	10	10	applications	application	NOUN
ejpam-5812	10	11	,	,	PUNCT
ejpam-5812	10	12	including	include	VERB
ejpam-5812	10	13	data	data	PROPN
ejpam-5812	10	14	base	base	PROPN
ejpam-5812	10	15	administration	administration	NOUN
ejpam-5812	10	16	,	,	PUNCT
ejpam-5812	10	17	x	x	NOUN
ejpam-5812	10	18	-	-	NOUN
ejpam-5812	10	19	ray	ray	NOUN
ejpam-5812	10	20	crystallography	crystallography	NOUN
ejpam-5812	10	21	,	,	PUNCT
ejpam-5812	10	22	radar	radar	NOUN
ejpam-5812	10	23	,	,	PUNCT
ejpam-5812	10	24	circuit	circuit	NOUN
ejpam-5812	10	25	design	design	NOUN
ejpam-5812	10	26	,	,	PUNCT
ejpam-5812	10	27	and	and	CCONJ
ejpam-5812	10	28	coding	code	VERB
ejpam-5812	10	29	theory	theory	NOUN
ejpam-5812	10	30	[	[	X
ejpam-5812	10	31	20	20	NUM
ejpam-5812	10	32	]	]	PUNCT
ejpam-5812	10	33	.	.	PUNCT
ejpam-5812	11	1	when	when	SCONJ
ejpam-5812	11	2	a	a	DET
ejpam-5812	11	3	specific	specific	ADJ
ejpam-5812	11	4	type	type	NOUN
ejpam-5812	11	5	of	of	ADP
ejpam-5812	11	6	graph	graph	NOUN
ejpam-5812	11	7	is	be	AUX
ejpam-5812	11	8	labelled	label	VERB
ejpam-5812	11	9	,	,	PUNCT
ejpam-5812	11	10	its	its	PRON
ejpam-5812	11	11	vertices	vertex	NOUN
ejpam-5812	11	12	are	be	AUX
ejpam-5812	11	13	given	give	VERB
ejpam-5812	11	14	values	value	NOUN
ejpam-5812	11	15	from	from	ADP
ejpam-5812	11	16	a	a	DET
ejpam-5812	11	17	predetermined	predetermine	VERB
ejpam-5812	11	18	set	set	NOUN
ejpam-5812	11	19	,	,	PUNCT
ejpam-5812	11	20	its	its	PRON
ejpam-5812	11	21	edges	edge	NOUN
ejpam-5812	11	22	have	have	VERB
ejpam-5812	11	23	a	a	DET
ejpam-5812	11	24	predetermined	predetermine	VERB
ejpam-5812	11	25	induced	induced	ADJ
ejpam-5812	11	26	labelling	labelling	NOUN
ejpam-5812	11	27	,	,	PUNCT
ejpam-5812	11	28	and	and	CCONJ
ejpam-5812	11	29	its	its	PRON
ejpam-5812	11	30	labelling	labelling	NOUN
ejpam-5812	11	31	must	must	AUX
ejpam-5812	11	32	adhere	adhere	VERB
ejpam-5812	11	33	to	to	ADP
ejpam-5812	11	34	specified	specify	VERB
ejpam-5812	11	35	requirements	requirement	NOUN
ejpam-5812	11	36	.	.	PUNCT
ejpam-5812	12	1	the	the	DET
ejpam-5812	12	2	study	study	NOUN
ejpam-5812	12	3	by	by	ADP
ejpam-5812	12	4	gallian	gallian	PROPN
ejpam-5812	12	5	[	[	X
ejpam-5812	12	6	17	17	NUM
ejpam-5812	12	7	]	]	PUNCT
ejpam-5812	12	8	is	be	AUX
ejpam-5812	12	9	a	a	DET
ejpam-5812	12	10	great	great	ADJ
ejpam-5812	12	11	resource	resource	NOUN
ejpam-5812	12	12	on	on	ADP
ejpam-5812	12	13	this	this	DET
ejpam-5812	12	14	topic	topic	NOUN
ejpam-5812	12	15	graceful	graceful	NOUN
ejpam-5812	12	16	and	and	CCONJ
ejpam-5812	12	17	harmonious	harmonious	ADJ
ejpam-5812	12	18	labelling	labelling	NOUN
ejpam-5812	12	19	are	be	AUX
ejpam-5812	12	20	two	two	NUM
ejpam-5812	12	21	of	of	ADP
ejpam-5812	12	22	the	the	DET
ejpam-5812	12	23	most	most	ADV
ejpam-5812	12	24	significant	significant	ADJ
ejpam-5812	12	25	categories	category	NOUN
ejpam-5812	12	26	.	.	PUNCT
ejpam-5812	13	1	rosa	rosa	PROPN
ejpam-5812	14	1	[	[	X
ejpam-5812	14	2	22	22	NUM
ejpam-5812	14	3	]	]	PUNCT
ejpam-5812	14	4	and	and	CCONJ
ejpam-5812	14	5	golomb	golomb	NOUN
ejpam-5812	14	6	∗corresponding	∗corresponde	VERB
ejpam-5812	14	7	author	author	NOUN
ejpam-5812	14	8	.	.	PUNCT
ejpam-5812	15	1	doi	doi	NOUN
ejpam-5812	15	2	:	:	PUNCT
ejpam-5812	15	3	https://doi.org/10.29020/nybg.ejpam.v18i1.5812	https://doi.org/10.29020/nybg.ejpam.v18i1.5812	NOUN
ejpam-5812	15	4	email	email	NOUN
ejpam-5812	15	5	addresses	address	NOUN
ejpam-5812	15	6	:	:	PUNCT
ejpam-5812	15	7	atef	atef	PROPN
ejpam-5812	15	8	1992@yahoo.com	1992@yahoo.com	X
ejpam-5812	15	9	(	(	PUNCT
ejpam-5812	15	10	a.	a.	PROPN
ejpam-5812	15	11	abd	abd	PROPN
ejpam-5812	15	12	el	el	PROPN
ejpam-5812	15	13	-	-	PROPN
ejpam-5812	15	14	hay	hay	PROPN
ejpam-5812	15	15	)	)	PUNCT
ejpam-5812	15	16	,	,	PUNCT
ejpam-5812	15	17	satamy@qu.edu.sa	satamy@qu.edu.sa	PROPN
ejpam-5812	15	18	(	(	PUNCT
ejpam-5812	15	19	k.	k.	PROPN
ejpam-5812	15	20	a.	a.	PROPN
ejpam-5812	15	21	alsatami	alsatami	PROPN
ejpam-5812	15	22	)	)	PUNCT
ejpam-5812	15	23	,	,	PUNCT
ejpam-5812	15	24	ashraf.hefnawy68@yahoo.com	ashraf.hefnawy68@yahoo.com	X
ejpam-5812	15	25	(	(	PUNCT
ejpam-5812	15	26	a.	a.	NOUN
ejpam-5812	15	27	elrokh	elrokh	NOUN
ejpam-5812	15	28	)	)	PUNCT
ejpam-5812	15	29	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-5812	15	30	1	1	NUM
ejpam-5812	16	1	copyright	copyright	NOUN
ejpam-5812	16	2	:	:	PUNCT
ejpam-5812	16	3	©	©	PROPN
ejpam-5812	16	4	2025	2025	NUM
ejpam-5812	16	5	the	the	DET
ejpam-5812	16	6	author(s	author(s	NOUN
ejpam-5812	16	7	)	)	PUNCT
ejpam-5812	16	8	.	.	PUNCT
ejpam-5812	17	1	(	(	PUNCT
ejpam-5812	17	2	cc	cc	NOUN
ejpam-5812	17	3	by	by	ADP
ejpam-5812	17	4	-	-	PUNCT
ejpam-5812	17	5	nc	nc	PROPN
ejpam-5812	17	6	4.0	4.0	NUM
ejpam-5812	17	7	)	)	PUNCT
ejpam-5812	17	8	a.	a.	NOUN
ejpam-5812	17	9	abd	abd	PROPN
ejpam-5812	17	10	el	el	PROPN
ejpam-5812	17	11	-	-	PROPN
ejpam-5812	17	12	hay	hay	PROPN
ejpam-5812	17	13	,	,	PUNCT
ejpam-5812	17	14	k.	k.	PROPN
ejpam-5812	17	15	a.	a.	PROPN
ejpam-5812	17	16	alsatami	alsatami	PROPN
ejpam-5812	17	17	,	,	PUNCT
ejpam-5812	17	18	a.	a.	NOUN
ejpam-5812	17	19	elrokh	elrokh	PROPN
ejpam-5812	17	20	/	/	SYM
ejpam-5812	17	21	eur	eur	PROPN
ejpam-5812	17	22	.	.	PUNCT
ejpam-5812	18	1	j.	j.	PROPN
ejpam-5812	18	2	pure	pure	PROPN
ejpam-5812	18	3	appl	appl	PROPN
ejpam-5812	18	4	.	.	PROPN
ejpam-5812	18	5	math	math	PROPN
ejpam-5812	18	6	,	,	PUNCT
ejpam-5812	18	7	18	18	NUM
ejpam-5812	18	8	(	(	PUNCT
ejpam-5812	18	9	1	1	NUM
ejpam-5812	18	10	)	)	PUNCT
ejpam-5812	18	11	(	(	PUNCT
ejpam-5812	18	12	2025	2025	NUM
ejpam-5812	18	13	)	)	PUNCT
ejpam-5812	18	14	,	,	PUNCT
ejpam-5812	18	15	5812	5812	NUM
ejpam-5812	18	16	2	2	NUM
ejpam-5812	18	17	of	of	ADP
ejpam-5812	18	18	14	14	NUM
ejpam-5812	18	19	[	[	SYM
ejpam-5812	18	20	18	18	NUM
ejpam-5812	18	21	]	]	PUNCT
ejpam-5812	18	22	independently	independently	ADV
ejpam-5812	18	23	created	create	VERB
ejpam-5812	18	24	graceful	graceful	ADJ
ejpam-5812	18	25	labelling	labelling	NOUN
ejpam-5812	18	26	in	in	ADP
ejpam-5812	18	27	1966	1966	NUM
ejpam-5812	18	28	and	and	CCONJ
ejpam-5812	18	29	1972	1972	NUM
ejpam-5812	18	30	,	,	PUNCT
ejpam-5812	18	31	respectively	respectively	ADV
ejpam-5812	18	32	,	,	PUNCT
ejpam-5812	18	33	while	while	SCONJ
ejpam-5812	18	34	graham	graham	PROPN
ejpam-5812	18	35	and	and	CCONJ
ejpam-5812	18	36	sloane	sloane	PROPN
ejpam-5812	18	37	[	[	X
ejpam-5812	18	38	19	19	NUM
ejpam-5812	18	39	]	]	PUNCT
ejpam-5812	18	40	conducted	conduct	VERB
ejpam-5812	18	41	the	the	DET
ejpam-5812	18	42	first	first	ADJ
ejpam-5812	18	43	study	study	NOUN
ejpam-5812	18	44	on	on	ADP
ejpam-5812	18	45	harmonic	harmonic	ADJ
ejpam-5812	18	46	labelling	labelling	NOUN
ejpam-5812	18	47	in	in	ADP
ejpam-5812	18	48	1980	1980	NUM
ejpam-5812	18	49	.	.	PUNCT
ejpam-5812	19	1	cordial	cordial	ADJ
ejpam-5812	19	2	labelling	labelling	NOUN
ejpam-5812	19	3	is	be	AUX
ejpam-5812	19	4	a	a	DET
ejpam-5812	19	5	third	third	ADJ
ejpam-5812	19	6	crucial	crucial	ADJ
ejpam-5812	19	7	sort	sort	NOUN
ejpam-5812	19	8	of	of	ADP
ejpam-5812	19	9	labelling	labelling	NOUN
ejpam-5812	19	10	that	that	PRON
ejpam-5812	19	11	cahit	cahit	ADJ
ejpam-5812	19	12	[	[	X
ejpam-5812	19	13	4	4	NUM
ejpam-5812	19	14	]	]	PUNCT
ejpam-5812	19	15	established	establish	VERB
ejpam-5812	19	16	in	in	ADP
ejpam-5812	19	17	1990	1990	NUM
ejpam-5812	19	18	and	and	CCONJ
ejpam-5812	19	19	which	which	PRON
ejpam-5812	19	20	combines	combine	VERB
ejpam-5812	19	21	elements	element	NOUN
ejpam-5812	19	22	of	of	ADP
ejpam-5812	19	23	the	the	DET
ejpam-5812	19	24	other	other	ADJ
ejpam-5812	19	25	two	two	NUM
ejpam-5812	19	26	.	.	PUNCT
ejpam-5812	20	1	unlike	unlike	ADP
ejpam-5812	20	2	graceful	graceful	ADJ
ejpam-5812	20	3	and	and	CCONJ
ejpam-5812	20	4	harmonious	harmonious	ADJ
ejpam-5812	20	5	labelling	labelling	NOUN
ejpam-5812	20	6	,	,	PUNCT
ejpam-5812	20	7	which	which	PRON
ejpam-5812	20	8	utilize	utilize	VERB
ejpam-5812	20	9	labels	label	NOUN
ejpam-5812	20	10	|f(v)−f(w)|	|f(v)−f(w)|	NOUN
ejpam-5812	20	11	and	and	CCONJ
ejpam-5812	20	12	(	(	PUNCT
ejpam-5812	20	13	f(v)+f(w	f(v)+f(w	NOUN
ejpam-5812	20	14	)	)	PUNCT
ejpam-5812	20	15	(	(	PUNCT
ejpam-5812	20	16	modulo	modulo	VERB
ejpam-5812	20	17	the	the	DET
ejpam-5812	20	18	number	number	NOUN
ejpam-5812	20	19	of	of	ADP
ejpam-5812	20	20	edges	edge	NOUN
ejpam-5812	20	21	)	)	PUNCT
ejpam-5812	20	22	,	,	PUNCT
ejpam-5812	20	23	respectively	respectively	ADV
ejpam-5812	20	24	,	,	PUNCT
ejpam-5812	20	25	cordial	cordial	ADJ
ejpam-5812	20	26	labelings	labeling	NOUN
ejpam-5812	20	27	simply	simply	ADV
ejpam-5812	20	28	use	use	VERB
ejpam-5812	20	29	labels	label	NOUN
ejpam-5812	20	30	0	0	PUNCT
ejpam-5812	20	31	and	and	CCONJ
ejpam-5812	20	32	1	1	NUM
ejpam-5812	20	33	,	,	PUNCT
ejpam-5812	20	34	as	as	ADV
ejpam-5812	20	35	well	well	ADV
ejpam-5812	20	36	as	as	ADP
ejpam-5812	20	37	the	the	DET
ejpam-5812	20	38	induced	induced	ADJ
ejpam-5812	20	39	label	label	NOUN
ejpam-5812	20	40	(	(	PUNCT
ejpam-5812	20	41	f(v)+f(w))(mod2	f(v)+f(w))(mod2	PROPN
ejpam-5812	20	42	)	)	PUNCT
ejpam-5812	20	43	,	,	PUNCT
ejpam-5812	20	44	which	which	PRON
ejpam-5812	20	45	naturally	naturally	ADV
ejpam-5812	20	46	equals	equal	VERB
ejpam-5812	20	47	|f(v)−	|f(v)−	ADJ
ejpam-5812	20	48	f(w)|	f(w)|	NOUN
ejpam-5812	20	49	.	.	PUNCT
ejpam-5812	21	1	the	the	DET
ejpam-5812	21	2	original	original	ADJ
ejpam-5812	21	3	concept	concept	NOUN
ejpam-5812	21	4	of	of	ADP
ejpam-5812	21	5	cordial	cordial	ADJ
ejpam-5812	21	6	graphs	graph	NOUN
ejpam-5812	21	7	is	be	AUX
ejpam-5812	21	8	due	due	ADJ
ejpam-5812	21	9	to	to	ADP
ejpam-5812	21	10	cahit[3	cahit[3	NUM
ejpam-5812	21	11	]	]	PUNCT
ejpam-5812	21	12	.	.	PUNCT
ejpam-5812	22	1	he	he	PRON
ejpam-5812	22	2	showed	show	VERB
ejpam-5812	22	3	that	that	SCONJ
ejpam-5812	22	4	each	each	DET
ejpam-5812	22	5	tree	tree	NOUN
ejpam-5812	22	6	is	be	AUX
ejpam-5812	22	7	cordial	cordial	ADJ
ejpam-5812	22	8	;	;	PUNCT
ejpam-5812	22	9	a	a	DET
ejpam-5812	22	10	complete	complete	ADJ
ejpam-5812	22	11	graph	graph	NOUN
ejpam-5812	22	12	kn	kn	PROPN
ejpam-5812	22	13	is	be	AUX
ejpam-5812	22	14	cordial	cordial	ADJ
ejpam-5812	22	15	if	if	SCONJ
ejpam-5812	23	1	and	and	CCONJ
ejpam-5812	23	2	only	only	ADV
ejpam-5812	23	3	if	if	SCONJ
ejpam-5812	23	4	n	n	PRON
ejpam-5812	23	5	≤	≤	ADV
ejpam-5812	23	6	3	3	NUM
ejpam-5812	23	7	and	and	CCONJ
ejpam-5812	23	8	a	a	DET
ejpam-5812	23	9	complete	complete	ADJ
ejpam-5812	23	10	bipartite	bipartite	PROPN
ejpam-5812	23	11	graph	graph	NOUN
ejpam-5812	23	12	kn	kn	PROPN
ejpam-5812	23	13	,	,	PUNCT
ejpam-5812	23	14	m	m	VERB
ejpam-5812	23	15	is	be	AUX
ejpam-5812	23	16	cordial	cordial	ADJ
ejpam-5812	23	17	for	for	ADP
ejpam-5812	23	18	all	all	DET
ejpam-5812	23	19	positive	positive	ADJ
ejpam-5812	23	20	integers	integer	NOUN
ejpam-5812	23	21	n	n	NOUN
ejpam-5812	23	22	and	and	CCONJ
ejpam-5812	23	23	m.	m.	VERB
ejpam-5812	23	24	the	the	DET
ejpam-5812	23	25	fifth	fifth	ADJ
ejpam-5812	23	26	power	power	NOUN
ejpam-5812	23	27	of	of	ADP
ejpam-5812	23	28	graphs	graph	NOUN
ejpam-5812	23	29	g5	g5	NOUN
ejpam-5812	23	30	is	be	AUX
ejpam-5812	23	31	the	the	DET
ejpam-5812	23	32	graph	graph	NOUN
ejpam-5812	23	33	obtained	obtain	VERB
ejpam-5812	23	34	from	from	ADP
ejpam-5812	23	35	the	the	DET
ejpam-5812	23	36	graph	graph	NOUN
ejpam-5812	23	37	g	g	NOUN
ejpam-5812	23	38	by	by	ADP
ejpam-5812	23	39	adding	add	VERB
ejpam-5812	23	40	edges	edge	NOUN
ejpam-5812	23	41	that	that	PRON
ejpam-5812	23	42	join	join	VERB
ejpam-5812	23	43	all	all	PRON
ejpam-5812	23	44	vertices	vertice	VERB
ejpam-5812	23	45	u	u	NOUN
ejpam-5812	23	46	and	and	CCONJ
ejpam-5812	23	47	v	v	NOUN
ejpam-5812	23	48	with	with	ADP
ejpam-5812	23	49	d(u	d(u	PROPN
ejpam-5812	23	50	,	,	PUNCT
ejpam-5812	23	51	v	v	NOUN
ejpam-5812	23	52	)	)	PUNCT
ejpam-5812	23	53	≤	≤	NOUN
ejpam-5812	23	54	5	5	NUM
ejpam-5812	23	55	.	.	PUNCT
ejpam-5812	24	1	more	more	ADV
ejpam-5812	24	2	precisely	precisely	ADV
ejpam-5812	24	3	,	,	PUNCT
ejpam-5812	24	4	and	and	CCONJ
ejpam-5812	24	5	with	with	ADP
ejpam-5812	24	6	the	the	DET
ejpam-5812	24	7	fifth	fifth	ADJ
ejpam-5812	24	8	power	power	NOUN
ejpam-5812	24	9	of	of	ADP
ejpam-5812	24	10	paths	path	NOUN
ejpam-5812	24	11	p	p	NOUN
ejpam-5812	24	12	5	5	NUM
ejpam-5812	24	13	n	n	NOUN
ejpam-5812	24	14	,	,	PUNCT
ejpam-5812	24	15	the	the	DET
ejpam-5812	24	16	fifth	fifth	ADJ
ejpam-5812	24	17	power	power	NOUN
ejpam-5812	24	18	of	of	ADP
ejpam-5812	24	19	cycles	cycle	NOUN
ejpam-5812	24	20	c5	c5	PROPN
ejpam-5812	24	21	n	n	CCONJ
ejpam-5812	24	22	,	,	PUNCT
ejpam-5812	24	23	the	the	DET
ejpam-5812	24	24	fifth	fifth	ADJ
ejpam-5812	24	25	power	power	NOUN
ejpam-5812	24	26	of	of	ADP
ejpam-5812	24	27	fans	fan	NOUN
ejpam-5812	24	28	f	f	X
ejpam-5812	24	29	5	5	NUM
ejpam-5812	24	30	n+1	n+1	PROPN
ejpam-5812	24	31	=	=	SYM
ejpam-5812	24	32	p1	p1	PROPN
ejpam-5812	24	33	+	+	CCONJ
ejpam-5812	24	34	p	p	NOUN
ejpam-5812	24	35	5	5	NUM
ejpam-5812	24	36	n	n	NOUN
ejpam-5812	24	37	,	,	PUNCT
ejpam-5812	24	38	the	the	DET
ejpam-5812	24	39	fifth	fifth	ADJ
ejpam-5812	24	40	power	power	NOUN
ejpam-5812	24	41	of	of	ADP
ejpam-5812	24	42	wheels	wheel	NOUN
ejpam-5812	24	43	w	w	PROPN
ejpam-5812	24	44	5	5	NUM
ejpam-5812	24	45	n+1	n+1	PROPN
ejpam-5812	24	46	=	=	SYM
ejpam-5812	24	47	p1	p1	PROPN
ejpam-5812	24	48	+	+	PROPN
ejpam-5812	24	49	c5	c5	PROPN
ejpam-5812	24	50	n	n	CCONJ
ejpam-5812	24	51	,	,	PUNCT
ejpam-5812	24	52	and	and	CCONJ
ejpam-5812	24	53	the	the	DET
ejpam-5812	24	54	fifth	fifth	ADJ
ejpam-5812	24	55	power	power	NOUN
ejpam-5812	24	56	of	of	ADP
ejpam-5812	24	57	a	a	DET
ejpam-5812	24	58	lemniscate	lemniscate	PROPN
ejpam-5812	24	59	graph	graph	NOUN
ejpam-5812	24	60	is	be	AUX
ejpam-5812	24	61	denoted	denote	VERB
ejpam-5812	24	62	by	by	ADP
ejpam-5812	24	63	l5	l5	PROPN
ejpam-5812	24	64	n	n	CCONJ
ejpam-5812	24	65	,	,	PUNCT
ejpam-5812	24	66	m	m	PROPN
ejpam-5812	24	67	=	=	NOUN
ejpam-5812	24	68	c5	c5	PROPN
ejpam-5812	24	69	n∪c5	n∪c5	PROPN
ejpam-5812	24	70	m	m	VERB
ejpam-5812	24	71	where	where	SCONJ
ejpam-5812	24	72	both	both	PRON
ejpam-5812	24	73	cycles	cycle	VERB
ejpam-5812	24	74	c5	c5	PROPN
ejpam-5812	24	75	n	n	PROPN
ejpam-5812	24	76	and	and	CCONJ
ejpam-5812	24	77	c5	c5	PROPN
ejpam-5812	24	78	m	m	VERB
ejpam-5812	24	79	have	have	VERB
ejpam-5812	24	80	a	a	DET
ejpam-5812	24	81	common	common	ADJ
ejpam-5812	24	82	vertex	vertex	NOUN
ejpam-5812	24	83	.	.	PUNCT
ejpam-5812	25	1	as	as	SCONJ
ejpam-5812	25	2	stated	state	VERB
ejpam-5812	25	3	in	in	ADP
ejpam-5812	25	4	[	[	X
ejpam-5812	25	5	17	17	NUM
ejpam-5812	25	6	]	]	PUNCT
ejpam-5812	25	7	,	,	PUNCT
ejpam-5812	25	8	every	every	DET
ejpam-5812	25	9	path	path	NOUN
ejpam-5812	25	10	pn	pn	PROPN
ejpam-5812	25	11	is	be	AUX
ejpam-5812	25	12	cordial	cordial	ADJ
ejpam-5812	25	13	for	for	ADP
ejpam-5812	25	14	every	every	DET
ejpam-5812	25	15	n	n	CCONJ
ejpam-5812	25	16	,	,	PUNCT
ejpam-5812	25	17	a	a	DET
ejpam-5812	25	18	cycle	cycle	NOUN
ejpam-5812	25	19	cn	cn	PROPN
ejpam-5812	25	20	is	be	AUX
ejpam-5812	25	21	cordial	cordial	ADJ
ejpam-5812	25	22	if	if	SCONJ
ejpam-5812	25	23	and	and	CCONJ
ejpam-5812	25	24	only	only	ADV
ejpam-5812	25	25	if	if	SCONJ
ejpam-5812	25	26	n	n	DET
ejpam-5812	25	27	̸=	̸=	PROPN
ejpam-5812	25	28	2(mod4	2(mod4	NUM
ejpam-5812	25	29	)	)	PUNCT
ejpam-5812	25	30	,	,	PUNCT
ejpam-5812	25	31	the	the	DET
ejpam-5812	25	32	complete	complete	ADJ
ejpam-5812	25	33	graph	graph	NOUN
ejpam-5812	25	34	kn	kn	PROPN
ejpam-5812	25	35	is	be	AUX
ejpam-5812	25	36	cordial	cordial	ADJ
ejpam-5812	25	37	if	if	SCONJ
ejpam-5812	26	1	and	and	CCONJ
ejpam-5812	26	2	only	only	ADV
ejpam-5812	26	3	if	if	SCONJ
ejpam-5812	26	4	n	n	PRON
ejpam-5812	26	5	≤	≤	ADV
ejpam-5812	26	6	3	3	NUM
ejpam-5812	26	7	.	.	PUNCT
ejpam-5812	27	1	p	p	NOUN
ejpam-5812	27	2	2	2	NUM
ejpam-5812	27	3	n	n	NOUN
ejpam-5812	27	4	is	be	AUX
ejpam-5812	27	5	cordial	cordial	ADJ
ejpam-5812	27	6	for	for	ADP
ejpam-5812	27	7	every	every	DET
ejpam-5812	27	8	n	n	NOUN
ejpam-5812	27	9	,	,	PUNCT
ejpam-5812	27	10	p	p	NOUN
ejpam-5812	27	11	3	3	NUM
ejpam-5812	27	12	n	n	NOUN
ejpam-5812	27	13	is	be	AUX
ejpam-5812	27	14	cordial	cordial	ADJ
ejpam-5812	27	15	if	if	SCONJ
ejpam-5812	27	16	and	and	CCONJ
ejpam-5812	27	17	only	only	ADV
ejpam-5812	27	18	if	if	SCONJ
ejpam-5812	27	19	n	n	PRON
ejpam-5812	27	20	̸=	̸=	PROPN
ejpam-5812	27	21	4	4	NUM
ejpam-5812	27	22	,	,	PUNCT
ejpam-5812	27	23	p	p	NOUN
ejpam-5812	27	24	4	4	NUM
ejpam-5812	27	25	n	n	NOUN
ejpam-5812	27	26	is	be	AUX
ejpam-5812	27	27	cordial	cordial	ADJ
ejpam-5812	27	28	if	if	SCONJ
ejpam-5812	27	29	and	and	CCONJ
ejpam-5812	27	30	only	only	ADV
ejpam-5812	27	31	if	if	SCONJ
ejpam-5812	27	32	m	m	VERB
ejpam-5812	27	33	̸=	̸=	PROPN
ejpam-5812	27	34	4	4	NUM
ejpam-5812	27	35	,	,	PUNCT
ejpam-5812	27	36	5	5	NUM
ejpam-5812	27	37	or	or	CCONJ
ejpam-5812	27	38	6	6	NUM
ejpam-5812	27	39	,	,	PUNCT
ejpam-5812	27	40	all	all	DET
ejpam-5812	27	41	fans	fan	NOUN
ejpam-5812	27	42	fn	fn	VERB
ejpam-5812	27	43	are	be	AUX
ejpam-5812	27	44	cordial	cordial	ADJ
ejpam-5812	27	45	and	and	CCONJ
ejpam-5812	27	46	the	the	DET
ejpam-5812	27	47	wheel	wheel	NOUN
ejpam-5812	27	48	wn	wn	PROPN
ejpam-5812	27	49	is	be	AUX
ejpam-5812	27	50	cordial	cordial	ADJ
ejpam-5812	27	51	if	if	SCONJ
ejpam-5812	27	52	and	and	CCONJ
ejpam-5812	27	53	only	only	ADV
ejpam-5812	27	54	if	if	SCONJ
ejpam-5812	27	55	n	n	PRON
ejpam-5812	27	56	̸=	̸=	PROPN
ejpam-5812	27	57	3(mod4	3(mod4	NUM
ejpam-5812	27	58	)	)	PUNCT
ejpam-5812	27	59	.	.	PUNCT
ejpam-5812	28	1	in	in	ADP
ejpam-5812	28	2	[	[	X
ejpam-5812	28	3	7	7	NUM
ejpam-5812	28	4	,	,	PUNCT
ejpam-5812	28	5	8	8	NUM
ejpam-5812	28	6	]	]	PUNCT
ejpam-5812	28	7	,	,	PUNCT
ejpam-5812	28	8	diab	diab	PROPN
ejpam-5812	28	9	has	have	AUX
ejpam-5812	28	10	reported	report	VERB
ejpam-5812	28	11	several	several	ADJ
ejpam-5812	28	12	results	result	NOUN
ejpam-5812	28	13	concerning	concern	VERB
ejpam-5812	28	14	the	the	DET
ejpam-5812	28	15	sum	sum	NOUN
ejpam-5812	28	16	and	and	CCONJ
ejpam-5812	28	17	union	union	NOUN
ejpam-5812	28	18	of	of	ADP
ejpam-5812	28	19	the	the	DET
ejpam-5812	28	20	cycles	cycle	NOUN
ejpam-5812	28	21	cn	cn	PROPN
ejpam-5812	28	22	and	and	CCONJ
ejpam-5812	28	23	paths	path	NOUN
ejpam-5812	28	24	pm	pm	VERB
ejpam-5812	28	25	together	together	ADV
ejpam-5812	28	26	and	and	CCONJ
ejpam-5812	28	27	with	with	ADP
ejpam-5812	28	28	other	other	ADJ
ejpam-5812	28	29	specific	specific	ADJ
ejpam-5812	28	30	graphs	graph	NOUN
ejpam-5812	28	31	.	.	PUNCT
ejpam-5812	29	1	he	he	PRON
ejpam-5812	29	2	introduced	introduce	VERB
ejpam-5812	29	3	the	the	DET
ejpam-5812	29	4	cordiality	cordiality	NOUN
ejpam-5812	29	5	of	of	ADP
ejpam-5812	29	6	the	the	DET
ejpam-5812	29	7	join	join	NOUN
ejpam-5812	29	8	and	and	CCONJ
ejpam-5812	29	9	the	the	DET
ejpam-5812	29	10	union	union	NOUN
ejpam-5812	29	11	of	of	ADP
ejpam-5812	29	12	pairs	pair	NOUN
ejpam-5812	29	13	of	of	ADP
ejpam-5812	29	14	wheels	wheel	NOUN
ejpam-5812	29	15	and	and	CCONJ
ejpam-5812	29	16	graphs	graph	NOUN
ejpam-5812	29	17	consisting	consist	VERB
ejpam-5812	29	18	of	of	ADP
ejpam-5812	29	19	a	a	DET
ejpam-5812	29	20	wheel	wheel	NOUN
ejpam-5812	29	21	and	and	CCONJ
ejpam-5812	29	22	a	a	DET
ejpam-5812	29	23	path	path	NOUN
ejpam-5812	29	24	or	or	CCONJ
ejpam-5812	29	25	a	a	DET
ejpam-5812	29	26	cycle	cycle	NOUN
ejpam-5812	29	27	he	he	PRON
ejpam-5812	29	28	investigated	investigate	VERB
ejpam-5812	29	29	that	that	SCONJ
ejpam-5812	29	30	the	the	DET
ejpam-5812	29	31	second	second	ADJ
ejpam-5812	29	32	power	power	NOUN
ejpam-5812	29	33	of	of	ADP
ejpam-5812	29	34	cycles	cycle	NOUN
ejpam-5812	29	35	is	be	AUX
ejpam-5812	29	36	cordial	cordial	ADJ
ejpam-5812	29	37	for	for	ADP
ejpam-5812	29	38	all	all	DET
ejpam-5812	29	39	n	n	PRON
ejpam-5812	29	40	≥	≥	NOUN
ejpam-5812	29	41	3	3	NUM
ejpam-5812	29	42	if	if	SCONJ
ejpam-5812	29	43	and	and	CCONJ
ejpam-5812	29	44	only	only	ADV
ejpam-5812	29	45	if	if	SCONJ
ejpam-5812	29	46	n	n	PROPN
ejpam-5812	29	47	=	=	SYM
ejpam-5812	29	48	3	3	NUM
ejpam-5812	29	49	or	or	CCONJ
ejpam-5812	29	50	even	even	ADV
ejpam-5812	29	51	n	n	CCONJ
ejpam-5812	29	52	>	>	X
ejpam-5812	29	53	4	4	X
ejpam-5812	29	54	.	.	PUNCT
ejpam-5812	30	1	moreover	moreover	ADV
ejpam-5812	30	2	,	,	PUNCT
ejpam-5812	30	3	he	he	PRON
ejpam-5812	30	4	studies	study	VERB
ejpam-5812	30	5	the	the	DET
ejpam-5812	30	6	cordiality	cordiality	NOUN
ejpam-5812	30	7	of	of	ADP
ejpam-5812	30	8	certain	certain	ADJ
ejpam-5812	30	9	combinations	combination	NOUN
ejpam-5812	30	10	of	of	ADP
ejpam-5812	30	11	second	second	ADJ
ejpam-5812	30	12	power	power	NOUN
ejpam-5812	30	13	of	of	ADP
ejpam-5812	30	14	cycles	cycle	NOUN
ejpam-5812	30	15	,	,	PUNCT
ejpam-5812	30	16	cycles	cycle	NOUN
ejpam-5812	30	17	and	and	CCONJ
ejpam-5812	30	18	paths	path	NOUN
ejpam-5812	30	19	.	.	PUNCT
ejpam-5812	31	1	specifically	specifically	ADV
ejpam-5812	31	2	,	,	PUNCT
ejpam-5812	31	3	he	he	PRON
ejpam-5812	31	4	discussed	discuss	VERB
ejpam-5812	31	5	the	the	DET
ejpam-5812	31	6	cordiality	cordiality	NOUN
ejpam-5812	31	7	of	of	ADP
ejpam-5812	31	8	the	the	DET
ejpam-5812	31	9	join	join	NOUN
ejpam-5812	31	10	and	and	CCONJ
ejpam-5812	31	11	union	union	NOUN
ejpam-5812	31	12	of	of	ADP
ejpam-5812	31	13	pairs	pair	NOUN
ejpam-5812	31	14	of	of	ADP
ejpam-5812	31	15	second	second	ADJ
ejpam-5812	31	16	power	power	NOUN
ejpam-5812	31	17	of	of	ADP
ejpam-5812	31	18	cycles	cycle	NOUN
ejpam-5812	31	19	and	and	CCONJ
ejpam-5812	31	20	graphs	graph	NOUN
ejpam-5812	31	21	consisting	consist	VERB
ejpam-5812	31	22	of	of	ADP
ejpam-5812	31	23	one	one	NUM
ejpam-5812	31	24	second	second	ADJ
ejpam-5812	31	25	power	power	NOUN
ejpam-5812	31	26	of	of	ADP
ejpam-5812	31	27	cycle	cycle	NOUN
ejpam-5812	31	28	with	with	ADP
ejpam-5812	31	29	one	one	NUM
ejpam-5812	31	30	cycle	cycle	NOUN
ejpam-5812	31	31	and	and	CCONJ
ejpam-5812	31	32	one	one	NUM
ejpam-5812	31	33	path	path	NOUN
ejpam-5812	31	34	.	.	PUNCT
ejpam-5812	32	1	in	in	ADP
ejpam-5812	32	2	[	[	X
ejpam-5812	32	3	16	16	NUM
ejpam-5812	32	4	]	]	PUNCT
ejpam-5812	32	5	the	the	DET
ejpam-5812	32	6	cordiality	cordiality	NOUN
ejpam-5812	32	7	of	of	ADP
ejpam-5812	32	8	the	the	DET
ejpam-5812	32	9	join	join	NOUN
ejpam-5812	32	10	and	and	CCONJ
ejpam-5812	32	11	union	union	NOUN
ejpam-5812	32	12	of	of	ADP
ejpam-5812	32	13	graphs	graph	NOUN
ejpam-5812	32	14	involving	involve	VERB
ejpam-5812	32	15	one	one	NUM
ejpam-5812	32	16	path	path	NOUN
ejpam-5812	32	17	and	and	CCONJ
ejpam-5812	32	18	one	one	NUM
ejpam-5812	32	19	cycle	cycle	NOUN
ejpam-5812	32	20	,	,	PUNCT
ejpam-5812	32	21	as	as	ADV
ejpam-5812	32	22	well	well	ADV
ejpam-5812	32	23	as	as	ADP
ejpam-5812	32	24	the	the	DET
ejpam-5812	32	25	third	third	ADJ
ejpam-5812	32	26	power	power	NOUN
ejpam-5812	32	27	of	of	ADP
ejpam-5812	32	28	paths	path	NOUN
ejpam-5812	32	29	.	.	PUNCT
ejpam-5812	33	1	elrokh	elrokh	VERB
ejpam-5812	33	2	and	and	CCONJ
ejpam-5812	33	3	rabie	rabie	VERB
ejpam-5812	33	4	[	[	X
ejpam-5812	33	5	14	14	NUM
ejpam-5812	33	6	]	]	PUNCT
ejpam-5812	33	7	proved	prove	VERB
ejpam-5812	33	8	p	p	NOUN
ejpam-5812	33	9	4	4	NUM
ejpam-5812	33	10	n	n	NOUN
ejpam-5812	33	11	+	+	CCONJ
ejpam-5812	33	12	p	p	X
ejpam-5812	33	13	4	4	NUM
ejpam-5812	33	14	m	m	NOUN
ejpam-5812	33	15	and	and	CCONJ
ejpam-5812	33	16	p	p	NOUN
ejpam-5812	33	17	4	4	NUM
ejpam-5812	33	18	n	n	NOUN
ejpam-5812	33	19	∪	∪	NOUN
ejpam-5812	33	20	p	p	PROPN
ejpam-5812	33	21	4	4	NUM
ejpam-5812	33	22	m	m	NOUN
ejpam-5812	33	23	are	be	AUX
ejpam-5812	33	24	cordial	cordial	ADJ
ejpam-5812	33	25	for	for	ADP
ejpam-5812	33	26	all	all	DET
ejpam-5812	33	27	n	n	CCONJ
ejpam-5812	33	28	,	,	PUNCT
ejpam-5812	33	29	m	m	VERB
ejpam-5812	33	30	≥	≥	NOUN
ejpam-5812	33	31	7	7	NUM
ejpam-5812	33	32	,	,	PUNCT
ejpam-5812	33	33	and	and	CCONJ
ejpam-5812	33	34	c4	c4	NOUN
ejpam-5812	33	35	n	n	PROPN
ejpam-5812	33	36	+	+	CCONJ
ejpam-5812	33	37	c4	c4	NOUN
ejpam-5812	33	38	m	m	PROPN
ejpam-5812	33	39	,	,	PUNCT
ejpam-5812	33	40	and	and	CCONJ
ejpam-5812	33	41	c4	c4	VERB
ejpam-5812	33	42	n	n	CCONJ
ejpam-5812	33	43	∪	∪	X
ejpam-5812	33	44	c4	c4	NOUN
ejpam-5812	33	45	m	m	VERB
ejpam-5812	33	46	are	be	AUX
ejpam-5812	33	47	cordial	cordial	ADJ
ejpam-5812	33	48	for	for	ADP
ejpam-5812	33	49	all	all	DET
ejpam-5812	33	50	n	n	NOUN
ejpam-5812	33	51	,	,	PUNCT
ejpam-5812	33	52	m	m	VERB
ejpam-5812	33	53	except	except	SCONJ
ejpam-5812	33	54	(	(	PUNCT
ejpam-5812	33	55	n	n	CCONJ
ejpam-5812	33	56	,	,	PUNCT
ejpam-5812	33	57	m	m	NOUN
ejpam-5812	33	58	)	)	PUNCT
ejpam-5812	33	59	=	=	SYM
ejpam-5812	33	60	(	(	PUNCT
ejpam-5812	33	61	7	7	NUM
ejpam-5812	33	62	,	,	PUNCT
ejpam-5812	33	63	7	7	NUM
ejpam-5812	33	64	)	)	PUNCT
ejpam-5812	33	65	.	.	PUNCT
ejpam-5812	34	1	cordial	cordial	ADJ
ejpam-5812	34	2	labelling	labelling	NOUN
ejpam-5812	34	3	has	have	VERB
ejpam-5812	34	4	significant	significant	ADJ
ejpam-5812	34	5	connections	connection	NOUN
ejpam-5812	34	6	to	to	PART
ejpam-5812	34	7	computer	computer	NOUN
ejpam-5812	34	8	science	science	NOUN
ejpam-5812	34	9	because	because	SCONJ
ejpam-5812	34	10	arithmetic	arithmetic	ADJ
ejpam-5812	34	11	modulo	modulo	NOUN
ejpam-5812	34	12	2	2	NUM
ejpam-5812	34	13	is	be	AUX
ejpam-5812	34	14	a	a	DET
ejpam-5812	34	15	fundamental	fundamental	ADJ
ejpam-5812	34	16	component	component	NOUN
ejpam-5812	34	17	of	of	ADP
ejpam-5812	34	18	that	that	DET
ejpam-5812	34	19	discipline	discipline	NOUN
ejpam-5812	34	20	.	.	PUNCT
ejpam-5812	35	1	cordial	cordial	ADJ
ejpam-5812	35	2	labeling	labeling	NOUN
ejpam-5812	35	3	has	have	VERB
ejpam-5812	35	4	applications	application	NOUN
ejpam-5812	35	5	in	in	ADP
ejpam-5812	35	6	various	various	ADJ
ejpam-5812	35	7	fields	field	NOUN
ejpam-5812	35	8	,	,	PUNCT
ejpam-5812	35	9	such	such	ADJ
ejpam-5812	35	10	as	as	ADP
ejpam-5812	35	11	coding	code	VERB
ejpam-5812	35	12	theory	theory	NOUN
ejpam-5812	35	13	,	,	PUNCT
ejpam-5812	35	14	communication	communication	NOUN
ejpam-5812	35	15	networks	network	NOUN
ejpam-5812	35	16	,	,	PUNCT
ejpam-5812	35	17	x	x	NOUN
ejpam-5812	35	18	-	-	NOUN
ejpam-5812	35	19	ray	ray	NOUN
ejpam-5812	35	20	crystallography	crystallography	NOUN
ejpam-5812	35	21	,	,	PUNCT
ejpam-5812	35	22	and	and	CCONJ
ejpam-5812	35	23	computational	computational	ADJ
ejpam-5812	35	24	and	and	CCONJ
ejpam-5812	35	25	communication	communication	NOUN
ejpam-5812	35	26	paradigms	paradigm	NOUN
ejpam-5812	35	27	.	.	PUNCT
ejpam-5812	36	1	one	one	NUM
ejpam-5812	36	2	interesting	interesting	ADJ
ejpam-5812	36	3	application	application	NOUN
ejpam-5812	36	4	is	be	AUX
ejpam-5812	36	5	to	to	PART
ejpam-5812	36	6	produce	produce	VERB
ejpam-5812	36	7	new	new	ADJ
ejpam-5812	36	8	cordial	cordial	ADJ
ejpam-5812	36	9	families	family	NOUN
ejpam-5812	36	10	by	by	ADP
ejpam-5812	36	11	using	use	VERB
ejpam-5812	36	12	a	a	DET
ejpam-5812	36	13	technique	technique	NOUN
ejpam-5812	36	14	called	call	VERB
ejpam-5812	36	15	balanced	balanced	ADJ
ejpam-5812	36	16	cordial	cordial	ADJ
ejpam-5812	36	17	labeling	labeling	NOUN
ejpam-5812	36	18	,	,	PUNCT
ejpam-5812	36	19	which	which	PRON
ejpam-5812	36	20	can	can	AUX
ejpam-5812	36	21	generate	generate	VERB
ejpam-5812	36	22	cordial	cordial	ADJ
ejpam-5812	36	23	graphs	graph	NOUN
ejpam-5812	36	24	from	from	ADP
ejpam-5812	36	25	two	two	NUM
ejpam-5812	36	26	given	give	VERB
ejpam-5812	36	27	graphs	graph	NOUN
ejpam-5812	36	28	by	by	ADP
ejpam-5812	36	29	taking	take	VERB
ejpam-5812	36	30	one	one	NUM
ejpam-5812	36	31	copy	copy	NOUN
ejpam-5812	36	32	of	of	ADP
ejpam-5812	36	33	one	one	NUM
ejpam-5812	36	34	graph	graph	NOUN
ejpam-5812	36	35	and	and	CCONJ
ejpam-5812	36	36	j	j	PROPN
ejpam-5812	36	37	copies	copy	NOUN
ejpam-5812	36	38	of	of	ADP
ejpam-5812	36	39	another	another	DET
ejpam-5812	36	40	graph	graph	NOUN
ejpam-5812	36	41	and	and	CCONJ
ejpam-5812	36	42	joining	join	VERB
ejpam-5812	36	43	them	they	PRON
ejpam-5812	36	44	by	by	ADP
ejpam-5812	36	45	an	an	DET
ejpam-5812	36	46	edge	edge	NOUN
ejpam-5812	36	47	.	.	PUNCT
ejpam-5812	37	1	for	for	ADP
ejpam-5812	37	2	more	more	ADJ
ejpam-5812	37	3	details	detail	NOUN
ejpam-5812	37	4	about	about	ADP
ejpam-5812	37	5	the	the	DET
ejpam-5812	37	6	cordial	cordial	ADJ
ejpam-5812	37	7	labeling	labeling	NOUN
ejpam-5812	37	8	and	and	CCONJ
ejpam-5812	37	9	types	type	NOUN
ejpam-5812	37	10	of	of	ADP
ejpam-5812	37	11	labeling	labeling	NOUN
ejpam-5812	37	12	,	,	PUNCT
ejpam-5812	37	13	the	the	DET
ejpam-5812	37	14	reader	reader	NOUN
ejpam-5812	37	15	can	can	AUX
ejpam-5812	37	16	refer	refer	VERB
ejpam-5812	37	17	to	to	ADP
ejpam-5812	37	18	[	[	X
ejpam-5812	37	19	1	1	NUM
ejpam-5812	37	20	,	,	PUNCT
ejpam-5812	37	21	2	2	NUM
ejpam-5812	37	22	,	,	PUNCT
ejpam-5812	37	23	9–13	9–13	NOUN
ejpam-5812	37	24	,	,	PUNCT
ejpam-5812	37	25	15	15	NUM
ejpam-5812	37	26	]	]	PUNCT
ejpam-5812	37	27	.	.	PUNCT
ejpam-5812	38	1	we	we	PRON
ejpam-5812	38	2	defined	define	VERB
ejpam-5812	38	3	cordial	cordial	ADJ
ejpam-5812	38	4	graphs	graph	NOUN
ejpam-5812	38	5	more	more	ADV
ejpam-5812	38	6	accurately	accurately	ADV
ejpam-5812	38	7	as	as	SCONJ
ejpam-5812	38	8	follows	follow	VERB
ejpam-5812	38	9	.	.	PUNCT
ejpam-5812	39	1	let	let	VERB
ejpam-5812	39	2	g	g	PROPN
ejpam-5812	39	3	=	=	SYM
ejpam-5812	39	4	(	(	PUNCT
ejpam-5812	39	5	v	v	NOUN
ejpam-5812	39	6	,	,	PUNCT
ejpam-5812	39	7	e	e	NOUN
ejpam-5812	39	8	)	)	PUNCT
ejpam-5812	39	9	be	be	AUX
ejpam-5812	39	10	a	a	DET
ejpam-5812	39	11	graph	graph	NOUN
ejpam-5812	39	12	,	,	PUNCT
ejpam-5812	39	13	let	let	VERB
ejpam-5812	39	14	f	f	PRON
ejpam-5812	39	15	:	:	PUNCT
ejpam-5812	39	16	v	v	X
ejpam-5812	39	17	→	→	SYM
ejpam-5812	39	18	{	{	PUNCT
ejpam-5812	39	19	0	0	NUM
ejpam-5812	39	20	,	,	PUNCT
ejpam-5812	39	21	1	1	X
ejpam-5812	39	22	}	}	PUNCT
ejpam-5812	39	23	labeling	labeling	NOUN
ejpam-5812	39	24	of	of	ADP
ejpam-5812	39	25	the	the	DET
ejpam-5812	39	26	vertices	vertex	NOUN
ejpam-5812	39	27	,	,	PUNCT
ejpam-5812	39	28	and	and	CCONJ
ejpam-5812	39	29	let	let	VERB
ejpam-5812	39	30	f∗	f∗	NOUN
ejpam-5812	39	31	:	:	PUNCT
ejpam-5812	39	32	e	e	X
ejpam-5812	39	33	→	→	PUNCT
ejpam-5812	39	34	{	{	PUNCT
ejpam-5812	39	35	0	0	NUM
ejpam-5812	39	36	,	,	PUNCT
ejpam-5812	39	37	1	1	NUM
ejpam-5812	39	38	}	}	PUNCT
ejpam-5812	39	39	be	be	AUX
ejpam-5812	39	40	the	the	DET
ejpam-5812	39	41	extension	extension	NOUN
ejpam-5812	39	42	of	of	ADP
ejpam-5812	39	43	f	f	PROPN
ejpam-5812	39	44	to	to	ADP
ejpam-5812	39	45	the	the	DET
ejpam-5812	39	46	edges	edge	NOUN
ejpam-5812	39	47	of	of	ADP
ejpam-5812	39	48	g	g	NOUN
ejpam-5812	39	49	by	by	ADP
ejpam-5812	39	50	the	the	DET
ejpam-5812	39	51	formula	formula	NOUN
ejpam-5812	39	52	f∗(vw	f∗(vw	NOUN
ejpam-5812	39	53	)	)	PUNCT
ejpam-5812	39	54	=	=	SYM
ejpam-5812	39	55	f(v	f(v	NOUN
ejpam-5812	39	56	)	)	PUNCT
ejpam-5812	39	57	+	+	PUNCT
ejpam-5812	39	58	f(w	f(w	PROPN
ejpam-5812	39	59	)	)	PUNCT
ejpam-5812	39	60	(	(	PUNCT
ejpam-5812	39	61	mod	mod	NOUN
ejpam-5812	39	62	2	2	NUM
ejpam-5812	39	63	)	)	PUNCT
ejpam-5812	39	64	.	.	PUNCT
ejpam-5812	40	1	(	(	PUNCT
ejpam-5812	40	2	thus	thus	ADV
ejpam-5812	40	3	for	for	ADP
ejpam-5812	40	4	any	any	DET
ejpam-5812	40	5	edges	edge	NOUN
ejpam-5812	40	6	e	e	X
ejpam-5812	40	7	=	=	SYM
ejpam-5812	40	8	vw	vw	PROPN
ejpam-5812	40	9	,	,	PUNCT
ejpam-5812	40	10	f∗(e	f∗(e	PROPN
ejpam-5812	40	11	)	)	PUNCT
ejpam-5812	40	12	=	=	SYM
ejpam-5812	40	13	0	0	PUNCT
ejpam-5812	40	14	if	if	SCONJ
ejpam-5812	40	15	its	its	PRON
ejpam-5812	40	16	two	two	NUM
ejpam-5812	40	17	vertices	vertex	NOUN
ejpam-5812	40	18	have	have	VERB
ejpam-5812	40	19	the	the	DET
ejpam-5812	40	20	same	same	ADJ
ejpam-5812	40	21	label	label	NOUN
ejpam-5812	40	22	and	and	CCONJ
ejpam-5812	40	23	f∗(e	f∗(e	NOUN
ejpam-5812	40	24	)	)	PUNCT
ejpam-5812	40	25	=	=	NOUN
ejpam-5812	40	26	1	1	NUM
ejpam-5812	40	27	if	if	SCONJ
ejpam-5812	40	28	they	they	PRON
ejpam-5812	40	29	have	have	VERB
ejpam-5812	40	30	different	different	ADJ
ejpam-5812	40	31	labels	label	NOUN
ejpam-5812	40	32	)	)	PUNCT
ejpam-5812	40	33	.	.	PUNCT
ejpam-5812	41	1	let	let	VERB
ejpam-5812	41	2	v0	v0	NOUN
ejpam-5812	41	3	and	and	CCONJ
ejpam-5812	41	4	v1	v1	NOUN
ejpam-5812	41	5	be	be	AUX
ejpam-5812	41	6	the	the	DET
ejpam-5812	41	7	numbers	number	NOUN
ejpam-5812	41	8	of	of	ADP
ejpam-5812	41	9	vertices	vertex	NOUN
ejpam-5812	41	10	labeled	label	VERB
ejpam-5812	41	11	0	0	NUM
ejpam-5812	41	12	and	and	CCONJ
ejpam-5812	41	13	1	1	NUM
ejpam-5812	41	14	respectively	respectively	ADV
ejpam-5812	41	15	,	,	PUNCT
ejpam-5812	41	16	and	and	CCONJ
ejpam-5812	41	17	let	let	VERB
ejpam-5812	41	18	e0	e0	PROPN
ejpam-5812	41	19	and	and	CCONJ
ejpam-5812	41	20	e1	e1	PROPN
ejpam-5812	41	21	be	be	VERB
ejpam-5812	41	22	the	the	DET
ejpam-5812	41	23	corresponding	corresponding	ADJ
ejpam-5812	41	24	numbers	number	NOUN
ejpam-5812	41	25	of	of	ADP
ejpam-5812	41	26	edges	edge	NOUN
ejpam-5812	41	27	.	.	PUNCT
ejpam-5812	42	1	such	such	DET
ejpam-5812	42	2	a	a	DET
ejpam-5812	42	3	labeling	labeling	NOUN
ejpam-5812	42	4	is	be	AUX
ejpam-5812	42	5	called	call	VERB
ejpam-5812	42	6	cordial	cordial	ADJ
ejpam-5812	42	7	a.	a.	NOUN
ejpam-5812	42	8	abd	abd	PROPN
ejpam-5812	42	9	el	el	PROPN
ejpam-5812	42	10	-	-	PROPN
ejpam-5812	42	11	hay	hay	PROPN
ejpam-5812	42	12	,	,	PUNCT
ejpam-5812	42	13	k.	k.	PROPN
ejpam-5812	42	14	a.	a.	PROPN
ejpam-5812	42	15	alsatami	alsatami	PROPN
ejpam-5812	42	16	,	,	PUNCT
ejpam-5812	42	17	a.	a.	NOUN
ejpam-5812	42	18	elrokh	elrokh	PROPN
ejpam-5812	42	19	/	/	SYM
ejpam-5812	42	20	eur	eur	PROPN
ejpam-5812	42	21	.	.	PUNCT
ejpam-5812	43	1	j.	j.	PROPN
ejpam-5812	43	2	pure	pure	PROPN
ejpam-5812	43	3	appl	appl	PROPN
ejpam-5812	43	4	.	.	PROPN
ejpam-5812	43	5	math	math	PROPN
ejpam-5812	43	6	,	,	PUNCT
ejpam-5812	43	7	18	18	NUM
ejpam-5812	43	8	(	(	PUNCT
ejpam-5812	43	9	1	1	NUM
ejpam-5812	43	10	)	)	PUNCT
ejpam-5812	43	11	(	(	PUNCT
ejpam-5812	43	12	2025	2025	NUM
ejpam-5812	43	13	)	)	PUNCT
ejpam-5812	43	14	,	,	PUNCT
ejpam-5812	43	15	5812	5812	NUM
ejpam-5812	43	16	3	3	NUM
ejpam-5812	43	17	of	of	ADP
ejpam-5812	43	18	14	14	NUM
ejpam-5812	43	19	if	if	SCONJ
ejpam-5812	43	20	both	both	PRON
ejpam-5812	43	21	|v0−	|v0−	VERB
ejpam-5812	43	22	v1|	v1|	NOUN
ejpam-5812	43	23	≤	≤	ADJ
ejpam-5812	43	24	1	1	NUM
ejpam-5812	43	25	and	and	CCONJ
ejpam-5812	43	26	|e0−	|e0−	ADJ
ejpam-5812	43	27	e1|	e1|	PROPN
ejpam-5812	43	28	≤	≤	PROPN
ejpam-5812	43	29	1	1	NUM
ejpam-5812	43	30	.	.	PUNCT
ejpam-5812	44	1	a	a	DET
ejpam-5812	44	2	graph	graph	NOUN
ejpam-5812	44	3	is	be	AUX
ejpam-5812	44	4	called	call	VERB
ejpam-5812	44	5	cordial	cordial	ADJ
ejpam-5812	44	6	if	if	SCONJ
ejpam-5812	44	7	it	it	PRON
ejpam-5812	44	8	has	have	VERB
ejpam-5812	44	9	a	a	DET
ejpam-5812	44	10	cordial	cordial	ADJ
ejpam-5812	44	11	labeling	labeling	NOUN
ejpam-5812	44	12	.	.	PUNCT
ejpam-5812	45	1	the	the	DET
ejpam-5812	45	2	main	main	ADJ
ejpam-5812	45	3	object	object	NOUN
ejpam-5812	45	4	of	of	ADP
ejpam-5812	45	5	this	this	DET
ejpam-5812	45	6	paper	paper	NOUN
ejpam-5812	45	7	is	be	AUX
ejpam-5812	45	8	to	to	PART
ejpam-5812	45	9	extend	extend	VERB
ejpam-5812	45	10	the	the	DET
ejpam-5812	45	11	above	above	ADJ
ejpam-5812	45	12	results	result	NOUN
ejpam-5812	45	13	as	as	SCONJ
ejpam-5812	45	14	follows	follow	VERB
ejpam-5812	45	15	.	.	PUNCT
ejpam-5812	46	1	in	in	ADP
ejpam-5812	46	2	section	section	NOUN
ejpam-5812	46	3	3	3	NUM
ejpam-5812	46	4	,	,	PUNCT
ejpam-5812	46	5	we	we	PRON
ejpam-5812	46	6	study	study	VERB
ejpam-5812	46	7	the	the	DET
ejpam-5812	46	8	cordiality	cordiality	NOUN
ejpam-5812	46	9	of	of	ADP
ejpam-5812	46	10	the	the	DET
ejpam-5812	46	11	fifth	fifth	ADJ
ejpam-5812	46	12	power	power	NOUN
ejpam-5812	46	13	of	of	ADP
ejpam-5812	46	14	paths	path	NOUN
ejpam-5812	46	15	,	,	PUNCT
ejpam-5812	46	16	cycles	cycle	NOUN
ejpam-5812	46	17	,	,	PUNCT
ejpam-5812	46	18	fans	fan	NOUN
ejpam-5812	46	19	,	,	PUNCT
ejpam-5812	46	20	wheels	wheel	NOUN
ejpam-5812	46	21	,	,	PUNCT
ejpam-5812	46	22	and	and	CCONJ
ejpam-5812	46	23	lemniscate	lemniscate	PROPN
ejpam-5812	46	24	graphs	graph	NOUN
ejpam-5812	46	25	.	.	PUNCT
ejpam-5812	47	1	section	section	NOUN
ejpam-5812	47	2	4	4	NUM
ejpam-5812	47	3	investigates	investigate	VERB
ejpam-5812	47	4	the	the	DET
ejpam-5812	47	5	cordiality	cordiality	NOUN
ejpam-5812	47	6	for	for	ADP
ejpam-5812	47	7	the	the	DET
ejpam-5812	47	8	union	union	NOUN
ejpam-5812	47	9	of	of	ADP
ejpam-5812	47	10	fifth	fifth	ADJ
ejpam-5812	47	11	power	power	NOUN
ejpam-5812	47	12	of	of	ADP
ejpam-5812	47	13	paths	path	NOUN
ejpam-5812	47	14	and	and	CCONJ
ejpam-5812	47	15	cycles	cycle	NOUN
ejpam-5812	47	16	.	.	PUNCT
ejpam-5812	48	1	section	section	NOUN
ejpam-5812	48	2	5	5	NUM
ejpam-5812	48	3	,	,	PUNCT
ejpam-5812	48	4	proposes	propose	VERB
ejpam-5812	48	5	an	an	DET
ejpam-5812	48	6	algorithm	algorithm	NOUN
ejpam-5812	48	7	for	for	ADP
ejpam-5812	48	8	determining	determine	VERB
ejpam-5812	48	9	the	the	DET
ejpam-5812	48	10	cordiality	cordiality	NOUN
ejpam-5812	48	11	of	of	ADP
ejpam-5812	48	12	a	a	DET
ejpam-5812	48	13	given	give	VERB
ejpam-5812	48	14	graph	graph	NOUN
ejpam-5812	48	15	.	.	PUNCT
ejpam-5812	49	1	the	the	DET
ejpam-5812	49	2	last	last	ADJ
ejpam-5812	49	3	section	section	NOUN
ejpam-5812	49	4	,	,	PUNCT
ejpam-5812	49	5	is	be	AUX
ejpam-5812	49	6	the	the	DET
ejpam-5812	49	7	conclusion	conclusion	NOUN
ejpam-5812	49	8	which	which	PRON
ejpam-5812	49	9	summarize	summarize	VERB
ejpam-5812	49	10	the	the	DET
ejpam-5812	49	11	important	important	ADJ
ejpam-5812	49	12	points	point	NOUN
ejpam-5812	49	13	of	of	ADP
ejpam-5812	49	14	our	our	PRON
ejpam-5812	49	15	finding	finding	NOUN
ejpam-5812	49	16	in	in	ADP
ejpam-5812	49	17	this	this	DET
ejpam-5812	49	18	paper	paper	NOUN
ejpam-5812	49	19	.	.	PUNCT
ejpam-5812	50	1	2	2	X
ejpam-5812	50	2	.	.	X
ejpam-5812	50	3	terminology	terminology	NOUN
ejpam-5812	50	4	and	and	CCONJ
ejpam-5812	50	5	notation	notation	NOUN
ejpam-5812	50	6	we	we	PRON
ejpam-5812	50	7	let	let	VERB
ejpam-5812	50	8	l4r	l4r	PRON
ejpam-5812	50	9	denote	denote	VERB
ejpam-5812	50	10	the	the	DET
ejpam-5812	50	11	labeling	labeling	NOUN
ejpam-5812	50	12	0011	0011	NUM
ejpam-5812	50	13	...	...	PUNCT
ejpam-5812	50	14	0011	0011	NUM
ejpam-5812	50	15	(	(	PUNCT
ejpam-5812	50	16	repeated	repeat	VERB
ejpam-5812	50	17	r	r	NOUN
ejpam-5812	50	18	-	-	PUNCT
ejpam-5812	50	19	times	time	NOUN
ejpam-5812	50	20	)	)	PUNCT
ejpam-5812	50	21	,	,	PUNCT
ejpam-5812	50	22	let	let	VERB
ejpam-5812	50	23	l	l	NOUN
ejpam-5812	50	24	′	′	NOUN
ejpam-5812	50	25	4r	4r	NUM
ejpam-5812	50	26	denote	denote	VERB
ejpam-5812	50	27	the	the	DET
ejpam-5812	50	28	labeling	labeling	NOUN
ejpam-5812	50	29	1100	1100	NUM
ejpam-5812	50	30	...	...	SYM
ejpam-5812	50	31	1100	1100	NUM
ejpam-5812	50	32	(	(	PUNCT
ejpam-5812	50	33	repeated	repeat	VERB
ejpam-5812	50	34	r	r	NOUN
ejpam-5812	50	35	times	time	NOUN
ejpam-5812	50	36	)	)	PUNCT
ejpam-5812	50	37	.	.	PUNCT
ejpam-5812	51	1	the	the	DET
ejpam-5812	51	2	labeling	labeling	NOUN
ejpam-5812	51	3	1001	1001	NUM
ejpam-5812	51	4	1001	1001	NUM
ejpam-5812	51	5	...	...	SYM
ejpam-5812	51	6	1001	1001	NUM
ejpam-5812	51	7	(	(	PUNCT
ejpam-5812	51	8	repeated	repeat	VERB
ejpam-5812	51	9	r	r	NOUN
ejpam-5812	51	10	times	time	NOUN
ejpam-5812	51	11	)	)	PUNCT
ejpam-5812	51	12	and	and	CCONJ
ejpam-5812	51	13	0110	0110	NUM
ejpam-5812	51	14	...	...	PUNCT
ejpam-5812	51	15	0110	0110	NUM
ejpam-5812	51	16	(	(	PUNCT
ejpam-5812	51	17	repeated	repeat	VERB
ejpam-5812	51	18	r	r	NOUN
ejpam-5812	51	19	times	time	NOUN
ejpam-5812	51	20	)	)	PUNCT
ejpam-5812	51	21	are	be	AUX
ejpam-5812	51	22	denoted	denote	VERB
ejpam-5812	51	23	by	by	ADP
ejpam-5812	51	24	s4r	s4r	PROPN
ejpam-5812	51	25	and	and	CCONJ
ejpam-5812	51	26	s′	s′	ADJ
ejpam-5812	51	27	4rrespectively	4rrespectively	NUM
ejpam-5812	51	28	.	.	PUNCT
ejpam-5812	52	1	let	let	VERB
ejpam-5812	52	2	m2r	m2r	NOUN
ejpam-5812	52	3	denote	denote	VERB
ejpam-5812	52	4	the	the	DET
ejpam-5812	52	5	labeling	labeling	NOUN
ejpam-5812	52	6	0101	0101	NUM
ejpam-5812	52	7	...	...	PUNCT
ejpam-5812	52	8	01	01	NUM
ejpam-5812	52	9	,	,	PUNCT
ejpam-5812	52	10	zero	zero	NUM
ejpam-5812	52	11	-	-	PUNCT
ejpam-5812	52	12	one	one	NUM
ejpam-5812	52	13	repeated	repeat	VERB
ejpam-5812	52	14	r−times	r−time	NOUN
ejpam-5812	52	15	if	if	SCONJ
ejpam-5812	52	16	r	r	NOUN
ejpam-5812	52	17	is	be	AUX
ejpam-5812	52	18	even	even	ADV
ejpam-5812	52	19	and	and	CCONJ
ejpam-5812	52	20	0101	0101	NUM
ejpam-5812	52	21	...	...	PUNCT
ejpam-5812	52	22	010	010	NUM
ejpam-5812	53	1	if	if	SCONJ
ejpam-5812	53	2	r	r	NOUN
ejpam-5812	53	3	is	be	AUX
ejpam-5812	53	4	odd	odd	ADJ
ejpam-5812	53	5	.	.	PUNCT
ejpam-5812	54	1	sometimes	sometimes	ADV
ejpam-5812	54	2	,	,	PUNCT
ejpam-5812	54	3	we	we	PRON
ejpam-5812	54	4	modify	modify	VERB
ejpam-5812	54	5	labeling	labeling	NOUN
ejpam-5812	54	6	by	by	ADP
ejpam-5812	54	7	adding	add	VERB
ejpam-5812	54	8	symbols	symbol	NOUN
ejpam-5812	54	9	at	at	ADP
ejpam-5812	54	10	one	one	NUM
ejpam-5812	54	11	end	end	NOUN
ejpam-5812	54	12	or	or	CCONJ
ejpam-5812	54	13	the	the	DET
ejpam-5812	54	14	other	other	ADJ
ejpam-5812	54	15	(	(	PUNCT
ejpam-5812	54	16	or	or	CCONJ
ejpam-5812	54	17	both	both	PRON
ejpam-5812	54	18	)	)	PUNCT
ejpam-5812	54	19	.	.	PUNCT
ejpam-5812	55	1	in	in	ADP
ejpam-5812	55	2	most	most	ADJ
ejpam-5812	55	3	cases	case	NOUN
ejpam-5812	55	4	,	,	PUNCT
ejpam-5812	55	5	we	we	PRON
ejpam-5812	55	6	then	then	ADV
ejpam-5812	55	7	modify	modify	VERB
ejpam-5812	55	8	this	this	PRON
ejpam-5812	55	9	by	by	ADP
ejpam-5812	55	10	adding	add	VERB
ejpam-5812	55	11	symbols	symbol	NOUN
ejpam-5812	55	12	at	at	ADP
ejpam-5812	55	13	one	one	NUM
ejpam-5812	55	14	end	end	NOUN
ejpam-5812	55	15	or	or	CCONJ
ejpam-5812	55	16	the	the	DET
ejpam-5812	55	17	other	other	ADJ
ejpam-5812	55	18	(	(	PUNCT
ejpam-5812	55	19	or	or	CCONJ
ejpam-5812	55	20	both	both	PRON
ejpam-5812	55	21	)	)	PUNCT
ejpam-5812	55	22	,	,	PUNCT
ejpam-5812	55	23	thus	thus	ADV
ejpam-5812	55	24	l4r101	l4r101	PROPN
ejpam-5812	55	25	denotes	denote	VERB
ejpam-5812	55	26	the	the	DET
ejpam-5812	55	27	labeling	labeling	NOUN
ejpam-5812	55	28	0011	0011	NUM
ejpam-5812	55	29	0011	0011	NUM
ejpam-5812	55	30	...	...	PUNCT
ejpam-5812	55	31	0011	0011	NUM
ejpam-5812	55	32	101	101	NUM
ejpam-5812	55	33	(	(	PUNCT
ejpam-5812	55	34	repeated	repeat	VERB
ejpam-5812	55	35	r	r	NOUN
ejpam-5812	55	36	-	-	PUNCT
ejpam-5812	55	37	times	time	NOUN
ejpam-5812	55	38	)	)	PUNCT
ejpam-5812	55	39	when	when	SCONJ
ejpam-5812	55	40	r≥1	r≥1	ADV
ejpam-5812	55	41	and	and	CCONJ
ejpam-5812	55	42	101	101	NUM
ejpam-5812	55	43	when	when	SCONJ
ejpam-5812	55	44	r=	r=	ADJ
ejpam-5812	55	45	0	0	NUM
ejpam-5812	55	46	.	.	PUNCT
ejpam-5812	56	1	similarly	similarly	ADV
ejpam-5812	56	2	,	,	PUNCT
ejpam-5812	56	3	1l	1l	NUM
ejpam-5812	56	4	′	′	NUM
ejpam-5812	56	5	4r	4r	NUM
ejpam-5812	56	6	is	be	AUX
ejpam-5812	56	7	the	the	DET
ejpam-5812	56	8	labeling	labeling	NOUN
ejpam-5812	56	9	1	1	NUM
ejpam-5812	56	10	1100	1100	NUM
ejpam-5812	56	11	1100	1100	NUM
ejpam-5812	56	12	...	...	SYM
ejpam-5812	56	13	1100	1100	NUM
ejpam-5812	56	14	(	(	PUNCT
ejpam-5812	56	15	repeated	repeat	VERB
ejpam-5812	56	16	r	r	NOUN
ejpam-5812	56	17	-	-	PUNCT
ejpam-5812	56	18	times	time	NOUN
ejpam-5812	56	19	)	)	PUNCT
ejpam-5812	56	20	when	when	SCONJ
ejpam-5812	56	21	r≥1	r≥1	ADJ
ejpam-5812	56	22	and	and	CCONJ
ejpam-5812	56	23	1	1	NUM
ejpam-5812	56	24	when	when	SCONJ
ejpam-5812	56	25	r=	r=	ADJ
ejpam-5812	56	26	0	0	NUM
ejpam-5812	56	27	.	.	PUNCT
ejpam-5812	57	1	similarly	similarly	ADV
ejpam-5812	57	2	,	,	PUNCT
ejpam-5812	57	3	0l	0l	NUM
ejpam-5812	57	4	′	′	NUM
ejpam-5812	57	5	4r1	4r1	NUM
ejpam-5812	57	6	is	be	AUX
ejpam-5812	57	7	the	the	DET
ejpam-5812	57	8	labeling	labeling	NOUN
ejpam-5812	57	9	0	0	NUM
ejpam-5812	57	10	1100	1100	NUM
ejpam-5812	57	11	1100	1100	NUM
ejpam-5812	57	12	...	...	PUNCT
ejpam-5812	57	13	1100	1100	NUM
ejpam-5812	57	14	1	1	NUM
ejpam-5812	57	15	when	when	SCONJ
ejpam-5812	57	16	r≥1	r≥1	ADV
ejpam-5812	57	17	and	and	CCONJ
ejpam-5812	57	18	01	01	NUM
ejpam-5812	57	19	when	when	SCONJ
ejpam-5812	57	20	r=	r=	ADJ
ejpam-5812	57	21	0	0	NUM
ejpam-5812	57	22	.	.	PUNCT
ejpam-5812	58	1	additional	additional	ADJ
ejpam-5812	58	2	notation	notation	NOUN
ejpam-5812	58	3	that	that	PRON
ejpam-5812	58	4	we	we	PRON
ejpam-5812	58	5	use	use	VERB
ejpam-5812	58	6	the	the	DET
ejpam-5812	58	7	following	following	NOUN
ejpam-5812	58	8	for	for	ADP
ejpam-5812	58	9	a	a	DET
ejpam-5812	58	10	given	give	VERB
ejpam-5812	58	11	labeling	labeling	NOUN
ejpam-5812	58	12	of	of	ADP
ejpam-5812	58	13	the	the	DET
ejpam-5812	58	14	union	union	NOUN
ejpam-5812	58	15	g∪h	g∪h	NOUN
ejpam-5812	58	16	,	,	PUNCT
ejpam-5812	58	17	we	we	PRON
ejpam-5812	58	18	let	let	VERB
ejpam-5812	58	19	vg	vg	NOUN
ejpam-5812	58	20	and	and	CCONJ
ejpam-5812	58	21	vh	vh	PROPN
ejpam-5812	58	22	be	be	AUX
ejpam-5812	58	23	the	the	DET
ejpam-5812	58	24	numbers	number	NOUN
ejpam-5812	58	25	of	of	ADP
ejpam-5812	58	26	vertices	vertex	NOUN
ejpam-5812	58	27	g	g	NOUN
ejpam-5812	58	28	and	and	CCONJ
ejpam-5812	58	29	h	h	NOUN
ejpam-5812	58	30	respectively	respectively	ADV
ejpam-5812	58	31	.	.	PUNCT
ejpam-5812	59	1	also	also	ADV
ejpam-5812	59	2	eg	eg	NOUN
ejpam-5812	59	3	and	and	CCONJ
ejpam-5812	59	4	eh	eh	INTJ
ejpam-5812	59	5	be	be	AUX
ejpam-5812	59	6	the	the	DET
ejpam-5812	59	7	numbers	number	NOUN
ejpam-5812	59	8	of	of	ADP
ejpam-5812	59	9	edges	edge	NOUN
ejpam-5812	59	10	g	g	NOUN
ejpam-5812	59	11	and	and	CCONJ
ejpam-5812	59	12	h	h	NOUN
ejpam-5812	59	13	respectively	respectively	ADV
ejpam-5812	59	14	.	.	PUNCT
ejpam-5812	60	1	it	it	PRON
ejpam-5812	60	2	is	be	AUX
ejpam-5812	60	3	follows	follow	VERB
ejpam-5812	60	4	that	that	SCONJ
ejpam-5812	60	5	vg∪h	vg∪h	NOUN
ejpam-5812	60	6	=	=	SYM
ejpam-5812	60	7	vg+	vg+	NOUN
ejpam-5812	60	8	vh	vh	PROPN
ejpam-5812	60	9	,	,	PUNCT
ejpam-5812	60	10	and	and	CCONJ
ejpam-5812	60	11	eg∪h	eg∪h	VERB
ejpam-5812	60	12	=	=	SYM
ejpam-5812	60	13	eg	eg	PROPN
ejpam-5812	60	14	+	+	CCONJ
ejpam-5812	60	15	eh	eh	INTJ
ejpam-5812	60	16	,	,	PUNCT
ejpam-5812	60	17	for	for	ADP
ejpam-5812	60	18	more	more	ADJ
ejpam-5812	60	19	details	detail	NOUN
ejpam-5812	60	20	see	see	VERB
ejpam-5812	60	21	[	[	X
ejpam-5812	60	22	6	6	NUM
ejpam-5812	60	23	]	]	PUNCT
ejpam-5812	60	24	.	.	PUNCT
ejpam-5812	61	1	moreover	moreover	ADV
ejpam-5812	61	2	,	,	PUNCT
ejpam-5812	61	3	we	we	PRON
ejpam-5812	61	4	used	use	VERB
ejpam-5812	61	5	the	the	DET
ejpam-5812	61	6	symbol	symbol	NOUN
ejpam-5812	61	7	[	[	X
ejpam-5812	61	8	l	l	NOUN
ejpam-5812	61	9	,	,	PUNCT
ejpam-5812	61	10	m	m	VERB
ejpam-5812	61	11	]	]	PUNCT
ejpam-5812	61	12	for	for	ADP
ejpam-5812	61	13	the	the	DET
ejpam-5812	61	14	union	union	NOUN
ejpam-5812	61	15	of	of	ADP
ejpam-5812	61	16	two	two	NUM
ejpam-5812	61	17	graphs	graph	NOUN
ejpam-5812	61	18	g	g	NOUN
ejpam-5812	61	19	and	and	CCONJ
ejpam-5812	61	20	h	h	NOUN
ejpam-5812	61	21	,	,	PUNCT
ejpam-5812	61	22	where	where	SCONJ
ejpam-5812	61	23	l	l	NOUN
ejpam-5812	61	24	is	be	AUX
ejpam-5812	61	25	the	the	DET
ejpam-5812	61	26	labeling	labeling	NOUN
ejpam-5812	61	27	of	of	ADP
ejpam-5812	61	28	g	g	PROPN
ejpam-5812	61	29	and	and	CCONJ
ejpam-5812	61	30	m	m	PROPN
ejpam-5812	61	31	is	be	AUX
ejpam-5812	61	32	the	the	DET
ejpam-5812	61	33	labeling	labeling	NOUN
ejpam-5812	61	34	of	of	ADP
ejpam-5812	61	35	h.	h.	PROPN
ejpam-5812	61	36	3	3	NUM
ejpam-5812	61	37	.	.	PUNCT
ejpam-5812	61	38	cordial	cordial	ADJ
ejpam-5812	61	39	labeling	labeling	NOUN
ejpam-5812	61	40	of	of	ADP
ejpam-5812	61	41	fifth	fifth	ADJ
ejpam-5812	61	42	power	power	NOUN
ejpam-5812	61	43	of	of	ADP
ejpam-5812	61	44	some	some	DET
ejpam-5812	61	45	graphs	graph	NOUN
ejpam-5812	61	46	in	in	ADP
ejpam-5812	61	47	this	this	DET
ejpam-5812	61	48	section	section	NOUN
ejpam-5812	61	49	we	we	PRON
ejpam-5812	61	50	shall	shall	AUX
ejpam-5812	61	51	prove	prove	VERB
ejpam-5812	61	52	that	that	SCONJ
ejpam-5812	61	53	the	the	DET
ejpam-5812	61	54	cordiality	cordiality	NOUN
ejpam-5812	61	55	of	of	ADP
ejpam-5812	61	56	the	the	DET
ejpam-5812	61	57	fifth	fifth	ADJ
ejpam-5812	61	58	power	power	NOUN
ejpam-5812	61	59	of	of	ADP
ejpam-5812	61	60	paths	path	NOUN
ejpam-5812	61	61	,	,	PUNCT
ejpam-5812	61	62	cycles	cycle	NOUN
ejpam-5812	61	63	,	,	PUNCT
ejpam-5812	61	64	fan	fan	NOUN
ejpam-5812	61	65	wheel	wheel	PROPN
ejpam-5812	61	66	and	and	CCONJ
ejpam-5812	61	67	lemniscate	lemniscate	PROPN
ejpam-5812	61	68	graphs	graph	NOUN
ejpam-5812	61	69	.	.	PUNCT
ejpam-5812	62	1	more	more	ADV
ejpam-5812	62	2	over	over	ADV
ejpam-5812	62	3	,	,	PUNCT
ejpam-5812	62	4	we	we	PRON
ejpam-5812	62	5	introduce	introduce	VERB
ejpam-5812	62	6	some	some	DET
ejpam-5812	62	7	illustrate	illustrate	ADJ
ejpam-5812	62	8	examples	example	NOUN
ejpam-5812	62	9	for	for	ADP
ejpam-5812	62	10	each	each	DET
ejpam-5812	62	11	graphs	graph	NOUN
ejpam-5812	62	12	.	.	PUNCT
ejpam-5812	63	1	3.1	3.1	NUM
ejpam-5812	63	2	.	.	PUNCT
ejpam-5812	63	3	cordial	cordial	ADJ
ejpam-5812	63	4	labeling	labeling	NOUN
ejpam-5812	63	5	of	of	ADP
ejpam-5812	63	6	fifth	fifth	ADJ
ejpam-5812	63	7	power	power	NOUN
ejpam-5812	63	8	of	of	ADP
ejpam-5812	63	9	cycles	cycle	NOUN
ejpam-5812	63	10	graphs	graph	NOUN
ejpam-5812	63	11	obviously	obviously	ADV
ejpam-5812	63	12	,	,	PUNCT
ejpam-5812	63	13	the	the	DET
ejpam-5812	63	14	order	order	NOUN
ejpam-5812	63	15	of	of	ADP
ejpam-5812	63	16	c5	c5	PROPN
ejpam-5812	63	17	n	n	PART
ejpam-5812	63	18	is	be	AUX
ejpam-5812	63	19	n	n	CCONJ
ejpam-5812	63	20	,	,	PUNCT
ejpam-5812	63	21	and	and	CCONJ
ejpam-5812	63	22	the	the	DET
ejpam-5812	63	23	size	size	NOUN
ejpam-5812	63	24	of	of	ADP
ejpam-5812	63	25	c5	c5	PROPN
ejpam-5812	63	26	n	n	NUM
ejpam-5812	63	27	is	be	AUX
ejpam-5812	63	28	5n	5n	NUM
ejpam-5812	63	29	−	−	PROPN
ejpam-5812	63	30	14	14	NUM
ejpam-5812	63	31	for	for	ADP
ejpam-5812	63	32	every	every	DET
ejpam-5812	63	33	n	n	NOUN
ejpam-5812	63	34	>	>	X
ejpam-5812	63	35	7	7	NUM
ejpam-5812	63	36	.	.	PUNCT
ejpam-5812	64	1	in	in	ADP
ejpam-5812	64	2	particular	particular	ADJ
ejpam-5812	64	3	,	,	PUNCT
ejpam-5812	64	4	c5	c5	PROPN
ejpam-5812	64	5	3	3	NUM
ejpam-5812	64	6	∼=	∼=	PROPN
ejpam-5812	64	7	c3	c3	NOUN
ejpam-5812	64	8	,	,	PUNCT
ejpam-5812	64	9	c	c	PROPN
ejpam-5812	64	10	5	5	NUM
ejpam-5812	64	11	4	4	NUM
ejpam-5812	64	12	∼=	∼=	NOUN
ejpam-5812	64	13	k4	k4	NOUN
ejpam-5812	64	14	,	,	PUNCT
ejpam-5812	64	15	c	c	NOUN
ejpam-5812	64	16	5	5	NUM
ejpam-5812	64	17	5	5	NUM
ejpam-5812	64	18	∼=	∼=	PROPN
ejpam-5812	64	19	k5	k5	NOUN
ejpam-5812	64	20	,	,	PUNCT
ejpam-5812	64	21	c	c	NOUN
ejpam-5812	64	22	5	5	NUM
ejpam-5812	64	23	6	6	NUM
ejpam-5812	64	24	∼=	∼=	NOUN
ejpam-5812	64	25	k6	k6	NOUN
ejpam-5812	64	26	and	and	CCONJ
ejpam-5812	64	27	c5	c5	PROPN
ejpam-5812	64	28	7	7	NUM
ejpam-5812	64	29	∼=	∼=	PROPN
ejpam-5812	64	30	k7	k7	NOUN
ejpam-5812	64	31	.	.	PUNCT
ejpam-5812	65	1	in	in	ADP
ejpam-5812	65	2	this	this	DET
ejpam-5812	65	3	subsection	subsection	NOUN
ejpam-5812	65	4	,	,	PUNCT
ejpam-5812	65	5	we	we	PRON
ejpam-5812	65	6	show	show	VERB
ejpam-5812	65	7	that	that	SCONJ
ejpam-5812	65	8	the	the	DET
ejpam-5812	65	9	cordiality	cordiality	NOUN
ejpam-5812	65	10	of	of	ADP
ejpam-5812	65	11	c5	c5	PROPN
ejpam-5812	65	12	n	n	CCONJ
ejpam-5812	65	13	if	if	SCONJ
ejpam-5812	65	14	and	and	CCONJ
ejpam-5812	65	15	only	only	ADV
ejpam-5812	65	16	if	if	SCONJ
ejpam-5812	65	17	n	n	PROPN
ejpam-5812	65	18	=	=	SYM
ejpam-5812	65	19	3	3	NUM
ejpam-5812	65	20	,	,	PUNCT
ejpam-5812	65	21	and	and	CCONJ
ejpam-5812	65	22	n	n	CCONJ
ejpam-5812	65	23	>	>	SYM
ejpam-5812	65	24	8	8	NUM
ejpam-5812	65	25	.	.	PUNCT
ejpam-5812	66	1	lemma	lemma	PROPN
ejpam-5812	66	2	3.1.1	3.1.1	NUM
ejpam-5812	66	3	.	.	PUNCT
ejpam-5812	67	1	the	the	DET
ejpam-5812	67	2	fifth	fifth	ADJ
ejpam-5812	67	3	power	power	NOUN
ejpam-5812	67	4	of	of	ADP
ejpam-5812	67	5	cycles	cycle	NOUN
ejpam-5812	67	6	graphs	graph	NOUN
ejpam-5812	67	7	c5	c5	PROPN
ejpam-5812	67	8	n	n	PRON
ejpam-5812	67	9	is	be	AUX
ejpam-5812	67	10	cordial	cordial	ADJ
ejpam-5812	67	11	for	for	ADP
ejpam-5812	67	12	all	all	PRON
ejpam-5812	67	13	n	n	CCONJ
ejpam-5812	67	14	>	>	ADP
ejpam-5812	67	15	8	8	NUM
ejpam-5812	67	16	.	.	PUNCT
ejpam-5812	68	1	proof	proof	NOUN
ejpam-5812	68	2	.	.	PUNCT
ejpam-5812	69	1	let	let	VERB
ejpam-5812	69	2	n=	n=	ADJ
ejpam-5812	69	3	4t+	4t+	ADP
ejpam-5812	69	4	i	i	PRON
ejpam-5812	69	5	(	(	PUNCT
ejpam-5812	69	6	0	0	NUM
ejpam-5812	69	7	≤	≤	NUM
ejpam-5812	69	8	i	i	NOUN
ejpam-5812	69	9	≤	≤	NOUN
ejpam-5812	69	10	3	3	NUM
ejpam-5812	69	11	and	and	CCONJ
ejpam-5812	69	12	t	t	PROPN
ejpam-5812	69	13	≥	≥	NUM
ejpam-5812	69	14	2	2	NUM
ejpam-5812	69	15	)	)	PUNCT
ejpam-5812	69	16	,	,	PUNCT
ejpam-5812	69	17	then	then	ADV
ejpam-5812	69	18	for	for	ADP
ejpam-5812	69	19	a	a	DET
ejpam-5812	69	20	given	give	VERB
ejpam-5812	69	21	value	value	NOUN
ejpam-5812	69	22	of	of	ADP
ejpam-5812	69	23	i	i	PRON
ejpam-5812	69	24	with	with	ADP
ejpam-5812	69	25	0	0	NUM
ejpam-5812	69	26	≤	≤	NUM
ejpam-5812	69	27	i	i	PRON
ejpam-5812	69	28	≤	≤	NOUN
ejpam-5812	69	29	3	3	NUM
ejpam-5812	69	30	,	,	PUNCT
ejpam-5812	69	31	we	we	PRON
ejpam-5812	69	32	use	use	VERB
ejpam-5812	69	33	the	the	DET
ejpam-5812	69	34	labeling	labeling	NOUN
ejpam-5812	69	35	ai	ai	VERB
ejpam-5812	69	36	or	or	CCONJ
ejpam-5812	69	37	a	a	DET
ejpam-5812	69	38	′	′	NUM
ejpam-5812	69	39	i	i	PRON
ejpam-5812	69	40	for	for	ADP
ejpam-5812	69	41	cn	cn	PROPN
ejpam-5812	69	42	as	as	SCONJ
ejpam-5812	69	43	shown	show	VERB
ejpam-5812	69	44	in	in	ADP
ejpam-5812	69	45	table	table	NOUN
ejpam-5812	69	46	1	1	NUM
ejpam-5812	69	47	.	.	PUNCT
ejpam-5812	70	1	it	it	PRON
ejpam-5812	70	2	is	be	AUX
ejpam-5812	70	3	easy	easy	ADJ
ejpam-5812	70	4	to	to	PART
ejpam-5812	70	5	see	see	VERB
ejpam-5812	70	6	that	that	SCONJ
ejpam-5812	70	7	c5	c5	PROPN
ejpam-5812	70	8	n	n	PROPN
ejpam-5812	70	9	for	for	ADP
ejpam-5812	70	10	every	every	DET
ejpam-5812	70	11	n	n	NOUN
ejpam-5812	70	12	>	>	SYM
ejpam-5812	70	13	8	8	NUM
ejpam-5812	70	14	is	be	AUX
ejpam-5812	70	15	cordial	cordial	ADJ
ejpam-5812	70	16	from	from	ADP
ejpam-5812	70	17	the	the	DET
ejpam-5812	70	18	last	last	ADJ
ejpam-5812	70	19	two	two	NUM
ejpam-5812	70	20	columns	column	NOUN
ejpam-5812	70	21	of	of	ADP
ejpam-5812	70	22	the	the	DET
ejpam-5812	70	23	table	table	NOUN
ejpam-5812	70	24	1	1	NUM
ejpam-5812	70	25	and	and	CCONJ
ejpam-5812	70	26	thus	thus	ADV
ejpam-5812	70	27	the	the	DET
ejpam-5812	70	28	lemma	lemma	PROPN
ejpam-5812	70	29	is	be	AUX
ejpam-5812	70	30	proved	prove	VERB
ejpam-5812	70	31	.	.	PUNCT
ejpam-5812	71	1	a.	a.	PROPN
ejpam-5812	71	2	abd	abd	PROPN
ejpam-5812	71	3	el	el	PROPN
ejpam-5812	71	4	-	-	PROPN
ejpam-5812	71	5	hay	hay	PROPN
ejpam-5812	71	6	,	,	PUNCT
ejpam-5812	71	7	k.	k.	PROPN
ejpam-5812	71	8	a.	a.	PROPN
ejpam-5812	71	9	alsatami	alsatami	PROPN
ejpam-5812	71	10	,	,	PUNCT
ejpam-5812	71	11	a.	a.	NOUN
ejpam-5812	71	12	elrokh	elrokh	PROPN
ejpam-5812	71	13	/	/	SYM
ejpam-5812	71	14	eur	eur	PROPN
ejpam-5812	71	15	.	.	PUNCT
ejpam-5812	72	1	j.	j.	PROPN
ejpam-5812	72	2	pure	pure	PROPN
ejpam-5812	72	3	appl	appl	PROPN
ejpam-5812	72	4	.	.	PROPN
ejpam-5812	72	5	math	math	PROPN
ejpam-5812	72	6	,	,	PUNCT
ejpam-5812	72	7	18	18	NUM
ejpam-5812	72	8	(	(	PUNCT
ejpam-5812	72	9	1	1	NUM
ejpam-5812	72	10	)	)	PUNCT
ejpam-5812	72	11	(	(	PUNCT
ejpam-5812	72	12	2025	2025	NUM
ejpam-5812	72	13	)	)	PUNCT
ejpam-5812	72	14	,	,	PUNCT
ejpam-5812	72	15	5812	5812	NUM
ejpam-5812	72	16	4	4	NUM
ejpam-5812	72	17	of	of	ADP
ejpam-5812	72	18	14	14	NUM
ejpam-5812	72	19	table	table	NOUN
ejpam-5812	72	20	1	1	NUM
ejpam-5812	72	21	:	:	PUNCT
ejpam-5812	72	22	labeling	labeling	NOUN
ejpam-5812	72	23	of	of	ADP
ejpam-5812	72	24	c5	c5	PROPN
ejpam-5812	72	25	n.	n.	PROPN
ejpam-5812	72	26	n	n	PROPN
ejpam-5812	72	27	=	=	SYM
ejpam-5812	72	28	4t+	4t+	PROPN
ejpam-5812	73	1	i	i	PRON
ejpam-5812	73	2	,	,	PUNCT
ejpam-5812	73	3	i	i	PRON
ejpam-5812	73	4	=	=	NOUN
ejpam-5812	73	5	0	0	NUM
ejpam-5812	73	6	,	,	PUNCT
ejpam-5812	73	7	1	1	NUM
ejpam-5812	73	8	,	,	PUNCT
ejpam-5812	73	9	2	2	NUM
ejpam-5812	73	10	,	,	PUNCT
ejpam-5812	73	11	3	3	NUM
ejpam-5812	73	12	labeling	labeling	NOUN
ejpam-5812	73	13	of	of	ADP
ejpam-5812	73	14	c5	c5	PROPN
ejpam-5812	73	15	n	n	CCONJ
ejpam-5812	73	16	v0	v0	NOUN
ejpam-5812	73	17	v1	v1	NOUN
ejpam-5812	73	18	e0	e0	PROPN
ejpam-5812	73	19	e1	e1	PROPN
ejpam-5812	73	20	v0	v0	NOUN
ejpam-5812	73	21	−	−	PROPN
ejpam-5812	73	22	v1	v1	PROPN
ejpam-5812	73	23	e0	e0	PROPN
ejpam-5812	73	24	−	−	PROPN
ejpam-5812	73	25	e1	e1	NOUN
ejpam-5812	73	26	i	i	NOUN
ejpam-5812	73	27	=	=	SYM
ejpam-5812	73	28	0	0	NUM
ejpam-5812	73	29	a0	a0	NOUN
ejpam-5812	73	30	=	=	SYM
ejpam-5812	73	31	0l4t120	0l4t120	NUM
ejpam-5812	73	32	2t+	2t+	NUM
ejpam-5812	73	33	2	2	NUM
ejpam-5812	73	34	2t+	2t+	NUM
ejpam-5812	73	35	2	2	NUM
ejpam-5812	73	36	10t+	10t+	NUM
ejpam-5812	73	37	3	3	NUM
ejpam-5812	73	38	10t+	10t+	NUM
ejpam-5812	73	39	3	3	NUM
ejpam-5812	73	40	0	0	NUM
ejpam-5812	73	41	0	0	NUM
ejpam-5812	74	1	i	i	NOUN
ejpam-5812	74	2	=	=	NOUN
ejpam-5812	74	3	1	1	NUM
ejpam-5812	74	4	a1	a1	NOUN
ejpam-5812	74	5	=	=	PUNCT
ejpam-5812	74	6	l4t1	l4t1	PROPN
ejpam-5812	74	7	2	2	NUM
ejpam-5812	74	8	t	t	NOUN
ejpam-5812	74	9	2t+	2t+	NUM
ejpam-5812	74	10	1	1	NUM
ejpam-5812	74	11	10t−	10t−	NUM
ejpam-5812	74	12	5	5	NUM
ejpam-5812	74	13	10t−	10t−	NUM
ejpam-5812	74	14	4	4	NUM
ejpam-5812	74	15	−1	−1	NOUN
ejpam-5812	74	16	−1	−1	NOUN
ejpam-5812	74	17	a	a	DET
ejpam-5812	74	18	′	′	NUM
ejpam-5812	74	19	1	1	NUM
ejpam-5812	74	20	=	=	SYM
ejpam-5812	74	21	12m4t−403	12m4t−403	NUM
ejpam-5812	74	22	2t+	2t+	NUM
ejpam-5812	74	23	1	1	NUM
ejpam-5812	74	24	2	2	NUM
ejpam-5812	74	25	t	t	NOUN
ejpam-5812	74	26	10t−	10t−	NUM
ejpam-5812	74	27	4	4	NUM
ejpam-5812	74	28	10t−	10t−	NUM
ejpam-5812	74	29	5	5	NUM
ejpam-5812	74	30	1	1	NUM
ejpam-5812	74	31	1	1	NUM
ejpam-5812	74	32	i	i	NOUN
ejpam-5812	74	33	=	=	SYM
ejpam-5812	74	34	2	2	NUM
ejpam-5812	74	35	a2	a2	NOUN
ejpam-5812	74	36	=	=	SYM
ejpam-5812	74	37	l	l	NOUN
ejpam-5812	74	38	′	′	NUM
ejpam-5812	74	39	4t10	4t10	NOUN
ejpam-5812	74	40	2t+	2t+	NUM
ejpam-5812	74	41	1	1	NUM
ejpam-5812	74	42	2t+	2t+	NUM
ejpam-5812	74	43	1	1	NUM
ejpam-5812	74	44	10t−	10t−	NUM
ejpam-5812	74	45	2	2	NUM
ejpam-5812	74	46	10t−	10t−	NUM
ejpam-5812	74	47	2	2	NUM
ejpam-5812	74	48	0	0	NUM
ejpam-5812	74	49	0	0	NUM
ejpam-5812	75	1	i	i	NOUN
ejpam-5812	75	2	=	=	SYM
ejpam-5812	75	3	3	3	NUM
ejpam-5812	75	4	a3	a3	NOUN
ejpam-5812	75	5	=	=	SYM
ejpam-5812	76	1	l4t100	l4t100	ADP
ejpam-5812	76	2	2t+	2t+	NUM
ejpam-5812	76	3	2	2	NUM
ejpam-5812	76	4	2t+	2t+	NUM
ejpam-5812	76	5	1	1	NUM
ejpam-5812	76	6	10	10	NUM
ejpam-5812	76	7	t	t	NOUN
ejpam-5812	76	8	10t+	10t+	NUM
ejpam-5812	76	9	1	1	NUM
ejpam-5812	76	10	1	1	NUM
ejpam-5812	76	11	−1	−1	NOUN
ejpam-5812	76	12	a′	a′	NOUN
ejpam-5812	76	13	3	3	NUM
ejpam-5812	76	14	=	=	SYM
ejpam-5812	76	15	11l′	11l′	NUM
ejpam-5812	76	16	4t0	4t0	NUM
ejpam-5812	76	17	2t+	2t+	NUM
ejpam-5812	76	18	1	1	NUM
ejpam-5812	76	19	2t+	2t+	NUM
ejpam-5812	76	20	2	2	NUM
ejpam-5812	76	21	10t+	10t+	NUM
ejpam-5812	76	22	1	1	NUM
ejpam-5812	76	23	10	10	NUM
ejpam-5812	76	24	t	t	NOUN
ejpam-5812	76	25	−1	−1	NOUN
ejpam-5812	76	26	1	1	NUM
ejpam-5812	76	27	example	example	NOUN
ejpam-5812	76	28	3.1.1.the	3.1.1.the	DET
ejpam-5812	76	29	graph	graph	NOUN
ejpam-5812	76	30	c5	c5	PROPN
ejpam-5812	76	31	3	3	NUM
ejpam-5812	76	32	is	be	AUX
ejpam-5812	76	33	cordial	cordial	ADJ
ejpam-5812	76	34	,	,	PUNCT
ejpam-5812	76	35	but	but	CCONJ
ejpam-5812	76	36	the	the	DET
ejpam-5812	76	37	graphs	graph	NOUN
ejpam-5812	76	38	c5	c5	PROPN
ejpam-5812	76	39	n	n	PRON
ejpam-5812	76	40	are	be	AUX
ejpam-5812	76	41	not	not	PART
ejpam-5812	76	42	cordial	cordial	ADJ
ejpam-5812	76	43	for	for	ADP
ejpam-5812	76	44	all	all	DET
ejpam-5812	76	45	4	4	NUM
ejpam-5812	76	46	≤	≤	NOUN
ejpam-5812	76	47	n	n	PRON
ejpam-5812	76	48	≤	≤	NUM
ejpam-5812	76	49	8	8	NUM
ejpam-5812	76	50	.	.	PUNCT
ejpam-5812	77	1	solution	solution	NOUN
ejpam-5812	77	2	.	.	PUNCT
ejpam-5812	78	1	since	since	SCONJ
ejpam-5812	78	2	c5	c5	PROPN
ejpam-5812	78	3	3	3	NUM
ejpam-5812	78	4	∼=	∼=	PROPN
ejpam-5812	78	5	c3	c3	NOUN
ejpam-5812	78	6	and	and	CCONJ
ejpam-5812	78	7	c3	c3	PROPN
ejpam-5812	78	8	is	be	AUX
ejpam-5812	78	9	cordial	cordial	ADJ
ejpam-5812	78	10	[	[	X
ejpam-5812	78	11	3	3	NUM
ejpam-5812	78	12	]	]	PUNCT
ejpam-5812	78	13	,	,	PUNCT
ejpam-5812	78	14	then	then	ADV
ejpam-5812	78	15	c5	c5	PROPN
ejpam-5812	78	16	3	3	NUM
ejpam-5812	78	17	is	be	AUX
ejpam-5812	78	18	cordial	cordial	ADJ
ejpam-5812	78	19	.	.	PUNCT
ejpam-5812	79	1	in	in	ADP
ejpam-5812	79	2	case	case	NOUN
ejpam-5812	79	3	of	of	ADP
ejpam-5812	79	4	4	4	NUM
ejpam-5812	79	5	≤	≤	NOUN
ejpam-5812	79	6	n	n	PRON
ejpam-5812	79	7	≤	≤	NOUN
ejpam-5812	79	8	7	7	NUM
ejpam-5812	79	9	,	,	PUNCT
ejpam-5812	79	10	it	it	PRON
ejpam-5812	79	11	is	be	AUX
ejpam-5812	79	12	easy	easy	ADJ
ejpam-5812	79	13	to	to	PART
ejpam-5812	79	14	verify	verify	VERB
ejpam-5812	79	15	that	that	SCONJ
ejpam-5812	79	16	c5	c5	PROPN
ejpam-5812	79	17	4	4	NUM
ejpam-5812	79	18	∼=	∼=	NOUN
ejpam-5812	79	19	k4	k4	NOUN
ejpam-5812	79	20	,	,	PUNCT
ejpam-5812	79	21	c	c	NOUN
ejpam-5812	79	22	5	5	NUM
ejpam-5812	79	23	5	5	NUM
ejpam-5812	79	24	∼=	∼=	PROPN
ejpam-5812	79	25	k5	k5	NOUN
ejpam-5812	79	26	,	,	PUNCT
ejpam-5812	79	27	c	c	NOUN
ejpam-5812	79	28	5	5	NUM
ejpam-5812	79	29	6	6	NUM
ejpam-5812	79	30	∼=	∼=	NOUN
ejpam-5812	79	31	k6	k6	NOUN
ejpam-5812	79	32	and	and	CCONJ
ejpam-5812	79	33	c5	c5	PROPN
ejpam-5812	79	34	7	7	NUM
ejpam-5812	79	35	∼=	∼=	PROPN
ejpam-5812	79	36	k7	k7	NOUN
ejpam-5812	79	37	are	be	AUX
ejpam-5812	79	38	not	not	PART
ejpam-5812	79	39	cordial	cordial	ADJ
ejpam-5812	79	40	by	by	ADP
ejpam-5812	79	41	cahit	cahit	ADJ
ejpam-5812	80	1	[	[	X
ejpam-5812	80	2	9	9	NUM
ejpam-5812	80	3	]	]	PUNCT
ejpam-5812	80	4	.	.	PUNCT
ejpam-5812	81	1	in	in	ADP
ejpam-5812	81	2	case	case	NOUN
ejpam-5812	81	3	of	of	ADP
ejpam-5812	81	4	n	n	NOUN
ejpam-5812	81	5	=	=	SYM
ejpam-5812	81	6	8	8	NUM
ejpam-5812	81	7	,	,	PUNCT
ejpam-5812	81	8	since	since	SCONJ
ejpam-5812	81	9	n	n	NOUN
ejpam-5812	81	10	=	=	SYM
ejpam-5812	81	11	8	8	NUM
ejpam-5812	81	12	,	,	PUNCT
ejpam-5812	81	13	then	then	ADV
ejpam-5812	81	14	by	by	ADP
ejpam-5812	81	15	investigation	investigation	NOUN
ejpam-5812	81	16	all	all	DET
ejpam-5812	81	17	possible	possible	ADJ
ejpam-5812	81	18	labelings	labeling	NOUN
ejpam-5812	81	19	of	of	ADP
ejpam-5812	81	20	vertices	vertex	NOUN
ejpam-5812	81	21	of	of	ADP
ejpam-5812	81	22	c5	c5	PROPN
ejpam-5812	81	23	8	8	NUM
ejpam-5812	81	24	with	with	ADP
ejpam-5812	81	25	v0	v0	NOUN
ejpam-5812	81	26	=	=	SYM
ejpam-5812	81	27	v1	v1	NOUN
ejpam-5812	81	28	=	=	SYM
ejpam-5812	81	29	4	4	NUM
ejpam-5812	81	30	,	,	PUNCT
ejpam-5812	81	31	we	we	PRON
ejpam-5812	81	32	obtained	obtain	VERB
ejpam-5812	81	33	that	that	PRON
ejpam-5812	81	34	|e0−e1|	|e0−e1|	NOUN
ejpam-5812	81	35	>	>	X
ejpam-5812	81	36	1	1	X
ejpam-5812	81	37	.	.	PUNCT
ejpam-5812	82	1	therefore	therefore	ADV
ejpam-5812	82	2	c5	c5	PROPN
ejpam-5812	82	3	8	8	NUM
ejpam-5812	82	4	is	be	AUX
ejpam-5812	82	5	not	not	PART
ejpam-5812	82	6	cordial	cordial	ADJ
ejpam-5812	82	7	.	.	PUNCT
ejpam-5812	83	1	theorem	theorem	VERB
ejpam-5812	83	2	3.1.1	3.1.1	NUM
ejpam-5812	83	3	.	.	PUNCT
ejpam-5812	84	1	the	the	DET
ejpam-5812	84	2	fifth	fifth	ADJ
ejpam-5812	84	3	power	power	NOUN
ejpam-5812	84	4	of	of	ADP
ejpam-5812	84	5	cycles	cycle	NOUN
ejpam-5812	84	6	graphs	graph	NOUN
ejpam-5812	84	7	c5	c5	PROPN
ejpam-5812	84	8	n	n	PRON
ejpam-5812	84	9	is	be	AUX
ejpam-5812	84	10	cordial	cordial	ADJ
ejpam-5812	84	11	if	if	SCONJ
ejpam-5812	84	12	and	and	CCONJ
ejpam-5812	84	13	only	only	ADV
ejpam-5812	84	14	if	if	SCONJ
ejpam-5812	84	15	n	n	PROPN
ejpam-5812	84	16	=	=	SYM
ejpam-5812	84	17	3	3	NUM
ejpam-5812	84	18	and	and	CCONJ
ejpam-5812	84	19	n	n	ADJ
ejpam-5812	84	20	>	>	ADP
ejpam-5812	84	21	8	8	NUM
ejpam-5812	84	22	.	.	PUNCT
ejpam-5812	85	1	proof	proof	NOUN
ejpam-5812	85	2	.	.	PUNCT
ejpam-5812	86	1	the	the	DET
ejpam-5812	86	2	proof	proof	NOUN
ejpam-5812	86	3	follows	follow	VERB
ejpam-5812	86	4	directly	directly	ADV
ejpam-5812	86	5	from	from	ADP
ejpam-5812	86	6	lemma	lemma	PROPN
ejpam-5812	86	7	3.1.1	3.1.1	NOUN
ejpam-5812	86	8	and	and	CCONJ
ejpam-5812	86	9	example	example	NOUN
ejpam-5812	86	10	3.1.1	3.1.1	NUM
ejpam-5812	86	11	.	.	PUNCT
ejpam-5812	87	1	3.2	3.2	NUM
ejpam-5812	87	2	.	.	PUNCT
ejpam-5812	88	1	cordial	cordial	ADJ
ejpam-5812	88	2	labeling	labeling	NOUN
ejpam-5812	88	3	of	of	ADP
ejpam-5812	88	4	fifth	fifth	ADJ
ejpam-5812	88	5	power	power	NOUN
ejpam-5812	88	6	of	of	ADP
ejpam-5812	88	7	paths	path	NOUN
ejpam-5812	88	8	graphs	graph	NOUN
ejpam-5812	88	9	clearly	clearly	ADV
ejpam-5812	88	10	,	,	PUNCT
ejpam-5812	88	11	the	the	DET
ejpam-5812	88	12	order	order	NOUN
ejpam-5812	88	13	of	of	ADP
ejpam-5812	88	14	p	p	PROPN
ejpam-5812	88	15	5	5	NUM
ejpam-5812	88	16	n	n	NOUN
ejpam-5812	88	17	is	be	AUX
ejpam-5812	88	18	n	n	CCONJ
ejpam-5812	88	19	,	,	PUNCT
ejpam-5812	88	20	and	and	CCONJ
ejpam-5812	88	21	the	the	DET
ejpam-5812	88	22	size	size	NOUN
ejpam-5812	88	23	of	of	ADP
ejpam-5812	88	24	p	p	PROPN
ejpam-5812	88	25	5	5	NUM
ejpam-5812	88	26	n	n	NOUN
ejpam-5812	88	27	is	be	AUX
ejpam-5812	88	28	5n−15	5n−15	NUM
ejpam-5812	88	29	for	for	ADP
ejpam-5812	88	30	every	every	DET
ejpam-5812	88	31	n	n	NOUN
ejpam-5812	88	32	>	>	X
ejpam-5812	88	33	7	7	NUM
ejpam-5812	88	34	.	.	PUNCT
ejpam-5812	89	1	in	in	ADP
ejpam-5812	89	2	particular	particular	ADJ
ejpam-5812	89	3	,	,	PUNCT
ejpam-5812	89	4	p	p	NOUN
ejpam-5812	89	5	5	5	NUM
ejpam-5812	89	6	1	1	NUM
ejpam-5812	89	7	∼=	∼=	PROPN
ejpam-5812	89	8	p1	p1	NOUN
ejpam-5812	89	9	,	,	PUNCT
ejpam-5812	89	10	p	p	NOUN
ejpam-5812	89	11	5	5	NUM
ejpam-5812	89	12	2	2	NUM
ejpam-5812	89	13	∼=	∼=	NOUN
ejpam-5812	89	14	p2	p2	NOUN
ejpam-5812	89	15	,	,	PUNCT
ejpam-5812	89	16	p	p	NOUN
ejpam-5812	89	17	5	5	NUM
ejpam-5812	89	18	3	3	NUM
ejpam-5812	89	19	∼=	∼=	PROPN
ejpam-5812	89	20	c3	c3	NOUN
ejpam-5812	89	21	,	,	PUNCT
ejpam-5812	89	22	p	p	NOUN
ejpam-5812	89	23	5	5	NUM
ejpam-5812	89	24	4	4	NUM
ejpam-5812	89	25	∼=	∼=	NOUN
ejpam-5812	89	26	k4	k4	NOUN
ejpam-5812	89	27	,	,	PUNCT
ejpam-5812	89	28	p	p	NOUN
ejpam-5812	89	29	5	5	NUM
ejpam-5812	89	30	5	5	NUM
ejpam-5812	89	31	∼=	∼=	NOUN
ejpam-5812	89	32	k5	k5	NOUN
ejpam-5812	89	33	and	and	CCONJ
ejpam-5812	89	34	p	p	NOUN
ejpam-5812	89	35	5	5	NUM
ejpam-5812	89	36	6	6	NUM
ejpam-5812	89	37	∼=	∼=	NOUN
ejpam-5812	89	38	k6	k6	NOUN
ejpam-5812	89	39	.	.	PUNCT
ejpam-5812	90	1	in	in	ADP
ejpam-5812	90	2	this	this	DET
ejpam-5812	90	3	subsection	subsection	NOUN
ejpam-5812	90	4	,	,	PUNCT
ejpam-5812	90	5	we	we	PRON
ejpam-5812	90	6	show	show	VERB
ejpam-5812	90	7	that	that	SCONJ
ejpam-5812	90	8	p	p	PROPN
ejpam-5812	90	9	5	5	NUM
ejpam-5812	90	10	n	n	NOUN
ejpam-5812	90	11	is	be	AUX
ejpam-5812	90	12	cordial	cordial	ADJ
ejpam-5812	90	13	if	if	SCONJ
ejpam-5812	90	14	and	and	CCONJ
ejpam-5812	90	15	only	only	ADV
ejpam-5812	90	16	if	if	SCONJ
ejpam-5812	90	17	1	1	NUM
ejpam-5812	90	18	≤	≤	NUM
ejpam-5812	90	19	n	n	PRON
ejpam-5812	90	20	≤	≤	NOUN
ejpam-5812	90	21	3	3	NUM
ejpam-5812	90	22	and	and	CCONJ
ejpam-5812	90	23	n	n	NOUN
ejpam-5812	90	24	>	>	X
ejpam-5812	90	25	7	7	X
ejpam-5812	90	26	.	.	PUNCT
ejpam-5812	91	1	lemma	lemma	PROPN
ejpam-5812	91	2	3.2.1.the	3.2.1.the	NUM
ejpam-5812	91	3	fifth	fifth	ADJ
ejpam-5812	91	4	power	power	NOUN
ejpam-5812	91	5	of	of	ADP
ejpam-5812	91	6	paths	path	NOUN
ejpam-5812	91	7	graphs	graph	VERB
ejpam-5812	91	8	p	p	PROPN
ejpam-5812	91	9	5	5	NUM
ejpam-5812	91	10	n	n	NOUN
ejpam-5812	91	11	is	be	AUX
ejpam-5812	91	12	cordial	cordial	ADJ
ejpam-5812	91	13	for	for	ADP
ejpam-5812	91	14	all	all	PRON
ejpam-5812	91	15	n	n	CCONJ
ejpam-5812	91	16	>	>	ADP
ejpam-5812	91	17	8	8	NUM
ejpam-5812	91	18	.	.	PUNCT
ejpam-5812	92	1	proof	proof	NOUN
ejpam-5812	92	2	.	.	PUNCT
ejpam-5812	93	1	let	let	VERB
ejpam-5812	93	2	n=	n=	ADJ
ejpam-5812	93	3	4t+	4t+	ADP
ejpam-5812	93	4	i	i	PRON
ejpam-5812	93	5	(	(	PUNCT
ejpam-5812	93	6	0	0	NUM
ejpam-5812	93	7	≤	≤	NUM
ejpam-5812	93	8	i	i	NOUN
ejpam-5812	93	9	≤	≤	NOUN
ejpam-5812	93	10	3	3	NUM
ejpam-5812	93	11	and	and	CCONJ
ejpam-5812	93	12	t	t	PROPN
ejpam-5812	93	13	≥	≥	NUM
ejpam-5812	93	14	2	2	NUM
ejpam-5812	93	15	)	)	PUNCT
ejpam-5812	93	16	,	,	PUNCT
ejpam-5812	93	17	then	then	ADV
ejpam-5812	93	18	for	for	ADP
ejpam-5812	93	19	a	a	DET
ejpam-5812	93	20	given	give	VERB
ejpam-5812	93	21	value	value	NOUN
ejpam-5812	93	22	of	of	ADP
ejpam-5812	93	23	i	i	PRON
ejpam-5812	93	24	with	with	ADP
ejpam-5812	93	25	0	0	NUM
ejpam-5812	93	26	≤	≤	NUM
ejpam-5812	93	27	i	i	PRON
ejpam-5812	93	28	≤	≤	NOUN
ejpam-5812	93	29	3	3	NUM
ejpam-5812	93	30	,	,	PUNCT
ejpam-5812	93	31	we	we	PRON
ejpam-5812	93	32	use	use	VERB
ejpam-5812	93	33	the	the	DET
ejpam-5812	93	34	labeling	labeling	NOUN
ejpam-5812	93	35	bi	bi	NOUN
ejpam-5812	93	36	or	or	CCONJ
ejpam-5812	93	37	b	b	NOUN
ejpam-5812	93	38	′	′	NUM
ejpam-5812	93	39	i	i	PRON
ejpam-5812	93	40	for	for	ADP
ejpam-5812	93	41	pn	pn	PROPN
ejpam-5812	93	42	as	as	SCONJ
ejpam-5812	93	43	shown	show	VERB
ejpam-5812	93	44	in	in	ADP
ejpam-5812	93	45	table	table	NOUN
ejpam-5812	93	46	2	2	NUM
ejpam-5812	93	47	.	.	PUNCT
ejpam-5812	94	1	it	it	PRON
ejpam-5812	94	2	is	be	AUX
ejpam-5812	94	3	easy	easy	ADJ
ejpam-5812	94	4	to	to	PART
ejpam-5812	94	5	see	see	VERB
ejpam-5812	94	6	that	that	SCONJ
ejpam-5812	94	7	p	p	PROPN
ejpam-5812	94	8	5	5	NUM
ejpam-5812	94	9	n	n	NOUN
ejpam-5812	94	10	for	for	ADP
ejpam-5812	94	11	every	every	DET
ejpam-5812	94	12	n	n	NOUN
ejpam-5812	94	13	>	>	SYM
ejpam-5812	94	14	8	8	NUM
ejpam-5812	94	15	is	be	AUX
ejpam-5812	94	16	cordial	cordial	ADJ
ejpam-5812	94	17	from	from	ADP
ejpam-5812	94	18	the	the	DET
ejpam-5812	94	19	last	last	ADJ
ejpam-5812	94	20	two	two	NUM
ejpam-5812	94	21	columns	column	NOUN
ejpam-5812	94	22	of	of	ADP
ejpam-5812	94	23	the	the	DET
ejpam-5812	94	24	table	table	NOUN
ejpam-5812	94	25	2	2	NUM
ejpam-5812	94	26	and	and	CCONJ
ejpam-5812	94	27	thus	thus	ADV
ejpam-5812	94	28	the	the	DET
ejpam-5812	94	29	lemma	lemma	PROPN
ejpam-5812	94	30	is	be	AUX
ejpam-5812	94	31	proved	prove	VERB
ejpam-5812	94	32	.	.	PUNCT
ejpam-5812	95	1	table	table	NOUN
ejpam-5812	95	2	2	2	NUM
ejpam-5812	95	3	:	:	PUNCT
ejpam-5812	95	4	labeling	labeling	NOUN
ejpam-5812	95	5	of	of	ADP
ejpam-5812	95	6	p	p	PROPN
ejpam-5812	95	7	5	5	NUM
ejpam-5812	95	8	n	n	NOUN
ejpam-5812	95	9	.	.	PUNCT
ejpam-5812	96	1	n	n	NOUN
ejpam-5812	96	2	=	=	SYM
ejpam-5812	96	3	4t+	4t+	PROPN
ejpam-5812	97	1	i	i	NOUN
ejpam-5812	97	2	,	,	PUNCT
ejpam-5812	97	3	n	n	PROPN
ejpam-5812	97	4	>	>	X
ejpam-5812	97	5	8	8	NUM
ejpam-5812	98	1	i	i	NOUN
ejpam-5812	98	2	=	=	NOUN
ejpam-5812	98	3	0	0	NUM
ejpam-5812	98	4	,	,	PUNCT
ejpam-5812	98	5	1	1	NUM
ejpam-5812	98	6	,	,	PUNCT
ejpam-5812	98	7	2	2	NUM
ejpam-5812	98	8	,	,	PUNCT
ejpam-5812	98	9	3	3	NUM
ejpam-5812	98	10	labeling	labeling	NOUN
ejpam-5812	98	11	of	of	ADP
ejpam-5812	98	12	p	p	PROPN
ejpam-5812	98	13	5	5	NUM
ejpam-5812	98	14	n	n	PRON
ejpam-5812	98	15	v0	v0	NOUN
ejpam-5812	98	16	v1	v1	NOUN
ejpam-5812	98	17	e0	e0	PROPN
ejpam-5812	98	18	e1	e1	PROPN
ejpam-5812	98	19	v0	v0	NOUN
ejpam-5812	98	20	−	−	PROPN
ejpam-5812	98	21	v1	v1	PROPN
ejpam-5812	98	22	e0	e0	PROPN
ejpam-5812	98	23	−	−	PROPN
ejpam-5812	98	24	e1	e1	VERB
ejpam-5812	98	25	i=	i=	PROPN
ejpam-5812	98	26	0	0	PUNCT
ejpam-5812	99	1	b0=	b0=	NOUN
ejpam-5812	99	2	0l4t120	0l4t120	NUM
ejpam-5812	99	3	2	2	NUM
ejpam-5812	99	4	t	t	NOUN
ejpam-5812	99	5	2	2	NUM
ejpam-5812	99	6	t	t	NOUN
ejpam-5812	99	7	10t+	10t+	NUM
ejpam-5812	99	8	2	2	NUM
ejpam-5812	99	9	10t+	10t+	NUM
ejpam-5812	99	10	3	3	NUM
ejpam-5812	99	11	0	0	NUM
ejpam-5812	99	12	1	1	NUM
ejpam-5812	99	13	i=	i=	NUM
ejpam-5812	99	14	1	1	NUM
ejpam-5812	99	15	b1	b1	NOUN
ejpam-5812	99	16	=	=	NOUN
ejpam-5812	99	17	l4t1	l4t1	PROPN
ejpam-5812	99	18	2	2	NUM
ejpam-5812	99	19	t	t	NOUN
ejpam-5812	99	20	2t+	2t+	NUM
ejpam-5812	99	21	1	1	NUM
ejpam-5812	99	22	10t−	10t−	NUM
ejpam-5812	99	23	5	5	NUM
ejpam-5812	99	24	10t−	10t−	NUM
ejpam-5812	99	25	5	5	NUM
ejpam-5812	99	26	−1	−1	NOUN
ejpam-5812	99	27	0	0	PUNCT
ejpam-5812	99	28	i=	i=	PROPN
ejpam-5812	99	29	2	2	NUM
ejpam-5812	99	30	b2	b2	NOUN
ejpam-5812	99	31	=	=	NOUN
ejpam-5812	99	32	l	l	NOUN
ejpam-5812	99	33	′	′	NUM
ejpam-5812	99	34	4t10	4t10	NOUN
ejpam-5812	99	35	2t+	2t+	NUM
ejpam-5812	99	36	1	1	NUM
ejpam-5812	99	37	2t+	2t+	NUM
ejpam-5812	99	38	1	1	NUM
ejpam-5812	99	39	10t−	10t−	NUM
ejpam-5812	99	40	2	2	NUM
ejpam-5812	99	41	10t−	10t−	NUM
ejpam-5812	99	42	3	3	NUM
ejpam-5812	99	43	0	0	NUM
ejpam-5812	99	44	1	1	NUM
ejpam-5812	99	45	i=	i=	PROPN
ejpam-5812	99	46	3	3	NUM
ejpam-5812	99	47	b3	b3	NOUN
ejpam-5812	99	48	=	=	SYM
ejpam-5812	99	49	l	l	NOUN
ejpam-5812	99	50	′	′	NUM
ejpam-5812	100	1	4t010	4t010	NUM
ejpam-5812	100	2	2t+	2t+	NUM
ejpam-5812	100	3	2	2	NUM
ejpam-5812	100	4	2t+	2t+	NUM
ejpam-5812	100	5	1	1	NUM
ejpam-5812	100	6	10	10	NUM
ejpam-5812	100	7	t	t	NOUN
ejpam-5812	100	8	10	10	NUM
ejpam-5812	100	9	t	t	PROPN
ejpam-5812	100	10	1	1	NUM
ejpam-5812	100	11	0	0	NUM
ejpam-5812	100	12	b′	b′	NUM
ejpam-5812	100	13	3=	3=	NUM
ejpam-5812	100	14	010l4	010l4	NUM
ejpam-5812	100	15	t	t	NOUN
ejpam-5812	100	16	2t+	2t+	NUM
ejpam-5812	100	17	2	2	NUM
ejpam-5812	100	18	2t+	2t+	NUM
ejpam-5812	100	19	1	1	NUM
ejpam-5812	100	20	10	10	NUM
ejpam-5812	100	21	t	t	NOUN
ejpam-5812	100	22	10	10	NUM
ejpam-5812	100	23	t	t	PROPN
ejpam-5812	100	24	1	1	NUM
ejpam-5812	100	25	0	0	NUM
ejpam-5812	100	26	a.	a.	PROPN
ejpam-5812	100	27	abd	abd	PROPN
ejpam-5812	100	28	el	el	PROPN
ejpam-5812	100	29	-	-	PROPN
ejpam-5812	100	30	hay	hay	PROPN
ejpam-5812	100	31	,	,	PUNCT
ejpam-5812	100	32	k.	k.	PROPN
ejpam-5812	100	33	a.	a.	PROPN
ejpam-5812	100	34	alsatami	alsatami	PROPN
ejpam-5812	100	35	,	,	PUNCT
ejpam-5812	100	36	a.	a.	NOUN
ejpam-5812	100	37	elrokh	elrokh	PROPN
ejpam-5812	100	38	/	/	SYM
ejpam-5812	100	39	eur	eur	PROPN
ejpam-5812	100	40	.	.	PUNCT
ejpam-5812	101	1	j.	j.	PROPN
ejpam-5812	101	2	pure	pure	PROPN
ejpam-5812	101	3	appl	appl	PROPN
ejpam-5812	101	4	.	.	PROPN
ejpam-5812	101	5	math	math	PROPN
ejpam-5812	101	6	,	,	PUNCT
ejpam-5812	101	7	18	18	NUM
ejpam-5812	101	8	(	(	PUNCT
ejpam-5812	101	9	1	1	NUM
ejpam-5812	101	10	)	)	PUNCT
ejpam-5812	101	11	(	(	PUNCT
ejpam-5812	101	12	2025	2025	NUM
ejpam-5812	101	13	)	)	PUNCT
ejpam-5812	101	14	,	,	PUNCT
ejpam-5812	101	15	5812	5812	NUM
ejpam-5812	101	16	5	5	NUM
ejpam-5812	101	17	of	of	ADP
ejpam-5812	101	18	14	14	NUM
ejpam-5812	101	19	example	example	NOUN
ejpam-5812	101	20	3.2.1	3.2.1	NUM
ejpam-5812	101	21	.	.	PUNCT
ejpam-5812	102	1	the	the	DET
ejpam-5812	102	2	graphs	graph	NOUN
ejpam-5812	102	3	p	p	X
ejpam-5812	102	4	5	5	NUM
ejpam-5812	102	5	1	1	NUM
ejpam-5812	102	6	,	,	PUNCT
ejpam-5812	102	7	p	p	NOUN
ejpam-5812	102	8	5	5	NUM
ejpam-5812	102	9	2	2	NUM
ejpam-5812	102	10	,	,	PUNCT
ejpam-5812	102	11	p	p	NOUN
ejpam-5812	102	12	5	5	NUM
ejpam-5812	102	13	3	3	NUM
ejpam-5812	102	14	and	and	CCONJ
ejpam-5812	102	15	p	p	NOUN
ejpam-5812	102	16	5	5	NUM
ejpam-5812	102	17	8	8	NUM
ejpam-5812	102	18	are	be	AUX
ejpam-5812	102	19	cordial	cordial	ADJ
ejpam-5812	102	20	,	,	PUNCT
ejpam-5812	102	21	but	but	CCONJ
ejpam-5812	102	22	the	the	DET
ejpam-5812	102	23	graphs	graph	NOUN
ejpam-5812	102	24	p	p	NOUN
ejpam-5812	102	25	5	5	NUM
ejpam-5812	102	26	n	n	NOUN
ejpam-5812	102	27	are	be	AUX
ejpam-5812	102	28	not	not	PART
ejpam-5812	102	29	cordial	cordial	ADJ
ejpam-5812	102	30	for	for	ADP
ejpam-5812	102	31	all	all	DET
ejpam-5812	102	32	4	4	NUM
ejpam-5812	102	33	≤	≤	NOUN
ejpam-5812	102	34	n	n	PRON
ejpam-5812	102	35	≤	≤	NUM
ejpam-5812	102	36	7	7	NUM
ejpam-5812	102	37	.	.	PUNCT
ejpam-5812	102	38	solution	solution	NOUN
ejpam-5812	102	39	.	.	PUNCT
ejpam-5812	103	1	since	since	SCONJ
ejpam-5812	103	2	p	p	NOUN
ejpam-5812	103	3	5	5	NUM
ejpam-5812	103	4	1	1	NUM
ejpam-5812	103	5	∼=	∼=	PROPN
ejpam-5812	103	6	p1	p1	NOUN
ejpam-5812	103	7	,	,	PUNCT
ejpam-5812	103	8	p	p	NOUN
ejpam-5812	103	9	5	5	NUM
ejpam-5812	103	10	2	2	NUM
ejpam-5812	103	11	∼=	∼=	NOUN
ejpam-5812	103	12	p2	p2	NOUN
ejpam-5812	103	13	,	,	PUNCT
ejpam-5812	103	14	p	p	NOUN
ejpam-5812	103	15	5	5	NUM
ejpam-5812	103	16	3	3	NUM
ejpam-5812	103	17	∼=	∼=	PROPN
ejpam-5812	103	18	c3	c3	NOUN
ejpam-5812	103	19	,	,	PUNCT
ejpam-5812	103	20	p	p	NOUN
ejpam-5812	103	21	5	5	NUM
ejpam-5812	103	22	8	8	NUM
ejpam-5812	103	23	the	the	DET
ejpam-5812	103	24	labeling	labeling	NOUN
ejpam-5812	103	25	[	[	X
ejpam-5812	103	26	0414	0414	NUM
ejpam-5812	103	27	]	]	PUNCT
ejpam-5812	103	28	is	be	AUX
ejpam-5812	103	29	sufficient	sufficient	ADJ
ejpam-5812	103	30	for	for	ADP
ejpam-5812	103	31	p	p	PROPN
ejpam-5812	103	32	5	5	NUM
ejpam-5812	103	33	8	8	NUM
ejpam-5812	103	34	and	and	CCONJ
ejpam-5812	103	35	p1	p1	NOUN
ejpam-5812	103	36	,	,	PUNCT
ejpam-5812	103	37	p2	p2	PROPN
ejpam-5812	103	38	and	and	CCONJ
ejpam-5812	103	39	c3	c3	PROPN
ejpam-5812	103	40	are	be	AUX
ejpam-5812	103	41	cordial	cordial	ADJ
ejpam-5812	104	1	[	[	X
ejpam-5812	104	2	3	3	NUM
ejpam-5812	104	3	]	]	PUNCT
ejpam-5812	104	4	,	,	PUNCT
ejpam-5812	104	5	then	then	ADV
ejpam-5812	104	6	p	p	X
ejpam-5812	104	7	5	5	NUM
ejpam-5812	104	8	1	1	NUM
ejpam-5812	104	9	,	,	PUNCT
ejpam-5812	104	10	p	p	NOUN
ejpam-5812	104	11	5	5	NUM
ejpam-5812	104	12	2	2	NUM
ejpam-5812	104	13	and	and	CCONJ
ejpam-5812	104	14	p	p	NOUN
ejpam-5812	104	15	5	5	NUM
ejpam-5812	104	16	3	3	NUM
ejpam-5812	104	17	are	be	AUX
ejpam-5812	104	18	cordial	cordial	ADJ
ejpam-5812	104	19	.	.	PUNCT
ejpam-5812	105	1	in	in	ADP
ejpam-5812	105	2	case	case	NOUN
ejpam-5812	105	3	of	of	ADP
ejpam-5812	105	4	4	4	NUM
ejpam-5812	105	5	≤	≤	NOUN
ejpam-5812	105	6	n	n	PRON
ejpam-5812	105	7	≤	≤	NOUN
ejpam-5812	105	8	7	7	NUM
ejpam-5812	105	9	,	,	PUNCT
ejpam-5812	105	10	it	it	PRON
ejpam-5812	105	11	is	be	AUX
ejpam-5812	105	12	easy	easy	ADJ
ejpam-5812	105	13	to	to	PART
ejpam-5812	105	14	verify	verify	VERB
ejpam-5812	105	15	that	that	SCONJ
ejpam-5812	105	16	p	p	NOUN
ejpam-5812	105	17	5	5	NUM
ejpam-5812	105	18	4	4	NUM
ejpam-5812	105	19	∼=	∼=	NOUN
ejpam-5812	105	20	k4	k4	NOUN
ejpam-5812	105	21	,	,	PUNCT
ejpam-5812	105	22	p	p	NOUN
ejpam-5812	105	23	5	5	NUM
ejpam-5812	105	24	5	5	NUM
ejpam-5812	105	25	∼=	∼=	NOUN
ejpam-5812	105	26	k5	k5	NOUN
ejpam-5812	105	27	,	,	PUNCT
ejpam-5812	105	28	p	p	NOUN
ejpam-5812	105	29	5	5	NUM
ejpam-5812	105	30	6	6	NUM
ejpam-5812	105	31	∼=	∼=	NOUN
ejpam-5812	105	32	k6	k6	NOUN
ejpam-5812	105	33	are	be	AUX
ejpam-5812	105	34	not	not	PART
ejpam-5812	105	35	cordial	cordial	ADJ
ejpam-5812	105	36	by	by	ADP
ejpam-5812	105	37	cahit	cahit	ADJ
ejpam-5812	106	1	[	[	X
ejpam-5812	106	2	9	9	NUM
ejpam-5812	106	3	]	]	PUNCT
ejpam-5812	106	4	.	.	PUNCT
ejpam-5812	107	1	since	since	SCONJ
ejpam-5812	107	2	n	n	NOUN
ejpam-5812	107	3	=	=	SYM
ejpam-5812	107	4	7	7	NUM
ejpam-5812	107	5	,	,	PUNCT
ejpam-5812	107	6	then	then	ADV
ejpam-5812	107	7	by	by	ADP
ejpam-5812	107	8	investigation	investigation	NOUN
ejpam-5812	107	9	all	all	DET
ejpam-5812	107	10	possible	possible	ADJ
ejpam-5812	107	11	labelings	labeling	NOUN
ejpam-5812	107	12	of	of	ADP
ejpam-5812	107	13	vertices	vertex	NOUN
ejpam-5812	107	14	of	of	ADP
ejpam-5812	107	15	p	p	PROPN
ejpam-5812	107	16	5	5	NUM
ejpam-5812	107	17	7	7	NUM
ejpam-5812	107	18	with	with	ADP
ejpam-5812	107	19	v0	v0	NOUN
ejpam-5812	107	20	=	=	SYM
ejpam-5812	107	21	3	3	NUM
ejpam-5812	107	22	,	,	PUNCT
ejpam-5812	107	23	v1	v1	NOUN
ejpam-5812	107	24	=	=	SYM
ejpam-5812	107	25	4	4	NUM
ejpam-5812	107	26	or	or	CCONJ
ejpam-5812	107	27	v0	v0	NOUN
ejpam-5812	107	28	=	=	SYM
ejpam-5812	107	29	4	4	NUM
ejpam-5812	107	30	,	,	PUNCT
ejpam-5812	107	31	v1	v1	NOUN
ejpam-5812	107	32	=	=	SYM
ejpam-5812	107	33	3	3	NUM
ejpam-5812	107	34	,	,	PUNCT
ejpam-5812	107	35	we	we	PRON
ejpam-5812	107	36	obtained	obtain	VERB
ejpam-5812	107	37	that	that	DET
ejpam-5812	107	38	|e0	|e0	NOUN
ejpam-5812	107	39	−	−	PROPN
ejpam-5812	107	40	e1|	e1|	PROPN
ejpam-5812	107	41	>	>	X
ejpam-5812	108	1	1	1	X
ejpam-5812	108	2	.	.	PUNCT
ejpam-5812	108	3	therefore	therefore	ADV
ejpam-5812	108	4	p	p	X
ejpam-5812	108	5	5	5	NUM
ejpam-5812	108	6	8	8	NUM
ejpam-5812	108	7	is	be	AUX
ejpam-5812	108	8	not	not	PART
ejpam-5812	108	9	cordial	cordial	ADJ
ejpam-5812	108	10	theorem	theorem	NOUN
ejpam-5812	108	11	3.2.1	3.2.1	NUM
ejpam-5812	108	12	.	.	PUNCT
ejpam-5812	109	1	the	the	DET
ejpam-5812	109	2	fifth	fifth	ADJ
ejpam-5812	109	3	power	power	NOUN
ejpam-5812	109	4	of	of	ADP
ejpam-5812	109	5	paths	path	NOUN
ejpam-5812	109	6	graphs	graph	VERB
ejpam-5812	109	7	p	p	PROPN
ejpam-5812	109	8	5	5	NUM
ejpam-5812	109	9	n	n	NOUN
ejpam-5812	109	10	are	be	AUX
ejpam-5812	109	11	cordial	cordial	ADJ
ejpam-5812	109	12	if	if	SCONJ
ejpam-5812	109	13	and	and	CCONJ
ejpam-5812	109	14	only	only	ADV
ejpam-5812	109	15	if	if	SCONJ
ejpam-5812	109	16	1	1	NUM
ejpam-5812	109	17	≤	≤	NUM
ejpam-5812	109	18	n	n	PRON
ejpam-5812	109	19	≤	≤	NOUN
ejpam-5812	109	20	3	3	NUM
ejpam-5812	109	21	and	and	CCONJ
ejpam-5812	109	22	n	n	NOUN
ejpam-5812	109	23	>	>	X
ejpam-5812	109	24	7	7	X
ejpam-5812	109	25	.	.	PUNCT
ejpam-5812	110	1	proof.the	proof.the	DET
ejpam-5812	110	2	proof	proof	NOUN
ejpam-5812	110	3	follows	follow	VERB
ejpam-5812	110	4	directly	directly	ADV
ejpam-5812	110	5	from	from	ADP
ejpam-5812	110	6	lemma	lemma	PROPN
ejpam-5812	110	7	3.2.1	3.2.1	NUM
ejpam-5812	110	8	and	and	CCONJ
ejpam-5812	110	9	example	example	NOUN
ejpam-5812	110	10	3.2.1	3.2.1	NUM
ejpam-5812	110	11	.	.	X
ejpam-5812	110	12	3.3	3.3	NUM
ejpam-5812	110	13	.	.	PUNCT
ejpam-5812	111	1	cordial	cordial	ADJ
ejpam-5812	111	2	labeling	labeling	NOUN
ejpam-5812	111	3	of	of	ADP
ejpam-5812	111	4	fifth	fifth	ADJ
ejpam-5812	111	5	power	power	NOUN
ejpam-5812	111	6	of	of	ADP
ejpam-5812	111	7	wheals	wheal	NOUN
ejpam-5812	111	8	graphs	graph	NOUN
ejpam-5812	111	9	obviously	obviously	ADV
ejpam-5812	111	10	,	,	PUNCT
ejpam-5812	111	11	the	the	DET
ejpam-5812	111	12	order	order	NOUN
ejpam-5812	111	13	of	of	ADP
ejpam-5812	111	14	w	w	PROPN
ejpam-5812	111	15	5	5	NUM
ejpam-5812	111	16	n+1	n+1	PROPN
ejpam-5812	111	17	is	be	AUX
ejpam-5812	111	18	n+1	n+1	PROPN
ejpam-5812	111	19	,	,	PUNCT
ejpam-5812	111	20	and	and	CCONJ
ejpam-5812	111	21	the	the	DET
ejpam-5812	111	22	size	size	NOUN
ejpam-5812	111	23	of	of	ADP
ejpam-5812	111	24	w	w	PROPN
ejpam-5812	111	25	5	5	NUM
ejpam-5812	111	26	n+1	n+1	PROPN
ejpam-5812	111	27	is	be	AUX
ejpam-5812	111	28	6n−	6n−	NUM
ejpam-5812	111	29	14	14	NUM
ejpam-5812	111	30	for	for	ADP
ejpam-5812	111	31	every	every	DET
ejpam-5812	111	32	n	n	NOUN
ejpam-5812	111	33	>	>	X
ejpam-5812	111	34	7	7	NUM
ejpam-5812	111	35	.	.	PUNCT
ejpam-5812	112	1	in	in	ADP
ejpam-5812	112	2	particular	particular	ADJ
ejpam-5812	112	3	,	,	PUNCT
ejpam-5812	112	4	w	w	PROPN
ejpam-5812	112	5	5	5	NUM
ejpam-5812	112	6	4	4	NUM
ejpam-5812	112	7	∼=	∼=	VERB
ejpam-5812	112	8	k4,w	k4,w	PROPN
ejpam-5812	112	9	5	5	NUM
ejpam-5812	112	10	5	5	NUM
ejpam-5812	112	11	∼=	∼=	ADP
ejpam-5812	112	12	k5,w	k5,w	PROPN
ejpam-5812	112	13	5	5	NUM
ejpam-5812	112	14	6	6	NUM
ejpam-5812	112	15	∼=	∼=	NOUN
ejpam-5812	112	16	k6,w	k6,w	NOUN
ejpam-5812	112	17	5	5	NUM
ejpam-5812	112	18	7	7	NUM
ejpam-5812	112	19	∼=	∼=	PROPN
ejpam-5812	112	20	k7	k7	PROPN
ejpam-5812	112	21	and	and	CCONJ
ejpam-5812	112	22	w	w	NOUN
ejpam-5812	112	23	5	5	NUM
ejpam-5812	112	24	8	8	NUM
ejpam-5812	112	25	∼=	∼=	NOUN
ejpam-5812	112	26	k8	k8	NOUN
ejpam-5812	112	27	.	.	PUNCT
ejpam-5812	113	1	in	in	ADP
ejpam-5812	113	2	this	this	DET
ejpam-5812	113	3	subsection	subsection	NOUN
ejpam-5812	113	4	,	,	PUNCT
ejpam-5812	113	5	we	we	PRON
ejpam-5812	113	6	show	show	VERB
ejpam-5812	113	7	that	that	SCONJ
ejpam-5812	113	8	w	w	NOUN
ejpam-5812	113	9	5	5	NUM
ejpam-5812	113	10	n+1	n+1	PROPN
ejpam-5812	113	11	is	be	AUX
ejpam-5812	113	12	cordial	cordial	ADJ
ejpam-5812	113	13	if	if	SCONJ
ejpam-5812	113	14	and	and	CCONJ
ejpam-5812	113	15	only	only	ADV
ejpam-5812	113	16	if	if	SCONJ
ejpam-5812	113	17	n≥	n≥	PROPN
ejpam-5812	113	18	3	3	NUM
ejpam-5812	113	19	except	except	SCONJ
ejpam-5812	113	20	3	3	NUM
ejpam-5812	113	21	≤	≤	NOUN
ejpam-5812	113	22	n	n	PRON
ejpam-5812	113	23	≤	≤	NUM
ejpam-5812	113	24	8	8	NUM
ejpam-5812	113	25	.	.	PUNCT
ejpam-5812	113	26	theorem	theorem	VERB
ejpam-5812	113	27	3.3.1	3.3.1	PROPN
ejpam-5812	113	28	.	.	PUNCT
ejpam-5812	114	1	the	the	DET
ejpam-5812	114	2	fifth	fifth	ADJ
ejpam-5812	114	3	power	power	NOUN
ejpam-5812	114	4	of	of	ADP
ejpam-5812	114	5	wheals	wheal	NOUN
ejpam-5812	114	6	graphs	graph	NOUN
ejpam-5812	114	7	w	w	ADP
ejpam-5812	114	8	5	5	NUM
ejpam-5812	114	9	n+1=	n+1=	PROPN
ejpam-5812	114	10	p	p	NOUN
ejpam-5812	114	11	1+c5	1+c5	PROPN
ejpam-5812	114	12	n	n	NOUN
ejpam-5812	114	13	are	be	AUX
ejpam-5812	114	14	cordial	cordial	ADJ
ejpam-5812	114	15	if	if	SCONJ
ejpam-5812	114	16	and	and	CCONJ
ejpam-5812	114	17	only	only	ADV
ejpam-5812	114	18	if	if	SCONJ
ejpam-5812	114	19	n≥	n≥	PROPN
ejpam-5812	114	20	3	3	NUM
ejpam-5812	114	21	except	except	SCONJ
ejpam-5812	114	22	3	3	NUM
ejpam-5812	114	23	≤	≤	NOUN
ejpam-5812	114	24	n	n	PRON
ejpam-5812	114	25	≤	≤	NOUN
ejpam-5812	114	26	8	8	NUM
ejpam-5812	114	27	.	.	PUNCT
ejpam-5812	115	1	proof	proof	NOUN
ejpam-5812	115	2	.	.	PUNCT
ejpam-5812	116	1	in	in	ADP
ejpam-5812	116	2	case	case	NOUN
ejpam-5812	116	3	of	of	ADP
ejpam-5812	116	4	3	3	NUM
ejpam-5812	116	5	≤	≤	NOUN
ejpam-5812	116	6	n	n	PRON
ejpam-5812	116	7	≤	≤	NOUN
ejpam-5812	116	8	7	7	NUM
ejpam-5812	116	9	,	,	PUNCT
ejpam-5812	116	10	it	it	PRON
ejpam-5812	116	11	is	be	AUX
ejpam-5812	116	12	easy	easy	ADJ
ejpam-5812	116	13	to	to	PART
ejpam-5812	116	14	verify	verify	VERB
ejpam-5812	116	15	that	that	SCONJ
ejpam-5812	116	16	w	w	NOUN
ejpam-5812	116	17	5	5	NUM
ejpam-5812	116	18	4	4	NUM
ejpam-5812	116	19	∼=	∼=	VERB
ejpam-5812	116	20	k4,w	k4,w	PROPN
ejpam-5812	116	21	5	5	NUM
ejpam-5812	116	22	5	5	NUM
ejpam-5812	116	23	∼=	∼=	ADP
ejpam-5812	116	24	k5,w	k5,w	PROPN
ejpam-5812	116	25	5	5	NUM
ejpam-5812	116	26	6	6	NUM
ejpam-5812	116	27	∼=	∼=	NOUN
ejpam-5812	116	28	k6,w	k6,w	NOUN
ejpam-5812	116	29	5	5	NUM
ejpam-5812	116	30	7	7	NUM
ejpam-5812	116	31	∼=	∼=	PROPN
ejpam-5812	116	32	k7	k7	PROPN
ejpam-5812	116	33	and	and	CCONJ
ejpam-5812	116	34	w	w	NOUN
ejpam-5812	116	35	5	5	NUM
ejpam-5812	116	36	8	8	NUM
ejpam-5812	116	37	∼=	∼=	PROPN
ejpam-5812	116	38	k8	k8	NOUN
ejpam-5812	116	39	are	be	AUX
ejpam-5812	116	40	not	not	PART
ejpam-5812	116	41	cordial	cordial	ADJ
ejpam-5812	116	42	by	by	ADP
ejpam-5812	116	43	cahit	cahit	ADJ
ejpam-5812	117	1	[	[	X
ejpam-5812	117	2	3	3	NUM
ejpam-5812	117	3	]	]	PUNCT
ejpam-5812	117	4	.	.	PUNCT
ejpam-5812	118	1	since	since	SCONJ
ejpam-5812	118	2	n	n	NOUN
ejpam-5812	118	3	=	=	SYM
ejpam-5812	118	4	8	8	NUM
ejpam-5812	118	5	,	,	PUNCT
ejpam-5812	118	6	then	then	ADV
ejpam-5812	118	7	by	by	ADP
ejpam-5812	118	8	investigation	investigation	NOUN
ejpam-5812	118	9	all	all	DET
ejpam-5812	118	10	possible	possible	ADJ
ejpam-5812	118	11	labelings	labeling	NOUN
ejpam-5812	118	12	of	of	ADP
ejpam-5812	118	13	vertices	vertex	NOUN
ejpam-5812	118	14	of	of	ADP
ejpam-5812	118	15	w	w	NOUN
ejpam-5812	118	16	5	5	NUM
ejpam-5812	118	17	9	9	NUM
ejpam-5812	118	18	with	with	ADP
ejpam-5812	118	19	v0	v0	NOUN
ejpam-5812	118	20	=	=	SYM
ejpam-5812	118	21	5	5	NUM
ejpam-5812	118	22	,	,	PUNCT
ejpam-5812	118	23	v1	v1	NOUN
ejpam-5812	118	24	=	=	SYM
ejpam-5812	118	25	4	4	NUM
ejpam-5812	118	26	or	or	CCONJ
ejpam-5812	118	27	v0	v0	NOUN
ejpam-5812	118	28	=	=	SYM
ejpam-5812	118	29	4	4	NUM
ejpam-5812	118	30	,	,	PUNCT
ejpam-5812	118	31	v1	v1	NOUN
ejpam-5812	118	32	=	=	SYM
ejpam-5812	118	33	5	5	NUM
ejpam-5812	118	34	,	,	PUNCT
ejpam-5812	118	35	we	we	PRON
ejpam-5812	118	36	obtained	obtain	VERB
ejpam-5812	118	37	that	that	DET
ejpam-5812	118	38	|e0	|e0	NOUN
ejpam-5812	118	39	−	−	PROPN
ejpam-5812	118	40	e1|	e1|	PROPN
ejpam-5812	118	41	>	>	X
ejpam-5812	119	1	1	1	X
ejpam-5812	119	2	.	.	PUNCT
ejpam-5812	119	3	therefore	therefore	ADV
ejpam-5812	119	4	w	w	NOUN
ejpam-5812	119	5	5	5	NUM
ejpam-5812	119	6	9	9	NUM
ejpam-5812	119	7	is	be	AUX
ejpam-5812	119	8	not	not	PART
ejpam-5812	119	9	cordial	cordial	ADJ
ejpam-5812	119	10	.	.	PUNCT
ejpam-5812	120	1	in	in	ADP
ejpam-5812	120	2	case	case	NOUN
ejpam-5812	120	3	of	of	ADP
ejpam-5812	120	4	n	n	PRON
ejpam-5812	120	5	≥	≥	NUM
ejpam-5812	120	6	9	9	NUM
ejpam-5812	120	7	,	,	PUNCT
ejpam-5812	120	8	let	let	VERB
ejpam-5812	120	9	n=	n=	ADJ
ejpam-5812	120	10	4t+	4t+	ADP
ejpam-5812	120	11	i	i	PRON
ejpam-5812	120	12	(	(	PUNCT
ejpam-5812	120	13	0	0	NUM
ejpam-5812	120	14	≤	≤	NUM
ejpam-5812	120	15	i	i	NOUN
ejpam-5812	120	16	≤	≤	NOUN
ejpam-5812	120	17	3	3	NUM
ejpam-5812	120	18	and	and	CCONJ
ejpam-5812	120	19	t	t	PROPN
ejpam-5812	120	20	>	>	X
ejpam-5812	120	21	2	2	NUM
ejpam-5812	120	22	)	)	PUNCT
ejpam-5812	120	23	,	,	PUNCT
ejpam-5812	120	24	then	then	ADV
ejpam-5812	120	25	for	for	ADP
ejpam-5812	120	26	a	a	DET
ejpam-5812	120	27	given	give	VERB
ejpam-5812	120	28	value	value	NOUN
ejpam-5812	120	29	of	of	ADP
ejpam-5812	120	30	i	i	PRON
ejpam-5812	120	31	with	with	ADP
ejpam-5812	120	32	0	0	NUM
ejpam-5812	120	33	≤	≤	NUM
ejpam-5812	120	34	i	i	PRON
ejpam-5812	120	35	≤	≤	NOUN
ejpam-5812	120	36	3	3	NUM
ejpam-5812	120	37	,	,	PUNCT
ejpam-5812	120	38	we	we	PRON
ejpam-5812	120	39	use	use	VERB
ejpam-5812	120	40	the	the	DET
ejpam-5812	120	41	labeling	labeling	NOUN
ejpam-5812	120	42	[	[	X
ejpam-5812	120	43	u	u	NOUN
ejpam-5812	120	44	,	,	PUNCT
ejpam-5812	120	45	v	v	NOUN
ejpam-5812	120	46	]	]	PUNCT
ejpam-5812	120	47	for	for	ADP
ejpam-5812	120	48	w	w	PROPN
ejpam-5812	120	49	5	5	NUM
ejpam-5812	120	50	n+1=	n+1=	PROPN
ejpam-5812	120	51	p	p	NOUN
ejpam-5812	120	52	1	1	NUM
ejpam-5812	120	53	+	+	CCONJ
ejpam-5812	120	54	c5	c5	PROPN
ejpam-5812	120	55	n	n	CCONJ
ejpam-5812	120	56	where	where	SCONJ
ejpam-5812	120	57	u	u	PRON
ejpam-5812	120	58	be	be	VERB
ejpam-5812	120	59	the	the	DET
ejpam-5812	120	60	labeling	labeling	NOUN
ejpam-5812	120	61	of	of	ADP
ejpam-5812	120	62	p1	p1	PROPN
ejpam-5812	120	63	and	and	CCONJ
ejpam-5812	120	64	v	v	NOUN
ejpam-5812	120	65	=	=	NOUN
ejpam-5812	120	66	ai	ai	NOUN
ejpam-5812	120	67	or	or	CCONJ
ejpam-5812	120	68	a	a	DET
ejpam-5812	120	69	′	′	NOUN
ejpam-5812	121	1	i	i	PRON
ejpam-5812	121	2	be	be	VERB
ejpam-5812	121	3	the	the	DET
ejpam-5812	121	4	labeling	labeling	NOUN
ejpam-5812	121	5	of	of	ADP
ejpam-5812	121	6	c5	c5	PROPN
ejpam-5812	121	7	n	n	CCONJ
ejpam-5812	121	8	as	as	SCONJ
ejpam-5812	121	9	shown	show	VERB
ejpam-5812	121	10	in	in	ADP
ejpam-5812	121	11	tables	table	NOUN
ejpam-5812	121	12	1	1	NUM
ejpam-5812	121	13	,	,	PUNCT
ejpam-5812	121	14	3	3	NUM
ejpam-5812	121	15	.	.	X
ejpam-5812	122	1	it	it	PRON
ejpam-5812	122	2	is	be	AUX
ejpam-5812	122	3	easy	easy	ADJ
ejpam-5812	122	4	to	to	PART
ejpam-5812	122	5	see	see	VERB
ejpam-5812	122	6	that	that	PRON
ejpam-5812	122	7	w	w	ADP
ejpam-5812	122	8	5	5	NUM
ejpam-5812	122	9	n+1	n+1	PROPN
ejpam-5812	122	10	for	for	ADP
ejpam-5812	122	11	every	every	DET
ejpam-5812	122	12	n	n	NOUN
ejpam-5812	122	13	>	>	SYM
ejpam-5812	122	14	8	8	NUM
ejpam-5812	122	15	is	be	AUX
ejpam-5812	122	16	cordial	cordial	ADJ
ejpam-5812	122	17	from	from	ADP
ejpam-5812	122	18	the	the	DET
ejpam-5812	122	19	last	last	ADJ
ejpam-5812	122	20	two	two	NUM
ejpam-5812	122	21	columns	column	NOUN
ejpam-5812	122	22	of	of	ADP
ejpam-5812	122	23	the	the	DET
ejpam-5812	122	24	table	table	NOUN
ejpam-5812	122	25	w	w	PROPN
ejpam-5812	122	26	and	and	CCONJ
ejpam-5812	122	27	the	the	DET
ejpam-5812	122	28	theorem	theorem	NOUN
ejpam-5812	122	29	is	be	AUX
ejpam-5812	122	30	proved	prove	VERB
ejpam-5812	122	31	.	.	PUNCT
ejpam-5812	123	1	table	table	NOUN
ejpam-5812	123	2	3	3	NUM
ejpam-5812	123	3	:	:	PUNCT
ejpam-5812	123	4	labeling	labeling	NOUN
ejpam-5812	123	5	of	of	ADP
ejpam-5812	123	6	w	w	PROPN
ejpam-5812	123	7	5	5	NUM
ejpam-5812	123	8	n+1	n+1	NOUN
ejpam-5812	123	9	.	.	PUNCT
ejpam-5812	124	1	n	n	NOUN
ejpam-5812	124	2	=	=	SYM
ejpam-5812	124	3	4t+	4t+	PROPN
ejpam-5812	125	1	i	i	NOUN
ejpam-5812	125	2	,	,	PUNCT
ejpam-5812	125	3	n	n	PROPN
ejpam-5812	125	4	≥	≥	NOUN
ejpam-5812	125	5	9	9	NUM
ejpam-5812	125	6	i	i	NOUN
ejpam-5812	125	7	=	=	PUNCT
ejpam-5812	125	8	0	0	NUM
ejpam-5812	125	9	,	,	PUNCT
ejpam-5812	125	10	1	1	NUM
ejpam-5812	125	11	,	,	PUNCT
ejpam-5812	125	12	2	2	NUM
ejpam-5812	125	13	,	,	PUNCT
ejpam-5812	125	14	3	3	NUM
ejpam-5812	125	15	labeling	labeling	NOUN
ejpam-5812	125	16	of	of	ADP
ejpam-5812	125	17	w	w	PROPN
ejpam-5812	125	18	5	5	NUM
ejpam-5812	125	19	n+1	n+1	PROPN
ejpam-5812	125	20	v0	v0	NOUN
ejpam-5812	125	21	v1	v1	NOUN
ejpam-5812	125	22	e0	e0	PROPN
ejpam-5812	125	23	e1	e1	PROPN
ejpam-5812	125	24	v0	v0	NOUN
ejpam-5812	125	25	−	−	PROPN
ejpam-5812	125	26	v1	v1	PROPN
ejpam-5812	125	27	e0	e0	PROPN
ejpam-5812	125	28	−	−	PROPN
ejpam-5812	125	29	e1	e1	VERB
ejpam-5812	125	30	i=	i=	NOUN
ejpam-5812	125	31	0	0	PUNCT
ejpam-5812	126	1	[	[	X
ejpam-5812	126	2	0,a0	0,a0	X
ejpam-5812	126	3	]	]	X
ejpam-5812	126	4	=	=	PUNCT
ejpam-5812	127	1	[	[	X
ejpam-5812	127	2	0,l4t120	0,l4t120	X
ejpam-5812	127	3	]	]	X
ejpam-5812	127	4	2t+	2t+	NUM
ejpam-5812	127	5	3	3	NUM
ejpam-5812	127	6	2t+	2t+	NUM
ejpam-5812	127	7	2	2	NUM
ejpam-5812	127	8	12t+	12t+	NUM
ejpam-5812	127	9	5	5	NUM
ejpam-5812	127	10	12t+	12t+	NUM
ejpam-5812	127	11	5	5	NUM
ejpam-5812	127	12	1	1	NUM
ejpam-5812	127	13	0	0	NUM
ejpam-5812	127	14	i=	i=	NUM
ejpam-5812	127	15	1	1	NUM
ejpam-5812	128	1	[	[	X
ejpam-5812	128	2	1,a′	1,a′	NOUN
ejpam-5812	128	3	1	1	NUM
ejpam-5812	128	4	]	]	PUNCT
ejpam-5812	128	5	=	=	PUNCT
ejpam-5812	129	1	[	[	X
ejpam-5812	129	2	1,12m4t−403	1,12m4t−403	NUM
ejpam-5812	129	3	]	]	SYM
ejpam-5812	129	4	2t+	2t+	NUM
ejpam-5812	129	5	1	1	NUM
ejpam-5812	129	6	2t+	2t+	NUM
ejpam-5812	129	7	1	1	NUM
ejpam-5812	129	8	12t−	12t−	NUM
ejpam-5812	129	9	4	4	NUM
ejpam-5812	129	10	12t−	12t−	NUM
ejpam-5812	129	11	4	4	NUM
ejpam-5812	129	12	0	0	NUM
ejpam-5812	129	13	0	0	NUM
ejpam-5812	129	14	i=	i=	NUM
ejpam-5812	129	15	2	2	NUM
ejpam-5812	130	1	[	[	NOUN
ejpam-5812	130	2	0,a2	0,a2	X
ejpam-5812	130	3	]	]	X
ejpam-5812	130	4	=	=	PUNCT
ejpam-5812	131	1	[	[	X
ejpam-5812	131	2	0,l	0,l	X
ejpam-5812	131	3	′	′	NUM
ejpam-5812	131	4	4t10	4t10	NOUN
ejpam-5812	131	5	]	]	PUNCT
ejpam-5812	131	6	2t+	2t+	NUM
ejpam-5812	131	7	2	2	NUM
ejpam-5812	131	8	2t+	2t+	NUM
ejpam-5812	131	9	1	1	NUM
ejpam-5812	131	10	12t−	12t−	NUM
ejpam-5812	131	11	1	1	NUM
ejpam-5812	131	12	10t−	10t−	NUM
ejpam-5812	131	13	1	1	NUM
ejpam-5812	131	14	1	1	NUM
ejpam-5812	131	15	0	0	NUM
ejpam-5812	131	16	i=	i=	NUM
ejpam-5812	131	17	3	3	NUM
ejpam-5812	132	1	[	[	X
ejpam-5812	132	2	0,a′	0,a′	NOUN
ejpam-5812	132	3	3	3	NUM
ejpam-5812	132	4	]	]	PUNCT
ejpam-5812	132	5	=	=	PUNCT
ejpam-5812	133	1	[	[	X
ejpam-5812	133	2	0	0	NUM
ejpam-5812	133	3	,	,	PUNCT
ejpam-5812	133	4	11l′	11l′	NUM
ejpam-5812	133	5	4t0	4t0	NUM
ejpam-5812	133	6	]	]	PUNCT
ejpam-5812	133	7	2t+	2t+	NUM
ejpam-5812	133	8	2	2	NUM
ejpam-5812	133	9	2t+	2t+	NUM
ejpam-5812	133	10	2	2	NUM
ejpam-5812	133	11	12t+	12t+	NUM
ejpam-5812	133	12	1	1	NUM
ejpam-5812	133	13	12t+	12t+	NUM
ejpam-5812	133	14	1	1	NUM
ejpam-5812	133	15	0	0	NUM
ejpam-5812	133	16	0	0	NUM
ejpam-5812	133	17	3.4	3.4	NUM
ejpam-5812	133	18	.	.	PUNCT
ejpam-5812	133	19	cordial	cordial	ADJ
ejpam-5812	133	20	labeling	labeling	NOUN
ejpam-5812	133	21	of	of	ADP
ejpam-5812	133	22	fifth	fifth	ADJ
ejpam-5812	133	23	power	power	NOUN
ejpam-5812	133	24	of	of	ADP
ejpam-5812	133	25	fans	fan	NOUN
ejpam-5812	133	26	graphs	graph	VERB
ejpam-5812	133	27	clearly	clearly	ADV
ejpam-5812	133	28	,	,	PUNCT
ejpam-5812	133	29	the	the	DET
ejpam-5812	133	30	order	order	NOUN
ejpam-5812	133	31	of	of	ADP
ejpam-5812	133	32	f	f	PROPN
ejpam-5812	133	33	5	5	NUM
ejpam-5812	133	34	n+1	n+1	PROPN
ejpam-5812	133	35	is	be	AUX
ejpam-5812	133	36	n	n	PRON
ejpam-5812	133	37	+	+	NUM
ejpam-5812	133	38	1	1	NUM
ejpam-5812	133	39	,	,	PUNCT
ejpam-5812	133	40	and	and	CCONJ
ejpam-5812	133	41	the	the	DET
ejpam-5812	133	42	size	size	NOUN
ejpam-5812	133	43	of	of	ADP
ejpam-5812	133	44	f	f	PROPN
ejpam-5812	133	45	5	5	NUM
ejpam-5812	133	46	n+1	n+1	PROPN
ejpam-5812	133	47	is	be	AUX
ejpam-5812	133	48	6n	6n	NUM
ejpam-5812	133	49	−	−	PROPN
ejpam-5812	133	50	15	15	NUM
ejpam-5812	133	51	for	for	ADP
ejpam-5812	133	52	every	every	DET
ejpam-5812	133	53	n	n	NOUN
ejpam-5812	133	54	>	>	X
ejpam-5812	133	55	7	7	NUM
ejpam-5812	133	56	.	.	PUNCT
ejpam-5812	134	1	in	in	ADP
ejpam-5812	134	2	particular	particular	ADJ
ejpam-5812	134	3	,	,	PUNCT
ejpam-5812	134	4	f	f	PROPN
ejpam-5812	134	5	5	5	NUM
ejpam-5812	134	6	2	2	NUM
ejpam-5812	134	7	∼=	∼=	NOUN
ejpam-5812	134	8	p2	p2	NOUN
ejpam-5812	134	9	,	,	PUNCT
ejpam-5812	134	10	f	f	PROPN
ejpam-5812	134	11	5	5	NUM
ejpam-5812	134	12	3	3	NUM
ejpam-5812	134	13	∼=	∼=	PROPN
ejpam-5812	134	14	c3	c3	NOUN
ejpam-5812	134	15	,	,	PUNCT
ejpam-5812	134	16	f	f	PROPN
ejpam-5812	134	17	5	5	NUM
ejpam-5812	134	18	4	4	NUM
ejpam-5812	134	19	∼=	∼=	NOUN
ejpam-5812	134	20	k4	k4	NOUN
ejpam-5812	134	21	,	,	PUNCT
ejpam-5812	134	22	f	f	PROPN
ejpam-5812	134	23	5	5	NUM
ejpam-5812	134	24	5	5	NUM
ejpam-5812	134	25	∼=	∼=	PROPN
ejpam-5812	134	26	k5	k5	NOUN
ejpam-5812	134	27	,	,	PUNCT
ejpam-5812	134	28	f	f	PROPN
ejpam-5812	134	29	5	5	NUM
ejpam-5812	134	30	6	6	NUM
ejpam-5812	134	31	∼=	∼=	NOUN
ejpam-5812	134	32	k6	k6	NOUN
ejpam-5812	134	33	and	and	CCONJ
ejpam-5812	134	34	f	f	PROPN
ejpam-5812	134	35	5	5	NUM
ejpam-5812	134	36	7	7	NUM
ejpam-5812	134	37	∼=	∼=	PROPN
ejpam-5812	134	38	k7	k7	NOUN
ejpam-5812	134	39	.	.	PUNCT
ejpam-5812	135	1	in	in	ADP
ejpam-5812	135	2	this	this	DET
ejpam-5812	135	3	subsection	subsection	NOUN
ejpam-5812	135	4	,	,	PUNCT
ejpam-5812	135	5	we	we	PRON
ejpam-5812	135	6	show	show	VERB
ejpam-5812	135	7	that	that	SCONJ
ejpam-5812	135	8	f	f	PROPN
ejpam-5812	135	9	5	5	NUM
ejpam-5812	135	10	n+1	n+1	PROPN
ejpam-5812	135	11	is	be	AUX
ejpam-5812	135	12	cordial	cordial	ADJ
ejpam-5812	135	13	if	if	SCONJ
ejpam-5812	135	14	and	and	CCONJ
ejpam-5812	135	15	only	only	ADV
ejpam-5812	135	16	if	if	SCONJ
ejpam-5812	135	17	n≥	n≥	PROPN
ejpam-5812	135	18	1	1	NUM
ejpam-5812	135	19	except	except	SCONJ
ejpam-5812	135	20	3	3	NUM
ejpam-5812	135	21	≤	≤	NOUN
ejpam-5812	135	22	n	n	PRON
ejpam-5812	135	23	≤	≤	NUM
ejpam-5812	135	24	7	7	NUM
ejpam-5812	135	25	.	.	PUNCT
ejpam-5812	135	26	theorem	theorem	VERB
ejpam-5812	135	27	3.4.1	3.4.1	NUM
ejpam-5812	135	28	.	.	PUNCT
ejpam-5812	136	1	the	the	DET
ejpam-5812	136	2	fifth	fifth	ADJ
ejpam-5812	136	3	power	power	NOUN
ejpam-5812	136	4	of	of	ADP
ejpam-5812	136	5	fans	fan	NOUN
ejpam-5812	136	6	graphs	graph	VERB
ejpam-5812	136	7	f	f	PROPN
ejpam-5812	136	8	5	5	NUM
ejpam-5812	136	9	n+1=	n+1=	PROPN
ejpam-5812	136	10	p	p	PROPN
ejpam-5812	136	11	1+p	1+p	NUM
ejpam-5812	136	12	5	5	NUM
ejpam-5812	136	13	n	n	PRON
ejpam-5812	136	14	is	be	AUX
ejpam-5812	136	15	cordial	cordial	ADJ
ejpam-5812	136	16	if	if	SCONJ
ejpam-5812	136	17	and	and	CCONJ
ejpam-5812	136	18	only	only	ADV
ejpam-5812	136	19	if	if	SCONJ
ejpam-5812	136	20	n≥	n≥	PROPN
ejpam-5812	136	21	1	1	NUM
ejpam-5812	136	22	except	except	SCONJ
ejpam-5812	136	23	3	3	NUM
ejpam-5812	136	24	≤	≤	NOUN
ejpam-5812	136	25	n	n	PRON
ejpam-5812	136	26	≤	≤	NOUN
ejpam-5812	136	27	7	7	NUM
ejpam-5812	136	28	.	.	PUNCT
ejpam-5812	136	29	a.	a.	PROPN
ejpam-5812	136	30	abd	abd	PROPN
ejpam-5812	136	31	el	el	PROPN
ejpam-5812	136	32	-	-	PROPN
ejpam-5812	136	33	hay	hay	PROPN
ejpam-5812	136	34	,	,	PUNCT
ejpam-5812	136	35	k.	k.	PROPN
ejpam-5812	136	36	a.	a.	PROPN
ejpam-5812	136	37	alsatami	alsatami	PROPN
ejpam-5812	136	38	,	,	PUNCT
ejpam-5812	136	39	a.	a.	NOUN
ejpam-5812	136	40	elrokh	elrokh	PROPN
ejpam-5812	136	41	/	/	SYM
ejpam-5812	136	42	eur	eur	PROPN
ejpam-5812	136	43	.	.	PUNCT
ejpam-5812	137	1	j.	j.	PROPN
ejpam-5812	137	2	pure	pure	PROPN
ejpam-5812	137	3	appl	appl	PROPN
ejpam-5812	137	4	.	.	PROPN
ejpam-5812	137	5	math	math	PROPN
ejpam-5812	137	6	,	,	PUNCT
ejpam-5812	137	7	18	18	NUM
ejpam-5812	137	8	(	(	PUNCT
ejpam-5812	137	9	1	1	NUM
ejpam-5812	137	10	)	)	PUNCT
ejpam-5812	137	11	(	(	PUNCT
ejpam-5812	137	12	2025	2025	NUM
ejpam-5812	137	13	)	)	PUNCT
ejpam-5812	137	14	,	,	PUNCT
ejpam-5812	137	15	5812	5812	NUM
ejpam-5812	137	16	6	6	NUM
ejpam-5812	137	17	of	of	ADP
ejpam-5812	137	18	14	14	NUM
ejpam-5812	137	19	proof	proof	NOUN
ejpam-5812	137	20	.	.	PUNCT
ejpam-5812	138	1	since	since	SCONJ
ejpam-5812	138	2	f	f	PROPN
ejpam-5812	138	3	5	5	NUM
ejpam-5812	138	4	2	2	NUM
ejpam-5812	138	5	∼=	∼=	NOUN
ejpam-5812	138	6	p2	p2	NOUN
ejpam-5812	138	7	,	,	PUNCT
ejpam-5812	138	8	f	f	PROPN
ejpam-5812	138	9	5	5	NUM
ejpam-5812	138	10	3	3	NUM
ejpam-5812	138	11	∼=	∼=	PROPN
ejpam-5812	138	12	c3	c3	NOUN
ejpam-5812	138	13	,	,	PUNCT
ejpam-5812	138	14	f	f	PROPN
ejpam-5812	138	15	5	5	NUM
ejpam-5812	138	16	9	9	NUM
ejpam-5812	138	17	the	the	DET
ejpam-5812	138	18	labeling	labeling	NOUN
ejpam-5812	138	19	[	[	X
ejpam-5812	138	20	1	1	NUM
ejpam-5812	138	21	;	;	PUNCT
ejpam-5812	138	22	0414	0414	NUM
ejpam-5812	138	23	]	]	PUNCT
ejpam-5812	138	24	is	be	AUX
ejpam-5812	138	25	sufficient	sufficient	ADJ
ejpam-5812	138	26	for	for	ADP
ejpam-5812	138	27	f	f	PROPN
ejpam-5812	138	28	5	5	NUM
ejpam-5812	138	29	9	9	NUM
ejpam-5812	138	30	and	and	CCONJ
ejpam-5812	138	31	p2	p2	PROPN
ejpam-5812	138	32	,	,	PUNCT
ejpam-5812	138	33	c3	c3	PROPN
ejpam-5812	138	34	are	be	AUX
ejpam-5812	138	35	cordial	cordial	ADJ
ejpam-5812	138	36	[	[	X
ejpam-5812	138	37	3	3	NUM
ejpam-5812	138	38	]	]	PUNCT
ejpam-5812	138	39	,	,	PUNCT
ejpam-5812	138	40	then	then	ADV
ejpam-5812	138	41	f	f	PROPN
ejpam-5812	138	42	5	5	NUM
ejpam-5812	138	43	2	2	NUM
ejpam-5812	138	44	,	,	PUNCT
ejpam-5812	138	45	f	f	PROPN
ejpam-5812	138	46	5	5	NUM
ejpam-5812	138	47	3	3	NUM
ejpam-5812	138	48	and	and	CCONJ
ejpam-5812	138	49	f	f	PROPN
ejpam-5812	138	50	5	5	NUM
ejpam-5812	138	51	8	8	NUM
ejpam-5812	138	52	are	be	AUX
ejpam-5812	138	53	cordial	cordial	ADJ
ejpam-5812	138	54	.	.	PUNCT
ejpam-5812	139	1	in	in	ADP
ejpam-5812	139	2	case	case	NOUN
ejpam-5812	139	3	of	of	ADP
ejpam-5812	139	4	3	3	NUM
ejpam-5812	139	5	≤	≤	NOUN
ejpam-5812	139	6	n	n	PRON
ejpam-5812	139	7	≤	≤	NOUN
ejpam-5812	139	8	6	6	NUM
ejpam-5812	139	9	,	,	PUNCT
ejpam-5812	139	10	it	it	PRON
ejpam-5812	139	11	is	be	AUX
ejpam-5812	139	12	easy	easy	ADJ
ejpam-5812	139	13	to	to	PART
ejpam-5812	139	14	verify	verify	VERB
ejpam-5812	139	15	that	that	SCONJ
ejpam-5812	139	16	f	f	PROPN
ejpam-5812	139	17	5	5	NUM
ejpam-5812	139	18	4	4	NUM
ejpam-5812	139	19	∼=	∼=	NOUN
ejpam-5812	139	20	k4	k4	NOUN
ejpam-5812	139	21	,	,	PUNCT
ejpam-5812	139	22	f	f	PROPN
ejpam-5812	139	23	5	5	NUM
ejpam-5812	139	24	5	5	NUM
ejpam-5812	139	25	∼=	∼=	PROPN
ejpam-5812	139	26	k5	k5	NOUN
ejpam-5812	139	27	,	,	PUNCT
ejpam-5812	139	28	f	f	PROPN
ejpam-5812	139	29	5	5	NUM
ejpam-5812	139	30	6	6	NUM
ejpam-5812	139	31	∼=	∼=	NOUN
ejpam-5812	139	32	k6	k6	NOUN
ejpam-5812	139	33	and	and	CCONJ
ejpam-5812	139	34	f	f	PROPN
ejpam-5812	139	35	5	5	NUM
ejpam-5812	139	36	7	7	NUM
ejpam-5812	139	37	∼=	∼=	PROPN
ejpam-5812	139	38	k7	k7	NOUN
ejpam-5812	139	39	are	be	AUX
ejpam-5812	139	40	not	not	PART
ejpam-5812	139	41	cordial	cordial	ADJ
ejpam-5812	139	42	by	by	ADP
ejpam-5812	139	43	cahit	cahit	ADJ
ejpam-5812	140	1	[	[	X
ejpam-5812	140	2	3	3	NUM
ejpam-5812	140	3	]	]	PUNCT
ejpam-5812	140	4	.	.	PUNCT
ejpam-5812	141	1	since	since	SCONJ
ejpam-5812	141	2	n	n	NOUN
ejpam-5812	141	3	=	=	SYM
ejpam-5812	141	4	7	7	NUM
ejpam-5812	141	5	,	,	PUNCT
ejpam-5812	141	6	then	then	ADV
ejpam-5812	141	7	by	by	ADP
ejpam-5812	141	8	investigation	investigation	NOUN
ejpam-5812	141	9	all	all	DET
ejpam-5812	141	10	possible	possible	ADJ
ejpam-5812	141	11	labelings	labeling	NOUN
ejpam-5812	141	12	of	of	ADP
ejpam-5812	141	13	vertices	vertex	NOUN
ejpam-5812	141	14	of	of	ADP
ejpam-5812	141	15	p	p	PROPN
ejpam-5812	141	16	5	5	NUM
ejpam-5812	141	17	8	8	NUM
ejpam-5812	141	18	with	with	ADP
ejpam-5812	141	19	v0	v0	NOUN
ejpam-5812	141	20	=	=	SYM
ejpam-5812	141	21	v1	v1	NOUN
ejpam-5812	141	22	=	=	SYM
ejpam-5812	141	23	4	4	NUM
ejpam-5812	141	24	,	,	PUNCT
ejpam-5812	141	25	we	we	PRON
ejpam-5812	141	26	obtained	obtain	VERB
ejpam-5812	141	27	that	that	DET
ejpam-5812	141	28	|e0	|e0	NOUN
ejpam-5812	141	29	−	−	PROPN
ejpam-5812	141	30	e1|	e1|	PROPN
ejpam-5812	141	31	>	>	X
ejpam-5812	142	1	1	1	X
ejpam-5812	142	2	.	.	PUNCT
ejpam-5812	142	3	therefore	therefore	ADV
ejpam-5812	142	4	f	f	PROPN
ejpam-5812	142	5	5	5	NUM
ejpam-5812	142	6	8	8	NUM
ejpam-5812	142	7	is	be	AUX
ejpam-5812	142	8	not	not	PART
ejpam-5812	142	9	cordial	cordial	ADJ
ejpam-5812	142	10	.	.	PUNCT
ejpam-5812	143	1	in	in	ADP
ejpam-5812	143	2	case	case	NOUN
ejpam-5812	143	3	of	of	ADP
ejpam-5812	143	4	n	n	NUM
ejpam-5812	143	5	≥	≥	NUM
ejpam-5812	143	6	8	8	NUM
ejpam-5812	143	7	,	,	PUNCT
ejpam-5812	143	8	let	let	VERB
ejpam-5812	143	9	n=	n=	ADJ
ejpam-5812	143	10	4	4	NUM
ejpam-5812	143	11	t	t	NOUN
ejpam-5812	144	1	+	+	X
ejpam-5812	144	2	i	i	PRON
ejpam-5812	144	3	(	(	PUNCT
ejpam-5812	144	4	0	0	NUM
ejpam-5812	144	5	≤	≤	NUM
ejpam-5812	144	6	i	i	NOUN
ejpam-5812	144	7	≤	≤	NOUN
ejpam-5812	144	8	3	3	NUM
ejpam-5812	144	9	and	and	CCONJ
ejpam-5812	144	10	t	t	PROPN
ejpam-5812	144	11	≥	≥	NUM
ejpam-5812	144	12	2	2	NUM
ejpam-5812	144	13	)	)	PUNCT
ejpam-5812	144	14	,	,	PUNCT
ejpam-5812	144	15	then	then	ADV
ejpam-5812	144	16	for	for	ADP
ejpam-5812	144	17	a	a	DET
ejpam-5812	144	18	given	give	VERB
ejpam-5812	144	19	value	value	NOUN
ejpam-5812	144	20	of	of	ADP
ejpam-5812	144	21	i	i	PRON
ejpam-5812	144	22	with	with	ADP
ejpam-5812	144	23	0	0	NUM
ejpam-5812	144	24	≤	≤	NUM
ejpam-5812	144	25	i	i	PRON
ejpam-5812	144	26	≤	≤	NOUN
ejpam-5812	144	27	3	3	NUM
ejpam-5812	144	28	,	,	PUNCT
ejpam-5812	144	29	we	we	PRON
ejpam-5812	144	30	use	use	VERB
ejpam-5812	144	31	the	the	DET
ejpam-5812	144	32	labeling	labeling	NOUN
ejpam-5812	144	33	[	[	X
ejpam-5812	144	34	u	u	NOUN
ejpam-5812	144	35	,	,	PUNCT
ejpam-5812	144	36	v	v	NOUN
ejpam-5812	144	37	]	]	PUNCT
ejpam-5812	144	38	for	for	ADP
ejpam-5812	144	39	f	f	PROPN
ejpam-5812	144	40	5	5	NUM
ejpam-5812	144	41	n+1=	n+1=	PROPN
ejpam-5812	144	42	p	p	NOUN
ejpam-5812	144	43	1	1	NUM
ejpam-5812	144	44	+	+	CCONJ
ejpam-5812	144	45	p	p	NOUN
ejpam-5812	144	46	5	5	NUM
ejpam-5812	144	47	nwhere	nwhere	ADV
ejpam-5812	144	48	u	u	NOUN
ejpam-5812	144	49	be	be	VERB
ejpam-5812	144	50	the	the	DET
ejpam-5812	144	51	labeling	labeling	NOUN
ejpam-5812	144	52	of	of	ADP
ejpam-5812	144	53	p1	p1	PROPN
ejpam-5812	144	54	and	and	CCONJ
ejpam-5812	144	55	v	v	NOUN
ejpam-5812	144	56	=	=	NOUN
ejpam-5812	144	57	bi	bi	NOUN
ejpam-5812	144	58	or	or	CCONJ
ejpam-5812	144	59	b	b	NOUN
ejpam-5812	144	60	′	′	NOUN
ejpam-5812	145	1	i	i	PRON
ejpam-5812	145	2	be	be	VERB
ejpam-5812	145	3	the	the	DET
ejpam-5812	145	4	labeling	labeling	NOUN
ejpam-5812	145	5	of	of	ADP
ejpam-5812	145	6	p	p	NOUN
ejpam-5812	145	7	5	5	NUM
ejpam-5812	145	8	n	n	NOUN
ejpam-5812	145	9	as	as	SCONJ
ejpam-5812	145	10	shown	show	VERB
ejpam-5812	145	11	in	in	ADP
ejpam-5812	145	12	tables	table	NOUN
ejpam-5812	145	13	2	2	NUM
ejpam-5812	145	14	,	,	PUNCT
ejpam-5812	145	15	4	4	NUM
ejpam-5812	145	16	.	.	PUNCT
ejpam-5812	146	1	it	it	PRON
ejpam-5812	146	2	is	be	AUX
ejpam-5812	146	3	easy	easy	ADJ
ejpam-5812	146	4	to	to	PART
ejpam-5812	146	5	see	see	VERB
ejpam-5812	146	6	that	that	SCONJ
ejpam-5812	146	7	f	f	PROPN
ejpam-5812	146	8	5	5	NUM
ejpam-5812	146	9	n+1	n+1	PROPN
ejpam-5812	146	10	for	for	ADP
ejpam-5812	146	11	every	every	DET
ejpam-5812	146	12	n	n	PRON
ejpam-5812	146	13	≥	≥	NOUN
ejpam-5812	146	14	8	8	NUM
ejpam-5812	146	15	is	be	AUX
ejpam-5812	146	16	cordial	cordial	ADJ
ejpam-5812	146	17	from	from	ADP
ejpam-5812	146	18	the	the	DET
ejpam-5812	146	19	last	last	ADJ
ejpam-5812	146	20	two	two	NUM
ejpam-5812	146	21	columns	column	NOUN
ejpam-5812	146	22	of	of	ADP
ejpam-5812	146	23	the	the	DET
ejpam-5812	146	24	table	table	NOUN
ejpam-5812	146	25	4	4	NUM
ejpam-5812	146	26	and	and	CCONJ
ejpam-5812	146	27	thus	thus	ADV
ejpam-5812	146	28	the	the	DET
ejpam-5812	146	29	theorem	theorem	NOUN
ejpam-5812	146	30	is	be	AUX
ejpam-5812	146	31	proved	prove	VERB
ejpam-5812	146	32	.	.	PUNCT
ejpam-5812	147	1	table	table	NOUN
ejpam-5812	147	2	4	4	NUM
ejpam-5812	147	3	:	:	PUNCT
ejpam-5812	147	4	labeling	labeling	NOUN
ejpam-5812	147	5	of	of	ADP
ejpam-5812	147	6	f	f	PROPN
ejpam-5812	147	7	5	5	NUM
ejpam-5812	147	8	n+1	n+1	PROPN
ejpam-5812	147	9	.	.	PUNCT
ejpam-5812	148	1	n	n	PROPN
ejpam-5812	148	2	=	=	SYM
ejpam-5812	148	3	4t+	4t+	PROPN
ejpam-5812	149	1	i	i	NOUN
ejpam-5812	149	2	,	,	PUNCT
ejpam-5812	149	3	n	n	PROPN
ejpam-5812	149	4	>	>	X
ejpam-5812	149	5	8	8	NUM
ejpam-5812	150	1	i	i	NOUN
ejpam-5812	150	2	=	=	NOUN
ejpam-5812	150	3	0	0	NUM
ejpam-5812	150	4	,	,	PUNCT
ejpam-5812	150	5	1	1	NUM
ejpam-5812	150	6	,	,	PUNCT
ejpam-5812	150	7	2	2	NUM
ejpam-5812	150	8	,	,	PUNCT
ejpam-5812	150	9	3	3	NUM
ejpam-5812	150	10	labeling	labeling	NOUN
ejpam-5812	150	11	of	of	ADP
ejpam-5812	150	12	f	f	PROPN
ejpam-5812	150	13	5	5	NUM
ejpam-5812	150	14	n+1	n+1	PROPN
ejpam-5812	150	15	v0	v0	NOUN
ejpam-5812	150	16	v1	v1	NOUN
ejpam-5812	150	17	e0	e0	PROPN
ejpam-5812	150	18	e1	e1	PROPN
ejpam-5812	150	19	v0	v0	NOUN
ejpam-5812	150	20	−	−	PROPN
ejpam-5812	150	21	v1	v1	PROPN
ejpam-5812	150	22	e0	e0	PROPN
ejpam-5812	150	23	−	−	PROPN
ejpam-5812	150	24	e1	e1	VERB
ejpam-5812	150	25	i=	i=	NOUN
ejpam-5812	150	26	0	0	PUNCT
ejpam-5812	151	1	[	[	X
ejpam-5812	151	2	0;b0=	0;b0=	NOUN
ejpam-5812	151	3	0l4t120	0l4t120	NUM
ejpam-5812	151	4	]	]	PUNCT
ejpam-5812	151	5	2t+	2t+	NUM
ejpam-5812	151	6	3	3	NUM
ejpam-5812	151	7	2t+	2t+	NUM
ejpam-5812	151	8	2	2	NUM
ejpam-5812	151	9	12t+	12t+	NUM
ejpam-5812	151	10	4	4	NUM
ejpam-5812	151	11	12t+	12t+	NUM
ejpam-5812	151	12	5	5	NUM
ejpam-5812	151	13	1	1	NUM
ejpam-5812	151	14	−1	−1	NOUN
ejpam-5812	151	15	i=	i=	NOUN
ejpam-5812	151	16	1	1	NUM
ejpam-5812	152	1	[	[	X
ejpam-5812	152	2	0;b1	0;b1	NUM
ejpam-5812	152	3	=	=	SYM
ejpam-5812	152	4	l4t1	l4t1	X
ejpam-5812	152	5	]	]	PUNCT
ejpam-5812	152	6	2t+	2t+	NUM
ejpam-5812	152	7	1	1	NUM
ejpam-5812	152	8	2t+	2t+	NUM
ejpam-5812	152	9	1	1	NUM
ejpam-5812	152	10	12t−	12t−	NUM
ejpam-5812	152	11	5	5	NUM
ejpam-5812	152	12	12t−	12t−	NUM
ejpam-5812	152	13	4	4	NUM
ejpam-5812	152	14	0	0	NUM
ejpam-5812	152	15	−1	−1	NOUN
ejpam-5812	152	16	i=	i=	NOUN
ejpam-5812	152	17	2	2	NUM
ejpam-5812	153	1	[	[	X
ejpam-5812	153	2	0;b2	0;b2	NUM
ejpam-5812	153	3	=	=	ADJ
ejpam-5812	153	4	l	l	NOUN
ejpam-5812	153	5	′	′	NUM
ejpam-5812	153	6	4t10	4t10	NOUN
ejpam-5812	153	7	]	]	PUNCT
ejpam-5812	153	8	2t+	2t+	NUM
ejpam-5812	153	9	2	2	NUM
ejpam-5812	153	10	2t+	2t+	NUM
ejpam-5812	153	11	1	1	NUM
ejpam-5812	153	12	12t−	12t−	NUM
ejpam-5812	153	13	1	1	NUM
ejpam-5812	153	14	12t−	12t−	NUM
ejpam-5812	153	15	2	2	NUM
ejpam-5812	153	16	1	1	NUM
ejpam-5812	153	17	1	1	NUM
ejpam-5812	153	18	i=	i=	NUM
ejpam-5812	153	19	3	3	NUM
ejpam-5812	154	1	[	[	X
ejpam-5812	154	2	1;b	1;b	NUM
ejpam-5812	154	3	′	′	NUM
ejpam-5812	154	4	3=	3=	NUM
ejpam-5812	154	5	010l4	010l4	NUM
ejpam-5812	154	6	t	t	NOUN
ejpam-5812	154	7	]	]	PUNCT
ejpam-5812	154	8	2t+	2t+	NUM
ejpam-5812	154	9	2	2	NUM
ejpam-5812	154	10	2t+	2t+	NUM
ejpam-5812	154	11	2	2	NUM
ejpam-5812	154	12	12t+	12t+	NUM
ejpam-5812	154	13	1	1	NUM
ejpam-5812	154	14	12t+	12t+	NUM
ejpam-5812	154	15	2	2	NUM
ejpam-5812	154	16	0	0	NUM
ejpam-5812	154	17	−1	−1	NOUN
ejpam-5812	154	18	3.5	3.5	NUM
ejpam-5812	154	19	.	.	PUNCT
ejpam-5812	155	1	cordial	cordial	ADJ
ejpam-5812	155	2	labeling	labeling	NOUN
ejpam-5812	155	3	of	of	ADP
ejpam-5812	155	4	fifth	fifth	ADJ
ejpam-5812	155	5	power	power	NOUN
ejpam-5812	155	6	of	of	ADP
ejpam-5812	155	7	lemniscate	lemniscate	PROPN
ejpam-5812	155	8	graphs	graph	NOUN
ejpam-5812	155	9	the	the	DET
ejpam-5812	155	10	fifth	fifth	ADJ
ejpam-5812	155	11	power	power	NOUN
ejpam-5812	155	12	of	of	ADP
ejpam-5812	155	13	a	a	DET
ejpam-5812	155	14	lemniscate	lemniscate	PROPN
ejpam-5812	155	15	graph	graph	NOUN
ejpam-5812	155	16	is	be	AUX
ejpam-5812	155	17	denoted	denote	VERB
ejpam-5812	155	18	by	by	ADP
ejpam-5812	155	19	l5	l5	PROPN
ejpam-5812	155	20	n	n	CCONJ
ejpam-5812	155	21	,	,	PUNCT
ejpam-5812	155	22	m	m	PROPN
ejpam-5812	155	23	=	=	NOUN
ejpam-5812	155	24	c5	c5	PROPN
ejpam-5812	155	25	n∪c5	n∪c5	PROPN
ejpam-5812	155	26	m	m	VERB
ejpam-5812	155	27	where	where	SCONJ
ejpam-5812	155	28	both	both	DET
ejpam-5812	155	29	cycles	cycle	NOUN
ejpam-5812	155	30	have	have	VERB
ejpam-5812	155	31	a	a	DET
ejpam-5812	155	32	common	common	ADJ
ejpam-5812	155	33	point	point	NOUN
ejpam-5812	155	34	.	.	PUNCT
ejpam-5812	156	1	so	so	ADV
ejpam-5812	156	2	,	,	PUNCT
ejpam-5812	156	3	the	the	DET
ejpam-5812	156	4	order	order	NOUN
ejpam-5812	156	5	of	of	ADP
ejpam-5812	156	6	the	the	DET
ejpam-5812	156	7	fifth	fifth	ADJ
ejpam-5812	156	8	power	power	NOUN
ejpam-5812	156	9	of	of	ADP
ejpam-5812	156	10	lemniscate	lemniscate	PROPN
ejpam-5812	156	11	is	be	AUX
ejpam-5812	156	12	n+m−	n+m−	NOUN
ejpam-5812	156	13	1	1	NUM
ejpam-5812	156	14	,	,	PUNCT
ejpam-5812	156	15	and	and	CCONJ
ejpam-5812	156	16	the	the	DET
ejpam-5812	156	17	size	size	NOUN
ejpam-5812	156	18	of	of	ADP
ejpam-5812	156	19	the	the	DET
ejpam-5812	156	20	fifth	fifth	ADJ
ejpam-5812	156	21	power	power	NOUN
ejpam-5812	156	22	of	of	ADP
ejpam-5812	156	23	lemniscate	lemniscate	PROPN
ejpam-5812	156	24	graph	graph	NOUN
ejpam-5812	156	25	l5	l5	PROPN
ejpam-5812	156	26	n	n	CCONJ
ejpam-5812	156	27	,	,	PUNCT
ejpam-5812	156	28	m	m	VERB
ejpam-5812	156	29	equals	equal	VERB
ejpam-5812	156	30	to	to	ADP
ejpam-5812	156	31	5(n+m)−	5(n+m)−	PROPN
ejpam-5812	156	32	28	28	NUM
ejpam-5812	156	33	.	.	PUNCT
ejpam-5812	157	1	in	in	ADP
ejpam-5812	157	2	the	the	DET
ejpam-5812	157	3	following	follow	VERB
ejpam-5812	157	4	section	section	NOUN
ejpam-5812	157	5	,	,	PUNCT
ejpam-5812	157	6	we	we	PRON
ejpam-5812	157	7	study	study	VERB
ejpam-5812	157	8	and	and	CCONJ
ejpam-5812	157	9	investigate	investigate	VERB
ejpam-5812	157	10	the	the	DET
ejpam-5812	157	11	cordiality	cordiality	NOUN
ejpam-5812	157	12	of	of	ADP
ejpam-5812	157	13	the	the	DET
ejpam-5812	157	14	fifth	fifth	ADJ
ejpam-5812	157	15	power	power	NOUN
ejpam-5812	157	16	of	of	ADP
ejpam-5812	157	17	lemniscate	lemniscate	PROPN
ejpam-5812	157	18	l5	l5	PROPN
ejpam-5812	157	19	n	n	CCONJ
ejpam-5812	157	20	,	,	PUNCT
ejpam-5812	157	21	m	m	VERB
ejpam-5812	157	22	for	for	ADP
ejpam-5812	157	23	all	all	DET
ejpam-5812	157	24	n	n	CCONJ
ejpam-5812	157	25	,	,	PUNCT
ejpam-5812	157	26	m	m	VERB
ejpam-5812	157	27	≥	≥	NOUN
ejpam-5812	157	28	3	3	NUM
ejpam-5812	157	29	.	.	PUNCT
ejpam-5812	158	1	the	the	DET
ejpam-5812	158	2	labeling	labeling	NOUN
ejpam-5812	158	3	of	of	ADP
ejpam-5812	158	4	l5	l5	PROPN
ejpam-5812	158	5	n	n	CCONJ
ejpam-5812	158	6	,	,	PUNCT
ejpam-5812	158	7	m	m	VERB
ejpam-5812	158	8	takes	take	VERB
ejpam-5812	158	9	the	the	DET
ejpam-5812	158	10	form	form	NOUN
ejpam-5812	158	11	[	[	X
ejpam-5812	158	12	a;b	a;b	X
ejpam-5812	158	13	]	]	X
ejpam-5812	158	14	where	where	SCONJ
ejpam-5812	158	15	the	the	DET
ejpam-5812	158	16	labeling	labeling	NOUN
ejpam-5812	158	17	a	a	PRON
ejpam-5812	158	18	is	be	AUX
ejpam-5812	158	19	given	give	VERB
ejpam-5812	158	20	to	to	ADP
ejpam-5812	158	21	n	n	NOUN
ejpam-5812	158	22	and	and	CCONJ
ejpam-5812	158	23	the	the	DET
ejpam-5812	158	24	labeling	labeling	NOUN
ejpam-5812	158	25	b	b	PROPN
ejpam-5812	158	26	is	be	AUX
ejpam-5812	158	27	given	give	VERB
ejpam-5812	158	28	to	to	AUX
ejpam-5812	158	29	m.	m.	NOUN
ejpam-5812	158	30	for	for	ADP
ejpam-5812	158	31	this	this	DET
ejpam-5812	158	32	purpose	purpose	NOUN
ejpam-5812	158	33	,	,	PUNCT
ejpam-5812	158	34	we	we	PRON
ejpam-5812	158	35	labeling	labeling	VERB
ejpam-5812	158	36	each	each	DET
ejpam-5812	158	37	fifth	fifth	ADJ
ejpam-5812	158	38	power	power	NOUN
ejpam-5812	158	39	of	of	ADP
ejpam-5812	158	40	cycle	cycle	NOUN
ejpam-5812	158	41	separately	separately	ADV
ejpam-5812	158	42	.	.	PUNCT
ejpam-5812	159	1	lemma	lemma	PROPN
ejpam-5812	159	2	3.5.1	3.5.1	NUM
ejpam-5812	159	3	.	.	PUNCT
ejpam-5812	160	1	if	if	SCONJ
ejpam-5812	160	2	3	3	NUM
ejpam-5812	160	3	≤	≤	NUM
ejpam-5812	160	4	n	n	PRON
ejpam-5812	160	5	≤	≤	NUM
ejpam-5812	160	6	8	8	NUM
ejpam-5812	160	7	,	,	PUNCT
ejpam-5812	160	8	and	and	CCONJ
ejpam-5812	160	9	m	m	PROPN
ejpam-5812	160	10	>	>	X
ejpam-5812	160	11	8	8	NUM
ejpam-5812	160	12	,	,	PUNCT
ejpam-5812	160	13	then	then	ADV
ejpam-5812	160	14	the	the	DET
ejpam-5812	160	15	fifth	fifth	ADJ
ejpam-5812	160	16	power	power	NOUN
ejpam-5812	160	17	of	of	ADP
ejpam-5812	160	18	lemniscate	lemniscate	PROPN
ejpam-5812	160	19	l5	l5	PROPN
ejpam-5812	160	20	n	n	CCONJ
ejpam-5812	160	21	,	,	PUNCT
ejpam-5812	160	22	m	m	VERB
ejpam-5812	160	23	is	be	AUX
ejpam-5812	160	24	cordial	cordial	ADJ
ejpam-5812	160	25	for	for	ADP
ejpam-5812	160	26	all	all	DET
ejpam-5812	160	27	3	3	NUM
ejpam-5812	160	28	≤	≤	NOUN
ejpam-5812	160	29	n	n	PRON
ejpam-5812	160	30	≤	≤	NUM
ejpam-5812	160	31	8	8	NUM
ejpam-5812	160	32	,	,	PUNCT
ejpam-5812	160	33	and	and	CCONJ
ejpam-5812	160	34	m	m	NOUN
ejpam-5812	160	35	>	>	X
ejpam-5812	160	36	8	8	NUM
ejpam-5812	160	37	.	.	PUNCT
ejpam-5812	161	1	considering	consider	VERB
ejpam-5812	161	2	that	that	SCONJ
ejpam-5812	161	3	l5	l5	PROPN
ejpam-5812	161	4	n	n	CCONJ
ejpam-5812	161	5	,	,	PUNCT
ejpam-5812	161	6	m	m	VERB
ejpam-5812	161	7	≊	≊	NOUN
ejpam-5812	161	8	l5	l5	PROPN
ejpam-5812	161	9	m	m	PROPN
ejpam-5812	161	10	,	,	PUNCT
ejpam-5812	161	11	n.	n.	NOUN
ejpam-5812	161	12	proof	proof	NOUN
ejpam-5812	161	13	.	.	PUNCT
ejpam-5812	162	1	let	let	VERB
ejpam-5812	162	2	3	3	NUM
ejpam-5812	162	3	≤	≤	NOUN
ejpam-5812	162	4	n	n	PRON
ejpam-5812	162	5	≤	≤	NOUN
ejpam-5812	162	6	8	8	NUM
ejpam-5812	162	7	and	and	CCONJ
ejpam-5812	162	8	m=	m=	X
ejpam-5812	162	9	4t+	4t+	NUM
ejpam-5812	162	10	j	j	PROPN
ejpam-5812	162	11	(	(	PUNCT
ejpam-5812	162	12	j=	j=	ADP
ejpam-5812	162	13	4	4	NUM
ejpam-5812	162	14	,	,	PUNCT
ejpam-5812	162	15	1	1	NUM
ejpam-5812	162	16	,	,	PUNCT
ejpam-5812	162	17	2	2	NUM
ejpam-5812	162	18	,	,	PUNCT
ejpam-5812	162	19	3	3	NUM
ejpam-5812	162	20	and	and	CCONJ
ejpam-5812	162	21	t	t	PROPN
ejpam-5812	162	22	≥	≥	NUM
ejpam-5812	162	23	2	2	NUM
ejpam-5812	162	24	)	)	PUNCT
ejpam-5812	162	25	,	,	PUNCT
ejpam-5812	162	26	then	then	ADV
ejpam-5812	162	27	using	use	VERB
ejpam-5812	162	28	tables	table	NOUN
ejpam-5812	162	29	1	1	NUM
ejpam-5812	162	30	,	,	PUNCT
ejpam-5812	162	31	5	5	NUM
ejpam-5812	162	32	and	and	CCONJ
ejpam-5812	162	33	formulas	formula	NOUN
ejpam-5812	162	34	v0	v0	NOUN
ejpam-5812	162	35	−	−	PROPN
ejpam-5812	162	36	v1and	v1and	NOUN
ejpam-5812	162	37	e0	e0	PROPN
ejpam-5812	162	38	−	−	PROPN
ejpam-5812	162	39	e1	e1	PROPN
ejpam-5812	162	40	,	,	PUNCT
ejpam-5812	162	41	we	we	PRON
ejpam-5812	162	42	can	can	AUX
ejpam-5812	162	43	compute	compute	VERB
ejpam-5812	162	44	the	the	DET
ejpam-5812	162	45	values	value	NOUN
ejpam-5812	162	46	shown	show	VERB
ejpam-5812	162	47	in	in	ADP
ejpam-5812	162	48	the	the	DET
ejpam-5812	162	49	last	last	ADJ
ejpam-5812	162	50	two	two	NUM
ejpam-5812	162	51	columns	column	NOUN
ejpam-5812	162	52	of	of	ADP
ejpam-5812	162	53	tables	table	NOUN
ejpam-5812	162	54	5	5	NUM
ejpam-5812	162	55	.	.	PUNCT
ejpam-5812	163	1	since	since	SCONJ
ejpam-5812	163	2	all	all	PRON
ejpam-5812	163	3	of	of	ADP
ejpam-5812	163	4	these	these	DET
ejpam-5812	163	5	values	value	NOUN
ejpam-5812	163	6	are	be	AUX
ejpam-5812	163	7	−1	−1	ADJ
ejpam-5812	163	8	,	,	PUNCT
ejpam-5812	163	9	0	0	NUM
ejpam-5812	163	10	or	or	CCONJ
ejpam-5812	163	11	1	1	NUM
ejpam-5812	163	12	,	,	PUNCT
ejpam-5812	163	13	the	the	DET
ejpam-5812	163	14	lemma	lemma	PROPN
ejpam-5812	163	15	is	be	AUX
ejpam-5812	163	16	proved	prove	VERB
ejpam-5812	163	17	.	.	PUNCT
ejpam-5812	164	1	a.	a.	PROPN
ejpam-5812	164	2	abd	abd	PROPN
ejpam-5812	164	3	el	el	PROPN
ejpam-5812	164	4	-	-	PROPN
ejpam-5812	164	5	hay	hay	PROPN
ejpam-5812	164	6	,	,	PUNCT
ejpam-5812	164	7	k.	k.	PROPN
ejpam-5812	164	8	a.	a.	PROPN
ejpam-5812	164	9	alsatami	alsatami	PROPN
ejpam-5812	164	10	,	,	PUNCT
ejpam-5812	164	11	a.	a.	NOUN
ejpam-5812	164	12	elrokh	elrokh	PROPN
ejpam-5812	164	13	/	/	SYM
ejpam-5812	164	14	eur	eur	PROPN
ejpam-5812	164	15	.	.	PUNCT
ejpam-5812	165	1	j.	j.	PROPN
ejpam-5812	165	2	pure	pure	PROPN
ejpam-5812	165	3	appl	appl	PROPN
ejpam-5812	165	4	.	.	PROPN
ejpam-5812	165	5	math	math	PROPN
ejpam-5812	165	6	,	,	PUNCT
ejpam-5812	165	7	18	18	NUM
ejpam-5812	165	8	(	(	PUNCT
ejpam-5812	165	9	1	1	NUM
ejpam-5812	165	10	)	)	PUNCT
ejpam-5812	165	11	(	(	PUNCT
ejpam-5812	165	12	2025	2025	NUM
ejpam-5812	165	13	)	)	PUNCT
ejpam-5812	165	14	,	,	PUNCT
ejpam-5812	165	15	5812	5812	NUM
ejpam-5812	165	16	7	7	NUM
ejpam-5812	165	17	of	of	ADP
ejpam-5812	165	18	14	14	NUM
ejpam-5812	165	19	table	table	NOUN
ejpam-5812	165	20	5	5	NUM
ejpam-5812	165	21	:	:	PUNCT
ejpam-5812	165	22	labeling	labeling	NOUN
ejpam-5812	165	23	of	of	ADP
ejpam-5812	165	24	l5	l5	PROPN
ejpam-5812	165	25	n	n	CCONJ
ejpam-5812	165	26	,	,	PUNCT
ejpam-5812	165	27	m;3	m;3	NOUN
ejpam-5812	165	28	≤	≤	NOUN
ejpam-5812	165	29	n	n	CCONJ
ejpam-5812	165	30	≤	≤	NUM
ejpam-5812	165	31	8	8	NUM
ejpam-5812	165	32	,	,	PUNCT
ejpam-5812	165	33	and	and	CCONJ
ejpam-5812	165	34	m	m	PROPN
ejpam-5812	165	35	>	>	X
ejpam-5812	165	36	8	8	NUM
ejpam-5812	165	37	3	3	NUM
ejpam-5812	165	38	≤	≤	NOUN
ejpam-5812	165	39	n	n	PRON
ejpam-5812	165	40	≤	≤	NUM
ejpam-5812	165	41	8	8	NUM
ejpam-5812	165	42	m	m	NOUN
ejpam-5812	165	43	=	=	SYM
ejpam-5812	165	44	4t+	4t+	PROPN
ejpam-5812	165	45	j	j	PROPN
ejpam-5812	165	46	,	,	PUNCT
ejpam-5812	165	47	t	t	PROPN
ejpam-5812	165	48	≥	≥	NUM
ejpam-5812	165	49	2,m	2,m	X
ejpam-5812	165	50	>	>	SYM
ejpam-5812	165	51	8	8	NUM
ejpam-5812	165	52	i	i	NOUN
ejpam-5812	165	53	=	=	NOUN
ejpam-5812	165	54	4	4	NUM
ejpam-5812	165	55	,	,	PUNCT
ejpam-5812	165	56	1	1	NUM
ejpam-5812	165	57	,	,	PUNCT
ejpam-5812	165	58	2	2	NUM
ejpam-5812	165	59	,	,	PUNCT
ejpam-5812	165	60	3	3	NUM
ejpam-5812	165	61	labeling	labeling	NOUN
ejpam-5812	165	62	of	of	ADP
ejpam-5812	165	63	l5	l5	PROPN
ejpam-5812	165	64	n	n	CCONJ
ejpam-5812	165	65	,	,	PUNCT
ejpam-5812	165	66	m	m	PROPN
ejpam-5812	165	67	v0	v0	NOUN
ejpam-5812	165	68	v1	v1	NOUN
ejpam-5812	165	69	e0	e0	PROPN
ejpam-5812	165	70	e1	e1	PROPN
ejpam-5812	165	71	v0	v0	NOUN
ejpam-5812	165	72	−	−	PROPN
ejpam-5812	165	73	v1	v1	PROPN
ejpam-5812	165	74	e0	e0	PROPN
ejpam-5812	165	75	−	−	PROPN
ejpam-5812	165	76	e1	e1	PROPN
ejpam-5812	165	77	3	3	NUM
ejpam-5812	165	78	m=	m=	X
ejpam-5812	165	79	4t+	4t+	NOUN
ejpam-5812	165	80	4	4	NUM
ejpam-5812	165	81	[	[	X
ejpam-5812	165	82	03	03	NUM
ejpam-5812	165	83	;	;	PUNCT
ejpam-5812	165	84	0l4t13	0l4t13	NUM
ejpam-5812	165	85	]	]	PUNCT
ejpam-5812	165	86	2t+	2t+	NUM
ejpam-5812	165	87	3	3	NUM
ejpam-5812	165	88	2t+	2t+	NUM
ejpam-5812	165	89	3	3	NUM
ejpam-5812	165	90	10t+	10t+	NUM
ejpam-5812	165	91	5	5	NUM
ejpam-5812	165	92	10t+	10t+	NUM
ejpam-5812	165	93	4	4	NUM
ejpam-5812	165	94	0	0	NUM
ejpam-5812	165	95	1	1	NUM
ejpam-5812	165	96	m=	m=	X
ejpam-5812	165	97	4t+	4t+	NOUN
ejpam-5812	165	98	1	1	NUM
ejpam-5812	166	1	[	[	X
ejpam-5812	166	2	010;l4	010;l4	NUM
ejpam-5812	166	3	t	t	X
ejpam-5812	166	4	]	]	PUNCT
ejpam-5812	166	5	2t+	2t+	NUM
ejpam-5812	166	6	2	2	NUM
ejpam-5812	166	7	2t+	2t+	NUM
ejpam-5812	166	8	1	1	NUM
ejpam-5812	166	9	10t−	10t−	NUM
ejpam-5812	166	10	3	3	NUM
ejpam-5812	166	11	10t−	10t−	NUM
ejpam-5812	166	12	3	3	NUM
ejpam-5812	166	13	1	1	NUM
ejpam-5812	166	14	0	0	NUM
ejpam-5812	166	15	m=	m=	X
ejpam-5812	166	16	4t+	4t+	NUM
ejpam-5812	166	17	2	2	NUM
ejpam-5812	167	1	[	[	X
ejpam-5812	167	2	010;012l	010;012l	NUM
ejpam-5812	167	3	′	′	NUM
ejpam-5812	167	4	4t−410	4t−410	NUM
ejpam-5812	167	5	]	]	PUNCT
ejpam-5812	167	6	2t+	2t+	NUM
ejpam-5812	167	7	2	2	NUM
ejpam-5812	167	8	2t+	2t+	NUM
ejpam-5812	167	9	2	2	NUM
ejpam-5812	167	10	10t−	10t−	NUM
ejpam-5812	167	11	1	1	NUM
ejpam-5812	167	12	10	10	NUM
ejpam-5812	167	13	t	t	NOUN
ejpam-5812	167	14	0	0	NUM
ejpam-5812	167	15	−1	−1	NOUN
ejpam-5812	167	16	m=	m=	ADJ
ejpam-5812	167	17	4t+	4t+	NOUN
ejpam-5812	167	18	3	3	NUM
ejpam-5812	168	1	[	[	X
ejpam-5812	168	2	101;l	101;l	NUM
ejpam-5812	168	3	′	′	NUM
ejpam-5812	168	4	4t01	4t01	NUM
ejpam-5812	168	5	]	]	PUNCT
ejpam-5812	168	6	2t+	2t+	NUM
ejpam-5812	168	7	2	2	NUM
ejpam-5812	168	8	2t+	2t+	NUM
ejpam-5812	168	9	3	3	NUM
ejpam-5812	168	10	10t+	10t+	NUM
ejpam-5812	168	11	2	2	NUM
ejpam-5812	168	12	10t+	10t+	NUM
ejpam-5812	168	13	2	2	NUM
ejpam-5812	168	14	−1	−1	NOUN
ejpam-5812	168	15	0	0	NUM
ejpam-5812	168	16	4	4	NUM
ejpam-5812	168	17	m=	m=	ADJ
ejpam-5812	168	18	4t+	4t+	NUM
ejpam-5812	168	19	4	4	NUM
ejpam-5812	169	1	[	[	SYM
ejpam-5812	169	2	130;02l	130;02l	NUM
ejpam-5812	169	3	′	′	NUM
ejpam-5812	169	4	4t02	4t02	NOUN
ejpam-5812	169	5	]	]	PUNCT
ejpam-5812	169	6	2t+	2t+	NUM
ejpam-5812	169	7	4	4	NUM
ejpam-5812	169	8	2t+	2t+	NUM
ejpam-5812	169	9	3	3	NUM
ejpam-5812	169	10	10t+	10t+	NUM
ejpam-5812	169	11	6	6	NUM
ejpam-5812	169	12	10t+	10t+	NUM
ejpam-5812	169	13	6	6	NUM
ejpam-5812	169	14	1	1	NUM
ejpam-5812	169	15	0	0	NUM
ejpam-5812	169	16	m=	m=	X
ejpam-5812	169	17	4t+	4t+	NUM
ejpam-5812	169	18	1	1	NUM
ejpam-5812	169	19	[	[	X
ejpam-5812	169	20	m4	m4	X
ejpam-5812	169	21	;	;	PUNCT
ejpam-5812	169	22	12	12	NUM
ejpam-5812	169	23	m	m	NOUN
ejpam-5812	169	24	′	′	NUM
ejpam-5812	169	25	4t−403	4t−403	NUM
ejpam-5812	169	26	]	]	PUNCT
ejpam-5812	169	27	2t+	2t+	NUM
ejpam-5812	169	28	2	2	NUM
ejpam-5812	169	29	2t+	2t+	NUM
ejpam-5812	169	30	2	2	NUM
ejpam-5812	169	31	10t−	10t−	NUM
ejpam-5812	169	32	2	2	NUM
ejpam-5812	169	33	10t−	10t−	NUM
ejpam-5812	169	34	1	1	NUM
ejpam-5812	169	35	0	0	NUM
ejpam-5812	169	36	−1	−1	NOUN
ejpam-5812	169	37	m=	m=	X
ejpam-5812	169	38	4t+	4t+	PROPN
ejpam-5812	169	39	2	2	NUM
ejpam-5812	169	40	[	[	X
ejpam-5812	169	41	031;0l4t1	031;0l4t1	X
ejpam-5812	169	42	]	]	PUNCT
ejpam-5812	169	43	2t+	2t+	NUM
ejpam-5812	169	44	3	3	NUM
ejpam-5812	169	45	2t+	2t+	NUM
ejpam-5812	169	46	2	2	NUM
ejpam-5812	169	47	10t+	10t+	NUM
ejpam-5812	169	48	1	1	NUM
ejpam-5812	169	49	10t+	10t+	NUM
ejpam-5812	169	50	1	1	NUM
ejpam-5812	169	51	1	1	NUM
ejpam-5812	169	52	0	0	NUM
ejpam-5812	169	53	m=	m=	X
ejpam-5812	169	54	4t+	4t+	NUM
ejpam-5812	169	55	3	3	NUM
ejpam-5812	170	1	[	[	X
ejpam-5812	170	2	031	031	NOUN
ejpam-5812	170	3	;	;	PUNCT
ejpam-5812	170	4	1l4t12	1l4t12	NUM
ejpam-5812	170	5	]	]	PUNCT
ejpam-5812	170	6	2t+	2t+	NUM
ejpam-5812	170	7	3	3	NUM
ejpam-5812	170	8	2t+	2t+	NUM
ejpam-5812	170	9	3	3	NUM
ejpam-5812	170	10	10t+	10t+	NUM
ejpam-5812	170	11	4	4	NUM
ejpam-5812	170	12	10t+	10t+	NUM
ejpam-5812	170	13	3	3	NUM
ejpam-5812	170	14	1	1	NUM
ejpam-5812	170	15	0	0	NUM
ejpam-5812	170	16	5	5	NUM
ejpam-5812	170	17	m=	m=	ADJ
ejpam-5812	170	18	4t+	4t+	NOUN
ejpam-5812	170	19	4	4	NUM
ejpam-5812	171	1	[	[	SYM
ejpam-5812	171	2	0103	0103	NUM
ejpam-5812	171	3	;	;	PUNCT
ejpam-5812	171	4	0l	0l	NUM
ejpam-5812	171	5	′	′	NUM
ejpam-5812	171	6	4t13	4t13	NOUN
ejpam-5812	171	7	]	]	PUNCT
ejpam-5812	171	8	2t+	2t+	NUM
ejpam-5812	171	9	4	4	NUM
ejpam-5812	171	10	2t+	2t+	NUM
ejpam-5812	171	11	4	4	NUM
ejpam-5812	171	12	10t+	10t+	NUM
ejpam-5812	171	13	8	8	NUM
ejpam-5812	171	14	10t+	10t+	NUM
ejpam-5812	171	15	8	8	NUM
ejpam-5812	171	16	0	0	NUM
ejpam-5812	171	17	0	0	NUM
ejpam-5812	172	1	m=	m=	X
ejpam-5812	172	2	4t+	4t+	PROPN
ejpam-5812	172	3	1	1	NUM
ejpam-5812	173	1	[	[	X
ejpam-5812	173	2	0103;0l	0103;0l	NOUN
ejpam-5812	173	3	′	′	NUM
ejpam-5812	173	4	4t−413	4t−413	NUM
ejpam-5812	173	5	]	]	SYM
ejpam-5812	173	6	2t+	2t+	NUM
ejpam-5812	173	7	3	3	NUM
ejpam-5812	173	8	2t+	2t+	NUM
ejpam-5812	173	9	2	2	NUM
ejpam-5812	173	10	10t+	10t+	NUM
ejpam-5812	173	11	1	1	NUM
ejpam-5812	173	12	10	10	NUM
ejpam-5812	173	13	t	t	NOUN
ejpam-5812	173	14	1	1	NUM
ejpam-5812	173	15	1	1	NUM
ejpam-5812	173	16	m=	m=	X
ejpam-5812	173	17	4t+	4t+	NOUN
ejpam-5812	173	18	2	2	NUM
ejpam-5812	174	1	[	[	X
ejpam-5812	174	2	0103;12l	0103;12l	NUM
ejpam-5812	175	1	′	′	NUM
ejpam-5812	175	2	4t120	4t120	NUM
ejpam-5812	175	3	]	]	PUNCT
ejpam-5812	175	4	2t+	2t+	NUM
ejpam-5812	175	5	3	3	NUM
ejpam-5812	175	6	2t+	2t+	NUM
ejpam-5812	175	7	3	3	NUM
ejpam-5812	175	8	10t+	10t+	NUM
ejpam-5812	175	9	3	3	NUM
ejpam-5812	175	10	10t+	10t+	NUM
ejpam-5812	175	11	3	3	NUM
ejpam-5812	175	12	0	0	NUM
ejpam-5812	175	13	0	0	NUM
ejpam-5812	176	1	m=	m=	X
ejpam-5812	176	2	4t+	4t+	PROPN
ejpam-5812	176	3	3	3	NUM
ejpam-5812	176	4	[	[	X
ejpam-5812	176	5	0312	0312	NUM
ejpam-5812	176	6	;	;	PUNCT
ejpam-5812	176	7	l	l	NOUN
ejpam-5812	176	8	′	′	NUM
ejpam-5812	176	9	4t01	4t01	VERB
ejpam-5812	176	10	]	]	PUNCT
ejpam-5812	176	11	2t+	2t+	NUM
ejpam-5812	176	12	4	4	NUM
ejpam-5812	176	13	2t+	2t+	NUM
ejpam-5812	176	14	3	3	NUM
ejpam-5812	176	15	10t+	10t+	NUM
ejpam-5812	176	16	5	5	NUM
ejpam-5812	176	17	10t+	10t+	NUM
ejpam-5812	176	18	6	6	NUM
ejpam-5812	176	19	1	1	NUM
ejpam-5812	176	20	−1	−1	NOUN
ejpam-5812	176	21	6	6	NUM
ejpam-5812	176	22	m=	m=	NOUN
ejpam-5812	176	23	4t+	4t+	NUM
ejpam-5812	176	24	4	4	NUM
ejpam-5812	176	25	[	[	SYM
ejpam-5812	176	26	10213;l	10213;l	NUM
ejpam-5812	176	27	′	′	NUM
ejpam-5812	176	28	4t−40210	4t−40210	PROPN
ejpam-5812	176	29	]	]	PUNCT
ejpam-5812	176	30	2t+	2t+	NUM
ejpam-5812	176	31	5	5	NUM
ejpam-5812	176	32	2t+	2t+	NUM
ejpam-5812	176	33	4	4	NUM
ejpam-5812	176	34	10t+	10t+	NUM
ejpam-5812	176	35	3	3	NUM
ejpam-5812	176	36	10t+	10t+	NUM
ejpam-5812	176	37	4	4	NUM
ejpam-5812	176	38	1	1	NUM
ejpam-5812	176	39	−1	−1	NOUN
ejpam-5812	176	40	m=	m=	ADJ
ejpam-5812	176	41	4t+	4t+	NOUN
ejpam-5812	176	42	1	1	NUM
ejpam-5812	177	1	[	[	X
ejpam-5812	177	2	10213	10213	NUM
ejpam-5812	177	3	;	;	PUNCT
ejpam-5812	177	4	12m4t−403	12m4t−403	NUM
ejpam-5812	177	5	]	]	SYM
ejpam-5812	177	6	2t+	2t+	NUM
ejpam-5812	177	7	3	3	NUM
ejpam-5812	177	8	2t+	2t+	NUM
ejpam-5812	177	9	3	3	NUM
ejpam-5812	177	10	10t+	10t+	NUM
ejpam-5812	177	11	3	3	NUM
ejpam-5812	177	12	10t+	10t+	NUM
ejpam-5812	177	13	3	3	NUM
ejpam-5812	177	14	0	0	NUM
ejpam-5812	177	15	0	0	NUM
ejpam-5812	178	1	m=	m=	X
ejpam-5812	178	2	4t+	4t+	NUM
ejpam-5812	178	3	2	2	NUM
ejpam-5812	178	4	[	[	X
ejpam-5812	178	5	0l40;012l4t−410	0l40;012l4t−410	NUM
ejpam-5812	178	6	]	]	PUNCT
ejpam-5812	178	7	2t+	2t+	NUM
ejpam-5812	178	8	4	4	NUM
ejpam-5812	178	9	2t+	2t+	NUM
ejpam-5812	178	10	3	3	NUM
ejpam-5812	178	11	10t+	10t+	NUM
ejpam-5812	178	12	5	5	NUM
ejpam-5812	178	13	10t+	10t+	NUM
ejpam-5812	178	14	6	6	NUM
ejpam-5812	178	15	1	1	NUM
ejpam-5812	178	16	−1	−1	NOUN
ejpam-5812	178	17	m=	m=	ADJ
ejpam-5812	178	18	4t+	4t+	NOUN
ejpam-5812	178	19	3	3	NUM
ejpam-5812	178	20	[	[	X
ejpam-5812	178	21	13010	13010	NUM
ejpam-5812	178	22	;	;	PUNCT
ejpam-5812	178	23	0l4t10	0l4t10	NUM
ejpam-5812	178	24	]	]	SYM
ejpam-5812	178	25	2t+	2t+	NUM
ejpam-5812	178	26	4	4	NUM
ejpam-5812	178	27	2t+	2t+	NUM
ejpam-5812	178	28	5	5	NUM
ejpam-5812	178	29	10t+	10t+	NUM
ejpam-5812	178	30	8	8	NUM
ejpam-5812	178	31	10t+	10t+	NUM
ejpam-5812	178	32	8	8	NUM
ejpam-5812	178	33	−1	−1	NOUN
ejpam-5812	178	34	0	0	NUM
ejpam-5812	178	35	7	7	NUM
ejpam-5812	178	36	m=	m=	ADJ
ejpam-5812	178	37	4t+	4t+	NUM
ejpam-5812	178	38	4	4	NUM
ejpam-5812	178	39	[	[	X
ejpam-5812	178	40	021203;l4t1201	021203;l4t1201	NUM
ejpam-5812	178	41	]	]	PUNCT
ejpam-5812	178	42	2t+	2t+	NUM
ejpam-5812	178	43	4	4	NUM
ejpam-5812	178	44	2t+	2t+	NUM
ejpam-5812	178	45	3	3	NUM
ejpam-5812	178	46	10t+	10t+	NUM
ejpam-5812	178	47	14	14	NUM
ejpam-5812	178	48	10t+	10t+	NUM
ejpam-5812	178	49	13	13	NUM
ejpam-5812	178	50	1	1	NUM
ejpam-5812	178	51	1	1	NUM
ejpam-5812	178	52	m=	m=	ADJ
ejpam-5812	178	53	4t+	4t+	NUM
ejpam-5812	178	54	1	1	NUM
ejpam-5812	178	55	021203;l4t1	021203;l4t1	NUM
ejpam-5812	178	56	2t+	2t+	NUM
ejpam-5812	178	57	4	4	NUM
ejpam-5812	178	58	2t+	2t+	NUM
ejpam-5812	178	59	3	3	NUM
ejpam-5812	178	60	10t+	10t+	NUM
ejpam-5812	178	61	6	6	NUM
ejpam-5812	178	62	10t+	10t+	NUM
ejpam-5812	178	63	6	6	NUM
ejpam-5812	178	64	1	1	NUM
ejpam-5812	178	65	−1	−1	NOUN
ejpam-5812	178	66	m=	m=	PUNCT
ejpam-5812	178	67	4t+	4t+	NUM
ejpam-5812	178	68	2	2	NUM
ejpam-5812	178	69	021203;l4t12	021203;l4t12	NOUN
ejpam-5812	178	70	2t+	2t+	NUM
ejpam-5812	178	71	4	4	NUM
ejpam-5812	178	72	2t+	2t+	NUM
ejpam-5812	178	73	4	4	NUM
ejpam-5812	178	74	10t+	10t+	NUM
ejpam-5812	178	75	9	9	NUM
ejpam-5812	178	76	10t+	10t+	NUM
ejpam-5812	178	77	8	8	NUM
ejpam-5812	178	78	0	0	NUM
ejpam-5812	178	79	1	1	NUM
ejpam-5812	178	80	m=	m=	X
ejpam-5812	178	81	4t+	4t+	PROPN
ejpam-5812	178	82	3	3	NUM
ejpam-5812	178	83	[	[	X
ejpam-5812	178	84	04101	04101	NUM
ejpam-5812	178	85	;	;	PUNCT
ejpam-5812	178	86	11l4t1	11l4t1	NUM
ejpam-5812	178	87	]	]	PUNCT
ejpam-5812	178	88	2t+	2t+	NUM
ejpam-5812	178	89	5	5	NUM
ejpam-5812	178	90	2t+	2t+	NUM
ejpam-5812	178	91	4	4	NUM
ejpam-5812	178	92	10t+	10t+	NUM
ejpam-5812	178	93	11	11	NUM
ejpam-5812	178	94	10t+	10t+	NUM
ejpam-5812	178	95	11	11	NUM
ejpam-5812	178	96	1	1	NUM
ejpam-5812	178	97	0	0	NUM
ejpam-5812	178	98	8	8	NUM
ejpam-5812	178	99	m=	m=	X
ejpam-5812	178	100	4t+	4t+	NUM
ejpam-5812	178	101	4	4	NUM
ejpam-5812	178	102	[	[	SYM
ejpam-5812	178	103	1031021	1031021	NUM
ejpam-5812	178	104	;	;	PUNCT
ejpam-5812	178	105	1012l4	1012l4	NUM
ejpam-5812	178	106	t	t	NOUN
ejpam-5812	178	107	]	]	PUNCT
ejpam-5812	178	108	2t+	2t+	NUM
ejpam-5812	178	109	6	6	NUM
ejpam-5812	178	110	2t+	2t+	NUM
ejpam-5812	178	111	5	5	NUM
ejpam-5812	178	112	10t+	10t+	NUM
ejpam-5812	178	113	16	16	NUM
ejpam-5812	178	114	10t+	10t+	NUM
ejpam-5812	178	115	16	16	NUM
ejpam-5812	178	116	1	1	NUM
ejpam-5812	178	117	0	0	NUM
ejpam-5812	179	1	m=	m=	X
ejpam-5812	179	2	4t+	4t+	NUM
ejpam-5812	179	3	1	1	NUM
ejpam-5812	179	4	0102	0102	NUM
ejpam-5812	179	5	m	m	VERB
ejpam-5812	179	6	′	′	NOUN
ejpam-5812	180	1	4;l4t1	4;l4t1	NUM
ejpam-5812	180	2	2t+	2t+	NUM
ejpam-5812	180	3	4	4	NUM
ejpam-5812	180	4	2t+	2t+	NUM
ejpam-5812	180	5	4	4	NUM
ejpam-5812	180	6	10t+	10t+	NUM
ejpam-5812	180	7	8	8	NUM
ejpam-5812	180	8	10t+	10t+	NUM
ejpam-5812	180	9	9	9	NUM
ejpam-5812	180	10	0	0	NUM
ejpam-5812	180	11	−1	−1	NOUN
ejpam-5812	180	12	m=	m=	X
ejpam-5812	180	13	4t+	4t+	NUM
ejpam-5812	180	14	2	2	NUM
ejpam-5812	180	15	1031021	1031021	NUM
ejpam-5812	180	16	;	;	PUNCT
ejpam-5812	180	17	12l4	12l4	NUM
ejpam-5812	180	18	t	t	NOUN
ejpam-5812	180	19	2t+	2t+	NUM
ejpam-5812	180	20	5	5	NUM
ejpam-5812	180	21	2t+	2t+	NUM
ejpam-5812	180	22	4	4	NUM
ejpam-5812	180	23	10t+	10t+	NUM
ejpam-5812	180	24	11	11	NUM
ejpam-5812	180	25	10t+	10t+	NUM
ejpam-5812	180	26	11	11	NUM
ejpam-5812	180	27	1	1	NUM
ejpam-5812	180	28	0	0	NUM
ejpam-5812	180	29	m=	m=	X
ejpam-5812	180	30	4t+	4t+	NUM
ejpam-5812	180	31	3	3	NUM
ejpam-5812	180	32	[	[	PUNCT
ejpam-5812	180	33	0102	0102	NUM
ejpam-5812	180	34	m	m	VERB
ejpam-5812	180	35	′	′	NUM
ejpam-5812	180	36	4	4	NUM
ejpam-5812	180	37	;	;	PUNCT
ejpam-5812	180	38	0l4t12	0l4t12	NUM
ejpam-5812	180	39	]	]	PUNCT
ejpam-5812	180	40	2t+	2t+	NUM
ejpam-5812	180	41	5	5	NUM
ejpam-5812	180	42	2t+	2t+	NUM
ejpam-5812	180	43	5	5	NUM
ejpam-5812	180	44	10t+	10t+	NUM
ejpam-5812	180	45	14	14	NUM
ejpam-5812	180	46	10t+	10t+	NUM
ejpam-5812	180	47	13	13	NUM
ejpam-5812	180	48	0	0	NUM
ejpam-5812	180	49	1	1	NUM
ejpam-5812	181	1	lemma	lemma	PROPN
ejpam-5812	181	2	3.5.2	3.5.2	NUM
ejpam-5812	181	3	.	.	PUNCT
ejpam-5812	182	1	if	if	SCONJ
ejpam-5812	182	2	n	n	CCONJ
ejpam-5812	182	3	,	,	PUNCT
ejpam-5812	182	4	m	m	VERB
ejpam-5812	182	5	≥	≥	NOUN
ejpam-5812	182	6	9	9	NUM
ejpam-5812	182	7	,	,	PUNCT
ejpam-5812	182	8	then	then	ADV
ejpam-5812	182	9	the	the	DET
ejpam-5812	182	10	fifth	fifth	ADJ
ejpam-5812	182	11	power	power	NOUN
ejpam-5812	182	12	of	of	ADP
ejpam-5812	182	13	lemniscate	lemniscate	PROPN
ejpam-5812	182	14	l5	l5	PROPN
ejpam-5812	182	15	n	n	CCONJ
ejpam-5812	182	16	,	,	PUNCT
ejpam-5812	182	17	m	m	VERB
ejpam-5812	182	18	is	be	AUX
ejpam-5812	182	19	cordial	cordial	ADJ
ejpam-5812	182	20	for	for	ADP
ejpam-5812	182	21	all	all	DET
ejpam-5812	182	22	n	n	PRON
ejpam-5812	182	23	≥	≥	NOUN
ejpam-5812	182	24	9	9	NUM
ejpam-5812	182	25	and	and	CCONJ
ejpam-5812	182	26	m	m	PRON
ejpam-5812	182	27	≥	≥	NOUN
ejpam-5812	182	28	9	9	NUM
ejpam-5812	182	29	.	.	PUNCT
ejpam-5812	183	1	proof	proof	NOUN
ejpam-5812	183	2	.	.	PUNCT
ejpam-5812	184	1	let	let	VERB
ejpam-5812	184	2	n=	n=	ADJ
ejpam-5812	184	3	4r	4r	NOUN
ejpam-5812	184	4	+	+	CCONJ
ejpam-5812	184	5	i	i	PRON
ejpam-5812	184	6	(	(	PUNCT
ejpam-5812	184	7	i=	i=	PROPN
ejpam-5812	184	8	0	0	NUM
ejpam-5812	184	9	,	,	PUNCT
ejpam-5812	184	10	1	1	NUM
ejpam-5812	184	11	,	,	PUNCT
ejpam-5812	184	12	2	2	NUM
ejpam-5812	184	13	,	,	PUNCT
ejpam-5812	184	14	3	3	NUM
ejpam-5812	184	15	and	and	CCONJ
ejpam-5812	184	16	r	r	NOUN
ejpam-5812	184	17	≥	≥	NOUN
ejpam-5812	184	18	1	1	NUM
ejpam-5812	184	19	)	)	PUNCT
ejpam-5812	184	20	and	and	CCONJ
ejpam-5812	184	21	m=	m=	X
ejpam-5812	184	22	4	4	NUM
ejpam-5812	184	23	t	t	NOUN
ejpam-5812	184	24	+	+	X
ejpam-5812	184	25	j	j	PROPN
ejpam-5812	184	26	(	(	PUNCT
ejpam-5812	184	27	j=	j=	NOUN
ejpam-5812	184	28	0	0	NUM
ejpam-5812	184	29	,	,	PUNCT
ejpam-5812	184	30	1	1	NUM
ejpam-5812	184	31	,	,	PUNCT
ejpam-5812	184	32	2	2	NUM
ejpam-5812	184	33	,	,	PUNCT
ejpam-5812	184	34	3	3	NUM
ejpam-5812	184	35	and	and	CCONJ
ejpam-5812	184	36	t	t	PROPN
ejpam-5812	184	37	≥	≥	NUM
ejpam-5812	184	38	1	1	NUM
ejpam-5812	184	39	)	)	PUNCT
ejpam-5812	184	40	,	,	PUNCT
ejpam-5812	184	41	then	then	ADV
ejpam-5812	184	42	using	use	VERB
ejpam-5812	184	43	tables	table	NOUN
ejpam-5812	184	44	1	1	NUM
ejpam-5812	184	45	,	,	PUNCT
ejpam-5812	184	46	6	6	NUM
ejpam-5812	184	47	and	and	CCONJ
ejpam-5812	184	48	formulas	formula	NOUN
ejpam-5812	184	49	v0	v0	NOUN
ejpam-5812	184	50	−	−	PROPN
ejpam-5812	184	51	v1and	v1and	NOUN
ejpam-5812	184	52	e0	e0	PROPN
ejpam-5812	184	53	−	−	PROPN
ejpam-5812	184	54	e1	e1	PROPN
ejpam-5812	184	55	,	,	PUNCT
ejpam-5812	184	56	we	we	PRON
ejpam-5812	184	57	can	can	AUX
ejpam-5812	184	58	compute	compute	VERB
ejpam-5812	184	59	the	the	DET
ejpam-5812	184	60	values	value	NOUN
ejpam-5812	184	61	shown	show	VERB
ejpam-5812	184	62	in	in	ADP
ejpam-5812	184	63	the	the	DET
ejpam-5812	184	64	last	last	ADJ
ejpam-5812	184	65	two	two	NUM
ejpam-5812	184	66	columns	column	NOUN
ejpam-5812	184	67	of	of	ADP
ejpam-5812	184	68	table	table	NOUN
ejpam-5812	184	69	6	6	NUM
ejpam-5812	184	70	.	.	PUNCT
ejpam-5812	185	1	since	since	SCONJ
ejpam-5812	185	2	all	all	PRON
ejpam-5812	185	3	of	of	ADP
ejpam-5812	185	4	these	these	DET
ejpam-5812	185	5	values	value	NOUN
ejpam-5812	185	6	are	be	AUX
ejpam-5812	185	7	−1	−1	ADJ
ejpam-5812	185	8	,	,	PUNCT
ejpam-5812	185	9	0	0	NUM
ejpam-5812	185	10	or	or	CCONJ
ejpam-5812	185	11	1	1	NUM
ejpam-5812	185	12	,	,	PUNCT
ejpam-5812	185	13	the	the	DET
ejpam-5812	185	14	lemma	lemma	PROPN
ejpam-5812	185	15	is	be	AUX
ejpam-5812	185	16	proved	prove	VERB
ejpam-5812	185	17	.	.	PUNCT
ejpam-5812	186	1	table	table	NOUN
ejpam-5812	186	2	6	6	NUM
ejpam-5812	186	3	:	:	PUNCT
ejpam-5812	186	4	labeling	labeling	NOUN
ejpam-5812	186	5	of	of	ADP
ejpam-5812	186	6	l5	l5	PROPN
ejpam-5812	186	7	n	n	CCONJ
ejpam-5812	186	8	,	,	PUNCT
ejpam-5812	186	9	m	m	VERB
ejpam-5812	186	10	n	n	NOUN
ejpam-5812	186	11	=	=	NOUN
ejpam-5812	186	12	4r	4r	NOUN
ejpam-5812	187	1	+	+	CCONJ
ejpam-5812	187	2	i	i	PROPN
ejpam-5812	187	3	,	,	PUNCT
ejpam-5812	187	4	n	n	PRON
ejpam-5812	187	5	≥	≥	NOUN
ejpam-5812	187	6	9	9	NUM
ejpam-5812	187	7	0	0	NUM
ejpam-5812	187	8	≤	≤	NUM
ejpam-5812	187	9	j	j	PROPN
ejpam-5812	187	10	≤	≤	ADV
ejpam-5812	187	11	3	3	NUM
ejpam-5812	187	12	m	m	NOUN
ejpam-5812	187	13	=	=	SYM
ejpam-5812	187	14	4t+	4t+	NUM
ejpam-5812	187	15	j	j	PROPN
ejpam-5812	187	16	m	m	VERB
ejpam-5812	187	17	≥	≥	NUM
ejpam-5812	187	18	9	9	NUM
ejpam-5812	187	19	0	0	NUM
ejpam-5812	187	20	≤	≤	NUM
ejpam-5812	187	21	j	j	PROPN
ejpam-5812	187	22	≤	≤	ADV
ejpam-5812	187	23	3	3	NUM
ejpam-5812	187	24	labeling	labeling	NOUN
ejpam-5812	187	25	of	of	ADP
ejpam-5812	187	26	l5	l5	PROPN
ejpam-5812	187	27	n	n	CCONJ
ejpam-5812	187	28	,	,	PUNCT
ejpam-5812	187	29	m	m	PROPN
ejpam-5812	187	30	v0	v0	NOUN
ejpam-5812	187	31	v1	v1	NOUN
ejpam-5812	187	32	e0	e0	PROPN
ejpam-5812	187	33	e1	e1	PROPN
ejpam-5812	187	34	v0	v0	NOUN
ejpam-5812	187	35	−	−	PROPN
ejpam-5812	187	36	v1	v1	PROPN
ejpam-5812	187	37	e0	e0	PROPN
ejpam-5812	187	38	−	−	PROPN
ejpam-5812	187	39	e1	e1	VERB
ejpam-5812	187	40	i=	i=	PROPN
ejpam-5812	187	41	0	0	PUNCT
ejpam-5812	188	1	j=	j=	NOUN
ejpam-5812	188	2	0	0	PUNCT
ejpam-5812	189	1	[	[	X
ejpam-5812	189	2	0l4r120	0l4r120	NUM
ejpam-5812	189	3	;	;	PUNCT
ejpam-5812	189	4	0l4t120	0l4t120	NUM
ejpam-5812	189	5	]	]	X
ejpam-5812	190	1	2(r	2(r	NUM
ejpam-5812	190	2	+	+	NUM
ejpam-5812	190	3	t	t	X
ejpam-5812	190	4	)	)	PUNCT
ejpam-5812	191	1	+	+	CCONJ
ejpam-5812	191	2	3	3	NUM
ejpam-5812	191	3	2(r	2(r	NUM
ejpam-5812	191	4	+	+	SYM
ejpam-5812	191	5	t	t	PROPN
ejpam-5812	191	6	)	)	PUNCT
ejpam-5812	192	1	+	+	CCONJ
ejpam-5812	192	2	4	4	NUM
ejpam-5812	192	3	10(r	10(r	NUM
ejpam-5812	192	4	+	+	NUM
ejpam-5812	192	5	t	t	PROPN
ejpam-5812	192	6	)	)	PUNCT
ejpam-5812	192	7	+	+	CCONJ
ejpam-5812	192	8	6	6	NUM
ejpam-5812	192	9	10(r	10(r	NUM
ejpam-5812	192	10	+	+	NUM
ejpam-5812	192	11	t	t	PROPN
ejpam-5812	192	12	)	)	PUNCT
ejpam-5812	193	1	+	+	CCONJ
ejpam-5812	193	2	6	6	NUM
ejpam-5812	193	3	−1	−1	NOUN
ejpam-5812	193	4	0	0	NUM
ejpam-5812	193	5	j=	j=	NOUN
ejpam-5812	193	6	1	1	NUM
ejpam-5812	194	1	[	[	X
ejpam-5812	194	2	0l4r120;03m4t−412	0l4r120;03m4t−412	X
ejpam-5812	194	3	]	]	X
ejpam-5812	194	4	2(r	2(r	NUM
ejpam-5812	195	1	+	+	NUM
ejpam-5812	195	2	t	t	X
ejpam-5812	195	3	)	)	PUNCT
ejpam-5812	196	1	+	+	CCONJ
ejpam-5812	196	2	2	2	NUM
ejpam-5812	196	3	2(r	2(r	NUM
ejpam-5812	196	4	+	+	SYM
ejpam-5812	196	5	t	t	NOUN
ejpam-5812	196	6	)	)	PUNCT
ejpam-5812	196	7	+	+	CCONJ
ejpam-5812	196	8	2	2	NUM
ejpam-5812	196	9	10(r	10(r	NUM
ejpam-5812	197	1	+	+	CCONJ
ejpam-5812	197	2	t)−	t)−	PROPN
ejpam-5812	197	3	1	1	NUM
ejpam-5812	197	4	10(r	10(r	NUM
ejpam-5812	198	1	+	+	CCONJ
ejpam-5812	198	2	t)−	t)−	PROPN
ejpam-5812	198	3	2	2	NUM
ejpam-5812	198	4	0	0	NUM
ejpam-5812	198	5	−1	−1	NOUN
ejpam-5812	198	6	j=	j=	NOUN
ejpam-5812	198	7	2	2	NUM
ejpam-5812	199	1	[	[	X
ejpam-5812	199	2	0l4r120	0l4r120	NUM
ejpam-5812	199	3	;	;	PUNCT
ejpam-5812	199	4	01l4	01l4	NUM
ejpam-5812	199	5	t	t	X
ejpam-5812	199	6	]	]	PUNCT
ejpam-5812	199	7	2(r	2(r	NUM
ejpam-5812	199	8	+	+	NUM
ejpam-5812	199	9	t	t	PROPN
ejpam-5812	199	10	)	)	PUNCT
ejpam-5812	200	1	+	+	CCONJ
ejpam-5812	200	2	2	2	NUM
ejpam-5812	200	3	2(r	2(r	NUM
ejpam-5812	200	4	+	+	SYM
ejpam-5812	200	5	t	t	PROPN
ejpam-5812	200	6	)	)	PUNCT
ejpam-5812	201	1	+	+	CCONJ
ejpam-5812	201	2	3	3	NUM
ejpam-5812	201	3	10(r	10(r	NUM
ejpam-5812	201	4	+	+	NUM
ejpam-5812	201	5	t	t	PROPN
ejpam-5812	201	6	)	)	PUNCT
ejpam-5812	201	7	+	+	CCONJ
ejpam-5812	201	8	1	1	NUM
ejpam-5812	201	9	10(r	10(r	NUM
ejpam-5812	201	10	+	+	NUM
ejpam-5812	201	11	t	t	PROPN
ejpam-5812	201	12	)	)	PUNCT
ejpam-5812	201	13	+	+	CCONJ
ejpam-5812	201	14	1	1	NUM
ejpam-5812	201	15	−1	−1	NOUN
ejpam-5812	201	16	0	0	NUM
ejpam-5812	201	17	j=	j=	NOUN
ejpam-5812	201	18	3	3	NUM
ejpam-5812	202	1	[	[	X
ejpam-5812	202	2	0l4r120	0l4r120	NUM
ejpam-5812	202	3	;	;	PUNCT
ejpam-5812	202	4	0l4t10	0l4t10	NUM
ejpam-5812	202	5	]	]	X
ejpam-5812	202	6	2(r	2(r	NUM
ejpam-5812	202	7	+	+	NUM
ejpam-5812	202	8	t	t	PROPN
ejpam-5812	202	9	)	)	PUNCT
ejpam-5812	202	10	+	+	CCONJ
ejpam-5812	202	11	3	3	NUM
ejpam-5812	202	12	2(r	2(r	NUM
ejpam-5812	202	13	+	+	SYM
ejpam-5812	202	14	t	t	NOUN
ejpam-5812	202	15	)	)	PUNCT
ejpam-5812	203	1	+	+	CCONJ
ejpam-5812	203	2	3	3	NUM
ejpam-5812	203	3	10(r	10(r	NUM
ejpam-5812	203	4	+	+	NUM
ejpam-5812	203	5	t	t	PROPN
ejpam-5812	203	6	)	)	PUNCT
ejpam-5812	203	7	+	+	CCONJ
ejpam-5812	203	8	4	4	NUM
ejpam-5812	203	9	10(r	10(r	NUM
ejpam-5812	203	10	+	+	NUM
ejpam-5812	203	11	t	t	PROPN
ejpam-5812	203	12	)	)	PUNCT
ejpam-5812	204	1	+	+	CCONJ
ejpam-5812	204	2	3	3	NUM
ejpam-5812	204	3	0	0	NUM
ejpam-5812	204	4	1	1	NUM
ejpam-5812	204	5	i=	i=	NUM
ejpam-5812	204	6	1	1	NUM
ejpam-5812	204	7	j=	j=	NOUN
ejpam-5812	204	8	1	1	NUM
ejpam-5812	204	9	[	[	X
ejpam-5812	204	10	l4r1;12	l4r1;12	NOUN
ejpam-5812	204	11	m	m	VERB
ejpam-5812	204	12	′	′	NUM
ejpam-5812	204	13	4t−403	4t−403	NUM
ejpam-5812	204	14	]	]	PUNCT
ejpam-5812	204	15	2(r	2(r	NUM
ejpam-5812	204	16	+	+	SYM
ejpam-5812	204	17	t	t	X
ejpam-5812	204	18	)	)	PUNCT
ejpam-5812	205	1	+	+	CCONJ
ejpam-5812	205	2	1	1	NUM
ejpam-5812	205	3	2(r	2(r	NUM
ejpam-5812	205	4	+	+	NUM
ejpam-5812	205	5	t	t	PROPN
ejpam-5812	205	6	)	)	PUNCT
ejpam-5812	205	7	10(r	10(r	PROPN
ejpam-5812	206	1	+	+	CCONJ
ejpam-5812	206	2	t)−	t)−	PROPN
ejpam-5812	206	3	9	9	NUM
ejpam-5812	206	4	10(r	10(r	NUM
ejpam-5812	207	1	+	+	CCONJ
ejpam-5812	207	2	t)−	t)−	PROPN
ejpam-5812	207	3	9	9	NUM
ejpam-5812	207	4	1	1	NUM
ejpam-5812	207	5	0	0	NUM
ejpam-5812	207	6	j=	j=	NOUN
ejpam-5812	207	7	2	2	NUM
ejpam-5812	208	1	[	[	X
ejpam-5812	208	2	l4r1	l4r1	X
ejpam-5812	208	3	;	;	PUNCT
ejpam-5812	208	4	10l	10l	NOUN
ejpam-5812	208	5	′	′	NUM
ejpam-5812	208	6	4	4	NUM
ejpam-5812	208	7	t	t	NOUN
ejpam-5812	208	8	]	]	PUNCT
ejpam-5812	208	9	2(r	2(r	NUM
ejpam-5812	208	10	+	+	NUM
ejpam-5812	208	11	t	t	X
ejpam-5812	208	12	)	)	PUNCT
ejpam-5812	208	13	+	+	CCONJ
ejpam-5812	208	14	1	1	NUM
ejpam-5812	208	15	2(r	2(r	NUM
ejpam-5812	208	16	+	+	NUM
ejpam-5812	208	17	t	t	PROPN
ejpam-5812	208	18	)	)	PUNCT
ejpam-5812	209	1	+	+	CCONJ
ejpam-5812	209	2	1	1	NUM
ejpam-5812	209	3	10(r	10(r	NUM
ejpam-5812	209	4	+	+	CCONJ
ejpam-5812	209	5	t)−	t)−	PROPN
ejpam-5812	209	6	7	7	NUM
ejpam-5812	209	7	10(r	10(r	NUM
ejpam-5812	209	8	+	+	CCONJ
ejpam-5812	209	9	t)−	t)−	PROPN
ejpam-5812	209	10	6	6	NUM
ejpam-5812	209	11	0	0	NUM
ejpam-5812	209	12	−1	−1	NOUN
ejpam-5812	209	13	j=	j=	NOUN
ejpam-5812	209	14	3	3	NUM
ejpam-5812	210	1	[	[	X
ejpam-5812	210	2	l′	l′	NOUN
ejpam-5812	210	3	4r0	4r0	NUM
ejpam-5812	210	4	;	;	PUNCT
ejpam-5812	210	5	0l4t10	0l4t10	NUM
ejpam-5812	210	6	]	]	X
ejpam-5812	210	7	2(r	2(r	NUM
ejpam-5812	210	8	+	+	NUM
ejpam-5812	210	9	t	t	PROPN
ejpam-5812	210	10	)	)	PUNCT
ejpam-5812	210	11	+	+	CCONJ
ejpam-5812	210	12	2	2	NUM
ejpam-5812	210	13	2(r	2(r	NUM
ejpam-5812	210	14	+	+	SYM
ejpam-5812	210	15	t	t	NOUN
ejpam-5812	210	16	)	)	PUNCT
ejpam-5812	211	1	+	+	CCONJ
ejpam-5812	211	2	1	1	NUM
ejpam-5812	211	3	10(r	10(r	NUM
ejpam-5812	211	4	+	+	CCONJ
ejpam-5812	211	5	t)−	t)−	PROPN
ejpam-5812	211	6	4	4	NUM
ejpam-5812	211	7	10(r	10(r	NUM
ejpam-5812	211	8	+	+	CCONJ
ejpam-5812	211	9	t)−	t)−	PROPN
ejpam-5812	211	10	4	4	NUM
ejpam-5812	211	11	1	1	NUM
ejpam-5812	211	12	0	0	NUM
ejpam-5812	211	13	i=	i=	NUM
ejpam-5812	211	14	2	2	NUM
ejpam-5812	211	15	j=	j=	NOUN
ejpam-5812	211	16	2	2	NUM
ejpam-5812	212	1	[	[	X
ejpam-5812	212	2	l′	l′	X
ejpam-5812	212	3	4r10	4r10	NOUN
ejpam-5812	212	4	;	;	PUNCT
ejpam-5812	212	5	01l4	01l4	NUM
ejpam-5812	212	6	t	t	X
ejpam-5812	212	7	]	]	PUNCT
ejpam-5812	212	8	2(r	2(r	NUM
ejpam-5812	213	1	+	+	NUM
ejpam-5812	213	2	t	t	X
ejpam-5812	213	3	)	)	PUNCT
ejpam-5812	214	1	+	+	CCONJ
ejpam-5812	214	2	1	1	NUM
ejpam-5812	214	3	2(r	2(r	NUM
ejpam-5812	214	4	+	+	NUM
ejpam-5812	214	5	t	t	NOUN
ejpam-5812	214	6	)	)	PUNCT
ejpam-5812	214	7	+	+	CCONJ
ejpam-5812	214	8	2	2	NUM
ejpam-5812	214	9	10(r	10(r	NUM
ejpam-5812	215	1	+	+	CCONJ
ejpam-5812	215	2	t)−	t)−	PROPN
ejpam-5812	215	3	4	4	NUM
ejpam-5812	215	4	10(r	10(r	NUM
ejpam-5812	215	5	+	+	CCONJ
ejpam-5812	215	6	t)−	t)−	PROPN
ejpam-5812	215	7	4	4	NUM
ejpam-5812	215	8	−1	−1	NOUN
ejpam-5812	215	9	0	0	NUM
ejpam-5812	215	10	j=	j=	NOUN
ejpam-5812	215	11	3	3	NUM
ejpam-5812	216	1	[	[	X
ejpam-5812	216	2	l′	l′	NUM
ejpam-5812	216	3	4r10	4r10	NOUN
ejpam-5812	216	4	;	;	PUNCT
ejpam-5812	216	5	0l4t10	0l4t10	NUM
ejpam-5812	216	6	]	]	X
ejpam-5812	217	1	2(r	2(r	NUM
ejpam-5812	217	2	+	+	NUM
ejpam-5812	217	3	t	t	PROPN
ejpam-5812	217	4	)	)	PUNCT
ejpam-5812	218	1	+	+	CCONJ
ejpam-5812	218	2	2	2	NUM
ejpam-5812	218	3	2(r	2(r	NUM
ejpam-5812	218	4	+	+	SYM
ejpam-5812	218	5	t	t	NOUN
ejpam-5812	218	6	)	)	PUNCT
ejpam-5812	218	7	+	+	CCONJ
ejpam-5812	218	8	2	2	NUM
ejpam-5812	218	9	10(r	10(r	NUM
ejpam-5812	219	1	+	+	CCONJ
ejpam-5812	219	2	t)−	t)−	PROPN
ejpam-5812	219	3	1	1	NUM
ejpam-5812	219	4	10(r	10(r	NUM
ejpam-5812	219	5	+	+	CCONJ
ejpam-5812	219	6	t)−	t)−	PROPN
ejpam-5812	219	7	2	2	NUM
ejpam-5812	219	8	0	0	NUM
ejpam-5812	219	9	1	1	NUM
ejpam-5812	219	10	i=	i=	NUM
ejpam-5812	219	11	3	3	NUM
ejpam-5812	219	12	j=	j=	NOUN
ejpam-5812	219	13	3	3	NUM
ejpam-5812	220	1	[	[	X
ejpam-5812	220	2	11l′	11l′	NUM
ejpam-5812	220	3	4r0;l4t100	4r0;l4t100	NUM
ejpam-5812	220	4	]	]	PUNCT
ejpam-5812	221	1	2(r	2(r	NUM
ejpam-5812	221	2	+	+	NUM
ejpam-5812	221	3	t	t	X
ejpam-5812	221	4	)	)	PUNCT
ejpam-5812	222	1	+	+	CCONJ
ejpam-5812	222	2	2	2	NUM
ejpam-5812	222	3	2(r	2(r	NUM
ejpam-5812	222	4	+	+	SYM
ejpam-5812	222	5	t	t	PROPN
ejpam-5812	222	6	)	)	PUNCT
ejpam-5812	223	1	+	+	CCONJ
ejpam-5812	223	2	3	3	NUM
ejpam-5812	223	3	10(r	10(r	NUM
ejpam-5812	223	4	+	+	NUM
ejpam-5812	223	5	t	t	PROPN
ejpam-5812	223	6	)	)	PUNCT
ejpam-5812	223	7	+	+	CCONJ
ejpam-5812	223	8	1	1	NUM
ejpam-5812	223	9	10(r	10(r	NUM
ejpam-5812	223	10	+	+	NUM
ejpam-5812	223	11	t	t	PROPN
ejpam-5812	223	12	)	)	PUNCT
ejpam-5812	223	13	+	+	CCONJ
ejpam-5812	223	14	1	1	NUM
ejpam-5812	223	15	−1	−1	NOUN
ejpam-5812	223	16	0	0	PUNCT
ejpam-5812	224	1	lemma	lemma	PROPN
ejpam-5812	224	2	3.5.3	3.5.3	NUM
ejpam-5812	224	3	.	.	PUNCT
ejpam-5812	225	1	if	if	SCONJ
ejpam-5812	225	2	3	3	NUM
ejpam-5812	225	3	≤	≤	NUM
ejpam-5812	225	4	n	n	PRON
ejpam-5812	225	5	≤	≤	NUM
ejpam-5812	225	6	8	8	NUM
ejpam-5812	225	7	,	,	PUNCT
ejpam-5812	225	8	and	and	CCONJ
ejpam-5812	225	9	3	3	NUM
ejpam-5812	225	10	≤	≤	NUM
ejpam-5812	225	11	m	m	VERB
ejpam-5812	225	12	≤	≤	NOUN
ejpam-5812	225	13	8	8	NUM
ejpam-5812	225	14	,	,	PUNCT
ejpam-5812	225	15	then	then	ADV
ejpam-5812	225	16	the	the	DET
ejpam-5812	225	17	fifth	fifth	ADJ
ejpam-5812	225	18	power	power	NOUN
ejpam-5812	225	19	of	of	ADP
ejpam-5812	225	20	lemniscate	lemniscate	PROPN
ejpam-5812	225	21	l5	l5	PROPN
ejpam-5812	225	22	n	n	CCONJ
ejpam-5812	225	23	,	,	PUNCT
ejpam-5812	225	24	m	m	VERB
ejpam-5812	225	25	is	be	AUX
ejpam-5812	225	26	cordial	cordial	ADJ
ejpam-5812	225	27	except	except	SCONJ
ejpam-5812	225	28	(	(	PUNCT
ejpam-5812	225	29	n	n	CCONJ
ejpam-5812	225	30	,	,	PUNCT
ejpam-5812	225	31	m	m	NOUN
ejpam-5812	225	32	)	)	PUNCT
ejpam-5812	226	1	=	=	SYM
ejpam-5812	226	2	(	(	PUNCT
ejpam-5812	226	3	3	3	NUM
ejpam-5812	226	4	,	,	PUNCT
ejpam-5812	226	5	3),(3	3),(3	PROPN
ejpam-5812	226	6	,	,	PUNCT
ejpam-5812	226	7	6),(4	6),(4	PROPN
ejpam-5812	226	8	,	,	PUNCT
ejpam-5812	226	9	5),(5	5),(5	NUM
ejpam-5812	226	10	,	,	PUNCT
ejpam-5812	226	11	4),(5	4),(5	NUM
ejpam-5812	226	12	,	,	PUNCT
ejpam-5812	226	13	6),(6	6),(6	NUM
ejpam-5812	226	14	,	,	PUNCT
ejpam-5812	226	15	3),(6	3),(6	PROPN
ejpam-5812	226	16	,	,	PUNCT
ejpam-5812	226	17	5	5	NUM
ejpam-5812	226	18	)	)	PUNCT
ejpam-5812	226	19	and	and	CCONJ
ejpam-5812	226	20	(	(	PUNCT
ejpam-5812	226	21	6	6	NUM
ejpam-5812	226	22	,	,	PUNCT
ejpam-5812	226	23	6	6	NUM
ejpam-5812	226	24	)	)	PUNCT
ejpam-5812	226	25	.	.	PUNCT
ejpam-5812	227	1	a.	a.	PROPN
ejpam-5812	227	2	abd	abd	PROPN
ejpam-5812	227	3	el	el	PROPN
ejpam-5812	227	4	-	-	PROPN
ejpam-5812	227	5	hay	hay	PROPN
ejpam-5812	227	6	,	,	PUNCT
ejpam-5812	227	7	k.	k.	PROPN
ejpam-5812	227	8	a.	a.	PROPN
ejpam-5812	227	9	alsatami	alsatami	PROPN
ejpam-5812	227	10	,	,	PUNCT
ejpam-5812	227	11	a.	a.	NOUN
ejpam-5812	227	12	elrokh	elrokh	PROPN
ejpam-5812	227	13	/	/	SYM
ejpam-5812	227	14	eur	eur	PROPN
ejpam-5812	227	15	.	.	PUNCT
ejpam-5812	228	1	j.	j.	PROPN
ejpam-5812	228	2	pure	pure	PROPN
ejpam-5812	228	3	appl	appl	PROPN
ejpam-5812	228	4	.	.	PROPN
ejpam-5812	228	5	math	math	PROPN
ejpam-5812	228	6	,	,	PUNCT
ejpam-5812	228	7	18	18	NUM
ejpam-5812	228	8	(	(	PUNCT
ejpam-5812	228	9	1	1	NUM
ejpam-5812	228	10	)	)	PUNCT
ejpam-5812	228	11	(	(	PUNCT
ejpam-5812	228	12	2025	2025	NUM
ejpam-5812	228	13	)	)	PUNCT
ejpam-5812	228	14	,	,	PUNCT
ejpam-5812	228	15	5812	5812	NUM
ejpam-5812	228	16	8	8	NUM
ejpam-5812	228	17	of	of	ADP
ejpam-5812	228	18	14	14	NUM
ejpam-5812	228	19	proof	proof	NOUN
ejpam-5812	228	20	.	.	PUNCT
ejpam-5812	229	1	let	let	VERB
ejpam-5812	229	2	3	3	NUM
ejpam-5812	229	3	≤	≤	NOUN
ejpam-5812	229	4	n	n	PRON
ejpam-5812	229	5	≤	≤	NOUN
ejpam-5812	229	6	8	8	NUM
ejpam-5812	229	7	,	,	PUNCT
ejpam-5812	229	8	and	and	CCONJ
ejpam-5812	229	9	3	3	NUM
ejpam-5812	229	10	≤	≤	NUM
ejpam-5812	229	11	m	m	VERB
ejpam-5812	229	12	≤	≤	NOUN
ejpam-5812	229	13	8	8	NUM
ejpam-5812	229	14	except	except	SCONJ
ejpam-5812	229	15	(	(	PUNCT
ejpam-5812	229	16	n	n	CCONJ
ejpam-5812	229	17	,	,	PUNCT
ejpam-5812	229	18	m	m	NOUN
ejpam-5812	229	19	)	)	PUNCT
ejpam-5812	229	20	=	=	SYM
ejpam-5812	229	21	(	(	PUNCT
ejpam-5812	229	22	3	3	NUM
ejpam-5812	229	23	,	,	PUNCT
ejpam-5812	229	24	3),(3	3),(3	PROPN
ejpam-5812	229	25	,	,	PUNCT
ejpam-5812	229	26	6),(4	6),(4	PROPN
ejpam-5812	229	27	,	,	PUNCT
ejpam-5812	229	28	5),(5	5),(5	NUM
ejpam-5812	229	29	,	,	PUNCT
ejpam-5812	229	30	4),(5	4),(5	NUM
ejpam-5812	229	31	,	,	PUNCT
ejpam-5812	229	32	6),(6	6),(6	NUM
ejpam-5812	229	33	,	,	PUNCT
ejpam-5812	229	34	3),(6	3),(6	PROPN
ejpam-5812	229	35	,	,	PUNCT
ejpam-5812	229	36	5	5	NUM
ejpam-5812	229	37	)	)	PUNCT
ejpam-5812	229	38	and	and	CCONJ
ejpam-5812	229	39	(	(	PUNCT
ejpam-5812	229	40	6	6	NUM
ejpam-5812	229	41	,	,	PUNCT
ejpam-5812	229	42	6	6	NUM
ejpam-5812	229	43	)	)	PUNCT
ejpam-5812	229	44	then	then	ADV
ejpam-5812	229	45	using	use	VERB
ejpam-5812	229	46	tables	table	NOUN
ejpam-5812	229	47	7	7	NUM
ejpam-5812	229	48	and	and	CCONJ
ejpam-5812	229	49	formulas	formula	NOUN
ejpam-5812	229	50	v0−	v0−	PROPN
ejpam-5812	229	51	v1and	v1and	PROPN
ejpam-5812	229	52	e0−	e0−	PROPN
ejpam-5812	229	53	e1	e1	NOUN
ejpam-5812	229	54	,	,	PUNCT
ejpam-5812	229	55	we	we	PRON
ejpam-5812	229	56	can	can	AUX
ejpam-5812	229	57	compute	compute	VERB
ejpam-5812	229	58	the	the	DET
ejpam-5812	229	59	values	value	NOUN
ejpam-5812	229	60	shown	show	VERB
ejpam-5812	229	61	in	in	ADP
ejpam-5812	229	62	the	the	DET
ejpam-5812	229	63	last	last	ADJ
ejpam-5812	229	64	two	two	NUM
ejpam-5812	229	65	columns	column	NOUN
ejpam-5812	229	66	of	of	ADP
ejpam-5812	229	67	table	table	NOUN
ejpam-5812	229	68	7	7	NUM
ejpam-5812	229	69	.	.	PUNCT
ejpam-5812	230	1	since	since	SCONJ
ejpam-5812	230	2	all	all	PRON
ejpam-5812	230	3	of	of	ADP
ejpam-5812	230	4	these	these	DET
ejpam-5812	230	5	values	value	NOUN
ejpam-5812	230	6	are	be	AUX
ejpam-5812	230	7	−1	−1	ADJ
ejpam-5812	230	8	,	,	PUNCT
ejpam-5812	230	9	0	0	NUM
ejpam-5812	230	10	or	or	CCONJ
ejpam-5812	230	11	1	1	NUM
ejpam-5812	230	12	,	,	PUNCT
ejpam-5812	230	13	then	then	ADV
ejpam-5812	230	14	l5	l5	PROPN
ejpam-5812	230	15	n	n	SYM
ejpam-5812	230	16	,	,	PUNCT
ejpam-5812	230	17	m	m	VERB
ejpam-5812	230	18	are	be	AUX
ejpam-5812	230	19	cordial	cordial	ADJ
ejpam-5812	230	20	except	except	SCONJ
ejpam-5812	230	21	(	(	PUNCT
ejpam-5812	230	22	n	n	CCONJ
ejpam-5812	230	23	,	,	PUNCT
ejpam-5812	230	24	m	m	NOUN
ejpam-5812	230	25	)	)	PUNCT
ejpam-5812	231	1	=	=	SYM
ejpam-5812	231	2	(	(	PUNCT
ejpam-5812	231	3	3	3	NUM
ejpam-5812	231	4	,	,	PUNCT
ejpam-5812	231	5	3),(3	3),(3	PROPN
ejpam-5812	231	6	,	,	PUNCT
ejpam-5812	231	7	6),(4	6),(4	PROPN
ejpam-5812	231	8	,	,	PUNCT
ejpam-5812	231	9	5),(5	5),(5	NUM
ejpam-5812	231	10	,	,	PUNCT
ejpam-5812	231	11	4),(5	4),(5	NUM
ejpam-5812	231	12	,	,	PUNCT
ejpam-5812	231	13	6),(6	6),(6	NUM
ejpam-5812	231	14	,	,	PUNCT
ejpam-5812	231	15	3),(6	3),(6	PROPN
ejpam-5812	231	16	,	,	PUNCT
ejpam-5812	231	17	5	5	NUM
ejpam-5812	231	18	)	)	PUNCT
ejpam-5812	231	19	and	and	CCONJ
ejpam-5812	231	20	(	(	PUNCT
ejpam-5812	231	21	6	6	NUM
ejpam-5812	231	22	,	,	PUNCT
ejpam-5812	231	23	6	6	NUM
ejpam-5812	231	24	)	)	PUNCT
ejpam-5812	231	25	.	.	PUNCT
ejpam-5812	232	1	in	in	ADP
ejpam-5812	232	2	case	case	NOUN
ejpam-5812	232	3	of	of	ADP
ejpam-5812	232	4	(	(	PUNCT
ejpam-5812	232	5	n	n	X
ejpam-5812	232	6	,	,	PUNCT
ejpam-5812	232	7	m	m	NOUN
ejpam-5812	232	8	)	)	PUNCT
ejpam-5812	232	9	=	=	SYM
ejpam-5812	232	10	(	(	PUNCT
ejpam-5812	232	11	3	3	NUM
ejpam-5812	232	12	,	,	PUNCT
ejpam-5812	232	13	3	3	NUM
ejpam-5812	232	14	)	)	PUNCT
ejpam-5812	232	15	,	,	PUNCT
ejpam-5812	232	16	it	it	PRON
ejpam-5812	232	17	is	be	AUX
ejpam-5812	232	18	easy	easy	ADJ
ejpam-5812	232	19	to	to	PART
ejpam-5812	232	20	verify	verify	VERB
ejpam-5812	232	21	that	that	SCONJ
ejpam-5812	232	22	l5	l5	ADJ
ejpam-5812	232	23	3,3	3,3	NUM
ejpam-5812	232	24	∼=	∼=	NOUN
ejpam-5812	232	25	l3,3	l3,3	NOUN
ejpam-5812	232	26	is	be	AUX
ejpam-5812	232	27	not	not	PART
ejpam-5812	232	28	cordial	cordial	ADJ
ejpam-5812	232	29	by	by	ADP
ejpam-5812	232	30	cahit	cahit	ADJ
ejpam-5812	233	1	[	[	X
ejpam-5812	233	2	3	3	NUM
ejpam-5812	233	3	]	]	PUNCT
ejpam-5812	233	4	.	.	PUNCT
ejpam-5812	234	1	in	in	ADP
ejpam-5812	234	2	case	case	NOUN
ejpam-5812	234	3	of	of	ADP
ejpam-5812	234	4	(	(	PUNCT
ejpam-5812	234	5	n	n	X
ejpam-5812	234	6	,	,	PUNCT
ejpam-5812	234	7	m	m	NOUN
ejpam-5812	234	8	)	)	PUNCT
ejpam-5812	234	9	=	=	SYM
ejpam-5812	234	10	(	(	PUNCT
ejpam-5812	234	11	3	3	NUM
ejpam-5812	234	12	,	,	PUNCT
ejpam-5812	234	13	6),(4	6),(4	PROPN
ejpam-5812	234	14	,	,	PUNCT
ejpam-5812	234	15	5),(5	5),(5	NUM
ejpam-5812	234	16	,	,	PUNCT
ejpam-5812	234	17	4),(5	4),(5	NUM
ejpam-5812	234	18	,	,	PUNCT
ejpam-5812	234	19	6),(6	6),(6	NUM
ejpam-5812	234	20	,	,	PUNCT
ejpam-5812	234	21	3	3	NUM
ejpam-5812	234	22	)	)	PUNCT
ejpam-5812	234	23	,	,	PUNCT
ejpam-5812	234	24	and	and	CCONJ
ejpam-5812	234	25	(	(	PUNCT
ejpam-5812	234	26	6	6	NUM
ejpam-5812	234	27	,	,	PUNCT
ejpam-5812	234	28	5	5	NUM
ejpam-5812	234	29	)	)	PUNCT
ejpam-5812	234	30	the	the	DET
ejpam-5812	234	31	graphs	graph	NOUN
ejpam-5812	234	32	l5	l5	PROPN
ejpam-5812	234	33	n	n	CCONJ
ejpam-5812	234	34	,	,	PUNCT
ejpam-5812	234	35	m	m	VERB
ejpam-5812	234	36	have	have	VERB
ejpam-5812	234	37	an	an	DET
ejpam-5812	234	38	even	even	ADJ
ejpam-5812	234	39	order	order	NOUN
ejpam-5812	234	40	.	.	PUNCT
ejpam-5812	235	1	if	if	SCONJ
ejpam-5812	235	2	these	these	DET
ejpam-5812	235	3	graphs	graph	NOUN
ejpam-5812	235	4	are	be	AUX
ejpam-5812	235	5	cordial	cordial	ADJ
ejpam-5812	235	6	,	,	PUNCT
ejpam-5812	235	7	it	it	PRON
ejpam-5812	235	8	would	would	AUX
ejpam-5812	235	9	have	have	VERB
ejpam-5812	235	10	an	an	DET
ejpam-5812	235	11	equal	equal	ADJ
ejpam-5812	235	12	number	number	NOUN
ejpam-5812	235	13	of	of	ADP
ejpam-5812	235	14	vertices	vertex	NOUN
ejpam-5812	235	15	that	that	PRON
ejpam-5812	235	16	are	be	AUX
ejpam-5812	235	17	labeled	label	VERB
ejpam-5812	235	18	ones	one	NOUN
ejpam-5812	235	19	and	and	CCONJ
ejpam-5812	235	20	that	that	PRON
ejpam-5812	235	21	are	be	AUX
ejpam-5812	235	22	labeled	label	VERB
ejpam-5812	235	23	zero.otherwise	zero.otherwise	NUM
ejpam-5812	235	24	|v0	|v0	NUM
ejpam-5812	235	25	−	−	PROPN
ejpam-5812	235	26	v1|	v1|	NOUN
ejpam-5812	235	27	>	>	X
ejpam-5812	235	28	1	1	NUM
ejpam-5812	235	29	and	and	CCONJ
ejpam-5812	235	30	also	also	ADV
ejpam-5812	235	31	fo	fo	ADP
ejpam-5812	235	32	the	the	DET
ejpam-5812	235	33	case	case	NOUN
ejpam-5812	235	34	(	(	PUNCT
ejpam-5812	235	35	n	n	CCONJ
ejpam-5812	235	36	,	,	PUNCT
ejpam-5812	235	37	m	m	NOUN
ejpam-5812	235	38	)	)	PUNCT
ejpam-5812	235	39	=	=	SYM
ejpam-5812	235	40	(	(	PUNCT
ejpam-5812	235	41	6	6	NUM
ejpam-5812	235	42	,	,	PUNCT
ejpam-5812	235	43	6	6	NUM
ejpam-5812	235	44	)	)	PUNCT
ejpam-5812	235	45	the	the	DET
ejpam-5812	235	46	graph	graph	NOUN
ejpam-5812	235	47	l5	l5	PROPN
ejpam-5812	235	48	6,6	6,6	NUM
ejpam-5812	235	49	has	have	VERB
ejpam-5812	235	50	an	an	DET
ejpam-5812	235	51	odd	odd	ADJ
ejpam-5812	235	52	order	order	NOUN
ejpam-5812	235	53	,	,	PUNCT
ejpam-5812	235	54	it	it	PRON
ejpam-5812	235	55	would	would	AUX
ejpam-5812	235	56	have	have	VERB
ejpam-5812	235	57	the	the	DET
ejpam-5812	235	58	absolute	absolute	ADJ
ejpam-5812	235	59	difference	difference	NOUN
ejpam-5812	235	60	of	of	ADP
ejpam-5812	235	61	the	the	DET
ejpam-5812	235	62	vertices	vertex	NOUN
ejpam-5812	235	63	labeled	label	VERB
ejpam-5812	235	64	one	one	NUM
ejpam-5812	235	65	from	from	ADP
ejpam-5812	235	66	those	those	DET
ejpam-5812	235	67	labeled	label	VERB
ejpam-5812	235	68	zero	zero	NUM
ejpam-5812	235	69	will	will	AUX
ejpam-5812	235	70	be	be	AUX
ejpam-5812	235	71	one	one	NUM
ejpam-5812	235	72	.	.	PUNCT
ejpam-5812	236	1	otherwise	otherwise	ADV
ejpam-5812	236	2	|v0	|v0	PROPN
ejpam-5812	237	1	−	−	PROPN
ejpam-5812	237	2	v1|	v1|	PROPN
ejpam-5812	237	3	>	>	X
ejpam-5812	237	4	1	1	X
ejpam-5812	237	5	.	.	PUNCT
ejpam-5812	238	1	the	the	DET
ejpam-5812	238	2	set	set	NOUN
ejpam-5812	238	3	of	of	ADP
ejpam-5812	238	4	all	all	DET
ejpam-5812	238	5	different	different	ADJ
ejpam-5812	238	6	possibilities	possibility	NOUN
ejpam-5812	238	7	of	of	ADP
ejpam-5812	238	8	labeling	labeling	NOUN
ejpam-5812	238	9	of	of	ADP
ejpam-5812	238	10	the	the	DET
ejpam-5812	238	11	vertices	vertex	NOUN
ejpam-5812	238	12	of	of	ADP
ejpam-5812	238	13	l5	l5	PROPN
ejpam-5812	238	14	6,6	6,6	NUM
ejpam-5812	238	15	,	,	PUNCT
ejpam-5812	238	16	follows	follow	VERB
ejpam-5812	238	17	that	that	SCONJ
ejpam-5812	238	18	|e0	|e0	NOUN
ejpam-5812	238	19	−	−	PROPN
ejpam-5812	238	20	e1|	e1|	PROPN
ejpam-5812	238	21	>	>	X
ejpam-5812	238	22	1	1	NUM
ejpam-5812	238	23	,	,	PUNCT
ejpam-5812	238	24	contradiction	contradiction	NOUN
ejpam-5812	238	25	.	.	PUNCT
ejpam-5812	239	1	hence	hence	ADV
ejpam-5812	239	2	l5	l5	PROPN
ejpam-5812	239	3	n	n	CCONJ
ejpam-5812	239	4	,	,	PUNCT
ejpam-5812	239	5	m	m	PRON
ejpam-5812	239	6	,	,	PUNCT
ejpam-5812	239	7	(	(	PUNCT
ejpam-5812	239	8	n	n	CCONJ
ejpam-5812	239	9	,	,	PUNCT
ejpam-5812	239	10	m	m	NOUN
ejpam-5812	239	11	)	)	PUNCT
ejpam-5812	240	1	=	=	SYM
ejpam-5812	240	2	(	(	PUNCT
ejpam-5812	240	3	3	3	NUM
ejpam-5812	240	4	,	,	PUNCT
ejpam-5812	240	5	3),(3	3),(3	PROPN
ejpam-5812	240	6	,	,	PUNCT
ejpam-5812	240	7	6),(4	6),(4	PROPN
ejpam-5812	240	8	,	,	PUNCT
ejpam-5812	240	9	5),(5	5),(5	NUM
ejpam-5812	240	10	,	,	PUNCT
ejpam-5812	240	11	4),(5	4),(5	NUM
ejpam-5812	240	12	,	,	PUNCT
ejpam-5812	240	13	6),(6	6),(6	NUM
ejpam-5812	240	14	,	,	PUNCT
ejpam-5812	240	15	3),(6	3),(6	PROPN
ejpam-5812	240	16	,	,	PUNCT
ejpam-5812	240	17	5	5	NUM
ejpam-5812	240	18	)	)	PUNCT
ejpam-5812	240	19	and	and	CCONJ
ejpam-5812	240	20	(	(	PUNCT
ejpam-5812	240	21	6	6	NUM
ejpam-5812	240	22	,	,	PUNCT
ejpam-5812	240	23	6	6	NUM
ejpam-5812	240	24	)	)	PUNCT
ejpam-5812	240	25	are	be	AUX
ejpam-5812	240	26	not	not	PART
ejpam-5812	240	27	cordial	cordial	ADJ
ejpam-5812	240	28	.	.	PUNCT
ejpam-5812	241	1	table	table	NOUN
ejpam-5812	241	2	7	7	NUM
ejpam-5812	241	3	:	:	PUNCT
ejpam-5812	241	4	labeling	labeling	NOUN
ejpam-5812	241	5	of	of	ADP
ejpam-5812	241	6	l5	l5	PROPN
ejpam-5812	241	7	n	n	CCONJ
ejpam-5812	241	8	,	,	PUNCT
ejpam-5812	241	9	m;3	m;3	NOUN
ejpam-5812	241	10	≤	≤	NOUN
ejpam-5812	241	11	n	n	CCONJ
ejpam-5812	241	12	≤	≤	NUM
ejpam-5812	241	13	8	8	NUM
ejpam-5812	241	14	,	,	PUNCT
ejpam-5812	241	15	and	and	CCONJ
ejpam-5812	241	16	m	m	PROPN
ejpam-5812	241	17	>	>	X
ejpam-5812	241	18	8	8	NUM
ejpam-5812	241	19	3	3	NUM
ejpam-5812	241	20	≤	≤	NOUN
ejpam-5812	241	21	n	n	PRON
ejpam-5812	241	22	≤	≤	NUM
ejpam-5812	241	23	8	8	NUM
ejpam-5812	241	24	3	3	NUM
ejpam-5812	241	25	≤	≤	NUM
ejpam-5812	241	26	m	m	VERB
ejpam-5812	241	27	≤	≤	NUM
ejpam-5812	241	28	8	8	NUM
ejpam-5812	241	29	labeling	labeling	NOUN
ejpam-5812	241	30	of	of	ADP
ejpam-5812	241	31	l5	l5	PROPN
ejpam-5812	241	32	n	n	CCONJ
ejpam-5812	241	33	,	,	PUNCT
ejpam-5812	241	34	m	m	PROPN
ejpam-5812	241	35	v0	v0	NOUN
ejpam-5812	241	36	v1	v1	NOUN
ejpam-5812	241	37	e0	e0	PROPN
ejpam-5812	241	38	e1	e1	PROPN
ejpam-5812	241	39	v0	v0	NOUN
ejpam-5812	241	40	−	−	PROPN
ejpam-5812	241	41	v1	v1	PROPN
ejpam-5812	241	42	e0	e0	PROPN
ejpam-5812	241	43	−	−	PROPN
ejpam-5812	241	44	e1	e1	PROPN
ejpam-5812	241	45	3	3	NUM
ejpam-5812	241	46	m=	m=	X
ejpam-5812	241	47	4	4	NUM
ejpam-5812	242	1	[	[	SYM
ejpam-5812	242	2	110	110	NUM
ejpam-5812	242	3	;	;	PUNCT
ejpam-5812	242	4	0001	0001	NUM
ejpam-5812	242	5	]	]	SYM
ejpam-5812	242	6	3	3	NUM
ejpam-5812	242	7	3	3	NUM
ejpam-5812	242	8	4	4	NUM
ejpam-5812	242	9	5	5	NUM
ejpam-5812	242	10	0	0	NUM
ejpam-5812	242	11	−1	−1	NOUN
ejpam-5812	242	12	m=	m=	X
ejpam-5812	242	13	5	5	NUM
ejpam-5812	243	1	[	[	SYM
ejpam-5812	243	2	111	111	NUM
ejpam-5812	243	3	;	;	PUNCT
ejpam-5812	243	4	10010	10010	NUM
ejpam-5812	243	5	]	]	PUNCT
ejpam-5812	243	6	3	3	NUM
ejpam-5812	243	7	4	4	NUM
ejpam-5812	243	8	7	7	NUM
ejpam-5812	243	9	6	6	NUM
ejpam-5812	243	10	−1	−1	NOUN
ejpam-5812	243	11	1	1	NUM
ejpam-5812	243	12	m	m	NOUN
ejpam-5812	243	13	=	=	NUM
ejpam-5812	243	14	7	7	NUM
ejpam-5812	244	1	[	[	X
ejpam-5812	244	2	001	001	NUM
ejpam-5812	244	3	;	;	PUNCT
ejpam-5812	244	4	1101110	1101110	NUM
ejpam-5812	244	5	]	]	PUNCT
ejpam-5812	245	1	4	4	NUM
ejpam-5812	245	2	5	5	NUM
ejpam-5812	245	3	12	12	NUM
ejpam-5812	245	4	12	12	NUM
ejpam-5812	245	5	−1	−1	NOUN
ejpam-5812	245	6	0	0	NUM
ejpam-5812	245	7	m	m	VERB
ejpam-5812	245	8	=	=	SYM
ejpam-5812	245	9	8	8	NUM
ejpam-5812	246	1	[	[	X
ejpam-5812	246	2	001	001	NUM
ejpam-5812	246	3	;	;	PUNCT
ejpam-5812	246	4	10110101	10110101	NUM
ejpam-5812	246	5	]	]	PUNCT
ejpam-5812	246	6	5	5	NUM
ejpam-5812	246	7	5	5	NUM
ejpam-5812	246	8	14	14	NUM
ejpam-5812	246	9	15	15	NUM
ejpam-5812	246	10	0	0	NUM
ejpam-5812	246	11	−1	−1	NOUN
ejpam-5812	246	12	4	4	NUM
ejpam-5812	246	13	m=	m=	SYM
ejpam-5812	246	14	4	4	NUM
ejpam-5812	247	1	[	[	SYM
ejpam-5812	247	2	1000	1000	NUM
ejpam-5812	247	3	;	;	PUNCT
ejpam-5812	247	4	0111	0111	NUM
ejpam-5812	247	5	]	]	PUNCT
ejpam-5812	247	6	3	3	NUM
ejpam-5812	247	7	4	4	NUM
ejpam-5812	247	8	6	6	NUM
ejpam-5812	247	9	6	6	NUM
ejpam-5812	247	10	−1	−1	NOUN
ejpam-5812	247	11	0	0	NUM
ejpam-5812	248	1	m=	m=	X
ejpam-5812	248	2	6	6	NUM
ejpam-5812	248	3	[	[	X
ejpam-5812	248	4	031;0311	031;0311	NUM
ejpam-5812	248	5	]	]	SYM
ejpam-5812	248	6	5	5	NUM
ejpam-5812	248	7	4	4	NUM
ejpam-5812	248	8	11	11	NUM
ejpam-5812	248	9	11	11	NUM
ejpam-5812	248	10	1	1	NUM
ejpam-5812	248	11	0	0	NUM
ejpam-5812	248	12	m=	m=	X
ejpam-5812	248	13	7	7	NUM
ejpam-5812	248	14	[	[	X
ejpam-5812	248	15	0140;010210	0140;010210	X
ejpam-5812	248	16	]	]	X
ejpam-5812	248	17	6	6	NUM
ejpam-5812	248	18	6	6	NUM
ejpam-5812	248	19	18	18	NUM
ejpam-5812	248	20	18	18	NUM
ejpam-5812	248	21	0	0	NUM
ejpam-5812	248	22	0	0	NUM
ejpam-5812	248	23	5	5	NUM
ejpam-5812	248	24	m	m	NOUN
ejpam-5812	248	25	=	=	SYM
ejpam-5812	248	26	5	5	NUM
ejpam-5812	249	1	[	[	X
ejpam-5812	249	2	01021	01021	NUM
ejpam-5812	249	3	;	;	PUNCT
ejpam-5812	249	4	140	140	NUM
ejpam-5812	249	5	]	]	SYM
ejpam-5812	249	6	4	4	NUM
ejpam-5812	249	7	5	5	NUM
ejpam-5812	249	8	10	10	NUM
ejpam-5812	249	9	10	10	NUM
ejpam-5812	249	10	−1	−1	NOUN
ejpam-5812	249	11	0	0	NUM
ejpam-5812	249	12	m	m	VERB
ejpam-5812	250	1	=	=	NOUN
ejpam-5812	250	2	7	7	NUM
ejpam-5812	251	1	[	[	X
ejpam-5812	251	2	02101	02101	NUM
ejpam-5812	251	3	;	;	PUNCT
ejpam-5812	251	4	1201201	1201201	NUM
ejpam-5812	251	5	]	]	PUNCT
ejpam-5812	251	6	5	5	NUM
ejpam-5812	251	7	6	6	NUM
ejpam-5812	251	8	15	15	NUM
ejpam-5812	251	9	16	16	NUM
ejpam-5812	251	10	−1	−1	NOUN
ejpam-5812	251	11	−1	−1	NOUN
ejpam-5812	251	12	m	m	VERB
ejpam-5812	251	13	=	=	NOUN
ejpam-5812	251	14	8	8	NUM
ejpam-5812	251	15	0103	0103	NUM
ejpam-5812	251	16	;	;	PUNCT
ejpam-5812	251	17	010214	010214	NUM
ejpam-5812	251	18	6	6	NUM
ejpam-5812	251	19	6	6	NUM
ejpam-5812	251	20	18	18	NUM
ejpam-5812	251	21	18	18	NUM
ejpam-5812	251	22	0	0	NUM
ejpam-5812	251	23	0	0	NUM
ejpam-5812	251	24	6	6	NUM
ejpam-5812	251	25	m	m	NOUN
ejpam-5812	251	26	=	=	NUM
ejpam-5812	251	27	7	7	NUM
ejpam-5812	252	1	[	[	X
ejpam-5812	252	2	13m4	13m4	NUM
ejpam-5812	252	3	;	;	PUNCT
ejpam-5812	252	4	102102	102102	NUM
ejpam-5812	252	5	]	]	PUNCT
ejpam-5812	252	6	6	6	NUM
ejpam-5812	252	7	6	6	NUM
ejpam-5812	252	8	18	18	NUM
ejpam-5812	252	9	18	18	NUM
ejpam-5812	252	10	0	0	NUM
ejpam-5812	252	11	0	0	NUM
ejpam-5812	252	12	m	m	NOUN
ejpam-5812	252	13	=	=	SYM
ejpam-5812	252	14	8	8	NUM
ejpam-5812	253	1	[	[	X
ejpam-5812	253	2	m	m	AUX
ejpam-5812	253	3	′	′	NUM
ejpam-5812	253	4	411	411	NUM
ejpam-5812	253	5	;	;	PUNCT
ejpam-5812	253	6	1031021	1031021	NUM
ejpam-5812	253	7	]	]	SYM
ejpam-5812	253	8	7	7	NUM
ejpam-5812	253	9	6	6	NUM
ejpam-5812	253	10	20	20	NUM
ejpam-5812	253	11	21	21	NUM
ejpam-5812	253	12	1	1	NUM
ejpam-5812	253	13	−1	−1	NOUN
ejpam-5812	253	14	7	7	NUM
ejpam-5812	253	15	m=	m=	X
ejpam-5812	253	16	7	7	NUM
ejpam-5812	254	1	[	[	X
ejpam-5812	254	2	04	04	NUM
ejpam-5812	254	3	m	m	VERB
ejpam-5812	254	4	′	′	NUM
ejpam-5812	254	5	3;l	3;l	NUM
ejpam-5812	254	6	′	′	NUM
ejpam-5812	255	1	412	412	NUM
ejpam-5812	255	2	]	]	SYM
ejpam-5812	255	3	7	7	NUM
ejpam-5812	255	4	6	6	NUM
ejpam-5812	255	5	21	21	NUM
ejpam-5812	255	6	21	21	NUM
ejpam-5812	255	7	1	1	NUM
ejpam-5812	255	8	0	0	NUM
ejpam-5812	255	9	m	m	NOUN
ejpam-5812	255	10	=	=	NOUN
ejpam-5812	255	11	8	8	NUM
ejpam-5812	255	12	1214	1214	NUM
ejpam-5812	255	13	;	;	PUNCT
ejpam-5812	255	14	1031021	1031021	NUM
ejpam-5812	255	15	7	7	NUM
ejpam-5812	255	16	7	7	NUM
ejpam-5812	255	17	24	24	NUM
ejpam-5812	255	18	23	23	NUM
ejpam-5812	255	19	0	0	NUM
ejpam-5812	255	20	1	1	NUM
ejpam-5812	255	21	8	8	NUM
ejpam-5812	255	22	m=	m=	SYM
ejpam-5812	255	23	8	8	NUM
ejpam-5812	255	24	[	[	SYM
ejpam-5812	255	25	1013021;103102	1013021;103102	NUM
ejpam-5812	255	26	]	]	SYM
ejpam-5812	255	27	8	8	NUM
ejpam-5812	255	28	7	7	NUM
ejpam-5812	255	29	26	26	NUM
ejpam-5812	255	30	26	26	NUM
ejpam-5812	255	31	1	1	NUM
ejpam-5812	255	32	0	0	NUM
ejpam-5812	255	33	theorem	theorem	VERB
ejpam-5812	255	34	3.5.1	3.5.1	NUM
ejpam-5812	255	35	.	.	PUNCT
ejpam-5812	256	1	the	the	DET
ejpam-5812	256	2	fifth	fifth	ADJ
ejpam-5812	256	3	power	power	NOUN
ejpam-5812	256	4	of	of	ADP
ejpam-5812	256	5	lemniscate	lemniscate	PROPN
ejpam-5812	256	6	l5	l5	PROPN
ejpam-5812	256	7	n	n	CCONJ
ejpam-5812	256	8	,	,	PUNCT
ejpam-5812	256	9	m	m	VERB
ejpam-5812	256	10	cordial	cordial	ADJ
ejpam-5812	256	11	if	if	SCONJ
ejpam-5812	256	12	and	and	CCONJ
ejpam-5812	256	13	only	only	ADV
ejpam-5812	256	14	if	if	SCONJ
ejpam-5812	256	15	n	n	CCONJ
ejpam-5812	256	16	,	,	PUNCT
ejpam-5812	256	17	m	m	VERB
ejpam-5812	256	18	≥	≥	NOUN
ejpam-5812	256	19	3	3	NUM
ejpam-5812	256	20	except	except	SCONJ
ejpam-5812	256	21	(	(	PUNCT
ejpam-5812	256	22	n	n	CCONJ
ejpam-5812	256	23	,	,	PUNCT
ejpam-5812	256	24	m	m	NOUN
ejpam-5812	256	25	)	)	PUNCT
ejpam-5812	256	26	=	=	SYM
ejpam-5812	256	27	(	(	PUNCT
ejpam-5812	256	28	3	3	NUM
ejpam-5812	256	29	,	,	PUNCT
ejpam-5812	256	30	3),(3	3),(3	PROPN
ejpam-5812	256	31	,	,	PUNCT
ejpam-5812	256	32	6),(4	6),(4	PROPN
ejpam-5812	256	33	,	,	PUNCT
ejpam-5812	256	34	5),(5	5),(5	NUM
ejpam-5812	256	35	,	,	PUNCT
ejpam-5812	256	36	4),(5	4),(5	NUM
ejpam-5812	256	37	,	,	PUNCT
ejpam-5812	256	38	6),(6	6),(6	NUM
ejpam-5812	256	39	,	,	PUNCT
ejpam-5812	256	40	3),(6	3),(6	PROPN
ejpam-5812	256	41	,	,	PUNCT
ejpam-5812	256	42	5	5	NUM
ejpam-5812	256	43	)	)	PUNCT
ejpam-5812	256	44	and	and	CCONJ
ejpam-5812	256	45	(	(	PUNCT
ejpam-5812	256	46	6	6	NUM
ejpam-5812	256	47	,	,	PUNCT
ejpam-5812	256	48	6	6	NUM
ejpam-5812	256	49	)	)	PUNCT
ejpam-5812	256	50	.	.	PUNCT
ejpam-5812	257	1	proof	proof	NOUN
ejpam-5812	257	2	.	.	PUNCT
ejpam-5812	258	1	the	the	DET
ejpam-5812	258	2	proof	proof	NOUN
ejpam-5812	258	3	follows	follow	VERB
ejpam-5812	258	4	directly	directly	ADV
ejpam-5812	258	5	from	from	ADP
ejpam-5812	258	6	lemma	lemma	PROPN
ejpam-5812	258	7	3.5.1	3.5.1	NUM
ejpam-5812	258	8	,	,	PUNCT
ejpam-5812	258	9	...	...	PUNCT
ejpam-5812	258	10	,	,	PUNCT
ejpam-5812	258	11	3.5.3	3.5.3	NUM
ejpam-5812	258	12	.	.	PUNCT
ejpam-5812	258	13	example	example	NOUN
ejpam-5812	258	14	3.1	3.1	NUM
ejpam-5812	258	15	the	the	DET
ejpam-5812	258	16	cordial	cordial	ADJ
ejpam-5812	258	17	graph	graph	NOUN
ejpam-5812	258	18	of	of	ADP
ejpam-5812	258	19	p	p	PROPN
ejpam-5812	258	20	5	5	NUM
ejpam-5812	258	21	8	8	NUM
ejpam-5812	258	22	,	,	PUNCT
ejpam-5812	258	23	c	c	NOUN
ejpam-5812	258	24	5	5	NUM
ejpam-5812	258	25	9	9	NUM
ejpam-5812	258	26	,	,	PUNCT
ejpam-5812	258	27	f	f	PROPN
ejpam-5812	258	28	5	5	NUM
ejpam-5812	258	29	9	9	NUM
ejpam-5812	258	30	,	,	PUNCT
ejpam-5812	258	31	w	w	PROPN
ejpam-5812	258	32	5	5	NUM
ejpam-5812	258	33	10	10	NUM
ejpam-5812	258	34	,	,	PUNCT
ejpam-5812	258	35	and	and	CCONJ
ejpam-5812	258	36	l5	l5	PROPN
ejpam-5812	258	37	8,8are	8,8are	NUM
ejpam-5812	258	38	illustrated	illustrate	VERB
ejpam-5812	258	39	in	in	ADP
ejpam-5812	258	40	figures	figure	NOUN
ejpam-5812	258	41	(	(	PUNCT
ejpam-5812	258	42	1	1	NUM
ejpam-5812	258	43	,	,	PUNCT
ejpam-5812	258	44	...	...	PUNCT
ejpam-5812	258	45	,	,	PUNCT
ejpam-5812	258	46	5	5	NUM
ejpam-5812	258	47	)	)	PUNCT
ejpam-5812	258	48	.	.	PUNCT
ejpam-5812	259	1	v0=	v0=	PROPN
ejpam-5812	259	2	4,v1=	4,v1=	NUM
ejpam-5812	259	3	4,e0=	4,e0=	NUM
ejpam-5812	259	4	12,e1=	12,e1=	NUM
ejpam-5812	259	5	13,v0	13,v0	NUM
ejpam-5812	259	6	−	−	PROPN
ejpam-5812	259	7	v1=	v1=	PUNCT
ejpam-5812	259	8	0,e0	0,e0	SYM
ejpam-5812	259	9	−	−	PROPN
ejpam-5812	259	10	e1=−	e1=−	ADJ
ejpam-5812	259	11	1	1	NUM
ejpam-5812	259	12	figure	figure	NOUN
ejpam-5812	259	13	1	1	NUM
ejpam-5812	259	14	.	.	PUNCT
ejpam-5812	260	1	p	p	NOUN
ejpam-5812	260	2	5	5	NUM
ejpam-5812	260	3	8	8	NUM
ejpam-5812	260	4	is	be	AUX
ejpam-5812	260	5	cordial	cordial	ADJ
ejpam-5812	260	6	graph	graph	NOUN
ejpam-5812	260	7	.	.	PUNCT
ejpam-5812	261	1	a.	a.	PROPN
ejpam-5812	261	2	abd	abd	PROPN
ejpam-5812	261	3	el	el	PROPN
ejpam-5812	261	4	-	-	PROPN
ejpam-5812	261	5	hay	hay	PROPN
ejpam-5812	261	6	,	,	PUNCT
ejpam-5812	261	7	k.	k.	PROPN
ejpam-5812	261	8	a.	a.	PROPN
ejpam-5812	261	9	alsatami	alsatami	PROPN
ejpam-5812	261	10	,	,	PUNCT
ejpam-5812	261	11	a.	a.	NOUN
ejpam-5812	261	12	elrokh	elrokh	PROPN
ejpam-5812	261	13	/	/	SYM
ejpam-5812	261	14	eur	eur	PROPN
ejpam-5812	261	15	.	.	PUNCT
ejpam-5812	262	1	j.	j.	PROPN
ejpam-5812	262	2	pure	pure	PROPN
ejpam-5812	262	3	appl	appl	PROPN
ejpam-5812	262	4	.	.	PROPN
ejpam-5812	262	5	math	math	PROPN
ejpam-5812	262	6	,	,	PUNCT
ejpam-5812	262	7	18	18	NUM
ejpam-5812	262	8	(	(	PUNCT
ejpam-5812	262	9	1	1	NUM
ejpam-5812	262	10	)	)	PUNCT
ejpam-5812	262	11	(	(	PUNCT
ejpam-5812	262	12	2025	2025	NUM
ejpam-5812	262	13	)	)	PUNCT
ejpam-5812	262	14	,	,	PUNCT
ejpam-5812	262	15	5812	5812	NUM
ejpam-5812	262	16	9	9	NUM
ejpam-5812	262	17	of	of	ADP
ejpam-5812	262	18	14	14	NUM
ejpam-5812	262	19	v0=	v0=	NOUN
ejpam-5812	262	20	4,v1=	4,v1=	NUM
ejpam-5812	262	21	5,e0=	5,e0=	NUM
ejpam-5812	262	22	15,e1=	15,e1=	NUM
ejpam-5812	262	23	16,v0	16,v0	NUM
ejpam-5812	262	24	−	−	PROPN
ejpam-5812	262	25	v1=−	v1=−	NOUN
ejpam-5812	262	26	1,e0	1,e0	NUM
ejpam-5812	262	27	−	−	NOUN
ejpam-5812	262	28	e1=−	e1=−	NOUN
ejpam-5812	262	29	1	1	NUM
ejpam-5812	262	30	figure	figure	NOUN
ejpam-5812	262	31	2	2	NUM
ejpam-5812	262	32	.	.	PUNCT
ejpam-5812	263	1	c5	c5	PROPN
ejpam-5812	263	2	9	9	NUM
ejpam-5812	263	3	is	be	AUX
ejpam-5812	263	4	cordial	cordial	ADJ
ejpam-5812	263	5	graph	graph	NOUN
ejpam-5812	263	6	.	.	PUNCT
ejpam-5812	264	1	v0=	v0=	ADJ
ejpam-5812	264	2	5,v1=	5,v1=	NUM
ejpam-5812	264	3	4,e0=	4,e0=	NUM
ejpam-5812	264	4	16,e1=	16,e1=	NUM
ejpam-5812	264	5	17,v0	17,v0	PROPN
ejpam-5812	265	1	−	−	NUM
ejpam-5812	266	1	v1=	v1=	NOUN
ejpam-5812	266	2	1,e0	1,e0	NUM
ejpam-5812	266	3	−	−	NOUN
ejpam-5812	266	4	e1=−	e1=−	NOUN
ejpam-5812	266	5	1	1	NUM
ejpam-5812	266	6	figure	figure	NOUN
ejpam-5812	266	7	3	3	NUM
ejpam-5812	266	8	.	.	PUNCT
ejpam-5812	267	1	f	f	NOUN
ejpam-5812	267	2	5	5	NUM
ejpam-5812	267	3	9	9	NUM
ejpam-5812	267	4	is	be	AUX
ejpam-5812	267	5	cordial	cordial	ADJ
ejpam-5812	267	6	graph	graph	NOUN
ejpam-5812	267	7	.	.	PUNCT
ejpam-5812	268	1	v0=	v0=	ADJ
ejpam-5812	268	2	5,v1=	5,v1=	NUM
ejpam-5812	268	3	5,e0=	5,e0=	NUM
ejpam-5812	268	4	20,e1=	20,e1=	NUM
ejpam-5812	268	5	20,v0	20,v0	NUM
ejpam-5812	268	6	−	−	PROPN
ejpam-5812	268	7	v1=	v1=	PUNCT
ejpam-5812	268	8	0,e0	0,e0	NOUN
ejpam-5812	269	1	−	−	ADP
ejpam-5812	269	2	e1=	e1=	NOUN
ejpam-5812	269	3	0	0	NUM
ejpam-5812	269	4	figure	figure	NOUN
ejpam-5812	269	5	4	4	NUM
ejpam-5812	269	6	.	.	PUNCT
ejpam-5812	270	1	w	w	NOUN
ejpam-5812	270	2	5	5	NUM
ejpam-5812	270	3	10	10	NUM
ejpam-5812	270	4	is	be	AUX
ejpam-5812	270	5	cordial	cordial	ADJ
ejpam-5812	270	6	graph	graph	NOUN
ejpam-5812	270	7	.	.	PUNCT
ejpam-5812	271	1	v0=	v0=	PROPN
ejpam-5812	271	2	8,v1=	8,v1=	NUM
ejpam-5812	271	3	7,e0=	7,e0=	NUM
ejpam-5812	271	4	26,e1=	26,e1=	NUM
ejpam-5812	271	5	26,v0	26,v0	NUM
ejpam-5812	271	6	−	−	NOUN
ejpam-5812	272	1	v1=	v1=	NOUN
ejpam-5812	272	2	1,e0	1,e0	NUM
ejpam-5812	272	3	−	−	NOUN
ejpam-5812	272	4	e1=	e1=	NOUN
ejpam-5812	272	5	0	0	NUM
ejpam-5812	272	6	figure	figure	NOUN
ejpam-5812	272	7	5	5	NUM
ejpam-5812	272	8	.	.	PUNCT
ejpam-5812	273	1	l5	l5	PROPN
ejpam-5812	273	2	8,8	8,8	NUM
ejpam-5812	273	3	is	be	AUX
ejpam-5812	273	4	cordial	cordial	ADJ
ejpam-5812	273	5	graph	graph	NOUN
ejpam-5812	273	6	.	.	PUNCT
ejpam-5812	274	1	a.	a.	PROPN
ejpam-5812	274	2	abd	abd	PROPN
ejpam-5812	274	3	el	el	PROPN
ejpam-5812	274	4	-	-	PROPN
ejpam-5812	274	5	hay	hay	PROPN
ejpam-5812	274	6	,	,	PUNCT
ejpam-5812	274	7	k.	k.	PROPN
ejpam-5812	274	8	a.	a.	PROPN
ejpam-5812	274	9	alsatami	alsatami	PROPN
ejpam-5812	274	10	,	,	PUNCT
ejpam-5812	274	11	a.	a.	NOUN
ejpam-5812	274	12	elrokh	elrokh	PROPN
ejpam-5812	274	13	/	/	SYM
ejpam-5812	274	14	eur	eur	PROPN
ejpam-5812	274	15	.	.	PUNCT
ejpam-5812	275	1	j.	j.	PROPN
ejpam-5812	275	2	pure	pure	PROPN
ejpam-5812	275	3	appl	appl	PROPN
ejpam-5812	275	4	.	.	PROPN
ejpam-5812	275	5	math	math	PROPN
ejpam-5812	275	6	,	,	PUNCT
ejpam-5812	275	7	18	18	NUM
ejpam-5812	275	8	(	(	PUNCT
ejpam-5812	275	9	1	1	NUM
ejpam-5812	275	10	)	)	PUNCT
ejpam-5812	275	11	(	(	PUNCT
ejpam-5812	275	12	2025	2025	NUM
ejpam-5812	275	13	)	)	PUNCT
ejpam-5812	275	14	,	,	PUNCT
ejpam-5812	275	15	5812	5812	NUM
ejpam-5812	275	16	10	10	NUM
ejpam-5812	275	17	of	of	ADP
ejpam-5812	275	18	14	14	NUM
ejpam-5812	275	19	4	4	NUM
ejpam-5812	275	20	.	.	PUNCT
ejpam-5812	276	1	the	the	DET
ejpam-5812	276	2	cordial	cordial	ADJ
ejpam-5812	276	3	labeling	labeling	NOUN
ejpam-5812	276	4	for	for	ADP
ejpam-5812	276	5	union	union	NOUN
ejpam-5812	276	6	of	of	ADP
ejpam-5812	276	7	fifth	fifth	ADJ
ejpam-5812	276	8	power	power	NOUN
ejpam-5812	276	9	of	of	ADP
ejpam-5812	276	10	paths	path	NOUN
ejpam-5812	276	11	and	and	CCONJ
ejpam-5812	276	12	cycles	cycle	NOUN
ejpam-5812	276	13	in	in	ADP
ejpam-5812	276	14	this	this	DET
ejpam-5812	276	15	section	section	NOUN
ejpam-5812	276	16	,	,	PUNCT
ejpam-5812	276	17	we	we	PRON
ejpam-5812	276	18	will	will	AUX
ejpam-5812	276	19	study	study	VERB
ejpam-5812	276	20	the	the	DET
ejpam-5812	276	21	cordiality	cordiality	NOUN
ejpam-5812	276	22	of	of	ADP
ejpam-5812	276	23	the	the	DET
ejpam-5812	276	24	union	union	NOUN
ejpam-5812	276	25	of	of	ADP
ejpam-5812	276	26	two	two	NUM
ejpam-5812	276	27	fifth	fifth	ADJ
ejpam-5812	276	28	power	power	NOUN
ejpam-5812	276	29	of	of	ADP
ejpam-5812	276	30	paths	path	NOUN
ejpam-5812	276	31	,	,	PUNCT
ejpam-5812	276	32	and	and	CCONJ
ejpam-5812	276	33	a	a	DET
ejpam-5812	276	34	similar	similar	ADJ
ejpam-5812	276	35	study	study	NOUN
ejpam-5812	276	36	will	will	AUX
ejpam-5812	276	37	be	be	AUX
ejpam-5812	276	38	performed	perform	VERB
ejpam-5812	276	39	of	of	ADP
ejpam-5812	276	40	two	two	NUM
ejpam-5812	276	41	fifth	fifth	ADJ
ejpam-5812	276	42	power	power	NOUN
ejpam-5812	276	43	of	of	ADP
ejpam-5812	276	44	cycles	cycle	NOUN
ejpam-5812	276	45	.	.	PUNCT
ejpam-5812	277	1	we	we	PRON
ejpam-5812	277	2	end	end	VERB
ejpam-5812	277	3	this	this	DET
ejpam-5812	277	4	section	section	NOUN
ejpam-5812	277	5	by	by	ADP
ejpam-5812	277	6	studying	study	VERB
ejpam-5812	277	7	the	the	DET
ejpam-5812	277	8	cordiality	cordiality	NOUN
ejpam-5812	277	9	of	of	ADP
ejpam-5812	277	10	the	the	DET
ejpam-5812	277	11	union	union	NOUN
ejpam-5812	277	12	fifth	fifth	ADJ
ejpam-5812	277	13	power	power	NOUN
ejpam-5812	277	14	of	of	ADP
ejpam-5812	277	15	paths	path	NOUN
ejpam-5812	277	16	with	with	ADP
ejpam-5812	277	17	cycles	cycle	NOUN
ejpam-5812	277	18	.	.	PUNCT
ejpam-5812	278	1	theorem	theorem	VERB
ejpam-5812	278	2	4.1	4.1	NUM
ejpam-5812	278	3	.	.	PUNCT
ejpam-5812	279	1	the	the	DET
ejpam-5812	279	2	union	union	NOUN
ejpam-5812	279	3	of	of	ADP
ejpam-5812	279	4	p	p	PROPN
ejpam-5812	279	5	5	5	NUM
ejpam-5812	279	6	n	n	NOUN
ejpam-5812	279	7	∪	∪	NOUN
ejpam-5812	279	8	p	p	PROPN
ejpam-5812	279	9	5	5	NUM
ejpam-5812	279	10	m	m	NOUN
ejpam-5812	279	11	,	,	PUNCT
ejpam-5812	279	12	admits	admit	VERB
ejpam-5812	279	13	a	a	DET
ejpam-5812	279	14	cordial	cordial	ADJ
ejpam-5812	279	15	labeling	labeling	NOUN
ejpam-5812	279	16	for	for	ADP
ejpam-5812	279	17	every	every	DET
ejpam-5812	279	18	n	n	CCONJ
ejpam-5812	279	19	,	,	PUNCT
ejpam-5812	279	20	m	m	VERB
ejpam-5812	279	21	>	>	X
ejpam-5812	279	22	7	7	X
ejpam-5812	279	23	.	.	PUNCT
ejpam-5812	280	1	proof	proof	NOUN
ejpam-5812	280	2	.	.	PUNCT
ejpam-5812	281	1	let	let	VERB
ejpam-5812	281	2	n=	n=	ADJ
ejpam-5812	281	3	4r+	4r+	NUM
ejpam-5812	281	4	i	i	NOUN
ejpam-5812	281	5	(	(	PUNCT
ejpam-5812	281	6	i=	i=	PROPN
ejpam-5812	281	7	0	0	NUM
ejpam-5812	281	8	,	,	PUNCT
ejpam-5812	281	9	1	1	NUM
ejpam-5812	281	10	,	,	PUNCT
ejpam-5812	281	11	2	2	NUM
ejpam-5812	281	12	,	,	PUNCT
ejpam-5812	281	13	3	3	NUM
ejpam-5812	281	14	and	and	CCONJ
ejpam-5812	281	15	r	r	NOUN
ejpam-5812	281	16	≥	≥	NOUN
ejpam-5812	281	17	1	1	NUM
ejpam-5812	281	18	)	)	PUNCT
ejpam-5812	281	19	and	and	CCONJ
ejpam-5812	281	20	m=	m=	X
ejpam-5812	281	21	4t+	4t+	NUM
ejpam-5812	281	22	j	j	PROPN
ejpam-5812	281	23	(	(	PUNCT
ejpam-5812	281	24	j=	j=	NOUN
ejpam-5812	281	25	0	0	NUM
ejpam-5812	281	26	,	,	PUNCT
ejpam-5812	281	27	1	1	NUM
ejpam-5812	281	28	,	,	PUNCT
ejpam-5812	281	29	2	2	NUM
ejpam-5812	281	30	,	,	PUNCT
ejpam-5812	281	31	3	3	NUM
ejpam-5812	281	32	and	and	CCONJ
ejpam-5812	281	33	t	t	PROPN
ejpam-5812	281	34	≥	≥	NUM
ejpam-5812	281	35	1	1	NUM
ejpam-5812	281	36	)	)	PUNCT
ejpam-5812	281	37	,	,	PUNCT
ejpam-5812	281	38	then	then	ADV
ejpam-5812	281	39	throughout	throughout	ADP
ejpam-5812	281	40	the	the	DET
ejpam-5812	281	41	table	table	NOUN
ejpam-5812	281	42	2	2	NUM
ejpam-5812	281	43	and	and	CCONJ
ejpam-5812	281	44	table	table	NOUN
ejpam-5812	281	45	8	8	NUM
ejpam-5812	281	46	.	.	PUNCT
ejpam-5812	281	47	using	use	VERB
ejpam-5812	281	48	table	table	NOUN
ejpam-5812	281	49	8	8	NUM
ejpam-5812	281	50	and	and	CCONJ
ejpam-5812	281	51	formulas	formula	NOUN
ejpam-5812	281	52	v0	v0	NOUN
ejpam-5812	281	53	−	−	PROPN
ejpam-5812	281	54	v1and	v1and	NOUN
ejpam-5812	281	55	e0	e0	PROPN
ejpam-5812	281	56	−	−	PROPN
ejpam-5812	281	57	e1	e1	PROPN
ejpam-5812	281	58	,	,	PUNCT
ejpam-5812	281	59	we	we	PRON
ejpam-5812	281	60	can	can	AUX
ejpam-5812	281	61	compute	compute	VERB
ejpam-5812	281	62	the	the	DET
ejpam-5812	281	63	values	value	NOUN
ejpam-5812	281	64	shown	show	VERB
ejpam-5812	281	65	in	in	ADP
ejpam-5812	281	66	the	the	DET
ejpam-5812	281	67	last	last	ADJ
ejpam-5812	281	68	two	two	NUM
ejpam-5812	281	69	columns	column	NOUN
ejpam-5812	281	70	of	of	ADP
ejpam-5812	281	71	table	table	NOUN
ejpam-5812	281	72	8	8	NUM
ejpam-5812	281	73	.	.	PUNCT
ejpam-5812	282	1	since	since	SCONJ
ejpam-5812	282	2	all	all	PRON
ejpam-5812	282	3	of	of	ADP
ejpam-5812	282	4	these	these	DET
ejpam-5812	282	5	values	value	NOUN
ejpam-5812	282	6	are	be	AUX
ejpam-5812	282	7	−1	−1	ADJ
ejpam-5812	282	8	,	,	PUNCT
ejpam-5812	282	9	0	0	NUM
ejpam-5812	282	10	or	or	CCONJ
ejpam-5812	282	11	1	1	NUM
ejpam-5812	282	12	,	,	PUNCT
ejpam-5812	282	13	the	the	DET
ejpam-5812	282	14	theorem	theorem	NOUN
ejpam-5812	282	15	is	be	AUX
ejpam-5812	282	16	proved	prove	VERB
ejpam-5812	282	17	.	.	PUNCT
ejpam-5812	283	1	table	table	NOUN
ejpam-5812	283	2	8	8	NUM
ejpam-5812	283	3	:	:	PUNCT
ejpam-5812	283	4	labeling	labeling	NOUN
ejpam-5812	283	5	of	of	ADP
ejpam-5812	283	6	p	p	PROPN
ejpam-5812	283	7	5	5	NUM
ejpam-5812	283	8	n	n	NOUN
ejpam-5812	283	9	∪	∪	NOUN
ejpam-5812	283	10	p	p	PROPN
ejpam-5812	283	11	5	5	NUM
ejpam-5812	283	12	m	m	NOUN
ejpam-5812	283	13	n	n	NOUN
ejpam-5812	283	14	=	=	NOUN
ejpam-5812	283	15	4r	4r	NOUN
ejpam-5812	284	1	+	+	CCONJ
ejpam-5812	284	2	i	i	PROPN
ejpam-5812	284	3	,	,	PUNCT
ejpam-5812	284	4	n	n	PRON
ejpam-5812	284	5	≥	≥	NUM
ejpam-5812	284	6	8	8	NUM
ejpam-5812	284	7	0	0	NUM
ejpam-5812	284	8	≤	≤	NUM
ejpam-5812	284	9	i	i	PRON
ejpam-5812	284	10	≤	≤	NOUN
ejpam-5812	284	11	3	3	NUM
ejpam-5812	284	12	m	m	NOUN
ejpam-5812	284	13	=	=	SYM
ejpam-5812	284	14	4t+	4t+	NUM
ejpam-5812	284	15	j	j	PROPN
ejpam-5812	284	16	m	m	VERB
ejpam-5812	284	17	≥	≥	NUM
ejpam-5812	284	18	8	8	NUM
ejpam-5812	284	19	0	0	NUM
ejpam-5812	284	20	≤	≤	NUM
ejpam-5812	284	21	j	j	PROPN
ejpam-5812	284	22	≤	≤	ADV
ejpam-5812	284	23	3	3	NUM
ejpam-5812	284	24	labeling	labeling	NOUN
ejpam-5812	284	25	of	of	ADP
ejpam-5812	284	26	p	p	PROPN
ejpam-5812	284	27	5	5	NUM
ejpam-5812	284	28	n	n	PRON
ejpam-5812	284	29	labeling	labeling	NOUN
ejpam-5812	284	30	of	of	ADP
ejpam-5812	284	31	p	p	PROPN
ejpam-5812	284	32	5	5	NUM
ejpam-5812	284	33	m	m	NOUN
ejpam-5812	284	34	v0	v0	NOUN
ejpam-5812	284	35	v1	v1	NOUN
ejpam-5812	284	36	e0	e0	PROPN
ejpam-5812	284	37	e1	e1	PROPN
ejpam-5812	284	38	v0	v0	NOUN
ejpam-5812	284	39	−	−	PROPN
ejpam-5812	284	40	v1	v1	PROPN
ejpam-5812	284	41	e0	e0	PROPN
ejpam-5812	284	42	−	−	PROPN
ejpam-5812	284	43	e1	e1	VERB
ejpam-5812	284	44	i=	i=	PROPN
ejpam-5812	284	45	0	0	PUNCT
ejpam-5812	285	1	j=	j=	NOUN
ejpam-5812	285	2	0	0	NUM
ejpam-5812	286	1	0l4r120	0l4r120	NUM
ejpam-5812	286	2	1l	1l	NUM
ejpam-5812	286	3	′	′	NUM
ejpam-5812	286	4	4tm3	4tm3	NUM
ejpam-5812	286	5	2(r	2(r	NUM
ejpam-5812	286	6	+	+	NUM
ejpam-5812	286	7	t	t	X
ejpam-5812	286	8	)	)	PUNCT
ejpam-5812	287	1	+	+	CCONJ
ejpam-5812	287	2	4	4	NUM
ejpam-5812	287	3	2(r	2(r	NUM
ejpam-5812	287	4	+	+	SYM
ejpam-5812	287	5	t	t	PROPN
ejpam-5812	287	6	)	)	PUNCT
ejpam-5812	288	1	+	+	CCONJ
ejpam-5812	288	2	4	4	NUM
ejpam-5812	288	3	10(r	10(r	NUM
ejpam-5812	288	4	+	+	NUM
ejpam-5812	288	5	t	t	PROPN
ejpam-5812	288	6	)	)	PUNCT
ejpam-5812	288	7	+	+	CCONJ
ejpam-5812	288	8	5	5	NUM
ejpam-5812	288	9	10(r	10(r	NUM
ejpam-5812	288	10	+	+	NUM
ejpam-5812	288	11	t	t	PROPN
ejpam-5812	288	12	)	)	PUNCT
ejpam-5812	289	1	+	+	CCONJ
ejpam-5812	290	1	5	5	NUM
ejpam-5812	290	2	0	0	NUM
ejpam-5812	290	3	0	0	NUM
ejpam-5812	290	4	j=	j=	NOUN
ejpam-5812	290	5	1	1	NUM
ejpam-5812	290	6	0l4r120	0l4r120	NUM
ejpam-5812	290	7	l4t1	l4t1	PUNCT
ejpam-5812	290	8	2(r	2(r	NUM
ejpam-5812	290	9	+	+	SYM
ejpam-5812	290	10	t	t	PROPN
ejpam-5812	290	11	)	)	PUNCT
ejpam-5812	290	12	+	+	CCONJ
ejpam-5812	290	13	2	2	NUM
ejpam-5812	290	14	2(r	2(r	NUM
ejpam-5812	290	15	+	+	SYM
ejpam-5812	290	16	t	t	PROPN
ejpam-5812	290	17	)	)	PUNCT
ejpam-5812	290	18	+	+	CCONJ
ejpam-5812	290	19	3	3	NUM
ejpam-5812	290	20	10(r	10(r	NUM
ejpam-5812	290	21	+	+	CCONJ
ejpam-5812	290	22	t)−	t)−	PROPN
ejpam-5812	290	23	3	3	NUM
ejpam-5812	290	24	10(r	10(r	NUM
ejpam-5812	290	25	+	+	CCONJ
ejpam-5812	290	26	t)−	t)−	PROPN
ejpam-5812	290	27	2	2	NUM
ejpam-5812	290	28	−1	−1	NOUN
ejpam-5812	290	29	−1	−1	NOUN
ejpam-5812	290	30	j=	j=	NOUN
ejpam-5812	290	31	2	2	NUM
ejpam-5812	290	32	0l4r120	0l4r120	NUM
ejpam-5812	290	33	l	l	NOUN
ejpam-5812	290	34	′	′	NUM
ejpam-5812	290	35	4t10	4t10	NOUN
ejpam-5812	290	36	2(r	2(r	NUM
ejpam-5812	291	1	+	+	NUM
ejpam-5812	291	2	t	t	PROPN
ejpam-5812	291	3	)	)	PUNCT
ejpam-5812	292	1	+	+	CCONJ
ejpam-5812	292	2	3	3	NUM
ejpam-5812	292	3	2(r	2(r	NUM
ejpam-5812	292	4	+	+	SYM
ejpam-5812	292	5	t	t	NOUN
ejpam-5812	292	6	)	)	PUNCT
ejpam-5812	293	1	+	+	CCONJ
ejpam-5812	293	2	3	3	NUM
ejpam-5812	293	3	10(r	10(r	NUM
ejpam-5812	293	4	+	+	NUM
ejpam-5812	293	5	t	t	PROPN
ejpam-5812	293	6	)	)	PUNCT
ejpam-5812	293	7	10(r	10(r	PROPN
ejpam-5812	294	1	+	+	NUM
ejpam-5812	294	2	t	t	PROPN
ejpam-5812	294	3	)	)	PUNCT
ejpam-5812	294	4	0	0	NUM
ejpam-5812	294	5	0	0	NUM
ejpam-5812	294	6	j=	j=	VERB
ejpam-5812	294	7	3	3	NUM
ejpam-5812	294	8	0l4r120	0l4r120	NUM
ejpam-5812	294	9	0l4t10	0l4t10	NUM
ejpam-5812	294	10	2(r	2(r	NUM
ejpam-5812	294	11	+	+	SYM
ejpam-5812	294	12	t	t	PROPN
ejpam-5812	294	13	)	)	PUNCT
ejpam-5812	295	1	+	+	CCONJ
ejpam-5812	295	2	4	4	NUM
ejpam-5812	295	3	2(r	2(r	NUM
ejpam-5812	295	4	+	+	SYM
ejpam-5812	295	5	t	t	NOUN
ejpam-5812	295	6	)	)	PUNCT
ejpam-5812	296	1	+	+	CCONJ
ejpam-5812	296	2	3	3	NUM
ejpam-5812	296	3	10(r	10(r	NUM
ejpam-5812	296	4	+	+	NUM
ejpam-5812	296	5	t	t	PROPN
ejpam-5812	296	6	)	)	PUNCT
ejpam-5812	296	7	+	+	CCONJ
ejpam-5812	296	8	2	2	NUM
ejpam-5812	296	9	10(r	10(r	NUM
ejpam-5812	296	10	+	+	NUM
ejpam-5812	296	11	t	t	PROPN
ejpam-5812	296	12	)	)	PUNCT
ejpam-5812	297	1	+	+	CCONJ
ejpam-5812	297	2	3	3	NUM
ejpam-5812	297	3	1	1	NUM
ejpam-5812	297	4	−1	−1	NOUN
ejpam-5812	297	5	i=	i=	ADJ
ejpam-5812	297	6	1	1	NUM
ejpam-5812	297	7	j=	j=	NOUN
ejpam-5812	297	8	1	1	NUM
ejpam-5812	297	9	l4r1	l4r1	PUNCT
ejpam-5812	297	10	0l4	0l4	NOUN
ejpam-5812	297	11	t	t	NOUN
ejpam-5812	297	12	2(r	2(r	NUM
ejpam-5812	297	13	+	+	SYM
ejpam-5812	297	14	t	t	PROPN
ejpam-5812	297	15	)	)	PUNCT
ejpam-5812	298	1	+	+	CCONJ
ejpam-5812	298	2	1	1	NUM
ejpam-5812	298	3	2(r	2(r	NUM
ejpam-5812	298	4	+	+	NUM
ejpam-5812	298	5	t	t	PROPN
ejpam-5812	298	6	)	)	PUNCT
ejpam-5812	299	1	+	+	CCONJ
ejpam-5812	299	2	1	1	NUM
ejpam-5812	299	3	10(r	10(r	NUM
ejpam-5812	299	4	+	+	CCONJ
ejpam-5812	299	5	t)−	t)−	PROPN
ejpam-5812	299	6	10	10	NUM
ejpam-5812	299	7	10(r	10(r	NUM
ejpam-5812	299	8	+	+	CCONJ
ejpam-5812	299	9	t)−	t)−	PROPN
ejpam-5812	299	10	10	10	NUM
ejpam-5812	299	11	0	0	NUM
ejpam-5812	299	12	0	0	NUM
ejpam-5812	299	13	j=	j=	NOUN
ejpam-5812	299	14	2	2	NUM
ejpam-5812	299	15	l4r1	l4r1	NOUN
ejpam-5812	299	16	l	l	NOUN
ejpam-5812	299	17	′	′	NUM
ejpam-5812	299	18	4t10	4t10	NOUN
ejpam-5812	299	19	2(r	2(r	NUM
ejpam-5812	299	20	+	+	NUM
ejpam-5812	299	21	t	t	X
ejpam-5812	299	22	)	)	PUNCT
ejpam-5812	300	1	+	+	CCONJ
ejpam-5812	300	2	1	1	NUM
ejpam-5812	300	3	2(r	2(r	NUM
ejpam-5812	300	4	+	+	NUM
ejpam-5812	300	5	t	t	NOUN
ejpam-5812	300	6	)	)	PUNCT
ejpam-5812	300	7	+	+	CCONJ
ejpam-5812	300	8	2	2	NUM
ejpam-5812	300	9	10(r	10(r	NUM
ejpam-5812	300	10	+	+	CCONJ
ejpam-5812	300	11	t)−	t)−	PROPN
ejpam-5812	300	12	7	7	NUM
ejpam-5812	300	13	10(r	10(r	NUM
ejpam-5812	300	14	+	+	CCONJ
ejpam-5812	300	15	t)−	t)−	PROPN
ejpam-5812	300	16	8	8	NUM
ejpam-5812	300	17	−1	−1	NOUN
ejpam-5812	300	18	1	1	NUM
ejpam-5812	300	19	j=	j=	NOUN
ejpam-5812	300	20	3	3	NUM
ejpam-5812	300	21	l4r1	l4r1	PRON
ejpam-5812	300	22	l	l	NOUN
ejpam-5812	300	23	′	′	NUM
ejpam-5812	300	24	4tm3	4tm3	NUM
ejpam-5812	300	25	2(r	2(r	NUM
ejpam-5812	300	26	+	+	NUM
ejpam-5812	300	27	t	t	X
ejpam-5812	300	28	)	)	PUNCT
ejpam-5812	301	1	+	+	CCONJ
ejpam-5812	301	2	2	2	NUM
ejpam-5812	301	3	2(r	2(r	NUM
ejpam-5812	301	4	+	+	SYM
ejpam-5812	301	5	t	t	NOUN
ejpam-5812	301	6	)	)	PUNCT
ejpam-5812	301	7	+	+	CCONJ
ejpam-5812	301	8	2	2	NUM
ejpam-5812	301	9	10(r	10(r	NUM
ejpam-5812	302	1	+	+	CCONJ
ejpam-5812	302	2	t)−	t)−	PROPN
ejpam-5812	302	3	5	5	NUM
ejpam-5812	302	4	10(r	10(r	NUM
ejpam-5812	302	5	+	+	CCONJ
ejpam-5812	302	6	t)−	t)−	PROPN
ejpam-5812	302	7	5	5	NUM
ejpam-5812	302	8	0	0	SYM
ejpam-5812	302	9	0	0	NUM
ejpam-5812	302	10	i=	i=	PROPN
ejpam-5812	302	11	2	2	NUM
ejpam-5812	302	12	j=	j=	NOUN
ejpam-5812	302	13	2	2	NUM
ejpam-5812	302	14	l′	l′	NOUN
ejpam-5812	302	15	4r10	4r10	NOUN
ejpam-5812	302	16	l4t10	l4t10	VERB
ejpam-5812	302	17	2(r	2(r	NUM
ejpam-5812	302	18	+	+	SYM
ejpam-5812	302	19	t	t	PROPN
ejpam-5812	302	20	)	)	PUNCT
ejpam-5812	303	1	+	+	CCONJ
ejpam-5812	303	2	2	2	NUM
ejpam-5812	303	3	2(r	2(r	NUM
ejpam-5812	303	4	+	+	SYM
ejpam-5812	303	5	t	t	NOUN
ejpam-5812	303	6	)	)	PUNCT
ejpam-5812	303	7	+	+	CCONJ
ejpam-5812	303	8	2	2	NUM
ejpam-5812	303	9	10(r	10(r	NUM
ejpam-5812	304	1	+	+	CCONJ
ejpam-5812	304	2	t)−	t)−	PROPN
ejpam-5812	304	3	5	5	NUM
ejpam-5812	304	4	10(r	10(r	NUM
ejpam-5812	304	5	+	+	CCONJ
ejpam-5812	304	6	t)−	t)−	PROPN
ejpam-5812	304	7	5	5	NUM
ejpam-5812	304	8	0	0	NUM
ejpam-5812	304	9	0	0	NUM
ejpam-5812	304	10	j=	j=	NOUN
ejpam-5812	304	11	3	3	NUM
ejpam-5812	304	12	l′	l′	X
ejpam-5812	304	13	4r10	4r10	NOUN
ejpam-5812	304	14	l	l	NOUN
ejpam-5812	304	15	′	′	NUM
ejpam-5812	304	16	4tm3	4tm3	NUM
ejpam-5812	304	17	2(r	2(r	NUM
ejpam-5812	304	18	+	+	NUM
ejpam-5812	304	19	t	t	X
ejpam-5812	304	20	)	)	PUNCT
ejpam-5812	305	1	+	+	CCONJ
ejpam-5812	305	2	3	3	NUM
ejpam-5812	305	3	2(r	2(r	NUM
ejpam-5812	305	4	+	+	SYM
ejpam-5812	305	5	t	t	NOUN
ejpam-5812	305	6	)	)	PUNCT
ejpam-5812	306	1	+	+	CCONJ
ejpam-5812	306	2	2	2	NUM
ejpam-5812	306	3	10(r	10(r	NUM
ejpam-5812	306	4	+	+	CCONJ
ejpam-5812	306	5	t)−	t)−	PROPN
ejpam-5812	306	6	2	2	NUM
ejpam-5812	306	7	10(r	10(r	NUM
ejpam-5812	306	8	+	+	CCONJ
ejpam-5812	306	9	t)−	t)−	PROPN
ejpam-5812	306	10	3	3	NUM
ejpam-5812	306	11	1	1	NUM
ejpam-5812	306	12	1	1	NUM
ejpam-5812	306	13	i=	i=	NUM
ejpam-5812	306	14	3	3	NUM
ejpam-5812	306	15	j=	j=	NOUN
ejpam-5812	306	16	3	3	NUM
ejpam-5812	306	17	0l4r10	0l4r10	NUM
ejpam-5812	306	18	l4t101	l4t101	NOUN
ejpam-5812	306	19	2(r	2(r	NUM
ejpam-5812	306	20	+	+	NUM
ejpam-5812	306	21	t	t	X
ejpam-5812	306	22	)	)	PUNCT
ejpam-5812	306	23	+	+	CCONJ
ejpam-5812	306	24	3	3	NUM
ejpam-5812	306	25	2(r	2(r	NUM
ejpam-5812	306	26	+	+	SYM
ejpam-5812	306	27	t	t	NOUN
ejpam-5812	306	28	)	)	PUNCT
ejpam-5812	307	1	+	+	CCONJ
ejpam-5812	307	2	3	3	NUM
ejpam-5812	307	3	10(r	10(r	NUM
ejpam-5812	307	4	+	+	NUM
ejpam-5812	307	5	t	t	PROPN
ejpam-5812	307	6	)	)	PUNCT
ejpam-5812	307	7	10(r	10(r	PROPN
ejpam-5812	308	1	+	+	NUM
ejpam-5812	308	2	t	t	PROPN
ejpam-5812	308	3	)	)	PUNCT
ejpam-5812	308	4	0	0	NUM
ejpam-5812	308	5	0	0	NUM
ejpam-5812	308	6	n=	n=	ADJ
ejpam-5812	308	7	8	8	NUM
ejpam-5812	308	8	m=	m=	SYM
ejpam-5812	308	9	8	8	NUM
ejpam-5812	308	10	1013021	1013021	NUM
ejpam-5812	308	11	1203102	1203102	NUM
ejpam-5812	308	12	8	8	NUM
ejpam-5812	308	13	8	8	NUM
ejpam-5812	308	14	25	25	NUM
ejpam-5812	308	15	25	25	NUM
ejpam-5812	308	16	0	0	NUM
ejpam-5812	308	17	0	0	NUM
ejpam-5812	308	18	j	j	PROPN
ejpam-5812	308	19	=	=	SYM
ejpam-5812	308	20	0,m	0,m	PROPN
ejpam-5812	308	21	>	>	X
ejpam-5812	308	22	8	8	NUM
ejpam-5812	308	23	0414	0414	NUM
ejpam-5812	308	24	1l	1l	NUM
ejpam-5812	308	25	′	′	NUM
ejpam-5812	308	26	4tm3	4tm3	NUM
ejpam-5812	308	27	2t+	2t+	NUM
ejpam-5812	308	28	6	6	NUM
ejpam-5812	308	29	2t+	2t+	NUM
ejpam-5812	308	30	6	6	NUM
ejpam-5812	308	31	10t+	10t+	NUM
ejpam-5812	308	32	6	6	NUM
ejpam-5812	308	33	10t+	10t+	NUM
ejpam-5812	308	34	6	6	NUM
ejpam-5812	308	35	0	0	NUM
ejpam-5812	308	36	0	0	NUM
ejpam-5812	308	37	j=	j=	NOUN
ejpam-5812	308	38	1	1	NUM
ejpam-5812	308	39	0414	0414	NUM
ejpam-5812	308	40	l4t1	l4t1	SYM
ejpam-5812	308	41	2t+	2t+	NUM
ejpam-5812	308	42	4	4	NUM
ejpam-5812	308	43	2t+	2t+	NUM
ejpam-5812	308	44	5	5	NUM
ejpam-5812	308	45	10t+	10t+	NUM
ejpam-5812	308	46	7	7	NUM
ejpam-5812	308	47	10t+	10t+	NUM
ejpam-5812	308	48	8	8	NUM
ejpam-5812	308	49	−1	−1	NOUN
ejpam-5812	308	50	−1	−1	NOUN
ejpam-5812	308	51	j=	j=	ADJ
ejpam-5812	308	52	2	2	NUM
ejpam-5812	308	53	0414	0414	NUM
ejpam-5812	308	54	l	l	NOUN
ejpam-5812	308	55	′	′	NUM
ejpam-5812	308	56	4t10	4t10	NOUN
ejpam-5812	308	57	2t+	2t+	NUM
ejpam-5812	308	58	5	5	NUM
ejpam-5812	308	59	2t+	2t+	NUM
ejpam-5812	308	60	5	5	NUM
ejpam-5812	308	61	10t+	10t+	NUM
ejpam-5812	308	62	10	10	NUM
ejpam-5812	308	63	10t+	10t+	NUM
ejpam-5812	308	64	10	10	NUM
ejpam-5812	308	65	0	0	NUM
ejpam-5812	308	66	0	0	NUM
ejpam-5812	308	67	j=	j=	NOUN
ejpam-5812	308	68	3	3	NUM
ejpam-5812	308	69	0414	0414	NUM
ejpam-5812	308	70	l	l	NOUN
ejpam-5812	308	71	′	′	NUM
ejpam-5812	308	72	4tm3	4tm3	NUM
ejpam-5812	308	73	2t+	2t+	NUM
ejpam-5812	308	74	6	6	NUM
ejpam-5812	308	75	2t+	2t+	NUM
ejpam-5812	308	76	5	5	NUM
ejpam-5812	308	77	10t+	10t+	NUM
ejpam-5812	308	78	12	12	NUM
ejpam-5812	308	79	10t+	10t+	NUM
ejpam-5812	308	80	13	13	NUM
ejpam-5812	308	81	1	1	NUM
ejpam-5812	308	82	−1	−1	NOUN
ejpam-5812	308	83	theorem	theorem	VERB
ejpam-5812	308	84	4.2	4.2	NUM
ejpam-5812	308	85	.	.	PUNCT
ejpam-5812	309	1	the	the	DET
ejpam-5812	309	2	union	union	NOUN
ejpam-5812	309	3	of	of	ADP
ejpam-5812	309	4	c5	c5	PROPN
ejpam-5812	309	5	n	n	PROPN
ejpam-5812	309	6	∪	∪	VERB
ejpam-5812	309	7	c5	c5	PROPN
ejpam-5812	309	8	m	m	PROPN
ejpam-5812	309	9	,	,	PUNCT
ejpam-5812	309	10	n	n	CCONJ
ejpam-5812	309	11	,	,	PUNCT
ejpam-5812	309	12	m	m	VERB
ejpam-5812	309	13	>	>	X
ejpam-5812	309	14	7	7	NUM
ejpam-5812	309	15	admits	admit	VERB
ejpam-5812	309	16	a	a	DET
ejpam-5812	309	17	cordial	cordial	ADJ
ejpam-5812	309	18	labeling	labeling	NOUN
ejpam-5812	309	19	for	for	ADP
ejpam-5812	309	20	every	every	DET
ejpam-5812	309	21	n	n	CCONJ
ejpam-5812	309	22	,	,	PUNCT
ejpam-5812	309	23	m	m	VERB
ejpam-5812	309	24	>	>	X
ejpam-5812	309	25	7	7	X
ejpam-5812	309	26	.	.	PUNCT
ejpam-5812	310	1	proof	proof	NOUN
ejpam-5812	310	2	.	.	PUNCT
ejpam-5812	311	1	let	let	VERB
ejpam-5812	311	2	n=	n=	ADJ
ejpam-5812	311	3	4r	4r	NOUN
ejpam-5812	311	4	+	+	CCONJ
ejpam-5812	312	1	i	i	PRON
ejpam-5812	312	2	(	(	PUNCT
ejpam-5812	312	3	0	0	NUM
ejpam-5812	312	4	≤	≤	NUM
ejpam-5812	312	5	i	i	NOUN
ejpam-5812	312	6	≤	≤	ADV
ejpam-5812	312	7	3	3	NUM
ejpam-5812	312	8	and	and	CCONJ
ejpam-5812	312	9	r	r	NOUN
ejpam-5812	312	10	≥	≥	NOUN
ejpam-5812	312	11	1	1	NUM
ejpam-5812	312	12	)	)	PUNCT
ejpam-5812	312	13	and	and	CCONJ
ejpam-5812	312	14	m=	m=	X
ejpam-5812	312	15	4	4	NUM
ejpam-5812	312	16	t	t	NOUN
ejpam-5812	312	17	+	+	X
ejpam-5812	312	18	j	j	X
ejpam-5812	312	19	(	(	PUNCT
ejpam-5812	312	20	0	0	NUM
ejpam-5812	312	21	≤	≤	NUM
ejpam-5812	312	22	j	j	PROPN
ejpam-5812	312	23	≤	≤	NUM
ejpam-5812	312	24	3	3	NUM
ejpam-5812	312	25	and	and	CCONJ
ejpam-5812	312	26	t	t	PROPN
ejpam-5812	312	27	≥	≥	NUM
ejpam-5812	312	28	1	1	NUM
ejpam-5812	312	29	)	)	PUNCT
ejpam-5812	312	30	,	,	PUNCT
ejpam-5812	312	31	then	then	ADV
ejpam-5812	312	32	throughout	throughout	ADP
ejpam-5812	312	33	the	the	DET
ejpam-5812	312	34	table	table	NOUN
ejpam-5812	312	35	1	1	NUM
ejpam-5812	312	36	and	and	CCONJ
ejpam-5812	312	37	table	table	NOUN
ejpam-5812	312	38	9	9	NUM
ejpam-5812	312	39	.	.	PUNCT
ejpam-5812	312	40	using	use	VERB
ejpam-5812	312	41	table	table	NOUN
ejpam-5812	312	42	9	9	NUM
ejpam-5812	312	43	and	and	CCONJ
ejpam-5812	312	44	formulas	formula	NOUN
ejpam-5812	312	45	v0	v0	NOUN
ejpam-5812	312	46	−	−	PROPN
ejpam-5812	312	47	v1	v1	PROPN
ejpam-5812	312	48	and	and	CCONJ
ejpam-5812	312	49	e0	e0	PROPN
ejpam-5812	312	50	−	−	PROPN
ejpam-5812	312	51	e1	e1	PROPN
ejpam-5812	312	52	,	,	PUNCT
ejpam-5812	312	53	we	we	PRON
ejpam-5812	312	54	can	can	AUX
ejpam-5812	312	55	compute	compute	VERB
ejpam-5812	312	56	the	the	DET
ejpam-5812	312	57	values	value	NOUN
ejpam-5812	312	58	shown	show	VERB
ejpam-5812	312	59	in	in	ADP
ejpam-5812	312	60	the	the	DET
ejpam-5812	312	61	last	last	ADJ
ejpam-5812	312	62	two	two	NUM
ejpam-5812	312	63	columns	column	NOUN
ejpam-5812	312	64	of	of	ADP
ejpam-5812	312	65	table	table	NOUN
ejpam-5812	312	66	9	9	NUM
ejpam-5812	312	67	.	.	PUNCT
ejpam-5812	313	1	since	since	SCONJ
ejpam-5812	313	2	all	all	PRON
ejpam-5812	313	3	of	of	ADP
ejpam-5812	313	4	these	these	DET
ejpam-5812	313	5	values	value	NOUN
ejpam-5812	313	6	are	be	AUX
ejpam-5812	313	7	−1	−1	ADJ
ejpam-5812	313	8	,	,	PUNCT
ejpam-5812	313	9	0	0	NUM
ejpam-5812	313	10	or	or	CCONJ
ejpam-5812	313	11	1	1	NUM
ejpam-5812	313	12	,	,	PUNCT
ejpam-5812	313	13	the	the	DET
ejpam-5812	313	14	theorem	theorem	NOUN
ejpam-5812	313	15	is	be	AUX
ejpam-5812	313	16	proved	prove	VERB
ejpam-5812	313	17	.	.	PUNCT
ejpam-5812	314	1	table	table	NOUN
ejpam-5812	314	2	9	9	NUM
ejpam-5812	314	3	:	:	PUNCT
ejpam-5812	314	4	labeling	labeling	NOUN
ejpam-5812	314	5	of	of	ADP
ejpam-5812	314	6	c5	c5	PROPN
ejpam-5812	314	7	n	n	PART
ejpam-5812	314	8	∪	∪	VERB
ejpam-5812	314	9	c5	c5	PROPN
ejpam-5812	314	10	m	m	PROPN
ejpam-5812	314	11	n	n	NOUN
ejpam-5812	314	12	=	=	NOUN
ejpam-5812	314	13	4r	4r	NOUN
ejpam-5812	315	1	+	+	CCONJ
ejpam-5812	315	2	i	i	PROPN
ejpam-5812	315	3	,	,	PUNCT
ejpam-5812	315	4	n	n	PRON
ejpam-5812	315	5	≥	≥	NUM
ejpam-5812	315	6	8	8	NUM
ejpam-5812	315	7	0	0	NUM
ejpam-5812	315	8	≤	≤	NUM
ejpam-5812	315	9	i	i	PRON
ejpam-5812	315	10	≤	≤	NOUN
ejpam-5812	315	11	3	3	NUM
ejpam-5812	315	12	m	m	NOUN
ejpam-5812	315	13	=	=	SYM
ejpam-5812	315	14	4t+	4t+	NUM
ejpam-5812	315	15	j	j	PROPN
ejpam-5812	315	16	m	m	VERB
ejpam-5812	315	17	≥	≥	NUM
ejpam-5812	315	18	8	8	NUM
ejpam-5812	315	19	0	0	NUM
ejpam-5812	315	20	≤	≤	NUM
ejpam-5812	315	21	j	j	PROPN
ejpam-5812	315	22	≤	≤	ADV
ejpam-5812	315	23	3	3	NUM
ejpam-5812	315	24	labeling	labeling	NOUN
ejpam-5812	315	25	of	of	ADP
ejpam-5812	315	26	c5	c5	PROPN
ejpam-5812	315	27	n	n	PRON
ejpam-5812	315	28	labeling	labeling	NOUN
ejpam-5812	315	29	of	of	ADP
ejpam-5812	315	30	c5	c5	PROPN
ejpam-5812	315	31	m	m	PROPN
ejpam-5812	315	32	v0	v0	NOUN
ejpam-5812	315	33	v1	v1	PROPN
ejpam-5812	315	34	e0	e0	PROPN
ejpam-5812	315	35	e1	e1	PROPN
ejpam-5812	315	36	v0	v0	NOUN
ejpam-5812	315	37	−	−	PROPN
ejpam-5812	315	38	v1	v1	PROPN
ejpam-5812	315	39	e0	e0	PROPN
ejpam-5812	315	40	−	−	PROPN
ejpam-5812	315	41	e1	e1	VERB
ejpam-5812	315	42	i=	i=	PRON
ejpam-5812	315	43	0	0	NUM
ejpam-5812	315	44	,	,	PUNCT
ejpam-5812	315	45	r	r	NOUN
ejpam-5812	315	46	>	>	X
ejpam-5812	315	47	1	1	NUM
ejpam-5812	315	48	j=	j=	NUM
ejpam-5812	315	49	0	0	NUM
ejpam-5812	315	50	,	,	PUNCT
ejpam-5812	315	51	t	t	X
ejpam-5812	315	52	>	>	X
ejpam-5812	315	53	1	1	NUM
ejpam-5812	315	54	0l4r120	0l4r120	NUM
ejpam-5812	315	55	0l4t120	0l4t120	NUM
ejpam-5812	316	1	2(r	2(r	NUM
ejpam-5812	316	2	+	+	NUM
ejpam-5812	316	3	t	t	PROPN
ejpam-5812	316	4	)	)	PUNCT
ejpam-5812	317	1	+	+	CCONJ
ejpam-5812	317	2	4	4	NUM
ejpam-5812	317	3	2(r	2(r	NUM
ejpam-5812	317	4	+	+	SYM
ejpam-5812	317	5	t	t	PROPN
ejpam-5812	317	6	)	)	PUNCT
ejpam-5812	318	1	+	+	CCONJ
ejpam-5812	318	2	4	4	NUM
ejpam-5812	318	3	10(r	10(r	NUM
ejpam-5812	318	4	+	+	NUM
ejpam-5812	318	5	t	t	PROPN
ejpam-5812	318	6	)	)	PUNCT
ejpam-5812	318	7	+	+	CCONJ
ejpam-5812	318	8	6	6	NUM
ejpam-5812	318	9	10(r	10(r	NUM
ejpam-5812	318	10	+	+	NUM
ejpam-5812	318	11	t	t	PROPN
ejpam-5812	318	12	)	)	PUNCT
ejpam-5812	319	1	+	+	CCONJ
ejpam-5812	319	2	6	6	NUM
ejpam-5812	319	3	0	0	NUM
ejpam-5812	319	4	0	0	NUM
ejpam-5812	319	5	j=	j=	ADP
ejpam-5812	319	6	1	1	NUM
ejpam-5812	319	7	,	,	PUNCT
ejpam-5812	319	8	t	t	X
ejpam-5812	319	9	>	>	X
ejpam-5812	319	10	1	1	NUM
ejpam-5812	319	11	0l4r120	0l4r120	NUM
ejpam-5812	319	12	03m4t−412	03m4t−412	VERB
ejpam-5812	320	1	2(r	2(r	NUM
ejpam-5812	320	2	+	+	SYM
ejpam-5812	320	3	t	t	X
ejpam-5812	320	4	)	)	PUNCT
ejpam-5812	321	1	+	+	CCONJ
ejpam-5812	321	2	3	3	NUM
ejpam-5812	321	3	2(r	2(r	NUM
ejpam-5812	321	4	+	+	SYM
ejpam-5812	321	5	t	t	NOUN
ejpam-5812	321	6	)	)	PUNCT
ejpam-5812	322	1	+	+	CCONJ
ejpam-5812	322	2	2	2	NUM
ejpam-5812	322	3	10(r	10(r	NUM
ejpam-5812	322	4	+	+	CCONJ
ejpam-5812	322	5	t)−	t)−	PROPN
ejpam-5812	322	6	1	1	NUM
ejpam-5812	322	7	10(r	10(r	NUM
ejpam-5812	322	8	+	+	CCONJ
ejpam-5812	322	9	t)−	t)−	PROPN
ejpam-5812	322	10	2	2	NUM
ejpam-5812	322	11	1	1	NUM
ejpam-5812	322	12	−1	−1	NOUN
ejpam-5812	322	13	j=	j=	ADJ
ejpam-5812	322	14	2	2	NUM
ejpam-5812	322	15	,	,	PUNCT
ejpam-5812	322	16	t	t	X
ejpam-5812	322	17	>	>	X
ejpam-5812	322	18	1	1	NUM
ejpam-5812	322	19	0l4r120	0l4r120	NUM
ejpam-5812	322	20	01l4	01l4	NUM
ejpam-5812	322	21	t	t	NOUN
ejpam-5812	322	22	2(r	2(r	NUM
ejpam-5812	322	23	+	+	SYM
ejpam-5812	322	24	t	t	PROPN
ejpam-5812	322	25	)	)	PUNCT
ejpam-5812	322	26	+	+	CCONJ
ejpam-5812	322	27	3	3	NUM
ejpam-5812	322	28	2(r	2(r	NUM
ejpam-5812	322	29	+	+	SYM
ejpam-5812	322	30	t	t	NOUN
ejpam-5812	322	31	)	)	PUNCT
ejpam-5812	323	1	+	+	CCONJ
ejpam-5812	323	2	3	3	NUM
ejpam-5812	323	3	10(r	10(r	NUM
ejpam-5812	323	4	+	+	NUM
ejpam-5812	323	5	t	t	PROPN
ejpam-5812	323	6	)	)	PUNCT
ejpam-5812	323	7	+	+	CCONJ
ejpam-5812	323	8	1	1	NUM
ejpam-5812	323	9	10(r	10(r	NUM
ejpam-5812	323	10	+	+	NUM
ejpam-5812	323	11	t	t	PROPN
ejpam-5812	323	12	)	)	PUNCT
ejpam-5812	323	13	+	+	CCONJ
ejpam-5812	323	14	1	1	NUM
ejpam-5812	323	15	0	0	NUM
ejpam-5812	323	16	0	0	NUM
ejpam-5812	323	17	j=	j=	CCONJ
ejpam-5812	323	18	3	3	NUM
ejpam-5812	323	19	,	,	PUNCT
ejpam-5812	323	20	t	t	X
ejpam-5812	323	21	>	>	X
ejpam-5812	323	22	1	1	NUM
ejpam-5812	323	23	0l4r120	0l4r120	NUM
ejpam-5812	323	24	0l4t10	0l4t10	NUM
ejpam-5812	323	25	2(r	2(r	NUM
ejpam-5812	323	26	+	+	SYM
ejpam-5812	323	27	t	t	PROPN
ejpam-5812	323	28	)	)	PUNCT
ejpam-5812	324	1	+	+	CCONJ
ejpam-5812	324	2	4	4	NUM
ejpam-5812	324	3	2(r	2(r	NUM
ejpam-5812	324	4	+	+	SYM
ejpam-5812	324	5	t	t	NOUN
ejpam-5812	324	6	)	)	PUNCT
ejpam-5812	325	1	+	+	CCONJ
ejpam-5812	325	2	3	3	NUM
ejpam-5812	325	3	10(r	10(r	NUM
ejpam-5812	325	4	+	+	NUM
ejpam-5812	325	5	t	t	PROPN
ejpam-5812	325	6	)	)	PUNCT
ejpam-5812	325	7	+	+	CCONJ
ejpam-5812	325	8	4	4	NUM
ejpam-5812	325	9	10(r	10(r	NUM
ejpam-5812	325	10	+	+	NUM
ejpam-5812	325	11	t	t	PROPN
ejpam-5812	325	12	)	)	PUNCT
ejpam-5812	326	1	+	+	CCONJ
ejpam-5812	326	2	3	3	NUM
ejpam-5812	326	3	1	1	NUM
ejpam-5812	326	4	1	1	NUM
ejpam-5812	326	5	i=	i=	NUM
ejpam-5812	326	6	1	1	NUM
ejpam-5812	326	7	j=	j=	NOUN
ejpam-5812	326	8	1	1	NUM
ejpam-5812	327	1	l4r1	l4r1	SYM
ejpam-5812	327	2	12	12	NUM
ejpam-5812	327	3	m	m	NOUN
ejpam-5812	327	4	′	′	NUM
ejpam-5812	327	5	4t−403	4t−403	NUM
ejpam-5812	327	6	2(r	2(r	NUM
ejpam-5812	327	7	+	+	NUM
ejpam-5812	327	8	t	t	X
ejpam-5812	327	9	)	)	PUNCT
ejpam-5812	327	10	+	+	CCONJ
ejpam-5812	327	11	1	1	NUM
ejpam-5812	327	12	2(r	2(r	NUM
ejpam-5812	327	13	+	+	NUM
ejpam-5812	327	14	t	t	PROPN
ejpam-5812	327	15	)	)	PUNCT
ejpam-5812	327	16	+	+	CCONJ
ejpam-5812	327	17	1	1	NUM
ejpam-5812	327	18	10(r	10(r	NUM
ejpam-5812	327	19	+	+	CCONJ
ejpam-5812	327	20	t)−	t)−	PROPN
ejpam-5812	327	21	9	9	NUM
ejpam-5812	327	22	10(r	10(r	NUM
ejpam-5812	327	23	+	+	CCONJ
ejpam-5812	327	24	t)−	t)−	PROPN
ejpam-5812	327	25	9	9	NUM
ejpam-5812	327	26	0	0	NUM
ejpam-5812	327	27	0	0	NUM
ejpam-5812	327	28	j=	j=	NOUN
ejpam-5812	327	29	2	2	NUM
ejpam-5812	328	1	l4r1	l4r1	DET
ejpam-5812	328	2	10l′	10l′	NUM
ejpam-5812	328	3	4	4	NUM
ejpam-5812	328	4	t	t	NOUN
ejpam-5812	328	5	2(r	2(r	NUM
ejpam-5812	328	6	+	+	SYM
ejpam-5812	328	7	t	t	PROPN
ejpam-5812	328	8	)	)	PUNCT
ejpam-5812	329	1	+	+	CCONJ
ejpam-5812	329	2	1	1	NUM
ejpam-5812	329	3	2(r	2(r	NUM
ejpam-5812	329	4	+	+	NUM
ejpam-5812	329	5	t	t	NOUN
ejpam-5812	329	6	)	)	PUNCT
ejpam-5812	329	7	+	+	CCONJ
ejpam-5812	329	8	2	2	NUM
ejpam-5812	329	9	10(r	10(r	NUM
ejpam-5812	329	10	+	+	CCONJ
ejpam-5812	329	11	t)−	t)−	PROPN
ejpam-5812	329	12	7	7	NUM
ejpam-5812	329	13	10(r	10(r	NUM
ejpam-5812	329	14	+	+	CCONJ
ejpam-5812	329	15	t)−	t)−	PROPN
ejpam-5812	329	16	6	6	NUM
ejpam-5812	329	17	−1	−1	NOUN
ejpam-5812	329	18	−1	−1	NOUN
ejpam-5812	329	19	j=	j=	NOUN
ejpam-5812	329	20	3	3	NUM
ejpam-5812	329	21	l4r1	l4r1	ADV
ejpam-5812	329	22	l4t10	l4t10	X
ejpam-5812	329	23	2(r	2(r	NUM
ejpam-5812	329	24	+	+	SYM
ejpam-5812	329	25	t	t	PROPN
ejpam-5812	329	26	)	)	PUNCT
ejpam-5812	329	27	+	+	CCONJ
ejpam-5812	330	1	2	2	NUM
ejpam-5812	330	2	2(r	2(r	NUM
ejpam-5812	330	3	+	+	SYM
ejpam-5812	330	4	t	t	NOUN
ejpam-5812	330	5	)	)	PUNCT
ejpam-5812	330	6	+	+	CCONJ
ejpam-5812	330	7	2	2	NUM
ejpam-5812	330	8	10(r	10(r	NUM
ejpam-5812	330	9	+	+	CCONJ
ejpam-5812	330	10	t)−	t)−	PROPN
ejpam-5812	330	11	4	4	NUM
ejpam-5812	330	12	10(r	10(r	NUM
ejpam-5812	330	13	+	+	CCONJ
ejpam-5812	330	14	t)−	t)−	PROPN
ejpam-5812	330	15	4	4	NUM
ejpam-5812	330	16	0	0	NUM
ejpam-5812	330	17	0	0	NUM
ejpam-5812	330	18	i=	i=	PROPN
ejpam-5812	330	19	2	2	NUM
ejpam-5812	330	20	j=	j=	NOUN
ejpam-5812	330	21	2	2	NUM
ejpam-5812	330	22	l′	l′	X
ejpam-5812	330	23	4r10	4r10	NOUN
ejpam-5812	331	1	01l4	01l4	NUM
ejpam-5812	331	2	t	t	NOUN
ejpam-5812	331	3	2(r	2(r	NUM
ejpam-5812	331	4	+	+	SYM
ejpam-5812	331	5	t	t	PROPN
ejpam-5812	331	6	)	)	PUNCT
ejpam-5812	332	1	+	+	CCONJ
ejpam-5812	332	2	2	2	NUM
ejpam-5812	332	3	2(r	2(r	NUM
ejpam-5812	332	4	+	+	SYM
ejpam-5812	332	5	t	t	NOUN
ejpam-5812	332	6	)	)	PUNCT
ejpam-5812	332	7	+	+	CCONJ
ejpam-5812	332	8	2	2	NUM
ejpam-5812	332	9	10(r	10(r	NUM
ejpam-5812	333	1	+	+	CCONJ
ejpam-5812	333	2	t)−	t)−	PROPN
ejpam-5812	333	3	4	4	NUM
ejpam-5812	333	4	10(r	10(r	NUM
ejpam-5812	333	5	+	+	CCONJ
ejpam-5812	333	6	t)−	t)−	PROPN
ejpam-5812	333	7	4	4	NUM
ejpam-5812	333	8	0	0	NUM
ejpam-5812	333	9	0	0	NUM
ejpam-5812	333	10	j=	j=	NOUN
ejpam-5812	333	11	3	3	NUM
ejpam-5812	333	12	l′	l′	VERB
ejpam-5812	333	13	4r10	4r10	NOUN
ejpam-5812	333	14	0l4t10	0l4t10	NUM
ejpam-5812	333	15	2(r	2(r	NUM
ejpam-5812	333	16	+	+	NUM
ejpam-5812	333	17	t	t	PROPN
ejpam-5812	333	18	)	)	PUNCT
ejpam-5812	334	1	+	+	CCONJ
ejpam-5812	334	2	3	3	NUM
ejpam-5812	334	3	2(r	2(r	NUM
ejpam-5812	334	4	+	+	SYM
ejpam-5812	334	5	t	t	NOUN
ejpam-5812	334	6	)	)	PUNCT
ejpam-5812	335	1	+	+	CCONJ
ejpam-5812	335	2	2	2	NUM
ejpam-5812	335	3	10(r	10(r	NUM
ejpam-5812	335	4	+	+	CCONJ
ejpam-5812	335	5	t)−	t)−	PROPN
ejpam-5812	335	6	1	1	NUM
ejpam-5812	335	7	10(r	10(r	NUM
ejpam-5812	335	8	+	+	CCONJ
ejpam-5812	335	9	t)−	t)−	PROPN
ejpam-5812	335	10	2	2	NUM
ejpam-5812	335	11	1	1	NUM
ejpam-5812	335	12	1	1	NUM
ejpam-5812	335	13	i=	i=	NUM
ejpam-5812	335	14	3	3	NUM
ejpam-5812	335	15	j=	j=	NOUN
ejpam-5812	335	16	3	3	NUM
ejpam-5812	335	17	l′	l′	NOUN
ejpam-5812	335	18	4rm3	4rm3	NUM
ejpam-5812	335	19	0l4t10	0l4t10	NUM
ejpam-5812	335	20	2(r	2(r	NUM
ejpam-5812	335	21	+	+	NUM
ejpam-5812	335	22	t	t	PROPN
ejpam-5812	335	23	)	)	PUNCT
ejpam-5812	335	24	+	+	CCONJ
ejpam-5812	335	25	3	3	NUM
ejpam-5812	335	26	2(r	2(r	NUM
ejpam-5812	335	27	+	+	SYM
ejpam-5812	335	28	t	t	NOUN
ejpam-5812	335	29	)	)	PUNCT
ejpam-5812	336	1	+	+	CCONJ
ejpam-5812	336	2	3	3	NUM
ejpam-5812	336	3	10(r	10(r	NUM
ejpam-5812	336	4	+	+	NUM
ejpam-5812	336	5	t	t	PROPN
ejpam-5812	336	6	)	)	PUNCT
ejpam-5812	336	7	+	+	CCONJ
ejpam-5812	336	8	1	1	NUM
ejpam-5812	336	9	10(r	10(r	NUM
ejpam-5812	336	10	+	+	NUM
ejpam-5812	336	11	t	t	PROPN
ejpam-5812	336	12	)	)	PUNCT
ejpam-5812	336	13	+	+	CCONJ
ejpam-5812	336	14	1	1	NUM
ejpam-5812	336	15	0	0	NUM
ejpam-5812	336	16	0	0	NUM
ejpam-5812	336	17	n=	n=	ADJ
ejpam-5812	336	18	8	8	NUM
ejpam-5812	336	19	m=	m=	SYM
ejpam-5812	336	20	8	8	NUM
ejpam-5812	336	21	1013021	1013021	NUM
ejpam-5812	336	22	1203102	1203102	NUM
ejpam-5812	336	23	8	8	NUM
ejpam-5812	336	24	8	8	NUM
ejpam-5812	336	25	26	26	NUM
ejpam-5812	336	26	26	26	NUM
ejpam-5812	336	27	0	0	NUM
ejpam-5812	336	28	0	0	NUM
ejpam-5812	336	29	j	j	PROPN
ejpam-5812	336	30	=	=	SYM
ejpam-5812	336	31	0,m	0,m	PROPN
ejpam-5812	336	32	>	>	X
ejpam-5812	336	33	8	8	NUM
ejpam-5812	336	34	0414	0414	NUM
ejpam-5812	336	35	04l	04l	NUM
ejpam-5812	337	1	′	′	NUM
ejpam-5812	338	1	4t−414	4t−414	NUM
ejpam-5812	338	2	2t+	2t+	NUM
ejpam-5812	338	3	6	6	NUM
ejpam-5812	338	4	2t+	2t+	NUM
ejpam-5812	338	5	6	6	NUM
ejpam-5812	338	6	10t+	10t+	NUM
ejpam-5812	338	7	7	7	NUM
ejpam-5812	338	8	10t+	10t+	NUM
ejpam-5812	338	9	7	7	NUM
ejpam-5812	338	10	0	0	NUM
ejpam-5812	338	11	0	0	NUM
ejpam-5812	338	12	j=	j=	NOUN
ejpam-5812	338	13	1	1	NUM
ejpam-5812	338	14	0414	0414	NUM
ejpam-5812	338	15	12m4t03	12m4t03	NUM
ejpam-5812	338	16	2t+	2t+	NUM
ejpam-5812	338	17	5	5	NUM
ejpam-5812	338	18	2t+	2t+	NUM
ejpam-5812	338	19	4	4	NUM
ejpam-5812	338	20	10t+	10t+	NUM
ejpam-5812	338	21	8	8	NUM
ejpam-5812	338	22	10t+	10t+	NUM
ejpam-5812	338	23	9	9	NUM
ejpam-5812	338	24	1	1	NUM
ejpam-5812	338	25	−1	−1	NOUN
ejpam-5812	338	26	j=	j=	ADP
ejpam-5812	338	27	2	2	NUM
ejpam-5812	338	28	0414	0414	NUM
ejpam-5812	339	1	031l4t−412	031l4t−412	NOUN
ejpam-5812	339	2	2t+	2t+	NUM
ejpam-5812	339	3	5	5	NUM
ejpam-5812	339	4	2t+	2t+	NUM
ejpam-5812	339	5	5	5	NUM
ejpam-5812	339	6	10t+	10t+	NUM
ejpam-5812	339	7	11	11	NUM
ejpam-5812	339	8	10t+	10t+	NUM
ejpam-5812	339	9	11	11	NUM
ejpam-5812	339	10	0	0	NUM
ejpam-5812	339	11	0	0	NUM
ejpam-5812	339	12	j=	j=	NOUN
ejpam-5812	339	13	3	3	NUM
ejpam-5812	339	14	0414	0414	NUM
ejpam-5812	339	15	l	l	NOUN
ejpam-5812	339	16	′	′	NUM
ejpam-5812	339	17	4tm3	4tm3	NUM
ejpam-5812	339	18	2t+	2t+	NUM
ejpam-5812	339	19	6	6	NUM
ejpam-5812	339	20	2t+	2t+	NUM
ejpam-5812	339	21	5	5	NUM
ejpam-5812	339	22	10t+	10t+	NUM
ejpam-5812	339	23	13	13	NUM
ejpam-5812	339	24	10t+	10t+	NUM
ejpam-5812	339	25	14	14	NUM
ejpam-5812	339	26	1	1	NUM
ejpam-5812	339	27	−1	−1	NOUN
ejpam-5812	339	28	a.	a.	PROPN
ejpam-5812	339	29	abd	abd	PROPN
ejpam-5812	339	30	el	el	PROPN
ejpam-5812	339	31	-	-	PROPN
ejpam-5812	339	32	hay	hay	PROPN
ejpam-5812	339	33	,	,	PUNCT
ejpam-5812	339	34	k.	k.	PROPN
ejpam-5812	339	35	a.	a.	PROPN
ejpam-5812	339	36	alsatami	alsatami	PROPN
ejpam-5812	339	37	,	,	PUNCT
ejpam-5812	339	38	a.	a.	NOUN
ejpam-5812	339	39	elrokh	elrokh	PROPN
ejpam-5812	339	40	/	/	SYM
ejpam-5812	339	41	eur	eur	PROPN
ejpam-5812	339	42	.	.	PUNCT
ejpam-5812	340	1	j.	j.	PROPN
ejpam-5812	340	2	pure	pure	PROPN
ejpam-5812	340	3	appl	appl	PROPN
ejpam-5812	340	4	.	.	PROPN
ejpam-5812	340	5	math	math	PROPN
ejpam-5812	340	6	,	,	PUNCT
ejpam-5812	340	7	18	18	NUM
ejpam-5812	340	8	(	(	PUNCT
ejpam-5812	340	9	1	1	NUM
ejpam-5812	340	10	)	)	PUNCT
ejpam-5812	340	11	(	(	PUNCT
ejpam-5812	340	12	2025	2025	NUM
ejpam-5812	340	13	)	)	PUNCT
ejpam-5812	340	14	,	,	PUNCT
ejpam-5812	340	15	5812	5812	NUM
ejpam-5812	340	16	11	11	NUM
ejpam-5812	340	17	of	of	ADP
ejpam-5812	340	18	14	14	NUM
ejpam-5812	340	19	theorem	theorem	VERB
ejpam-5812	340	20	4.3	4.3	NUM
ejpam-5812	340	21	.	.	PUNCT
ejpam-5812	341	1	the	the	DET
ejpam-5812	341	2	union	union	NOUN
ejpam-5812	341	3	of	of	ADP
ejpam-5812	341	4	p	p	PROPN
ejpam-5812	341	5	5	5	NUM
ejpam-5812	341	6	n	n	NOUN
ejpam-5812	341	7	∪	∪	NOUN
ejpam-5812	341	8	c5	c5	PROPN
ejpam-5812	341	9	m	m	PROPN
ejpam-5812	341	10	,	,	PUNCT
ejpam-5812	341	11	n	n	CCONJ
ejpam-5812	341	12	,	,	PUNCT
ejpam-5812	341	13	m	m	VERB
ejpam-5812	341	14	>	>	X
ejpam-5812	341	15	7	7	NUM
ejpam-5812	341	16	admits	admit	VERB
ejpam-5812	341	17	a	a	DET
ejpam-5812	341	18	cordial	cordial	ADJ
ejpam-5812	341	19	labeling	labeling	NOUN
ejpam-5812	341	20	for	for	ADP
ejpam-5812	341	21	every	every	DET
ejpam-5812	341	22	n	n	CCONJ
ejpam-5812	341	23	,	,	PUNCT
ejpam-5812	341	24	m	m	VERB
ejpam-5812	341	25	>	>	X
ejpam-5812	341	26	7	7	X
ejpam-5812	341	27	.	.	PUNCT
ejpam-5812	342	1	proof	proof	NOUN
ejpam-5812	342	2	.	.	PUNCT
ejpam-5812	343	1	let	let	VERB
ejpam-5812	343	2	n=	n=	ADJ
ejpam-5812	343	3	4r+	4r+	NUM
ejpam-5812	343	4	i	i	NOUN
ejpam-5812	343	5	(	(	PUNCT
ejpam-5812	343	6	i=	i=	PROPN
ejpam-5812	343	7	0	0	NUM
ejpam-5812	343	8	,	,	PUNCT
ejpam-5812	343	9	1	1	NUM
ejpam-5812	343	10	,	,	PUNCT
ejpam-5812	343	11	2	2	NUM
ejpam-5812	343	12	,	,	PUNCT
ejpam-5812	343	13	3	3	NUM
ejpam-5812	343	14	and	and	CCONJ
ejpam-5812	343	15	r	r	NOUN
ejpam-5812	343	16	≥	≥	NOUN
ejpam-5812	343	17	1	1	NUM
ejpam-5812	343	18	)	)	PUNCT
ejpam-5812	343	19	and	and	CCONJ
ejpam-5812	343	20	m=	m=	X
ejpam-5812	343	21	4t+	4t+	NUM
ejpam-5812	343	22	j	j	PROPN
ejpam-5812	343	23	(	(	PUNCT
ejpam-5812	343	24	j=	j=	NOUN
ejpam-5812	343	25	0	0	NUM
ejpam-5812	343	26	,	,	PUNCT
ejpam-5812	343	27	1	1	NUM
ejpam-5812	343	28	,	,	PUNCT
ejpam-5812	343	29	2	2	NUM
ejpam-5812	343	30	,	,	PUNCT
ejpam-5812	343	31	3	3	NUM
ejpam-5812	343	32	and	and	CCONJ
ejpam-5812	343	33	t	t	PROPN
ejpam-5812	343	34	≥	≥	NUM
ejpam-5812	343	35	1	1	NUM
ejpam-5812	343	36	)	)	PUNCT
ejpam-5812	343	37	,	,	PUNCT
ejpam-5812	343	38	then	then	ADV
ejpam-5812	343	39	throughout	throughout	ADP
ejpam-5812	343	40	the	the	DET
ejpam-5812	343	41	tables	table	NOUN
ejpam-5812	343	42	1	1	NUM
ejpam-5812	343	43	,	,	PUNCT
ejpam-5812	343	44	2	2	NUM
ejpam-5812	343	45	and	and	CCONJ
ejpam-5812	343	46	table	table	NOUN
ejpam-5812	343	47	10	10	NUM
ejpam-5812	343	48	.	.	PUNCT
ejpam-5812	344	1	using	use	VERB
ejpam-5812	344	2	table	table	NOUN
ejpam-5812	344	3	10	10	NUM
ejpam-5812	344	4	and	and	CCONJ
ejpam-5812	344	5	formulas	formula	NOUN
ejpam-5812	344	6	v0−	v0−	PROPN
ejpam-5812	344	7	v1and	v1and	PROPN
ejpam-5812	344	8	e0−	e0−	PROPN
ejpam-5812	344	9	e1	e1	NOUN
ejpam-5812	344	10	,	,	PUNCT
ejpam-5812	344	11	we	we	PRON
ejpam-5812	344	12	can	can	AUX
ejpam-5812	344	13	compute	compute	VERB
ejpam-5812	344	14	the	the	DET
ejpam-5812	344	15	values	value	NOUN
ejpam-5812	344	16	shown	show	VERB
ejpam-5812	344	17	in	in	ADP
ejpam-5812	344	18	the	the	DET
ejpam-5812	344	19	last	last	ADJ
ejpam-5812	344	20	two	two	NUM
ejpam-5812	344	21	columns	column	NOUN
ejpam-5812	344	22	of	of	ADP
ejpam-5812	344	23	table	table	NOUN
ejpam-5812	344	24	10	10	NUM
ejpam-5812	344	25	.	.	PUNCT
ejpam-5812	345	1	since	since	SCONJ
ejpam-5812	345	2	all	all	PRON
ejpam-5812	345	3	of	of	ADP
ejpam-5812	345	4	these	these	DET
ejpam-5812	345	5	values	value	NOUN
ejpam-5812	345	6	are	be	AUX
ejpam-5812	345	7	−1	−1	ADJ
ejpam-5812	345	8	,	,	PUNCT
ejpam-5812	345	9	0	0	NUM
ejpam-5812	345	10	or	or	CCONJ
ejpam-5812	345	11	1	1	NUM
ejpam-5812	345	12	,	,	PUNCT
ejpam-5812	345	13	the	the	DET
ejpam-5812	345	14	theorem	theorem	NOUN
ejpam-5812	345	15	is	be	AUX
ejpam-5812	345	16	proved	prove	VERB
ejpam-5812	345	17	.	.	PUNCT
ejpam-5812	346	1	table	table	NOUN
ejpam-5812	346	2	10	10	NUM
ejpam-5812	346	3	:	:	PUNCT
ejpam-5812	346	4	labeling	labeling	NOUN
ejpam-5812	346	5	of	of	ADP
ejpam-5812	346	6	p	p	PROPN
ejpam-5812	346	7	5	5	NUM
ejpam-5812	346	8	n	n	NOUN
ejpam-5812	346	9	∪	∪	NOUN
ejpam-5812	346	10	c5	c5	PROPN
ejpam-5812	346	11	m	m	PROPN
ejpam-5812	346	12	n	n	NOUN
ejpam-5812	346	13	=	=	NOUN
ejpam-5812	346	14	4r	4r	NOUN
ejpam-5812	347	1	+	+	CCONJ
ejpam-5812	347	2	i	i	PROPN
ejpam-5812	347	3	,	,	PUNCT
ejpam-5812	347	4	n	n	PRON
ejpam-5812	347	5	≥	≥	NUM
ejpam-5812	347	6	8	8	NUM
ejpam-5812	347	7	0	0	NUM
ejpam-5812	347	8	≤	≤	NUM
ejpam-5812	347	9	i	i	PRON
ejpam-5812	347	10	≤	≤	NOUN
ejpam-5812	347	11	3	3	NUM
ejpam-5812	347	12	m	m	NOUN
ejpam-5812	347	13	=	=	SYM
ejpam-5812	347	14	4t+	4t+	NUM
ejpam-5812	347	15	j	j	PROPN
ejpam-5812	347	16	m	m	VERB
ejpam-5812	347	17	≥	≥	NUM
ejpam-5812	347	18	8	8	NUM
ejpam-5812	347	19	0	0	NUM
ejpam-5812	347	20	≤	≤	NUM
ejpam-5812	347	21	j	j	PROPN
ejpam-5812	347	22	≤	≤	ADV
ejpam-5812	347	23	3	3	NUM
ejpam-5812	347	24	labeling	labeling	NOUN
ejpam-5812	347	25	of	of	ADP
ejpam-5812	347	26	p	p	PROPN
ejpam-5812	347	27	5	5	NUM
ejpam-5812	347	28	n	n	PRON
ejpam-5812	347	29	labeling	labeling	NOUN
ejpam-5812	347	30	of	of	ADP
ejpam-5812	347	31	c5	c5	PROPN
ejpam-5812	347	32	m	m	PROPN
ejpam-5812	347	33	v0	v0	NOUN
ejpam-5812	347	34	v1	v1	PROPN
ejpam-5812	347	35	e0	e0	PROPN
ejpam-5812	347	36	e1	e1	PROPN
ejpam-5812	347	37	v0	v0	NOUN
ejpam-5812	347	38	−	−	PROPN
ejpam-5812	347	39	v1	v1	PROPN
ejpam-5812	347	40	e0	e0	PROPN
ejpam-5812	347	41	−	−	PROPN
ejpam-5812	347	42	e1	e1	VERB
ejpam-5812	347	43	i=	i=	PROPN
ejpam-5812	347	44	0	0	PUNCT
ejpam-5812	348	1	j=	j=	NOUN
ejpam-5812	348	2	0	0	NUM
ejpam-5812	349	1	0l4r120	0l4r120	NUM
ejpam-5812	349	2	0l4t120	0l4t120	NUM
ejpam-5812	349	3	2(r	2(r	NUM
ejpam-5812	349	4	+	+	NUM
ejpam-5812	349	5	t	t	PROPN
ejpam-5812	349	6	)	)	PUNCT
ejpam-5812	350	1	+	+	CCONJ
ejpam-5812	350	2	4	4	NUM
ejpam-5812	350	3	2(r	2(r	NUM
ejpam-5812	350	4	+	+	SYM
ejpam-5812	350	5	t	t	PROPN
ejpam-5812	350	6	)	)	PUNCT
ejpam-5812	351	1	+	+	CCONJ
ejpam-5812	351	2	4	4	NUM
ejpam-5812	351	3	10(r	10(r	NUM
ejpam-5812	351	4	+	+	NUM
ejpam-5812	351	5	t	t	PROPN
ejpam-5812	351	6	)	)	PUNCT
ejpam-5812	351	7	+	+	CCONJ
ejpam-5812	351	8	5	5	NUM
ejpam-5812	351	9	10(r	10(r	NUM
ejpam-5812	351	10	+	+	NUM
ejpam-5812	351	11	t	t	PROPN
ejpam-5812	351	12	)	)	PUNCT
ejpam-5812	352	1	+	+	CCONJ
ejpam-5812	352	2	6	6	NUM
ejpam-5812	352	3	0	0	NUM
ejpam-5812	352	4	−1	−1	NOUN
ejpam-5812	352	5	j=	j=	NOUN
ejpam-5812	352	6	1	1	NUM
ejpam-5812	352	7	0l4r120	0l4r120	NUM
ejpam-5812	352	8	03m4t−412	03m4t−412	X
ejpam-5812	353	1	2(r	2(r	NUM
ejpam-5812	353	2	+	+	SYM
ejpam-5812	353	3	t	t	X
ejpam-5812	353	4	)	)	PUNCT
ejpam-5812	354	1	+	+	CCONJ
ejpam-5812	354	2	3	3	NUM
ejpam-5812	354	3	2(r	2(r	NUM
ejpam-5812	354	4	+	+	SYM
ejpam-5812	354	5	t	t	NOUN
ejpam-5812	354	6	)	)	PUNCT
ejpam-5812	355	1	+	+	CCONJ
ejpam-5812	355	2	2	2	NUM
ejpam-5812	355	3	10(r	10(r	NUM
ejpam-5812	355	4	+	+	CCONJ
ejpam-5812	355	5	t)−	t)−	PROPN
ejpam-5812	355	6	2	2	NUM
ejpam-5812	355	7	10(r	10(r	NUM
ejpam-5812	355	8	+	+	CCONJ
ejpam-5812	355	9	t)−	t)−	PROPN
ejpam-5812	355	10	2	2	NUM
ejpam-5812	355	11	1	1	NUM
ejpam-5812	355	12	0	0	NUM
ejpam-5812	355	13	j=	j=	ADP
ejpam-5812	355	14	2	2	NUM
ejpam-5812	355	15	0l4r120	0l4r120	NUM
ejpam-5812	355	16	01l4	01l4	NUM
ejpam-5812	355	17	t	t	NOUN
ejpam-5812	355	18	2(r	2(r	NUM
ejpam-5812	355	19	+	+	SYM
ejpam-5812	355	20	t	t	PROPN
ejpam-5812	355	21	)	)	PUNCT
ejpam-5812	355	22	+	+	CCONJ
ejpam-5812	355	23	3	3	NUM
ejpam-5812	355	24	2(r	2(r	NUM
ejpam-5812	355	25	+	+	SYM
ejpam-5812	355	26	t	t	NOUN
ejpam-5812	355	27	)	)	PUNCT
ejpam-5812	356	1	+	+	CCONJ
ejpam-5812	356	2	3	3	NUM
ejpam-5812	356	3	10(r	10(r	NUM
ejpam-5812	356	4	+	+	NUM
ejpam-5812	356	5	t	t	PROPN
ejpam-5812	356	6	)	)	PUNCT
ejpam-5812	356	7	10(r	10(r	PROPN
ejpam-5812	357	1	+	+	NUM
ejpam-5812	357	2	t	t	PROPN
ejpam-5812	357	3	)	)	PUNCT
ejpam-5812	357	4	+	+	CCONJ
ejpam-5812	357	5	1	1	NUM
ejpam-5812	357	6	0	0	NUM
ejpam-5812	357	7	−1	−1	NOUN
ejpam-5812	357	8	j=	j=	NOUN
ejpam-5812	357	9	3	3	NUM
ejpam-5812	357	10	0l4r120	0l4r120	NUM
ejpam-5812	357	11	0l4t10	0l4t10	NUM
ejpam-5812	358	1	2(r	2(r	NUM
ejpam-5812	358	2	+	+	SYM
ejpam-5812	358	3	t	t	PROPN
ejpam-5812	358	4	)	)	PUNCT
ejpam-5812	359	1	+	+	CCONJ
ejpam-5812	359	2	4	4	NUM
ejpam-5812	359	3	2(r	2(r	NUM
ejpam-5812	359	4	+	+	SYM
ejpam-5812	359	5	t	t	NOUN
ejpam-5812	359	6	)	)	PUNCT
ejpam-5812	360	1	+	+	CCONJ
ejpam-5812	360	2	3	3	NUM
ejpam-5812	360	3	10(r	10(r	NUM
ejpam-5812	360	4	+	+	NUM
ejpam-5812	360	5	t	t	PROPN
ejpam-5812	360	6	)	)	PUNCT
ejpam-5812	360	7	+	+	CCONJ
ejpam-5812	360	8	3	3	NUM
ejpam-5812	360	9	10(r	10(r	NUM
ejpam-5812	360	10	+	+	NUM
ejpam-5812	360	11	t	t	PROPN
ejpam-5812	360	12	)	)	PUNCT
ejpam-5812	361	1	+	+	CCONJ
ejpam-5812	361	2	3	3	NUM
ejpam-5812	361	3	1	1	NUM
ejpam-5812	361	4	0	0	NUM
ejpam-5812	361	5	i=	i=	PROPN
ejpam-5812	361	6	1	1	NUM
ejpam-5812	361	7	j=	j=	NOUN
ejpam-5812	361	8	0	0	NUM
ejpam-5812	362	1	l4r1	l4r1	DET
ejpam-5812	362	2	0l4t120	0l4t120	NUM
ejpam-5812	363	1	2(r	2(r	NUM
ejpam-5812	363	2	+	+	NUM
ejpam-5812	363	3	t	t	PROPN
ejpam-5812	363	4	)	)	PUNCT
ejpam-5812	364	1	+	+	CCONJ
ejpam-5812	364	2	2	2	NUM
ejpam-5812	364	3	2(r	2(r	NUM
ejpam-5812	364	4	+	+	SYM
ejpam-5812	364	5	t	t	PROPN
ejpam-5812	364	6	)	)	PUNCT
ejpam-5812	365	1	+	+	CCONJ
ejpam-5812	365	2	3	3	NUM
ejpam-5812	365	3	10(r	10(r	NUM
ejpam-5812	365	4	+	+	CCONJ
ejpam-5812	365	5	t)−	t)−	PROPN
ejpam-5812	365	6	2	2	NUM
ejpam-5812	365	7	10(r	10(r	NUM
ejpam-5812	365	8	+	+	CCONJ
ejpam-5812	365	9	t)−	t)−	PROPN
ejpam-5812	365	10	2	2	NUM
ejpam-5812	365	11	−1	−1	NOUN
ejpam-5812	365	12	0	0	NUM
ejpam-5812	365	13	j=	j=	NOUN
ejpam-5812	365	14	1	1	NUM
ejpam-5812	366	1	l4r1	l4r1	PRON
ejpam-5812	366	2	12	12	NUM
ejpam-5812	366	3	m	m	NOUN
ejpam-5812	366	4	′	′	NUM
ejpam-5812	366	5	4t−403	4t−403	NUM
ejpam-5812	366	6	2(r	2(r	NUM
ejpam-5812	366	7	+	+	NUM
ejpam-5812	366	8	t	t	X
ejpam-5812	366	9	)	)	PUNCT
ejpam-5812	366	10	+	+	CCONJ
ejpam-5812	366	11	1	1	NUM
ejpam-5812	366	12	2(r	2(r	NUM
ejpam-5812	366	13	+	+	NUM
ejpam-5812	366	14	t	t	PROPN
ejpam-5812	366	15	)	)	PUNCT
ejpam-5812	366	16	+	+	CCONJ
ejpam-5812	366	17	1	1	NUM
ejpam-5812	366	18	10(r	10(r	NUM
ejpam-5812	366	19	+	+	CCONJ
ejpam-5812	366	20	t)−	t)−	PROPN
ejpam-5812	366	21	9	9	NUM
ejpam-5812	366	22	10(r	10(r	NUM
ejpam-5812	366	23	+	+	CCONJ
ejpam-5812	366	24	t)−	t)−	PROPN
ejpam-5812	366	25	10	10	NUM
ejpam-5812	366	26	0	0	NUM
ejpam-5812	366	27	1	1	NUM
ejpam-5812	366	28	j=	j=	ADP
ejpam-5812	366	29	2	2	NUM
ejpam-5812	366	30	l4r1	l4r1	PRON
ejpam-5812	366	31	10l′	10l′	NUM
ejpam-5812	366	32	4	4	NUM
ejpam-5812	366	33	t	t	NOUN
ejpam-5812	366	34	2(r	2(r	NUM
ejpam-5812	366	35	+	+	SYM
ejpam-5812	366	36	t	t	PROPN
ejpam-5812	366	37	)	)	PUNCT
ejpam-5812	367	1	+	+	CCONJ
ejpam-5812	367	2	1	1	NUM
ejpam-5812	367	3	2(r	2(r	NUM
ejpam-5812	367	4	+	+	NUM
ejpam-5812	367	5	t	t	NOUN
ejpam-5812	367	6	)	)	PUNCT
ejpam-5812	367	7	+	+	CCONJ
ejpam-5812	367	8	2	2	NUM
ejpam-5812	367	9	10(r	10(r	NUM
ejpam-5812	367	10	+	+	CCONJ
ejpam-5812	367	11	t)−	t)−	PROPN
ejpam-5812	367	12	7	7	NUM
ejpam-5812	367	13	10(r	10(r	NUM
ejpam-5812	367	14	+	+	CCONJ
ejpam-5812	367	15	t)−	t)−	PROPN
ejpam-5812	367	16	7	7	NUM
ejpam-5812	367	17	−1	−1	NOUN
ejpam-5812	367	18	0	0	NUM
ejpam-5812	367	19	j=	j=	NOUN
ejpam-5812	367	20	3	3	NUM
ejpam-5812	367	21	l4r1	l4r1	ADV
ejpam-5812	367	22	l4t10	l4t10	X
ejpam-5812	367	23	2(r	2(r	NUM
ejpam-5812	367	24	+	+	SYM
ejpam-5812	367	25	t	t	PROPN
ejpam-5812	367	26	)	)	PUNCT
ejpam-5812	367	27	+	+	CCONJ
ejpam-5812	368	1	2	2	NUM
ejpam-5812	368	2	2(r	2(r	NUM
ejpam-5812	368	3	+	+	SYM
ejpam-5812	368	4	t	t	NOUN
ejpam-5812	368	5	)	)	PUNCT
ejpam-5812	368	6	+	+	CCONJ
ejpam-5812	368	7	2	2	NUM
ejpam-5812	368	8	10(r	10(r	NUM
ejpam-5812	368	9	+	+	CCONJ
ejpam-5812	368	10	t)−	t)−	PROPN
ejpam-5812	368	11	4	4	NUM
ejpam-5812	368	12	10(r	10(r	NUM
ejpam-5812	368	13	+	+	CCONJ
ejpam-5812	368	14	t)−	t)−	PROPN
ejpam-5812	368	15	5	5	NUM
ejpam-5812	368	16	0	0	NUM
ejpam-5812	368	17	1	1	NUM
ejpam-5812	368	18	i=	i=	NUM
ejpam-5812	368	19	2	2	NUM
ejpam-5812	368	20	j=	j=	NOUN
ejpam-5812	368	21	0	0	NUM
ejpam-5812	368	22	l′	l′	NOUN
ejpam-5812	368	23	4r10	4r10	NOUN
ejpam-5812	368	24	0l4t110	0l4t110	NOUN
ejpam-5812	369	1	2(r	2(r	NUM
ejpam-5812	369	2	+	+	NUM
ejpam-5812	369	3	t	t	PROPN
ejpam-5812	369	4	)	)	PUNCT
ejpam-5812	370	1	+	+	CCONJ
ejpam-5812	370	2	3	3	NUM
ejpam-5812	370	3	2(r	2(r	NUM
ejpam-5812	370	4	+	+	SYM
ejpam-5812	370	5	t	t	NOUN
ejpam-5812	370	6	)	)	PUNCT
ejpam-5812	371	1	+	+	CCONJ
ejpam-5812	371	2	3	3	NUM
ejpam-5812	371	3	10(r	10(r	NUM
ejpam-5812	371	4	+	+	NUM
ejpam-5812	371	5	t	t	PROPN
ejpam-5812	371	6	)	)	PUNCT
ejpam-5812	371	7	+	+	CCONJ
ejpam-5812	372	1	1	1	NUM
ejpam-5812	372	2	10(r	10(r	NUM
ejpam-5812	372	3	+	+	NUM
ejpam-5812	372	4	t	t	PROPN
ejpam-5812	372	5	)	)	PUNCT
ejpam-5812	372	6	0	0	NUM
ejpam-5812	372	7	1	1	NUM
ejpam-5812	372	8	j=	j=	ADP
ejpam-5812	372	9	1	1	NUM
ejpam-5812	372	10	l′	l′	NOUN
ejpam-5812	372	11	4r10	4r10	NOUN
ejpam-5812	373	1	l4t1	l4t1	X
ejpam-5812	373	2	2(r	2(r	NUM
ejpam-5812	373	3	+	+	SYM
ejpam-5812	373	4	t	t	PROPN
ejpam-5812	373	5	)	)	PUNCT
ejpam-5812	374	1	+	+	CCONJ
ejpam-5812	374	2	1	1	NUM
ejpam-5812	374	3	2(r	2(r	NUM
ejpam-5812	374	4	+	+	NUM
ejpam-5812	374	5	t	t	PROPN
ejpam-5812	374	6	)	)	PUNCT
ejpam-5812	375	1	+	+	CCONJ
ejpam-5812	375	2	1	1	NUM
ejpam-5812	375	3	10(r	10(r	NUM
ejpam-5812	375	4	+	+	CCONJ
ejpam-5812	375	5	t)−	t)−	PROPN
ejpam-5812	375	6	7	7	NUM
ejpam-5812	375	7	10(r	10(r	NUM
ejpam-5812	375	8	+	+	CCONJ
ejpam-5812	375	9	t)−	t)−	PROPN
ejpam-5812	375	10	7	7	NUM
ejpam-5812	375	11	0	0	NUM
ejpam-5812	375	12	0	0	NUM
ejpam-5812	375	13	j=	j=	NOUN
ejpam-5812	375	14	2	2	NUM
ejpam-5812	375	15	l′	l′	X
ejpam-5812	375	16	4r10	4r10	NOUN
ejpam-5812	376	1	01l4	01l4	NUM
ejpam-5812	376	2	t	t	NOUN
ejpam-5812	376	3	2(r	2(r	NUM
ejpam-5812	376	4	+	+	SYM
ejpam-5812	376	5	t	t	PROPN
ejpam-5812	376	6	)	)	PUNCT
ejpam-5812	377	1	+	+	CCONJ
ejpam-5812	377	2	2	2	NUM
ejpam-5812	377	3	2(r	2(r	NUM
ejpam-5812	377	4	+	+	SYM
ejpam-5812	377	5	t	t	NOUN
ejpam-5812	377	6	)	)	PUNCT
ejpam-5812	377	7	+	+	CCONJ
ejpam-5812	377	8	2	2	NUM
ejpam-5812	377	9	10(r	10(r	NUM
ejpam-5812	378	1	+	+	CCONJ
ejpam-5812	378	2	t)−	t)−	PROPN
ejpam-5812	378	3	4	4	NUM
ejpam-5812	378	4	10(r	10(r	NUM
ejpam-5812	378	5	+	+	CCONJ
ejpam-5812	378	6	t)−	t)−	PROPN
ejpam-5812	378	7	5	5	NUM
ejpam-5812	378	8	0	0	NUM
ejpam-5812	378	9	1	1	NUM
ejpam-5812	378	10	j=	j=	ADP
ejpam-5812	378	11	3	3	NUM
ejpam-5812	378	12	l′	l′	NOUN
ejpam-5812	378	13	4r10	4r10	NOUN
ejpam-5812	378	14	l4t101	l4t101	X
ejpam-5812	378	15	2(r	2(r	NUM
ejpam-5812	378	16	+	+	NUM
ejpam-5812	378	17	t	t	X
ejpam-5812	378	18	)	)	PUNCT
ejpam-5812	379	1	+	+	CCONJ
ejpam-5812	379	2	2	2	NUM
ejpam-5812	379	3	2(r	2(r	NUM
ejpam-5812	379	4	+	+	SYM
ejpam-5812	379	5	t	t	PROPN
ejpam-5812	379	6	)	)	PUNCT
ejpam-5812	380	1	+	+	CCONJ
ejpam-5812	380	2	3	3	NUM
ejpam-5812	380	3	10(r	10(r	NUM
ejpam-5812	380	4	+	+	CCONJ
ejpam-5812	380	5	t)−	t)−	PROPN
ejpam-5812	380	6	2	2	NUM
ejpam-5812	380	7	10(r	10(r	NUM
ejpam-5812	380	8	+	+	CCONJ
ejpam-5812	380	9	t)−	t)−	PROPN
ejpam-5812	380	10	2	2	NUM
ejpam-5812	380	11	−1	−1	NOUN
ejpam-5812	380	12	0	0	NUM
ejpam-5812	380	13	i=	i=	PROPN
ejpam-5812	380	14	3	3	NUM
ejpam-5812	380	15	j=	j=	NOUN
ejpam-5812	380	16	0	0	NUM
ejpam-5812	381	1	0l4r10	0l4r10	NUM
ejpam-5812	381	2	0l4t110	0l4t110	NOUN
ejpam-5812	381	3	2(r	2(r	NUM
ejpam-5812	381	4	+	+	NUM
ejpam-5812	381	5	t	t	PROPN
ejpam-5812	381	6	)	)	PUNCT
ejpam-5812	382	1	+	+	CCONJ
ejpam-5812	382	2	4	4	NUM
ejpam-5812	382	3	2(r	2(r	NUM
ejpam-5812	382	4	+	+	SYM
ejpam-5812	382	5	t	t	NOUN
ejpam-5812	382	6	)	)	PUNCT
ejpam-5812	383	1	+	+	CCONJ
ejpam-5812	383	2	3	3	NUM
ejpam-5812	383	3	10(r	10(r	NUM
ejpam-5812	383	4	+	+	NUM
ejpam-5812	383	5	t	t	PROPN
ejpam-5812	383	6	)	)	PUNCT
ejpam-5812	383	7	+	+	CCONJ
ejpam-5812	383	8	3	3	NUM
ejpam-5812	383	9	10(r	10(r	NUM
ejpam-5812	383	10	+	+	NUM
ejpam-5812	383	11	t	t	PROPN
ejpam-5812	383	12	)	)	PUNCT
ejpam-5812	384	1	+	+	CCONJ
ejpam-5812	384	2	3	3	NUM
ejpam-5812	384	3	1	1	NUM
ejpam-5812	384	4	0	0	NUM
ejpam-5812	384	5	j=	j=	ADP
ejpam-5812	384	6	1	1	NUM
ejpam-5812	384	7	0l4r10	0l4r10	NUM
ejpam-5812	384	8	l4t1	l4t1	NOUN
ejpam-5812	384	9	2(r	2(r	NUM
ejpam-5812	384	10	+	+	SYM
ejpam-5812	384	11	t	t	PROPN
ejpam-5812	384	12	)	)	PUNCT
ejpam-5812	384	13	+	+	CCONJ
ejpam-5812	384	14	2	2	NUM
ejpam-5812	384	15	2(r	2(r	NUM
ejpam-5812	384	16	+	+	SYM
ejpam-5812	384	17	t	t	NOUN
ejpam-5812	384	18	)	)	PUNCT
ejpam-5812	385	1	+	+	CCONJ
ejpam-5812	385	2	2	2	NUM
ejpam-5812	385	3	10(r	10(r	NUM
ejpam-5812	385	4	+	+	CCONJ
ejpam-5812	385	5	t)−	t)−	PROPN
ejpam-5812	385	6	5	5	NUM
ejpam-5812	385	7	10(r	10(r	NUM
ejpam-5812	385	8	+	+	CCONJ
ejpam-5812	385	9	t)−	t)−	PROPN
ejpam-5812	385	10	4	4	NUM
ejpam-5812	385	11	0	0	NUM
ejpam-5812	385	12	−1	−1	NOUN
ejpam-5812	385	13	j=	j=	NOUN
ejpam-5812	385	14	2	2	NUM
ejpam-5812	385	15	0l4r10	0l4r10	NUM
ejpam-5812	385	16	l′	l′	NOUN
ejpam-5812	385	17	4t10	4t10	NOUN
ejpam-5812	385	18	2(r	2(r	NUM
ejpam-5812	385	19	+	+	NUM
ejpam-5812	385	20	t	t	PROPN
ejpam-5812	385	21	)	)	PUNCT
ejpam-5812	386	1	+	+	CCONJ
ejpam-5812	386	2	3	3	NUM
ejpam-5812	386	3	2(r	2(r	NUM
ejpam-5812	386	4	+	+	SYM
ejpam-5812	386	5	t	t	NOUN
ejpam-5812	386	6	)	)	PUNCT
ejpam-5812	387	1	+	+	CCONJ
ejpam-5812	387	2	2	2	NUM
ejpam-5812	387	3	10(r	10(r	NUM
ejpam-5812	387	4	+	+	CCONJ
ejpam-5812	387	5	t)−	t)−	PROPN
ejpam-5812	387	6	2	2	NUM
ejpam-5812	387	7	10(r	10(r	NUM
ejpam-5812	387	8	+	+	CCONJ
ejpam-5812	387	9	t)−	t)−	PROPN
ejpam-5812	387	10	2	2	NUM
ejpam-5812	387	11	1	1	NUM
ejpam-5812	387	12	0	0	NUM
ejpam-5812	387	13	j=	j=	ADP
ejpam-5812	387	14	3	3	NUM
ejpam-5812	387	15	l′	l′	NOUN
ejpam-5812	387	16	4rm3	4rm3	NUM
ejpam-5812	387	17	0l4t10	0l4t10	NUM
ejpam-5812	387	18	2(r	2(r	NUM
ejpam-5812	387	19	+	+	NUM
ejpam-5812	387	20	t	t	PROPN
ejpam-5812	387	21	)	)	PUNCT
ejpam-5812	388	1	+	+	CCONJ
ejpam-5812	388	2	3	3	NUM
ejpam-5812	388	3	2(r	2(r	NUM
ejpam-5812	388	4	+	+	SYM
ejpam-5812	388	5	t	t	NOUN
ejpam-5812	388	6	)	)	PUNCT
ejpam-5812	389	1	+	+	CCONJ
ejpam-5812	389	2	3	3	NUM
ejpam-5812	389	3	10(r	10(r	NUM
ejpam-5812	389	4	+	+	NUM
ejpam-5812	389	5	t	t	PROPN
ejpam-5812	389	6	)	)	PUNCT
ejpam-5812	389	7	+	+	CCONJ
ejpam-5812	389	8	1	1	NUM
ejpam-5812	389	9	10(r	10(r	NUM
ejpam-5812	389	10	+	+	NUM
ejpam-5812	389	11	t	t	PROPN
ejpam-5812	389	12	)	)	PUNCT
ejpam-5812	389	13	0	0	NUM
ejpam-5812	389	14	1	1	NUM
ejpam-5812	389	15	n=	n=	ADJ
ejpam-5812	389	16	8	8	NUM
ejpam-5812	389	17	m=	m=	SYM
ejpam-5812	389	18	8	8	NUM
ejpam-5812	389	19	1013021	1013021	NUM
ejpam-5812	389	20	1203102	1203102	NUM
ejpam-5812	389	21	8	8	NUM
ejpam-5812	389	22	8	8	NUM
ejpam-5812	389	23	25	25	NUM
ejpam-5812	389	24	26	26	NUM
ejpam-5812	389	25	0	0	NUM
ejpam-5812	389	26	−1	−1	NOUN
ejpam-5812	389	27	j	j	PROPN
ejpam-5812	389	28	=	=	SYM
ejpam-5812	389	29	0,m	0,m	PROPN
ejpam-5812	389	30	>	>	X
ejpam-5812	389	31	8	8	NUM
ejpam-5812	389	32	0414	0414	NUM
ejpam-5812	389	33	1l	1l	NUM
ejpam-5812	389	34	′	′	NUM
ejpam-5812	389	35	4tm3	4tm3	NUM
ejpam-5812	389	36	2t+	2t+	NUM
ejpam-5812	389	37	6	6	NUM
ejpam-5812	389	38	2t+	2t+	NUM
ejpam-5812	389	39	6	6	NUM
ejpam-5812	389	40	10t+	10t+	NUM
ejpam-5812	389	41	6	6	NUM
ejpam-5812	389	42	10t+	10t+	NUM
ejpam-5812	389	43	7	7	NUM
ejpam-5812	389	44	0	0	NUM
ejpam-5812	389	45	−1	−1	NOUN
ejpam-5812	389	46	j=	j=	NOUN
ejpam-5812	389	47	1	1	NUM
ejpam-5812	389	48	0414	0414	NUM
ejpam-5812	389	49	12m4t03	12m4t03	NUM
ejpam-5812	389	50	2t+	2t+	NUM
ejpam-5812	389	51	5	5	NUM
ejpam-5812	389	52	2t+	2t+	NUM
ejpam-5812	389	53	4	4	NUM
ejpam-5812	389	54	10t+	10t+	NUM
ejpam-5812	389	55	8	8	NUM
ejpam-5812	389	56	10t+	10t+	NUM
ejpam-5812	389	57	8	8	NUM
ejpam-5812	389	58	1	1	NUM
ejpam-5812	389	59	0	0	NUM
ejpam-5812	389	60	j=	j=	NOUN
ejpam-5812	389	61	2	2	NUM
ejpam-5812	389	62	0414	0414	NUM
ejpam-5812	389	63	l	l	NOUN
ejpam-5812	389	64	′	′	NUM
ejpam-5812	389	65	4t10	4t10	NOUN
ejpam-5812	389	66	2t+	2t+	NUM
ejpam-5812	389	67	5	5	NUM
ejpam-5812	389	68	2t+	2t+	NUM
ejpam-5812	389	69	5	5	NUM
ejpam-5812	389	70	10t+	10t+	NUM
ejpam-5812	389	71	10	10	NUM
ejpam-5812	389	72	10t+	10t+	NUM
ejpam-5812	389	73	11	11	NUM
ejpam-5812	389	74	0	0	NUM
ejpam-5812	389	75	−1	−1	NOUN
ejpam-5812	389	76	j=	j=	NOUN
ejpam-5812	389	77	3	3	NUM
ejpam-5812	389	78	0414	0414	NUM
ejpam-5812	389	79	l	l	NOUN
ejpam-5812	389	80	′	′	NUM
ejpam-5812	389	81	4tm3	4tm3	NUM
ejpam-5812	389	82	2t+	2t+	NUM
ejpam-5812	389	83	6	6	NUM
ejpam-5812	389	84	2t+	2t+	NUM
ejpam-5812	389	85	5	5	NUM
ejpam-5812	389	86	10t+	10t+	NUM
ejpam-5812	389	87	13	13	NUM
ejpam-5812	389	88	10t+	10t+	NUM
ejpam-5812	389	89	13	13	NUM
ejpam-5812	389	90	1	1	NUM
ejpam-5812	389	91	0	0	NUM
ejpam-5812	390	1	i	i	NOUN
ejpam-5812	390	2	=	=	NOUN
ejpam-5812	390	3	0	0	NUM
ejpam-5812	390	4	,	,	PUNCT
ejpam-5812	390	5	n	n	X
ejpam-5812	390	6	>	>	X
ejpam-5812	390	7	8	8	NUM
ejpam-5812	390	8	m=	m=	SYM
ejpam-5812	390	9	8	8	NUM
ejpam-5812	390	10	04l	04l	NOUN
ejpam-5812	391	1	′	′	NUM
ejpam-5812	392	1	4r−414	4r−414	NUM
ejpam-5812	392	2	0414	0414	NUM
ejpam-5812	392	3	2r	2r	NUM
ejpam-5812	392	4	+	+	CCONJ
ejpam-5812	392	5	6	6	NUM
ejpam-5812	392	6	2r	2r	NUM
ejpam-5812	392	7	+	+	CCONJ
ejpam-5812	392	8	6	6	NUM
ejpam-5812	392	9	10r	10r	NOUN
ejpam-5812	392	10	+	+	CCONJ
ejpam-5812	392	11	7	7	NUM
ejpam-5812	392	12	10r	10r	NOUN
ejpam-5812	392	13	+	+	CCONJ
ejpam-5812	392	14	6	6	NUM
ejpam-5812	392	15	0	0	NUM
ejpam-5812	392	16	1	1	NUM
ejpam-5812	392	17	j=	j=	ADP
ejpam-5812	392	18	1	1	NUM
ejpam-5812	392	19	12m4r03	12m4r03	NUM
ejpam-5812	392	20	0414	0414	NUM
ejpam-5812	392	21	2r	2r	NUM
ejpam-5812	393	1	+	+	CCONJ
ejpam-5812	393	2	5	5	NUM
ejpam-5812	393	3	2r	2r	NUM
ejpam-5812	393	4	+	+	CCONJ
ejpam-5812	393	5	4	4	NUM
ejpam-5812	393	6	10r	10r	NOUN
ejpam-5812	393	7	+	+	CCONJ
ejpam-5812	393	8	8	8	NUM
ejpam-5812	393	9	10r	10r	NOUN
ejpam-5812	393	10	+	+	CCONJ
ejpam-5812	393	11	8	8	NUM
ejpam-5812	393	12	1	1	NUM
ejpam-5812	393	13	0	0	NUM
ejpam-5812	393	14	j=	j=	NOUN
ejpam-5812	393	15	2	2	NUM
ejpam-5812	393	16	031l4r−412	031l4r−412	NUM
ejpam-5812	393	17	0414	0414	NUM
ejpam-5812	394	1	2r	2r	NUM
ejpam-5812	395	1	+	+	CCONJ
ejpam-5812	395	2	5	5	NUM
ejpam-5812	395	3	2r	2r	NUM
ejpam-5812	395	4	+	+	CCONJ
ejpam-5812	395	5	5	5	NUM
ejpam-5812	395	6	10r	10r	NOUN
ejpam-5812	395	7	+	+	CCONJ
ejpam-5812	395	8	11	11	NUM
ejpam-5812	395	9	10r	10r	NOUN
ejpam-5812	395	10	+	+	CCONJ
ejpam-5812	395	11	10	10	NUM
ejpam-5812	395	12	0	0	NUM
ejpam-5812	395	13	1	1	NUM
ejpam-5812	395	14	j=	j=	ADP
ejpam-5812	395	15	3	3	NUM
ejpam-5812	395	16	l	l	NOUN
ejpam-5812	395	17	′	′	NUM
ejpam-5812	395	18	4rm3	4rm3	NUM
ejpam-5812	395	19	0414	0414	NUM
ejpam-5812	396	1	2r	2r	NUM
ejpam-5812	397	1	+	+	CCONJ
ejpam-5812	397	2	6	6	NUM
ejpam-5812	397	3	2r	2r	NUM
ejpam-5812	397	4	+	+	CCONJ
ejpam-5812	397	5	5	5	NUM
ejpam-5812	397	6	10r	10r	NOUN
ejpam-5812	397	7	+	+	CCONJ
ejpam-5812	397	8	13	13	NUM
ejpam-5812	397	9	10r	10r	NOUN
ejpam-5812	397	10	+	+	CCONJ
ejpam-5812	397	11	13	13	NUM
ejpam-5812	397	12	1	1	NUM
ejpam-5812	397	13	0	0	NUM
ejpam-5812	397	14	5	5	NUM
ejpam-5812	397	15	.	.	PUNCT
ejpam-5812	397	16	algorithm	algorithm	NOUN
ejpam-5812	397	17	in	in	ADP
ejpam-5812	397	18	this	this	DET
ejpam-5812	397	19	section	section	NOUN
ejpam-5812	397	20	,	,	PUNCT
ejpam-5812	397	21	we	we	PRON
ejpam-5812	397	22	propose	propose	VERB
ejpam-5812	397	23	an	an	DET
ejpam-5812	397	24	algorithm	algorithm	NOUN
ejpam-5812	397	25	for	for	ADP
ejpam-5812	397	26	calculating	calculate	VERB
ejpam-5812	397	27	the	the	DET
ejpam-5812	397	28	cordial	cordial	ADJ
ejpam-5812	397	29	labeling	labeling	NOUN
ejpam-5812	397	30	for	for	ADP
ejpam-5812	397	31	any	any	DET
ejpam-5812	397	32	graph	graph	NOUN
ejpam-5812	397	33	g	g	NOUN
ejpam-5812	397	34	.	.	PUNCT
ejpam-5812	398	1	this	this	DET
ejpam-5812	398	2	algorithm	algorithm	NOUN
ejpam-5812	398	3	provides	provide	VERB
ejpam-5812	398	4	a	a	DET
ejpam-5812	398	5	framework	framework	NOUN
ejpam-5812	398	6	for	for	ADP
ejpam-5812	398	7	attempting	attempt	VERB
ejpam-5812	398	8	to	to	PART
ejpam-5812	398	9	find	find	VERB
ejpam-5812	398	10	a	a	DET
ejpam-5812	398	11	cordial	cordial	ADJ
ejpam-5812	398	12	labeling	labeling	NOUN
ejpam-5812	398	13	for	for	ADP
ejpam-5812	398	14	a	a	DET
ejpam-5812	398	15	given	give	VERB
ejpam-5812	398	16	graph	graph	NOUN
ejpam-5812	398	17	.	.	PUNCT
ejpam-5812	399	1	it	it	PRON
ejpam-5812	399	2	’s	’	VERB
ejpam-5812	399	3	important	important	ADJ
ejpam-5812	399	4	to	to	PART
ejpam-5812	399	5	note	note	VERB
ejpam-5812	399	6	that	that	SCONJ
ejpam-5812	399	7	not	not	PART
ejpam-5812	399	8	all	all	DET
ejpam-5812	399	9	graphs	graph	NOUN
ejpam-5812	399	10	will	will	AUX
ejpam-5812	399	11	admit	admit	VERB
ejpam-5812	399	12	a	a	DET
ejpam-5812	399	13	cordial	cordial	ADJ
ejpam-5812	399	14	labeling	labeling	NOUN
ejpam-5812	399	15	,	,	PUNCT
ejpam-5812	399	16	and	and	CCONJ
ejpam-5812	399	17	the	the	DET
ejpam-5812	399	18	specific	specific	ADJ
ejpam-5812	399	19	method	method	NOUN
ejpam-5812	399	20	of	of	ADP
ejpam-5812	399	21	assigning	assign	VERB
ejpam-5812	399	22	labels	label	NOUN
ejpam-5812	399	23	to	to	PART
ejpam-5812	399	24	vertices	vertex	NOUN
ejpam-5812	399	25	in	in	ADP
ejpam-5812	399	26	step	step	NOUN
ejpam-5812	399	27	3	3	NUM
ejpam-5812	399	28	can	can	AUX
ejpam-5812	399	29	vary	vary	VERB
ejpam-5812	399	30	based	base	VERB
ejpam-5812	399	31	on	on	ADP
ejpam-5812	399	32	the	the	DET
ejpam-5812	399	33	graph	graph	NOUN
ejpam-5812	399	34	’s	’s	PART
ejpam-5812	399	35	structure	structure	NOUN
ejpam-5812	399	36	and	and	CCONJ
ejpam-5812	399	37	properties	property	NOUN
ejpam-5812	399	38	.	.	PUNCT
ejpam-5812	400	1	we	we	PRON
ejpam-5812	400	2	assume	assume	VERB
ejpam-5812	400	3	that	that	SCONJ
ejpam-5812	400	4	labeling	label	VERB
ejpam-5812	400	5	each	each	DET
ejpam-5812	400	6	vertex	vertex	NOUN
ejpam-5812	400	7	and	and	CCONJ
ejpam-5812	400	8	edge	edge	NOUN
ejpam-5812	400	9	takes	take	VERB
ejpam-5812	400	10	constant	constant	ADJ
ejpam-5812	400	11	time	time	NOUN
ejpam-5812	400	12	,	,	PUNCT
ejpam-5812	400	13	then	then	ADV
ejpam-5812	400	14	the	the	DET
ejpam-5812	400	15	time	time	NOUN
ejpam-5812	400	16	complexity	complexity	NOUN
ejpam-5812	400	17	of	of	ADP
ejpam-5812	400	18	algorithm	algorithm	NOUN
ejpam-5812	400	19	1	1	NUM
ejpam-5812	400	20	is	be	AUX
ejpam-5812	400	21	o(n	o(n	NUM
ejpam-5812	400	22	)	)	PUNCT
ejpam-5812	400	23	,	,	PUNCT
ejpam-5812	400	24	since	since	SCONJ
ejpam-5812	400	25	each	each	DET
ejpam-5812	400	26	vertex	vertex	NOUN
ejpam-5812	400	27	and	and	CCONJ
ejpam-5812	400	28	edge	edge	NOUN
ejpam-5812	400	29	is	be	AUX
ejpam-5812	400	30	visited	visit	VERB
ejpam-5812	400	31	once	once	ADV
ejpam-5812	400	32	.	.	PUNCT
ejpam-5812	401	1	a.	a.	PROPN
ejpam-5812	401	2	abd	abd	PROPN
ejpam-5812	401	3	el	el	PROPN
ejpam-5812	401	4	-	-	PROPN
ejpam-5812	401	5	hay	hay	PROPN
ejpam-5812	401	6	,	,	PUNCT
ejpam-5812	401	7	k.	k.	PROPN
ejpam-5812	401	8	a.	a.	PROPN
ejpam-5812	401	9	alsatami	alsatami	PROPN
ejpam-5812	401	10	,	,	PUNCT
ejpam-5812	401	11	a.	a.	NOUN
ejpam-5812	401	12	elrokh	elrokh	PROPN
ejpam-5812	401	13	/	/	SYM
ejpam-5812	401	14	eur	eur	PROPN
ejpam-5812	401	15	.	.	PUNCT
ejpam-5812	402	1	j.	j.	PROPN
ejpam-5812	402	2	pure	pure	PROPN
ejpam-5812	402	3	appl	appl	PROPN
ejpam-5812	402	4	.	.	PROPN
ejpam-5812	402	5	math	math	PROPN
ejpam-5812	402	6	,	,	PUNCT
ejpam-5812	402	7	18	18	NUM
ejpam-5812	402	8	(	(	PUNCT
ejpam-5812	402	9	1	1	NUM
ejpam-5812	402	10	)	)	PUNCT
ejpam-5812	402	11	(	(	PUNCT
ejpam-5812	402	12	2025	2025	NUM
ejpam-5812	402	13	)	)	PUNCT
ejpam-5812	402	14	,	,	PUNCT
ejpam-5812	402	15	5812	5812	NUM
ejpam-5812	402	16	12	12	NUM
ejpam-5812	402	17	of	of	ADP
ejpam-5812	402	18	14	14	NUM
ejpam-5812	402	19	algorithm1	algorithm1	NOUN
ejpam-5812	402	20	:	:	PUNCT
ejpam-5812	402	21	cordial	cordial	ADJ
ejpam-5812	402	22	labeling	labeling	NOUN
ejpam-5812	402	23	of	of	ADP
ejpam-5812	402	24	a	a	DET
ejpam-5812	402	25	graph	graph	NOUN
ejpam-5812	402	26	input	input	NOUN
ejpam-5812	402	27	:	:	PUNCT
ejpam-5812	402	28	a	a	DET
ejpam-5812	402	29	graph	graph	NOUN
ejpam-5812	402	30	g(v	g(v	NOUN
ejpam-5812	402	31	,	,	PUNCT
ejpam-5812	402	32	e	e	NOUN
ejpam-5812	402	33	)	)	PUNCT
ejpam-5812	402	34	output	output	NOUN
ejpam-5812	402	35	:	:	PUNCT
ejpam-5812	402	36	a	a	DET
ejpam-5812	402	37	cordial	cordial	ADJ
ejpam-5812	402	38	labeling	labeling	NOUN
ejpam-5812	402	39	of	of	ADP
ejpam-5812	402	40	g	g	PROPN
ejpam-5812	402	41	if	if	SCONJ
ejpam-5812	402	42	it	it	PRON
ejpam-5812	402	43	exists	exist	VERB
ejpam-5812	402	44	begin	begin	VERB
ejpam-5812	402	45	step	step	NOUN
ejpam-5812	402	46	1	1	NUM
ejpam-5812	402	47	.	.	PUNCT
ejpam-5812	402	48	initialize	initialize	VERB
ejpam-5812	402	49	two	two	NUM
ejpam-5812	402	50	counters	counter	NOUN
ejpam-5812	402	51	,	,	PUNCT
ejpam-5812	402	52	v(0	v(0	PROPN
ejpam-5812	402	53	)	)	PUNCT
ejpam-5812	402	54	and	and	CCONJ
ejpam-5812	402	55	v(1	v(1	NUM
ejpam-5812	402	56	)	)	PUNCT
ejpam-5812	402	57	,	,	PUNCT
ejpam-5812	402	58	to	to	ADP
ejpam-5812	402	59	0	0	NUM
ejpam-5812	402	60	.	.	PUNCT
ejpam-5812	403	1	step	step	NOUN
ejpam-5812	403	2	2	2	NUM
ejpam-5812	403	3	.	.	PUNCT
ejpam-5812	403	4	initialize	initialize	VERB
ejpam-5812	403	5	two	two	NUM
ejpam-5812	403	6	counters	counter	NOUN
ejpam-5812	403	7	,	,	PUNCT
ejpam-5812	403	8	e(0	e(0	NOUN
ejpam-5812	403	9	)	)	PUNCT
ejpam-5812	403	10	and	and	CCONJ
ejpam-5812	403	11	e(1	e(1	NOUN
ejpam-5812	403	12	)	)	PUNCT
ejpam-5812	403	13	,	,	PUNCT
ejpam-5812	403	14	to	to	ADP
ejpam-5812	403	15	0	0	NUM
ejpam-5812	403	16	.	.	PUNCT
ejpam-5812	403	17	step	step	NOUN
ejpam-5812	403	18	3	3	NUM
ejpam-5812	403	19	.	.	PUNCT
ejpam-5812	404	1	for	for	ADP
ejpam-5812	404	2	each	each	DET
ejpam-5812	404	3	vertex	vertex	NOUN
ejpam-5812	404	4	v	v	NOUN
ejpam-5812	404	5	in	in	ADP
ejpam-5812	404	6	v	v	NOUN
ejpam-5812	404	7	:	:	PUNCT
ejpam-5812	404	8	a.	a.	NOUN
ejpam-5812	404	9	assign	assign	VERB
ejpam-5812	404	10	a	a	DET
ejpam-5812	404	11	label	label	NOUN
ejpam-5812	404	12	f(v	f(v	NOUN
ejpam-5812	404	13	)	)	PUNCT
ejpam-5812	404	14	∈	∈	PROPN
ejpam-5812	404	15	{	{	PUNCT
ejpam-5812	404	16	0	0	NUM
ejpam-5812	404	17	,	,	PUNCT
ejpam-5812	404	18	1	1	NUM
ejpam-5812	404	19	}	}	PUNCT
ejpam-5812	404	20	to	to	ADP
ejpam-5812	404	21	the	the	DET
ejpam-5812	404	22	vertex	vertex	NOUN
ejpam-5812	404	23	v.	v.	ADP
ejpam-5812	404	24	b.	b.	PROPN
ejpam-5812	405	1	if	if	SCONJ
ejpam-5812	405	2	f(v	f(v	NOUN
ejpam-5812	405	3	)	)	PUNCT
ejpam-5812	406	1	=	=	SYM
ejpam-5812	406	2	=	=	SYM
ejpam-5812	406	3	0	0	NUM
ejpam-5812	406	4	,	,	PUNCT
ejpam-5812	406	5	increment	increment	VERB
ejpam-5812	406	6	v(0	v(0	PROPN
ejpam-5812	406	7	)	)	PUNCT
ejpam-5812	406	8	;	;	PUNCT
ejpam-5812	406	9	else	else	ADV
ejpam-5812	406	10	increment	increment	VERB
ejpam-5812	406	11	v(1	v(1	PROPN
ejpam-5812	406	12	)	)	PUNCT
ejpam-5812	406	13	.	.	PUNCT
ejpam-5812	407	1	step	step	NOUN
ejpam-5812	407	2	4	4	NUM
ejpam-5812	407	3	.	.	PUNCT
ejpam-5812	408	1	for	for	ADP
ejpam-5812	408	2	each	each	DET
ejpam-5812	408	3	edge	edge	NOUN
ejpam-5812	408	4	e(u	e(u	PROPN
ejpam-5812	408	5	,	,	PUNCT
ejpam-5812	408	6	v	v	NOUN
ejpam-5812	408	7	)	)	PUNCT
ejpam-5812	408	8	in	in	ADP
ejpam-5812	408	9	e	e	NOUN
ejpam-5812	408	10	:	:	PUNCT
ejpam-5812	408	11	a.	a.	NOUN
ejpam-5812	408	12	assign	assign	VERB
ejpam-5812	408	13	a	a	DET
ejpam-5812	408	14	label	label	NOUN
ejpam-5812	408	15	f(e	f(e	NOUN
ejpam-5812	408	16	)	)	PUNCT
ejpam-5812	409	1	=	=	PUNCT
ejpam-5812	409	2	|f(u)−	|f(u)−	PRON
ejpam-5812	409	3	f(v)|	f(v)|	NOUN
ejpam-5812	409	4	to	to	ADP
ejpam-5812	409	5	the	the	DET
ejpam-5812	409	6	edge	edge	NOUN
ejpam-5812	409	7	e.	e.	PROPN
ejpam-5812	409	8	b.	b.	PROPN
ejpam-5812	410	1	if	if	SCONJ
ejpam-5812	410	2	f(e	f(e	NOUN
ejpam-5812	410	3	)	)	PUNCT
ejpam-5812	411	1	=	=	SYM
ejpam-5812	411	2	=	=	SYM
ejpam-5812	411	3	0	0	NUM
ejpam-5812	411	4	,	,	PUNCT
ejpam-5812	411	5	increment	increment	VERB
ejpam-5812	411	6	e(0	e(0	NOUN
ejpam-5812	411	7	)	)	PUNCT
ejpam-5812	411	8	;	;	PUNCT
ejpam-5812	411	9	else	else	ADV
ejpam-5812	411	10	increment	increment	VERB
ejpam-5812	411	11	e(1	e(1	PROPN
ejpam-5812	411	12	)	)	PUNCT
ejpam-5812	411	13	.	.	PUNCT
ejpam-5812	412	1	step	step	NOUN
ejpam-5812	412	2	5	5	NUM
ejpam-5812	412	3	.	.	PUNCT
ejpam-5812	412	4	check	check	VERB
ejpam-5812	412	5	the	the	DET
ejpam-5812	412	6	cordiality	cordiality	NOUN
ejpam-5812	412	7	condition	condition	NOUN
ejpam-5812	412	8	:	:	PUNCT
ejpam-5812	413	1	a.	a.	NOUN
ejpam-5812	413	2	if	if	SCONJ
ejpam-5812	413	3	|v(0)−	|v(0)−	PROPN
ejpam-5812	413	4	v(1)≤	v(1)≤	ADP
ejpam-5812	413	5	1	1	NUM
ejpam-5812	413	6	and	and	CCONJ
ejpam-5812	413	7	|e(0)−	|e(0)−	PROPN
ejpam-5812	413	8	e(1)≤1	e(1)≤1	NOUN
ejpam-5812	413	9	:	:	PUNCT
ejpam-5812	413	10	i.	i.	NOUN
ejpam-5812	413	11	the	the	DET
ejpam-5812	413	12	labeling	labeling	NOUN
ejpam-5812	413	13	is	be	AUX
ejpam-5812	413	14	cordial	cordial	ADJ
ejpam-5812	413	15	.	.	PUNCT
ejpam-5812	414	1	ii	ii	PROPN
ejpam-5812	414	2	.	.	PUNCT
ejpam-5812	414	3	output	output	VERB
ejpam-5812	414	4	the	the	DET
ejpam-5812	414	5	labeling	labeling	NOUN
ejpam-5812	414	6	of	of	ADP
ejpam-5812	414	7	vertices	vertex	NOUN
ejpam-5812	414	8	and	and	CCONJ
ejpam-5812	414	9	edges	edge	NOUN
ejpam-5812	414	10	.	.	PUNCT
ejpam-5812	415	1	b.	b.	PROPN
ejpam-5812	415	2	else	else	ADV
ejpam-5812	415	3	:	:	PUNCT
ejpam-5812	415	4	i.	i.	NOUN
ejpam-5812	415	5	the	the	DET
ejpam-5812	415	6	graph	graph	NOUN
ejpam-5812	415	7	g	g	NOUN
ejpam-5812	415	8	does	do	AUX
ejpam-5812	415	9	not	not	PART
ejpam-5812	415	10	admit	admit	VERB
ejpam-5812	415	11	a	a	DET
ejpam-5812	415	12	cordial	cordial	ADJ
ejpam-5812	415	13	labeling	labeling	NOUN
ejpam-5812	415	14	.	.	PUNCT
ejpam-5812	416	1	ii	ii	PROPN
ejpam-5812	416	2	.	.	PUNCT
ejpam-5812	417	1	output	output	NOUN
ejpam-5812	417	2	that	that	PRON
ejpam-5812	417	3	no	no	DET
ejpam-5812	417	4	cordial	cordial	ADJ
ejpam-5812	417	5	labeling	labeling	NOUN
ejpam-5812	417	6	exists	exist	VERB
ejpam-5812	417	7	.	.	PUNCT
ejpam-5812	418	1	end	end	NOUN
ejpam-5812	418	2	algorithm	algorithm	NOUN
ejpam-5812	418	3	6	6	NUM
ejpam-5812	418	4	.	.	PUNCT
ejpam-5812	419	1	conclusion	conclusion	NOUN
ejpam-5812	419	2	we	we	PRON
ejpam-5812	419	3	proved	prove	VERB
ejpam-5812	419	4	that	that	SCONJ
ejpam-5812	419	5	each	each	DET
ejpam-5812	419	6	fifth	fifth	ADJ
ejpam-5812	419	7	power	power	NOUN
ejpam-5812	419	8	of	of	ADP
ejpam-5812	419	9	path	path	NOUN
ejpam-5812	419	10	p	p	PROPN
ejpam-5812	419	11	5	5	NUM
ejpam-5812	419	12	n	n	NOUN
ejpam-5812	419	13	,	,	PUNCT
ejpam-5812	419	14	admits	admit	VERB
ejpam-5812	419	15	cordial	cordial	ADJ
ejpam-5812	419	16	labeling	labeling	NOUN
ejpam-5812	419	17	if	if	SCONJ
ejpam-5812	419	18	and	and	CCONJ
ejpam-5812	419	19	only	only	ADV
ejpam-5812	419	20	if	if	SCONJ
ejpam-5812	419	21	1	1	NUM
ejpam-5812	419	22	≤	≤	NUM
ejpam-5812	419	23	n	n	PRON
ejpam-5812	419	24	≤	≤	NOUN
ejpam-5812	419	25	3	3	NUM
ejpam-5812	419	26	and	and	CCONJ
ejpam-5812	419	27	n	n	NOUN
ejpam-5812	419	28	>	>	X
ejpam-5812	419	29	7	7	X
ejpam-5812	419	30	.	.	PUNCT
ejpam-5812	420	1	each	each	DET
ejpam-5812	420	2	fifth	fifth	ADJ
ejpam-5812	420	3	power	power	NOUN
ejpam-5812	420	4	of	of	ADP
ejpam-5812	420	5	cycle	cycle	NOUN
ejpam-5812	420	6	c5	c5	PROPN
ejpam-5812	420	7	n	n	CCONJ
ejpam-5812	420	8	,	,	PUNCT
ejpam-5812	420	9	admits	admit	VERB
ejpam-5812	420	10	cordial	cordial	ADJ
ejpam-5812	420	11	labeling	labeling	NOUN
ejpam-5812	420	12	if	if	SCONJ
ejpam-5812	420	13	and	and	CCONJ
ejpam-5812	420	14	only	only	ADV
ejpam-5812	420	15	if	if	SCONJ
ejpam-5812	420	16	n	n	PROPN
ejpam-5812	420	17	=	=	SYM
ejpam-5812	420	18	3	3	NUM
ejpam-5812	420	19	and	and	CCONJ
ejpam-5812	420	20	n	n	ADJ
ejpam-5812	420	21	>	>	ADP
ejpam-5812	420	22	8	8	NUM
ejpam-5812	420	23	.	.	PUNCT
ejpam-5812	421	1	each	each	DET
ejpam-5812	421	2	fifth	fifth	ADJ
ejpam-5812	421	3	power	power	NOUN
ejpam-5812	421	4	of	of	ADP
ejpam-5812	421	5	fan	fan	PROPN
ejpam-5812	421	6	f	f	PROPN
ejpam-5812	421	7	5	5	NUM
ejpam-5812	421	8	n+1	n+1	PROPN
ejpam-5812	421	9	,	,	PUNCT
ejpam-5812	421	10	admits	admit	VERB
ejpam-5812	421	11	a	a	DET
ejpam-5812	421	12	cordial	cordial	ADJ
ejpam-5812	421	13	labeling	labeling	NOUN
ejpam-5812	421	14	if	if	SCONJ
ejpam-5812	421	15	and	and	CCONJ
ejpam-5812	421	16	only	only	ADV
ejpam-5812	421	17	if	if	SCONJ
ejpam-5812	421	18	n≥	n≥	PROPN
ejpam-5812	421	19	1	1	NUM
ejpam-5812	421	20	except	except	SCONJ
ejpam-5812	421	21	3	3	NUM
ejpam-5812	421	22	≤	≤	NOUN
ejpam-5812	421	23	n	n	PRON
ejpam-5812	421	24	≤	≤	NOUN
ejpam-5812	421	25	6	6	NUM
ejpam-5812	421	26	.	.	PUNCT
ejpam-5812	422	1	the	the	DET
ejpam-5812	422	2	fifth	fifth	ADJ
ejpam-5812	422	3	power	power	NOUN
ejpam-5812	422	4	of	of	ADP
ejpam-5812	422	5	wheel	wheel	NOUN
ejpam-5812	422	6	graph	graph	NOUN
ejpam-5812	422	7	wn+1	wn+1	NOUN
ejpam-5812	422	8	admits	admit	VERB
ejpam-5812	422	9	cordial	cordial	ADJ
ejpam-5812	422	10	labeling	labeling	NOUN
ejpam-5812	422	11	if	if	SCONJ
ejpam-5812	422	12	and	and	CCONJ
ejpam-5812	422	13	only	only	ADV
ejpam-5812	422	14	if	if	SCONJ
ejpam-5812	422	15	n≥	n≥	PROPN
ejpam-5812	422	16	3	3	NUM
ejpam-5812	422	17	except	except	SCONJ
ejpam-5812	422	18	3	3	NUM
ejpam-5812	422	19	≤	≤	NOUN
ejpam-5812	422	20	n	n	PRON
ejpam-5812	422	21	≤	≤	NOUN
ejpam-5812	422	22	8	8	NUM
ejpam-5812	422	23	.	.	PUNCT
ejpam-5812	423	1	moreover	moreover	ADV
ejpam-5812	423	2	,	,	PUNCT
ejpam-5812	423	3	we	we	PRON
ejpam-5812	423	4	proved	prove	VERB
ejpam-5812	423	5	that	that	SCONJ
ejpam-5812	423	6	the	the	DET
ejpam-5812	423	7	fifth	fifth	ADJ
ejpam-5812	423	8	power	power	NOUN
ejpam-5812	423	9	of	of	ADP
ejpam-5812	423	10	lemniscate	lemniscate	PROPN
ejpam-5812	423	11	l5	l5	PROPN
ejpam-5812	423	12	n	n	CCONJ
ejpam-5812	423	13	,	,	PUNCT
ejpam-5812	423	14	m	m	PROPN
ejpam-5812	423	15	,	,	PUNCT
ejpam-5812	423	16	admits	admit	VERB
ejpam-5812	423	17	a	a	DET
ejpam-5812	423	18	cordial	cordial	ADJ
ejpam-5812	423	19	labeling	labeling	NOUN
ejpam-5812	423	20	if	if	SCONJ
ejpam-5812	423	21	and	and	CCONJ
ejpam-5812	423	22	only	only	ADV
ejpam-5812	423	23	if	if	SCONJ
ejpam-5812	423	24	n	n	CCONJ
ejpam-5812	423	25	,	,	PUNCT
ejpam-5812	423	26	m	m	VERB
ejpam-5812	423	27	≥	≥	NOUN
ejpam-5812	423	28	3	3	NUM
ejpam-5812	423	29	except	except	SCONJ
ejpam-5812	423	30	(	(	PUNCT
ejpam-5812	423	31	n	n	CCONJ
ejpam-5812	423	32	,	,	PUNCT
ejpam-5812	423	33	m	m	NOUN
ejpam-5812	423	34	)	)	PUNCT
ejpam-5812	423	35	=	=	SYM
ejpam-5812	423	36	(	(	PUNCT
ejpam-5812	423	37	3	3	NUM
ejpam-5812	423	38	,	,	PUNCT
ejpam-5812	423	39	3),(3	3),(3	PROPN
ejpam-5812	423	40	,	,	PUNCT
ejpam-5812	423	41	6),(4	6),(4	PROPN
ejpam-5812	423	42	,	,	PUNCT
ejpam-5812	423	43	5),(5	5),(5	NUM
ejpam-5812	423	44	,	,	PUNCT
ejpam-5812	423	45	4),(5	4),(5	NUM
ejpam-5812	423	46	,	,	PUNCT
ejpam-5812	423	47	6),(6	6),(6	NUM
ejpam-5812	423	48	,	,	PUNCT
ejpam-5812	423	49	3),(6	3),(6	PROPN
ejpam-5812	423	50	,	,	PUNCT
ejpam-5812	423	51	5	5	NUM
ejpam-5812	423	52	)	)	PUNCT
ejpam-5812	423	53	and	and	CCONJ
ejpam-5812	423	54	(	(	PUNCT
ejpam-5812	423	55	6	6	NUM
ejpam-5812	423	56	,	,	PUNCT
ejpam-5812	423	57	6	6	NUM
ejpam-5812	423	58	)	)	PUNCT
ejpam-5812	423	59	.	.	PUNCT
ejpam-5812	424	1	also	also	ADV
ejpam-5812	424	2	,	,	PUNCT
ejpam-5812	424	3	we	we	PRON
ejpam-5812	424	4	investigated	investigate	VERB
ejpam-5812	424	5	the	the	DET
ejpam-5812	424	6	cordiality	cordiality	NOUN
ejpam-5812	424	7	for	for	ADP
ejpam-5812	424	8	the	the	DET
ejpam-5812	424	9	union	union	NOUN
ejpam-5812	424	10	of	of	ADP
ejpam-5812	424	11	fifth	fifth	ADJ
ejpam-5812	424	12	power	power	NOUN
ejpam-5812	424	13	of	of	ADP
ejpam-5812	424	14	paths	path	NOUN
ejpam-5812	424	15	and	and	CCONJ
ejpam-5812	424	16	cycles	cycle	NOUN
ejpam-5812	424	17	.	.	PUNCT
ejpam-5812	425	1	we	we	PRON
ejpam-5812	425	2	proposed	propose	VERB
ejpam-5812	425	3	an	an	DET
ejpam-5812	425	4	algorithm	algorithm	NOUN
ejpam-5812	425	5	for	for	ADP
ejpam-5812	425	6	determining	determine	VERB
ejpam-5812	425	7	the	the	DET
ejpam-5812	425	8	cordiality	cordiality	NOUN
ejpam-5812	425	9	of	of	ADP
ejpam-5812	425	10	a	a	DET
ejpam-5812	425	11	given	give	VERB
ejpam-5812	425	12	graph	graph	NOUN
ejpam-5812	425	13	.	.	PUNCT
ejpam-5812	426	1	in	in	ADP
ejpam-5812	426	2	the	the	DET
ejpam-5812	426	3	future	future	NOUN
ejpam-5812	426	4	,	,	PUNCT
ejpam-5812	426	5	we	we	PRON
ejpam-5812	426	6	will	will	AUX
ejpam-5812	426	7	apply	apply	VERB
ejpam-5812	426	8	cordial	cordial	ADJ
ejpam-5812	426	9	labeling	labeling	NOUN
ejpam-5812	426	10	to	to	ADP
ejpam-5812	426	11	other	other	ADJ
ejpam-5812	426	12	types	type	NOUN
ejpam-5812	426	13	of	of	ADP
ejpam-5812	426	14	graphs	graph	NOUN
ejpam-5812	426	15	.	.	PUNCT
ejpam-5812	427	1	acknowledgements	acknowledgement	NOUN
ejpam-5812	427	2	the	the	DET
ejpam-5812	427	3	researchers	researcher	NOUN
ejpam-5812	427	4	would	would	AUX
ejpam-5812	427	5	like	like	VERB
ejpam-5812	427	6	to	to	PART
ejpam-5812	427	7	thank	thank	VERB
ejpam-5812	427	8	the	the	DET
ejpam-5812	427	9	deanship	deanship	NOUN
ejpam-5812	427	10	of	of	ADP
ejpam-5812	427	11	graduate	graduate	NOUN
ejpam-5812	427	12	studies	study	NOUN
ejpam-5812	427	13	and	and	CCONJ
ejpam-5812	427	14	scientific	scientific	ADJ
ejpam-5812	427	15	research	research	NOUN
ejpam-5812	427	16	at	at	ADP
ejpam-5812	427	17	qassim	qassim	PROPN
ejpam-5812	427	18	university	university	PROPN
ejpam-5812	427	19	for	for	ADP
ejpam-5812	427	20	financial	financial	ADJ
ejpam-5812	427	21	support	support	NOUN
ejpam-5812	427	22	(	(	PUNCT
ejpam-5812	427	23	qu	qu	NOUN
ejpam-5812	427	24	-	-	NOUN
ejpam-5812	427	25	apc-2024	apc-2024	NOUN
ejpam-5812	427	26	-	-	PUNCT
ejpam-5812	427	27	9/1	9/1	NUM
ejpam-5812	427	28	)	)	PUNCT
ejpam-5812	427	29	.	.	PUNCT
ejpam-5812	428	1	data	datum	NOUN
ejpam-5812	428	2	availability	availability	NOUN
ejpam-5812	428	3	statement	statement	NOUN
ejpam-5812	428	4	all	all	DET
ejpam-5812	428	5	data	datum	NOUN
ejpam-5812	428	6	generated	generate	VERB
ejpam-5812	428	7	or	or	CCONJ
ejpam-5812	428	8	analyzed	analyze	VERB
ejpam-5812	428	9	during	during	ADP
ejpam-5812	428	10	this	this	DET
ejpam-5812	428	11	study	study	NOUN
ejpam-5812	428	12	are	be	AUX
ejpam-5812	428	13	included	include	VERB
ejpam-5812	428	14	in	in	ADP
ejpam-5812	428	15	this	this	DET
ejpam-5812	428	16	published	publish	VERB
ejpam-5812	428	17	article	article	NOUN
ejpam-5812	428	18	.	.	PUNCT
ejpam-5812	429	1	a.	a.	PROPN
ejpam-5812	429	2	abd	abd	PROPN
ejpam-5812	429	3	el	el	PROPN
ejpam-5812	429	4	-	-	PROPN
ejpam-5812	429	5	hay	hay	PROPN
ejpam-5812	429	6	,	,	PUNCT
ejpam-5812	429	7	k.	k.	PROPN
ejpam-5812	429	8	a.	a.	PROPN
ejpam-5812	429	9	alsatami	alsatami	PROPN
ejpam-5812	429	10	,	,	PUNCT
ejpam-5812	429	11	a.	a.	NOUN
ejpam-5812	429	12	elrokh	elrokh	PROPN
ejpam-5812	429	13	/	/	SYM
ejpam-5812	429	14	eur	eur	PROPN
ejpam-5812	429	15	.	.	PUNCT
ejpam-5812	430	1	j.	j.	PROPN
ejpam-5812	430	2	pure	pure	PROPN
ejpam-5812	430	3	appl	appl	PROPN
ejpam-5812	430	4	.	.	PROPN
ejpam-5812	430	5	math	math	PROPN
ejpam-5812	430	6	,	,	PUNCT
ejpam-5812	430	7	18	18	NUM
ejpam-5812	430	8	(	(	PUNCT
ejpam-5812	430	9	1	1	NUM
ejpam-5812	430	10	)	)	PUNCT
ejpam-5812	430	11	(	(	PUNCT
ejpam-5812	430	12	2025	2025	NUM
ejpam-5812	430	13	)	)	PUNCT
ejpam-5812	430	14	,	,	PUNCT
ejpam-5812	430	15	5812	5812	NUM
ejpam-5812	430	16	13	13	NUM
ejpam-5812	430	17	of	of	ADP
ejpam-5812	430	18	14	14	NUM
ejpam-5812	430	19	conflicts	conflict	NOUN
ejpam-5812	430	20	of	of	ADP
ejpam-5812	430	21	interest	interest	NOUN
ejpam-5812	430	22	the	the	DET
ejpam-5812	430	23	author	author	NOUN
ejpam-5812	430	24	declares	declare	VERB
ejpam-5812	430	25	no	no	DET
ejpam-5812	430	26	conflict	conflict	NOUN
ejpam-5812	430	27	of	of	ADP
ejpam-5812	430	28	interest	interest	NOUN
ejpam-5812	430	29	.	.	PUNCT
ejpam-5812	431	1	references	reference	NOUN
ejpam-5812	431	2	[	[	X
ejpam-5812	431	3	1	1	NUM
ejpam-5812	431	4	]	]	PUNCT
ejpam-5812	431	5	mohammed	mohammed	PROPN
ejpam-5812	431	6	m.	m.	PROPN
ejpam-5812	431	7	ali	ali	PROPN
ejpam-5812	431	8	al	al	PROPN
ejpam-5812	431	9	-	-	PUNCT
ejpam-5812	431	10	shamiri	shamiri	PROPN
ejpam-5812	431	11	a.	a.	NOUN
ejpam-5812	431	12	elrokh	elrokh	PROPN
ejpam-5812	431	13	and	and	CCONJ
ejpam-5812	431	14	atef	atef	PROPN
ejpam-5812	431	15	abd	abd	PROPN
ejpam-5812	431	16	el	el	PROPN
ejpam-5812	431	17	-	-	PROPN
ejpam-5812	431	18	hay	hay	PROPN
ejpam-5812	431	19	.	.	PUNCT
ejpam-5812	432	1	a	a	DET
ejpam-5812	432	2	novel	novel	ADJ
ejpam-5812	432	3	radio	radio	NOUN
ejpam-5812	432	4	geometric	geometric	ADJ
ejpam-5812	432	5	mean	mean	NOUN
ejpam-5812	432	6	algorithm	algorithm	NOUN
ejpam-5812	432	7	for	for	ADP
ejpam-5812	432	8	a	a	DET
ejpam-5812	432	9	graph	graph	NOUN
ejpam-5812	432	10	.	.	PUNCT
ejpam-5812	432	11	symmetry	symmetry	NOUN
ejpam-5812	432	12	,	,	PUNCT
ejpam-5812	432	13	15(3):570	15(3):570	NOUN
ejpam-5812	432	14	,	,	PUNCT
ejpam-5812	432	15	2023	2023	NUM
ejpam-5812	432	16	.	.	PUNCT
ejpam-5812	433	1	[	[	X
ejpam-5812	433	2	2	2	X
ejpam-5812	433	3	]	]	PUNCT
ejpam-5812	433	4	k.	k.	PROPN
ejpam-5812	433	5	a.	a.	PROPN
ejpam-5812	433	6	alsatami	alsatami	PROPN
ejpam-5812	433	7	,	,	PUNCT
ejpam-5812	433	8	y.	y.	PROPN
ejpam-5812	433	9	algrawani	algrawani	PROPN
ejpam-5812	433	10	,	,	PUNCT
ejpam-5812	433	11	and	and	CCONJ
ejpam-5812	433	12	a.	a.	PROPN
ejpam-5812	433	13	abd	abd	PROPN
ejpam-5812	433	14	el	el	PROPN
ejpam-5812	433	15	-	-	PROPN
ejpam-5812	433	16	hay	hay	PROPN
ejpam-5812	433	17	.	.	PUNCT
ejpam-5812	434	1	a	a	DET
ejpam-5812	434	2	novel	novel	ADJ
ejpam-5812	434	3	problem	problem	NOUN
ejpam-5812	434	4	and	and	CCONJ
ejpam-5812	434	5	algorithm	algorithm	NOUN
ejpam-5812	434	6	for	for	ADP
ejpam-5812	434	7	solving	solve	VERB
ejpam-5812	434	8	permuted	permute	VERB
ejpam-5812	434	9	cordial	cordial	ADJ
ejpam-5812	434	10	labeling	labeling	NOUN
ejpam-5812	434	11	of	of	ADP
ejpam-5812	434	12	corona	corona	NOUN
ejpam-5812	434	13	product	product	NOUN
ejpam-5812	434	14	between	between	ADP
ejpam-5812	434	15	two	two	NUM
ejpam-5812	434	16	graphs	graph	NOUN
ejpam-5812	434	17	.	.	PUNCT
ejpam-5812	435	1	mathematical	mathematical	ADJ
ejpam-5812	435	2	models	model	NOUN
ejpam-5812	435	3	in	in	ADP
ejpam-5812	435	4	engineering	engineering	NOUN
ejpam-5812	435	5	,	,	PUNCT
ejpam-5812	435	6	11(1):–11	11(1):–11	NUM
ejpam-5812	435	7	,	,	PUNCT
ejpam-5812	435	8	2025	2025	NUM
ejpam-5812	435	9	.	.	PUNCT
ejpam-5812	436	1	[	[	X
ejpam-5812	436	2	3	3	NUM
ejpam-5812	436	3	]	]	X
ejpam-5812	436	4	i.	i.	PROPN
ejpam-5812	436	5	cahit	cahit	PROPN
ejpam-5812	436	6	.	.	PUNCT
ejpam-5812	437	1	cordial	cordial	ADJ
ejpam-5812	437	2	graphs	graph	NOUN
ejpam-5812	437	3	:	:	PUNCT
ejpam-5812	437	4	a	a	DET
ejpam-5812	437	5	weaker	weak	ADJ
ejpam-5812	437	6	version	version	NOUN
ejpam-5812	437	7	of	of	ADP
ejpam-5812	437	8	graceful	graceful	ADJ
ejpam-5812	437	9	and	and	CCONJ
ejpam-5812	437	10	harmonious	harmonious	ADJ
ejpam-5812	437	11	graphs	graph	NOUN
ejpam-5812	437	12	.	.	PUNCT
ejpam-5812	438	1	ars	ar	NOUN
ejpam-5812	438	2	combinatoria	combinatoria	PROPN
ejpam-5812	438	3	,	,	PUNCT
ejpam-5812	438	4	23:201–207	23:201–207	PROPN
ejpam-5812	438	5	,	,	PUNCT
ejpam-5812	438	6	1987	1987	NUM
ejpam-5812	438	7	.	.	PUNCT
ejpam-5812	439	1	[	[	X
ejpam-5812	439	2	4	4	NUM
ejpam-5812	439	3	]	]	X
ejpam-5812	439	4	i.	i.	PROPN
ejpam-5812	439	5	cahit	cahit	PROPN
ejpam-5812	439	6	.	.	PUNCT
ejpam-5812	440	1	on	on	ADP
ejpam-5812	440	2	cordial	cordial	ADJ
ejpam-5812	440	3	and	and	CCONJ
ejpam-5812	440	4	3	3	NUM
ejpam-5812	440	5	-	-	PUNCT
ejpam-5812	440	6	equitable	equitable	ADJ
ejpam-5812	440	7	labeling	labeling	NOUN
ejpam-5812	440	8	of	of	ADP
ejpam-5812	440	9	graphs	graph	NOUN
ejpam-5812	440	10	.	.	PUNCT
ejpam-5812	441	1	utilities	utility	NOUN
ejpam-5812	441	2	mathematics	mathematic	NOUN
ejpam-5812	441	3	,	,	PUNCT
ejpam-5812	441	4	37:189	37:189	NUM
ejpam-5812	441	5	–	–	PUNCT
ejpam-5812	441	6	198	198	NUM
ejpam-5812	441	7	,	,	PUNCT
ejpam-5812	441	8	1990	1990	NUM
ejpam-5812	441	9	.	.	PUNCT
ejpam-5812	442	1	[	[	X
ejpam-5812	442	2	5	5	X
ejpam-5812	442	3	]	]	X
ejpam-5812	442	4	narsingh	narsingh	PROPN
ejpam-5812	442	5	deo	deo	NOUN
ejpam-5812	442	6	.	.	PUNCT
ejpam-5812	443	1	graph	graph	NOUN
ejpam-5812	443	2	theory	theory	NOUN
ejpam-5812	443	3	with	with	ADP
ejpam-5812	443	4	application	application	NOUN
ejpam-5812	443	5	to	to	ADP
ejpam-5812	443	6	engineering	engineering	NOUN
ejpam-5812	443	7	and	and	CCONJ
ejpam-5812	443	8	computer	computer	NOUN
ejpam-5812	443	9	science	science	NOUN
ejpam-5812	443	10	.	.	PUNCT
ejpam-5812	444	1	prentice	prentice	PROPN
ejpam-5812	444	2	hall	hall	PROPN
ejpam-5812	444	3	of	of	ADP
ejpam-5812	444	4	india	india	PROPN
ejpam-5812	444	5	pvt	pvt	PROPN
ejpam-5812	444	6	.	.	PROPN
ejpam-5812	444	7	,	,	PUNCT
ejpam-5812	444	8	new	new	PROPN
ejpam-5812	444	9	delhi	delhi	PROPN
ejpam-5812	444	10	,	,	PUNCT
ejpam-5812	444	11	india	india	PROPN
ejpam-5812	444	12	,	,	PUNCT
ejpam-5812	444	13	2003	2003	NUM
ejpam-5812	444	14	.	.	PUNCT
ejpam-5812	445	1	[	[	X
ejpam-5812	445	2	6	6	NUM
ejpam-5812	445	3	]	]	PUNCT
ejpam-5812	445	4	a.	a.	NOUN
ejpam-5812	445	5	t.	t.	PROPN
ejpam-5812	445	6	diab	diab	PROPN
ejpam-5812	445	7	.	.	PUNCT
ejpam-5812	446	1	study	study	NOUN
ejpam-5812	446	2	of	of	ADP
ejpam-5812	446	3	some	some	DET
ejpam-5812	446	4	problems	problem	NOUN
ejpam-5812	446	5	of	of	ADP
ejpam-5812	446	6	cordial	cordial	ADJ
ejpam-5812	446	7	.	.	PUNCT
ejpam-5812	447	1	ars	ars	PROPN
ejpam-5812	447	2	combinatoria	combinatoria	PROPN
ejpam-5812	447	3	,	,	PUNCT
ejpam-5812	447	4	92:255–261	92:255–261	NUM
ejpam-5812	447	5	,	,	PUNCT
ejpam-5812	447	6	2009	2009	NUM
ejpam-5812	447	7	.	.	PUNCT
ejpam-5812	448	1	[	[	X
ejpam-5812	448	2	7	7	NUM
ejpam-5812	448	3	]	]	PUNCT
ejpam-5812	448	4	a.	a.	NOUN
ejpam-5812	448	5	t.	t.	PROPN
ejpam-5812	448	6	diab	diab	PROPN
ejpam-5812	448	7	.	.	PUNCT
ejpam-5812	449	1	on	on	ADP
ejpam-5812	449	2	cordial	cordial	ADJ
ejpam-5812	449	3	labeling	labeling	NOUN
ejpam-5812	449	4	of	of	ADP
ejpam-5812	449	5	the	the	DET
ejpam-5812	449	6	second	second	ADJ
ejpam-5812	449	7	power	power	NOUN
ejpam-5812	449	8	of	of	ADP
ejpam-5812	449	9	paths	path	NOUN
ejpam-5812	449	10	with	with	ADP
ejpam-5812	449	11	other	other	ADJ
ejpam-5812	449	12	graphs	graph	NOUN
ejpam-5812	449	13	.	.	PUNCT
ejpam-5812	450	1	ars	ar	NOUN
ejpam-5812	450	2	combinatoria	combinatoria	PROPN
ejpam-5812	450	3	,	,	PUNCT
ejpam-5812	450	4	97a:327–343	97a:327–343	PROPN
ejpam-5812	450	5	,	,	PUNCT
ejpam-5812	450	6	2010	2010	NUM
ejpam-5812	450	7	.	.	PUNCT
ejpam-5812	451	1	[	[	X
ejpam-5812	451	2	8	8	NUM
ejpam-5812	451	3	]	]	PUNCT
ejpam-5812	451	4	a.	a.	NOUN
ejpam-5812	451	5	t.	t.	PROPN
ejpam-5812	451	6	diab	diab	PROPN
ejpam-5812	451	7	.	.	PUNCT
ejpam-5812	452	1	on	on	ADP
ejpam-5812	452	2	cordial	cordial	ADJ
ejpam-5812	452	3	labeling	labeling	NOUN
ejpam-5812	452	4	of	of	ADP
ejpam-5812	452	5	wheels	wheel	NOUN
ejpam-5812	452	6	with	with	ADP
ejpam-5812	452	7	other	other	ADJ
ejpam-5812	452	8	graphs	graph	NOUN
ejpam-5812	452	9	.	.	PUNCT
ejpam-5812	453	1	ars	ars	PROPN
ejpam-5812	453	2	combinatoria	combinatoria	PROPN
ejpam-5812	453	3	,	,	PUNCT
ejpam-5812	453	4	100:265–279	100:265–279	NUM
ejpam-5812	453	5	,	,	PUNCT
ejpam-5812	453	6	2011	2011	NUM
ejpam-5812	453	7	.	.	PUNCT
ejpam-5812	454	1	[	[	X
ejpam-5812	454	2	9	9	NUM
ejpam-5812	454	3	]	]	X
ejpam-5812	454	4	atef	atef	PROPN
ejpam-5812	454	5	abd	abd	PROPN
ejpam-5812	454	6	el	el	PROPN
ejpam-5812	454	7	-	-	PROPN
ejpam-5812	454	8	hay	hay	PROPN
ejpam-5812	454	9	,	,	PUNCT
ejpam-5812	454	10	khalid	khalid	PROPN
ejpam-5812	454	11	a.	a.	PROPN
ejpam-5812	454	12	alsatami	alsatami	PROPN
ejpam-5812	454	13	,	,	PUNCT
ejpam-5812	454	14	ashraf	ashraf	PROPN
ejpam-5812	454	15	elrokh	elrokh	VERB
ejpam-5812	454	16	,	,	PUNCT
ejpam-5812	454	17	and	and	CCONJ
ejpam-5812	454	18	aya	aya	PROPN
ejpam-5812	454	19	rabie	rabie	PROPN
ejpam-5812	454	20	.	.	PUNCT
ejpam-5812	455	1	cordial	cordial	ADJ
ejpam-5812	455	2	labeling	labeling	NOUN
ejpam-5812	455	3	of	of	ADP
ejpam-5812	455	4	corona	corona	NOUN
ejpam-5812	455	5	product	product	NOUN
ejpam-5812	455	6	of	of	ADP
ejpam-5812	455	7	paths	path	NOUN
ejpam-5812	455	8	and	and	CCONJ
ejpam-5812	455	9	fourth	fourth	ADJ
ejpam-5812	455	10	order	order	NOUN
ejpam-5812	455	11	of	of	ADP
ejpam-5812	455	12	lemniscate	lemniscate	PROPN
ejpam-5812	455	13	graphs	graph	NOUN
ejpam-5812	455	14	.	.	PUNCT
ejpam-5812	456	1	european	european	ADJ
ejpam-5812	456	2	journal	journal	PROPN
ejpam-5812	456	3	of	of	ADP
ejpam-5812	456	4	pure	pure	ADJ
ejpam-5812	456	5	and	and	CCONJ
ejpam-5812	456	6	applied	applied	ADJ
ejpam-5812	456	7	mathematics	mathematic	NOUN
ejpam-5812	456	8	,	,	PUNCT
ejpam-5812	456	9	18(1):5470	18(1):5470	NUM
ejpam-5812	456	10	,	,	PUNCT
ejpam-5812	456	11	2025	2025	NUM
ejpam-5812	456	12	.	.	PUNCT
ejpam-5812	457	1	[	[	X
ejpam-5812	457	2	10	10	NUM
ejpam-5812	457	3	]	]	X
ejpam-5812	457	4	atef	atef	PROPN
ejpam-5812	457	5	abd	abd	PROPN
ejpam-5812	457	6	el	el	PROPN
ejpam-5812	457	7	-	-	PROPN
ejpam-5812	457	8	hay	hay	PROPN
ejpam-5812	457	9	,	,	PUNCT
ejpam-5812	457	10	yasser	yasser	PROPN
ejpam-5812	457	11	elmshtaye	elmshtaye	VERB
ejpam-5812	457	12	,	,	PUNCT
ejpam-5812	457	13	and	and	CCONJ
ejpam-5812	457	14	ashraf	ashraf	PROPN
ejpam-5812	457	15	elrokh	elrokh	VERB
ejpam-5812	457	16	.	.	PUNCT
ejpam-5812	458	1	solving	solve	VERB
ejpam-5812	458	2	signed	sign	VERB
ejpam-5812	458	3	product	product	NOUN
ejpam-5812	458	4	cordial	cordial	ADJ
ejpam-5812	458	5	labeling	labeling	NOUN
ejpam-5812	458	6	of	of	ADP
ejpam-5812	458	7	corona	corona	NOUN
ejpam-5812	458	8	products	product	NOUN
ejpam-5812	458	9	of	of	ADP
ejpam-5812	458	10	paths	path	NOUN
ejpam-5812	458	11	and	and	CCONJ
ejpam-5812	458	12	the	the	DET
ejpam-5812	458	13	third	third	ADJ
ejpam-5812	458	14	power	power	NOUN
ejpam-5812	458	15	of	of	ADP
ejpam-5812	458	16	lemniscate	lemniscate	PROPN
ejpam-5812	458	17	graphs	graph	NOUN
ejpam-5812	458	18	.	.	PUNCT
ejpam-5812	459	1	turkish	turkish	ADJ
ejpam-5812	459	2	journal	journal	NOUN
ejpam-5812	459	3	of	of	ADP
ejpam-5812	459	4	computer	computer	NOUN
ejpam-5812	459	5	and	and	CCONJ
ejpam-5812	459	6	mathematics	mathematics	PROPN
ejpam-5812	459	7	education	education	NOUN
ejpam-5812	459	8	(	(	PUNCT
ejpam-5812	459	9	turcomat	turcomat	NOUN
ejpam-5812	459	10	)	)	PUNCT
ejpam-5812	459	11	,	,	PUNCT
ejpam-5812	459	12	14:806–823	14:806–823	NUM
ejpam-5812	459	13	,	,	PUNCT
ejpam-5812	459	14	2023	2023	NUM
ejpam-5812	459	15	.	.	PUNCT
ejpam-5812	460	1	[	[	X
ejpam-5812	460	2	11	11	NUM
ejpam-5812	460	3	]	]	X
ejpam-5812	460	4	atef	atef	PROPN
ejpam-5812	460	5	abd	abd	PROPN
ejpam-5812	460	6	el	el	PROPN
ejpam-5812	460	7	-	-	PROPN
ejpam-5812	460	8	hay	hay	PROPN
ejpam-5812	460	9	and	and	CCONJ
ejpam-5812	460	10	a.	a.	NOUN
ejpam-5812	460	11	elrokh	elrokh	PROPN
ejpam-5812	460	12	.	.	PUNCT
ejpam-5812	461	1	total	total	ADJ
ejpam-5812	461	2	cordial	cordial	ADJ
ejpam-5812	461	3	labeling	labeling	NOUN
ejpam-5812	461	4	of	of	ADP
ejpam-5812	461	5	corona	corona	NOUN
ejpam-5812	461	6	product	product	NOUN
ejpam-5812	461	7	of	of	ADP
ejpam-5812	461	8	paths	path	NOUN
ejpam-5812	461	9	and	and	CCONJ
ejpam-5812	461	10	second	second	ADJ
ejpam-5812	461	11	power	power	NOUN
ejpam-5812	461	12	of	of	ADP
ejpam-5812	461	13	fan	fan	NOUN
ejpam-5812	461	14	graph	graph	NOUN
ejpam-5812	461	15	.	.	PUNCT
ejpam-5812	462	1	turkish	turkish	ADJ
ejpam-5812	462	2	journal	journal	NOUN
ejpam-5812	462	3	of	of	ADP
ejpam-5812	462	4	computer	computer	NOUN
ejpam-5812	462	5	and	and	CCONJ
ejpam-5812	462	6	mathematics	mathematics	PROPN
ejpam-5812	462	7	education	education	NOUN
ejpam-5812	462	8	(	(	PUNCT
ejpam-5812	462	9	turcomat	turcomat	NOUN
ejpam-5812	462	10	)	)	PUNCT
ejpam-5812	462	11	,	,	PUNCT
ejpam-5812	462	12	13(3):681–690	13(3):681–690	PROPN
ejpam-5812	462	13	,	,	PUNCT
ejpam-5812	462	14	2022	2022	NUM
ejpam-5812	462	15	.	.	PUNCT
ejpam-5812	463	1	[	[	X
ejpam-5812	463	2	12	12	NUM
ejpam-5812	463	3	]	]	PUNCT
ejpam-5812	463	4	a.	a.	NOUN
ejpam-5812	463	5	elrokh	elrokh	NOUN
ejpam-5812	463	6	,	,	PUNCT
ejpam-5812	463	7	mohammed	mohammed	PROPN
ejpam-5812	463	8	m.	m.	PROPN
ejpam-5812	463	9	ali	ali	PROPN
ejpam-5812	463	10	al	al	PROPN
ejpam-5812	463	11	-	-	PUNCT
ejpam-5812	463	12	shamiri	shamiri	PROPN
ejpam-5812	463	13	,	,	PUNCT
ejpam-5812	463	14	mohammed	mohammed	PROPN
ejpam-5812	463	15	m.	m.	PROPN
ejpam-5812	463	16	a.	a.	PROPN
ejpam-5812	463	17	almazah	almazah	PROPN
ejpam-5812	463	18	,	,	PUNCT
ejpam-5812	463	19	and	and	CCONJ
ejpam-5812	463	20	atef	atef	PROPN
ejpam-5812	463	21	abd	abd	PROPN
ejpam-5812	463	22	el	el	PROPN
ejpam-5812	463	23	-	-	PROPN
ejpam-5812	463	24	hay	hay	PROPN
ejpam-5812	463	25	.	.	PUNCT
ejpam-5812	464	1	a	a	DET
ejpam-5812	464	2	novel	novel	ADJ
ejpam-5812	464	3	problem	problem	NOUN
ejpam-5812	464	4	for	for	ADP
ejpam-5812	464	5	solving	solve	VERB
ejpam-5812	464	6	permuted	permute	VERB
ejpam-5812	464	7	cordial	cordial	ADJ
ejpam-5812	464	8	labeling	labeling	NOUN
ejpam-5812	464	9	of	of	ADP
ejpam-5812	464	10	graphs	graph	NOUN
ejpam-5812	464	11	.	.	PUNCT
ejpam-5812	465	1	symmetry	symmetry	NOUN
ejpam-5812	465	2	,	,	PUNCT
ejpam-5812	465	3	15(4):825	15(4):825	PROPN
ejpam-5812	465	4	,	,	PUNCT
ejpam-5812	465	5	2023	2023	NUM
ejpam-5812	465	6	.	.	PUNCT
ejpam-5812	466	1	[	[	X
ejpam-5812	466	2	13	13	NUM
ejpam-5812	466	3	]	]	PUNCT
ejpam-5812	466	4	a.	a.	NOUN
ejpam-5812	466	5	elrokh	elrokh	NOUN
ejpam-5812	466	6	,	,	PUNCT
ejpam-5812	466	7	y.	y.	PROPN
ejpam-5812	466	8	elmshtaye	elmshtaye	VERB
ejpam-5812	466	9	,	,	PUNCT
ejpam-5812	466	10	and	and	CCONJ
ejpam-5812	466	11	atef	atef	PROPN
ejpam-5812	466	12	abd	abd	PROPN
ejpam-5812	466	13	el	el	PROPN
ejpam-5812	466	14	-	-	PROPN
ejpam-5812	466	15	hay	hay	PROPN
ejpam-5812	466	16	.	.	PUNCT
ejpam-5812	467	1	the	the	DET
ejpam-5812	467	2	cordiality	cordiality	NOUN
ejpam-5812	467	3	of	of	ADP
ejpam-5812	467	4	cone	cone	NOUN
ejpam-5812	467	5	and	and	CCONJ
ejpam-5812	467	6	lemniscate	lemniscate	PROPN
ejpam-5812	467	7	graphs	graph	NOUN
ejpam-5812	467	8	.	.	PUNCT
ejpam-5812	468	1	applied	apply	VERB
ejpam-5812	468	2	mathematics	mathematics	PROPN
ejpam-5812	468	3	&	&	CCONJ
ejpam-5812	468	4	information	information	NOUN
ejpam-5812	468	5	sciences	sciences	PROPN
ejpam-5812	468	6	,	,	PUNCT
ejpam-5812	468	7	16:1027–1034	16:1027–1034	NUM
ejpam-5812	468	8	,	,	PUNCT
ejpam-5812	468	9	2022	2022	NUM
ejpam-5812	468	10	.	.	PUNCT
ejpam-5812	469	1	[	[	X
ejpam-5812	469	2	14	14	NUM
ejpam-5812	469	3	]	]	PUNCT
ejpam-5812	469	4	a.	a.	NOUN
ejpam-5812	469	5	elrokh	elrokh	NOUN
ejpam-5812	469	6	and	and	CCONJ
ejpam-5812	469	7	a.	a.	NOUN
ejpam-5812	469	8	rabie	rabie	PROPN
ejpam-5812	469	9	.	.	PUNCT
ejpam-5812	470	1	the	the	DET
ejpam-5812	470	2	cordiality	cordiality	NOUN
ejpam-5812	470	3	of	of	ADP
ejpam-5812	470	4	the	the	DET
ejpam-5812	470	5	sum	sum	NOUN
ejpam-5812	470	6	and	and	CCONJ
ejpam-5812	470	7	union	union	NOUN
ejpam-5812	470	8	of	of	ADP
ejpam-5812	470	9	two	two	NUM
ejpam-5812	470	10	fourth	fourth	ADJ
ejpam-5812	470	11	power	power	NOUN
ejpam-5812	470	12	of	of	ADP
ejpam-5812	470	13	paths	path	NOUN
ejpam-5812	470	14	and	and	CCONJ
ejpam-5812	470	15	cycles	cycle	NOUN
ejpam-5812	470	16	.	.	PUNCT
ejpam-5812	471	1	journal	journal	NOUN
ejpam-5812	471	2	of	of	ADP
ejpam-5812	471	3	the	the	DET
ejpam-5812	471	4	egyptian	egyptian	PROPN
ejpam-5812	471	5	mathematical	mathematical	PROPN
ejpam-5812	471	6	society	society	NOUN
ejpam-5812	471	7	,	,	PUNCT
ejpam-5812	471	8	29(3):1–13	29(3):1–13	NUM
ejpam-5812	471	9	,	,	PUNCT
ejpam-5812	471	10	2021	2021	NUM
ejpam-5812	471	11	.	.	PUNCT
ejpam-5812	472	1	[	[	X
ejpam-5812	472	2	15	15	NUM
ejpam-5812	472	3	]	]	X
ejpam-5812	472	4	ashraf	ashraf	NOUN
ejpam-5812	472	5	elrokh	elrokh	VERB
ejpam-5812	472	6	,	,	PUNCT
ejpam-5812	472	7	mohammed	mohammed	PROPN
ejpam-5812	472	8	m.	m.	PROPN
ejpam-5812	472	9	ali	ali	PROPN
ejpam-5812	472	10	al	al	PROPN
ejpam-5812	472	11	-	-	PUNCT
ejpam-5812	472	12	shamiri	shamiri	PROPN
ejpam-5812	472	13	,	,	PUNCT
ejpam-5812	472	14	and	and	CCONJ
ejpam-5812	472	15	atef	atef	PROPN
ejpam-5812	472	16	abd	abd	PROPN
ejpam-5812	472	17	el	el	PROPN
ejpam-5812	472	18	-	-	PROPN
ejpam-5812	472	19	hay	hay	PROPN
ejpam-5812	472	20	.	.	PUNCT
ejpam-5812	473	1	a	a	DET
ejpam-5812	473	2	novel	novel	ADJ
ejpam-5812	473	3	problem	problem	NOUN
ejpam-5812	473	4	to	to	PART
ejpam-5812	473	5	solve	solve	VERB
ejpam-5812	473	6	the	the	DET
ejpam-5812	473	7	logically	logically	ADV
ejpam-5812	473	8	labeling	labeling	NOUN
ejpam-5812	473	9	of	of	ADP
ejpam-5812	473	10	corona	corona	NOUN
ejpam-5812	473	11	between	between	ADP
ejpam-5812	473	12	paths	path	NOUN
ejpam-5812	473	13	and	and	CCONJ
ejpam-5812	473	14	cycles	cycle	NOUN
ejpam-5812	473	15	.	.	PUNCT
ejpam-5812	474	1	journal	journal	NOUN
ejpam-5812	474	2	of	of	ADP
ejpam-5812	474	3	mathematics	mathematic	NOUN
ejpam-5812	474	4	,	,	PUNCT
ejpam-5812	474	5	2022	2022	NUM
ejpam-5812	474	6	:	:	PUNCT
ejpam-5812	474	7	article	article	NOUN
ejpam-5812	474	8	i	i	PROPN
ejpam-5812	474	9	d	d	PROPN
ejpam-5812	474	10	2312206	2312206	NUM
ejpam-5812	474	11	,	,	PUNCT
ejpam-5812	474	12	11	11	NUM
ejpam-5812	474	13	pages	page	NOUN
ejpam-5812	474	14	,	,	PUNCT
ejpam-5812	474	15	2022	2022	NUM
ejpam-5812	474	16	.	.	PUNCT
ejpam-5812	475	1	[	[	X
ejpam-5812	475	2	16	16	NUM
ejpam-5812	475	3	]	]	X
ejpam-5812	475	4	e.	e.	PROPN
ejpam-5812	475	5	a.	a.	PROPN
ejpam-5812	475	6	elsakhawy	elsakhawy	PROPN
ejpam-5812	475	7	and	and	CCONJ
ejpam-5812	475	8	a.	a.	NOUN
ejpam-5812	475	9	t.	t.	PROPN
ejpam-5812	475	10	diab	diab	PROPN
ejpam-5812	475	11	.	.	PUNCT
ejpam-5812	476	1	on	on	ADP
ejpam-5812	476	2	cordial	cordial	ADJ
ejpam-5812	476	3	labeling	labeling	NOUN
ejpam-5812	476	4	of	of	ADP
ejpam-5812	476	5	third	third	ADJ
ejpam-5812	476	6	power	power	NOUN
ejpam-5812	476	7	of	of	ADP
ejpam-5812	476	8	path	path	NOUN
ejpam-5812	476	9	with	with	ADP
ejpam-5812	476	10	other	other	ADJ
ejpam-5812	476	11	graphs	graph	NOUN
ejpam-5812	476	12	.	.	PUNCT
ejpam-5812	477	1	applied	apply	VERB
ejpam-5812	477	2	mathematics	mathematics	PROPN
ejpam-5812	477	3	&	&	CCONJ
ejpam-5812	477	4	information	information	NOUN
ejpam-5812	477	5	sciences	sciences	PROPN
ejpam-5812	477	6	,	,	PUNCT
ejpam-5812	477	7	18:1195–1207	18:1195–1207	NUM
ejpam-5812	477	8	,	,	PUNCT
ejpam-5812	477	9	2024	2024	NUM
ejpam-5812	477	10	.	.	PUNCT
ejpam-5812	478	1	a.	a.	PROPN
ejpam-5812	478	2	abd	abd	PROPN
ejpam-5812	478	3	el	el	PROPN
ejpam-5812	478	4	-	-	PROPN
ejpam-5812	478	5	hay	hay	PROPN
ejpam-5812	478	6	,	,	PUNCT
ejpam-5812	478	7	k.	k.	PROPN
ejpam-5812	478	8	a.	a.	PROPN
ejpam-5812	478	9	alsatami	alsatami	PROPN
ejpam-5812	478	10	,	,	PUNCT
ejpam-5812	478	11	a.	a.	NOUN
ejpam-5812	478	12	elrokh	elrokh	PROPN
ejpam-5812	478	13	/	/	SYM
ejpam-5812	478	14	eur	eur	PROPN
ejpam-5812	478	15	.	.	PUNCT
ejpam-5812	479	1	j.	j.	PROPN
ejpam-5812	479	2	pure	pure	PROPN
ejpam-5812	479	3	appl	appl	PROPN
ejpam-5812	479	4	.	.	PROPN
ejpam-5812	479	5	math	math	PROPN
ejpam-5812	479	6	,	,	PUNCT
ejpam-5812	479	7	18	18	NUM
ejpam-5812	479	8	(	(	PUNCT
ejpam-5812	479	9	1	1	NUM
ejpam-5812	479	10	)	)	PUNCT
ejpam-5812	479	11	(	(	PUNCT
ejpam-5812	479	12	2025	2025	NUM
ejpam-5812	479	13	)	)	PUNCT
ejpam-5812	479	14	,	,	PUNCT
ejpam-5812	479	15	5812	5812	NUM
ejpam-5812	479	16	14	14	NUM
ejpam-5812	479	17	of	of	ADP
ejpam-5812	479	18	14	14	NUM
ejpam-5812	479	19	[	[	X
ejpam-5812	479	20	17	17	NUM
ejpam-5812	479	21	]	]	PUNCT
ejpam-5812	479	22	j.	j.	PROPN
ejpam-5812	479	23	a.	a.	PROPN
ejpam-5812	479	24	gallian	gallian	PROPN
ejpam-5812	479	25	.	.	PUNCT
ejpam-5812	480	1	a	a	DET
ejpam-5812	480	2	dynamic	dynamic	ADJ
ejpam-5812	480	3	survey	survey	NOUN
ejpam-5812	480	4	of	of	ADP
ejpam-5812	480	5	graph	graph	NOUN
ejpam-5812	480	6	labeling	labeling	NOUN
ejpam-5812	480	7	.	.	PUNCT
ejpam-5812	481	1	electronic	electronic	ADJ
ejpam-5812	481	2	journal	journal	NOUN
ejpam-5812	481	3	of	of	ADP
ejpam-5812	481	4	combinatorics	combinatoric	NOUN
ejpam-5812	481	5	,	,	PUNCT
ejpam-5812	481	6	1(dynamic	1(dynamic	NUM
ejpam-5812	481	7	surveys):ds6	surveys):ds6	NOUN
ejpam-5812	481	8	.	.	PUNCT
ejpam-5812	482	1	[	[	X
ejpam-5812	482	2	18	18	NUM
ejpam-5812	482	3	]	]	PUNCT
ejpam-5812	482	4	s.	s.	PROPN
ejpam-5812	482	5	w.	w.	PROPN
ejpam-5812	482	6	golomb	golomb	PROPN
ejpam-5812	482	7	.	.	PUNCT
ejpam-5812	483	1	how	how	SCONJ
ejpam-5812	483	2	to	to	PART
ejpam-5812	483	3	number	number	VERB
ejpam-5812	483	4	a	a	DET
ejpam-5812	483	5	graph	graph	NOUN
ejpam-5812	483	6	in	in	ADP
ejpam-5812	483	7	graph	graph	NOUN
ejpam-5812	483	8	theory	theory	NOUN
ejpam-5812	483	9	and	and	CCONJ
ejpam-5812	483	10	computing	computing	NOUN
ejpam-5812	483	11	.	.	PUNCT
ejpam-5812	484	1	in	in	ADP
ejpam-5812	484	2	r.	r.	PROPN
ejpam-5812	484	3	c.	c.	PROPN
ejpam-5812	484	4	read	read	PROPN
ejpam-5812	484	5	,	,	PUNCT
ejpam-5812	484	6	editor	editor	NOUN
ejpam-5812	484	7	,	,	PUNCT
ejpam-5812	484	8	graph	graph	NOUN
ejpam-5812	484	9	theory	theory	NOUN
ejpam-5812	484	10	and	and	CCONJ
ejpam-5812	484	11	computing	computing	NOUN
ejpam-5812	484	12	,	,	PUNCT
ejpam-5812	484	13	page	page	NOUN
ejpam-5812	484	14	2337	2337	NUM
ejpam-5812	484	15	.	.	PUNCT
ejpam-5812	485	1	academic	academic	ADJ
ejpam-5812	485	2	press	press	NOUN
ejpam-5812	485	3	,	,	PUNCT
ejpam-5812	485	4	new	new	PROPN
ejpam-5812	485	5	york	york	PROPN
ejpam-5812	485	6	,	,	PUNCT
ejpam-5812	485	7	1972	1972	NUM
ejpam-5812	485	8	.	.	PUNCT
ejpam-5812	486	1	[	[	X
ejpam-5812	486	2	19	19	NUM
ejpam-5812	486	3	]	]	X
ejpam-5812	486	4	r.	r.	PROPN
ejpam-5812	486	5	l.	l.	PROPN
ejpam-5812	486	6	graham	graham	PROPN
ejpam-5812	486	7	and	and	CCONJ
ejpam-5812	486	8	n.	n.	PROPN
ejpam-5812	486	9	j.	j.	PROPN
ejpam-5812	486	10	a.	a.	PROPN
ejpam-5812	486	11	sloane	sloane	PROPN
ejpam-5812	486	12	.	.	PUNCT
ejpam-5812	487	1	on	on	ADP
ejpam-5812	487	2	additive	additive	ADJ
ejpam-5812	487	3	bases	basis	NOUN
ejpam-5812	487	4	and	and	CCONJ
ejpam-5812	487	5	harmonious	harmonious	ADJ
ejpam-5812	487	6	graphs	graph	NOUN
ejpam-5812	487	7	.	.	PUNCT
ejpam-5812	488	1	siam	siam	PROPN
ejpam-5812	488	2	journal	journal	PROPN
ejpam-5812	488	3	on	on	ADP
ejpam-5812	488	4	algebraic	algebraic	ADJ
ejpam-5812	488	5	discrete	discrete	ADJ
ejpam-5812	488	6	mathematics	mathematic	NOUN
ejpam-5812	488	7	,	,	PUNCT
ejpam-5812	488	8	1:382–404	1:382–404	NUM
ejpam-5812	488	9	,	,	PUNCT
ejpam-5812	488	10	1980	1980	NUM
ejpam-5812	488	11	.	.	PUNCT
ejpam-5812	489	1	[	[	X
ejpam-5812	489	2	20	20	NUM
ejpam-5812	489	3	]	]	X
ejpam-5812	489	4	n.	n.	PROPN
ejpam-5812	489	5	hartsfield	hartsfield	PROPN
ejpam-5812	489	6	and	and	CCONJ
ejpam-5812	489	7	g.	g.	PROPN
ejpam-5812	489	8	ringel	ringel	NOUN
ejpam-5812	489	9	.	.	PUNCT
ejpam-5812	490	1	pearls	pearl	NOUN
ejpam-5812	490	2	in	in	ADP
ejpam-5812	490	3	graph	graph	NOUN
ejpam-5812	490	4	theory	theory	NOUN
ejpam-5812	490	5	:	:	PUNCT
ejpam-5812	490	6	a	a	DET
ejpam-5812	490	7	comprehensive	comprehensive	ADJ
ejpam-5812	490	8	introduction	introduction	NOUN
ejpam-5812	490	9	.	.	PUNCT
ejpam-5812	491	1	academic	academic	PROPN
ejpam-5812	491	2	press	press	PROPN
ejpam-5812	491	3	inc	inc	PROPN
ejpam-5812	491	4	.	.	PROPN
ejpam-5812	491	5	,	,	PUNCT
ejpam-5812	491	6	boston	boston	PROPN
ejpam-5812	491	7	,	,	PUNCT
ejpam-5812	491	8	usa	usa	PROPN
ejpam-5812	491	9	,	,	PUNCT
ejpam-5812	491	10	1990	1990	NUM
ejpam-5812	491	11	.	.	PUNCT
ejpam-5812	492	1	[	[	X
ejpam-5812	492	2	21	21	NUM
ejpam-5812	492	3	]	]	PUNCT
ejpam-5812	492	4	a.	a.	NOUN
ejpam-5812	492	5	krishnaa	krishnaa	PROPN
ejpam-5812	492	6	.	.	PUNCT
ejpam-5812	493	1	some	some	DET
ejpam-5812	493	2	applications	application	NOUN
ejpam-5812	493	3	of	of	ADP
ejpam-5812	493	4	labelled	label	VERB
ejpam-5812	493	5	graphs	graph	NOUN
ejpam-5812	493	6	.	.	PUNCT
ejpam-5812	494	1	international	international	ADJ
ejpam-5812	494	2	journal	journal	PROPN
ejpam-5812	494	3	of	of	ADP
ejpam-5812	494	4	mathematics	mathematics	NOUN
ejpam-5812	494	5	trends	trend	NOUN
ejpam-5812	494	6	and	and	CCONJ
ejpam-5812	494	7	technology	technology	NOUN
ejpam-5812	494	8	(	(	PUNCT
ejpam-5812	494	9	ijmtt	ijmtt	ADJ
ejpam-5812	494	10	)	)	PUNCT
ejpam-5812	494	11	,	,	PUNCT
ejpam-5812	494	12	37(3):209–213	37(3):209–213	PROPN
ejpam-5812	494	13	,	,	PUNCT
ejpam-5812	494	14	2016	2016	NUM
ejpam-5812	494	15	.	.	PUNCT
ejpam-5812	495	1	[	[	X
ejpam-5812	495	2	22	22	NUM
ejpam-5812	495	3	]	]	PUNCT
ejpam-5812	495	4	a.	a.	PROPN
ejpam-5812	495	5	rosa	rosa	PROPN
ejpam-5812	495	6	.	.	PUNCT
ejpam-5812	496	1	on	on	ADP
ejpam-5812	496	2	certain	certain	ADJ
ejpam-5812	496	3	valuations	valuation	NOUN
ejpam-5812	496	4	of	of	ADP
ejpam-5812	496	5	the	the	DET
ejpam-5812	496	6	vertices	vertex	NOUN
ejpam-5812	496	7	of	of	ADP
ejpam-5812	496	8	a	a	DET
ejpam-5812	496	9	graph	graph	NOUN
ejpam-5812	496	10	.	.	PUNCT
ejpam-5812	497	1	in	in	ADP
ejpam-5812	497	2	theory	theory	NOUN
ejpam-5812	497	3	of	of	ADP
ejpam-5812	497	4	graphs	graph	NOUN
ejpam-5812	497	5	(	(	PUNCT
ejpam-5812	497	6	internet	internet	NOUN
ejpam-5812	497	7	.	.	PUNCT
ejpam-5812	498	1	symposium	symposium	PROPN
ejpam-5812	498	2	,	,	PUNCT
ejpam-5812	498	3	rome	rome	PROPN
ejpam-5812	498	4	,	,	PUNCT
ejpam-5812	498	5	july	july	PROPN
ejpam-5812	498	6	1966	1966	NUM
ejpam-5812	498	7	)	)	PUNCT
ejpam-5812	498	8	,	,	PUNCT
ejpam-5812	498	9	pages	page	NOUN
ejpam-5812	498	10	349–355	349–355	NUM
ejpam-5812	498	11	.	.	PUNCT
ejpam-5812	499	1	gordon	gordon	PROPN
ejpam-5812	499	2	and	and	CCONJ
ejpam-5812	499	3	breach	breach	PROPN
ejpam-5812	499	4	,	,	PUNCT
ejpam-5812	499	5	n.y	n.y	PROPN
ejpam-5812	499	6	.	.	PROPN
ejpam-5812	499	7	and	and	CCONJ
ejpam-5812	499	8	dunod	dunod	PROPN
ejpam-5812	499	9	paris	paris	PROPN
ejpam-5812	499	10	,	,	PUNCT
ejpam-5812	499	11	1967	1967	NUM
ejpam-5812	499	12	.	.	PUNCT