id	sid	tid	token	lemma	pos
ejpam-6438	1	1	european	european	PROPN
ejpam-6438	1	2	journal	journal	PROPN
ejpam-6438	1	3	of	of	ADP
ejpam-6438	1	4	pure	pure	ADJ
ejpam-6438	1	5	and	and	CCONJ
ejpam-6438	1	6	applied	applied	ADJ
ejpam-6438	1	7	mathematics	mathematic	NOUN
ejpam-6438	1	8	2025	2025	NUM
ejpam-6438	1	9	,	,	PUNCT
ejpam-6438	1	10	vol	vol	NOUN
ejpam-6438	1	11	.	.	PROPN
ejpam-6438	1	12	18	18	NUM
ejpam-6438	1	13	,	,	PUNCT
ejpam-6438	1	14	issue	issue	NOUN
ejpam-6438	1	15	3	3	NUM
ejpam-6438	1	16	,	,	PUNCT
ejpam-6438	1	17	article	article	NOUN
ejpam-6438	1	18	number	number	NOUN
ejpam-6438	1	19	6438	6438	NUM
ejpam-6438	1	20	issn	issn	PROPN
ejpam-6438	1	21	1307	1307	NUM
ejpam-6438	1	22	-	-	SYM
ejpam-6438	1	23	5543	5543	NUM
ejpam-6438	1	24	–	–	PUNCT
ejpam-6438	1	25	ejpam.com	ejpam.com	X
ejpam-6438	1	26	published	publish	VERB
ejpam-6438	1	27	by	by	ADP
ejpam-6438	1	28	new	new	PROPN
ejpam-6438	1	29	york	york	PROPN
ejpam-6438	1	30	business	business	PROPN
ejpam-6438	1	31	global	global	PROPN
ejpam-6438	1	32	computing	computing	PROPN
ejpam-6438	1	33	metric	metric	ADJ
ejpam-6438	1	34	and	and	CCONJ
ejpam-6438	1	35	connected	connected	ADJ
ejpam-6438	1	36	metric	metric	ADJ
ejpam-6438	1	37	dimension	dimension	NOUN
ejpam-6438	1	38	of	of	ADP
ejpam-6438	1	39	some	some	DET
ejpam-6438	1	40	graphs	graph	NOUN
ejpam-6438	1	41	ashraf	ashraf	VERB
ejpam-6438	1	42	elrokh1,∗	elrokh1,∗	PROPN
ejpam-6438	1	43	,	,	PUNCT
ejpam-6438	1	44	eman	eman	PROPN
ejpam-6438	1	45	s.	s.	PROPN
ejpam-6438	1	46	almotairi2	almotairi2	PROPN
ejpam-6438	1	47	,	,	PUNCT
ejpam-6438	1	48	hoda	hoda	PROPN
ejpam-6438	1	49	mostafa3	mostafa3	PROPN
ejpam-6438	1	50	1	1	NUM
ejpam-6438	1	51	mathematics	mathematic	NOUN
ejpam-6438	1	52	and	and	CCONJ
ejpam-6438	1	53	computer	computer	NOUN
ejpam-6438	1	54	science	science	PROPN
ejpam-6438	1	55	department	department	PROPN
ejpam-6438	1	56	,	,	PUNCT
ejpam-6438	1	57	faculty	faculty	NOUN
ejpam-6438	1	58	of	of	ADP
ejpam-6438	1	59	science	science	PROPN
ejpam-6438	1	60	menoufia	menoufia	PROPN
ejpam-6438	1	61	university	university	PROPN
ejpam-6438	1	62	,	,	PUNCT
ejpam-6438	1	63	menoufia	menoufia	PROPN
ejpam-6438	1	64	,	,	PUNCT
ejpam-6438	1	65	egypt	egypt	PROPN
ejpam-6438	1	66	2	2	NUM
ejpam-6438	1	67	department	department	NOUN
ejpam-6438	1	68	of	of	ADP
ejpam-6438	1	69	mathematics	mathematic	NOUN
ejpam-6438	1	70	,	,	PUNCT
ejpam-6438	1	71	college	college	NOUN
ejpam-6438	1	72	of	of	ADP
ejpam-6438	1	73	science	science	NOUN
ejpam-6438	1	74	,	,	PUNCT
ejpam-6438	1	75	qassim	qassim	PROPN
ejpam-6438	1	76	university	university	PROPN
ejpam-6438	1	77	,	,	PUNCT
ejpam-6438	1	78	buraydah	buraydah	NOUN
ejpam-6438	1	79	51452	51452	NUM
ejpam-6438	1	80	,	,	PUNCT
ejpam-6438	1	81	saudi	saudi	PROPN
ejpam-6438	1	82	arabia	arabia	PROPN
ejpam-6438	1	83	3	3	NUM
ejpam-6438	1	84	department	department	NOUN
ejpam-6438	1	85	of	of	ADP
ejpam-6438	1	86	basic	basic	ADJ
ejpam-6438	1	87	science	science	NOUN
ejpam-6438	1	88	,	,	PUNCT
ejpam-6438	1	89	giza	giza	PROPN
ejpam-6438	1	90	higher	high	ADJ
ejpam-6438	1	91	institute	institute	PROPN
ejpam-6438	1	92	of	of	ADP
ejpam-6438	1	93	engineering	engineering	NOUN
ejpam-6438	1	94	and	and	CCONJ
ejpam-6438	1	95	technology	technology	NOUN
ejpam-6438	1	96	,	,	PUNCT
ejpam-6438	1	97	giza	giza	PROPN
ejpam-6438	1	98	,	,	PUNCT
ejpam-6438	1	99	egypt	egypt	PROPN
ejpam-6438	1	100	abstract	abstract	PROPN
ejpam-6438	1	101	.	.	PUNCT
ejpam-6438	2	1	for	for	ADP
ejpam-6438	2	2	a	a	DET
ejpam-6438	2	3	connected	connected	ADJ
ejpam-6438	2	4	graph	graph	NOUN
ejpam-6438	2	5	g	g	PROPN
ejpam-6438	2	6	=	=	PUNCT
ejpam-6438	2	7	(	(	PUNCT
ejpam-6438	2	8	v	v	NOUN
ejpam-6438	2	9	,	,	PUNCT
ejpam-6438	2	10	e	e	NOUN
ejpam-6438	2	11	)	)	PUNCT
ejpam-6438	2	12	,	,	PUNCT
ejpam-6438	2	13	a	a	DET
ejpam-6438	2	14	set	set	NOUN
ejpam-6438	2	15	b	b	NOUN
ejpam-6438	2	16	⊆	⊆	NUM
ejpam-6438	2	17	v	v	NOUN
ejpam-6438	2	18	(	(	PUNCT
ejpam-6438	2	19	g	g	NOUN
ejpam-6438	2	20	)	)	PUNCT
ejpam-6438	2	21	is	be	AUX
ejpam-6438	2	22	a	a	DET
ejpam-6438	2	23	resolving	resolving	NOUN
ejpam-6438	2	24	set	set	VERB
ejpam-6438	2	25	if	if	SCONJ
ejpam-6438	2	26	every	every	DET
ejpam-6438	2	27	vertex	vertex	NOUN
ejpam-6438	2	28	in	in	ADP
ejpam-6438	2	29	g	g	PROPN
ejpam-6438	2	30	is	be	AUX
ejpam-6438	2	31	uniquely	uniquely	ADV
ejpam-6438	2	32	identified	identify	VERB
ejpam-6438	2	33	by	by	ADP
ejpam-6438	2	34	its	its	PRON
ejpam-6438	2	35	distances	distance	NOUN
ejpam-6438	2	36	to	to	ADP
ejpam-6438	2	37	the	the	DET
ejpam-6438	2	38	vertices	vertex	NOUN
ejpam-6438	2	39	in	in	ADP
ejpam-6438	2	40	b.	b.	PROPN
ejpam-6438	2	41	a	a	DET
ejpam-6438	2	42	resolving	resolving	NOUN
ejpam-6438	2	43	set	set	NOUN
ejpam-6438	2	44	that	that	PRON
ejpam-6438	2	45	induces	induce	VERB
ejpam-6438	2	46	a	a	DET
ejpam-6438	2	47	connected	connected	ADJ
ejpam-6438	2	48	subgraph	subgraph	NOUN
ejpam-6438	2	49	is	be	AUX
ejpam-6438	2	50	called	call	VERB
ejpam-6438	2	51	a	a	DET
ejpam-6438	2	52	connected	connected	ADJ
ejpam-6438	2	53	resolving	resolving	NOUN
ejpam-6438	2	54	set	set	NOUN
ejpam-6438	2	55	.	.	PUNCT
ejpam-6438	3	1	the	the	DET
ejpam-6438	3	2	minimum	minimum	ADJ
ejpam-6438	3	3	cardinality	cardinality	NOUN
ejpam-6438	3	4	of	of	ADP
ejpam-6438	3	5	such	such	DET
ejpam-6438	3	6	a	a	DET
ejpam-6438	3	7	set	set	NOUN
ejpam-6438	3	8	is	be	AUX
ejpam-6438	3	9	the	the	DET
ejpam-6438	3	10	connected	connected	ADJ
ejpam-6438	3	11	metric	metric	ADJ
ejpam-6438	3	12	dimension	dimension	NOUN
ejpam-6438	3	13	,	,	PUNCT
ejpam-6438	3	14	denoted	denote	VERB
ejpam-6438	3	15	cdim(g	cdim(g	NOUN
ejpam-6438	3	16	)	)	PUNCT
ejpam-6438	3	17	.	.	PUNCT
ejpam-6438	4	1	in	in	ADP
ejpam-6438	4	2	this	this	DET
ejpam-6438	4	3	paper	paper	NOUN
ejpam-6438	4	4	,	,	PUNCT
ejpam-6438	4	5	we	we	PRON
ejpam-6438	4	6	compute	compute	VERB
ejpam-6438	4	7	the	the	DET
ejpam-6438	4	8	metric	metric	ADJ
ejpam-6438	4	9	and	and	CCONJ
ejpam-6438	4	10	connected	connected	ADJ
ejpam-6438	4	11	metric	metric	ADJ
ejpam-6438	4	12	dimensions	dimension	NOUN
ejpam-6438	4	13	for	for	ADP
ejpam-6438	4	14	several	several	ADJ
ejpam-6438	4	15	classes	class	NOUN
ejpam-6438	4	16	of	of	ADP
ejpam-6438	4	17	corona	corona	NOUN
ejpam-6438	4	18	product	product	NOUN
ejpam-6438	4	19	graphs	graph	NOUN
ejpam-6438	4	20	and	and	CCONJ
ejpam-6438	4	21	propose	propose	VERB
ejpam-6438	4	22	an	an	DET
ejpam-6438	4	23	approximate	approximate	ADJ
ejpam-6438	4	24	algorithm	algorithm	NOUN
ejpam-6438	4	25	to	to	PART
ejpam-6438	4	26	determine	determine	VERB
ejpam-6438	4	27	the	the	DET
ejpam-6438	4	28	connected	connected	ADJ
ejpam-6438	4	29	metric	metric	ADJ
ejpam-6438	4	30	dimension	dimension	NOUN
ejpam-6438	4	31	of	of	ADP
ejpam-6438	4	32	arbitrary	arbitrary	ADJ
ejpam-6438	4	33	graphs	graph	NOUN
ejpam-6438	4	34	.	.	PUNCT
ejpam-6438	5	1	2020	2020	NUM
ejpam-6438	5	2	mathematics	mathematic	NOUN
ejpam-6438	5	3	subject	subject	NOUN
ejpam-6438	5	4	classifications	classification	NOUN
ejpam-6438	5	5	:	:	PUNCT
ejpam-6438	5	6	05c78	05c78	NUM
ejpam-6438	5	7	,	,	PUNCT
ejpam-6438	5	8	05c15	05c15	NOUN
ejpam-6438	5	9	key	key	ADJ
ejpam-6438	5	10	words	word	NOUN
ejpam-6438	5	11	and	and	CCONJ
ejpam-6438	5	12	phrases	phrase	NOUN
ejpam-6438	5	13	:	:	PUNCT
ejpam-6438	5	14	algebraic	algebraic	ADJ
ejpam-6438	5	15	graph	graph	NOUN
ejpam-6438	5	16	,	,	PUNCT
ejpam-6438	5	17	metric	metric	ADJ
ejpam-6438	5	18	basis	basis	NOUN
ejpam-6438	5	19	,	,	PUNCT
ejpam-6438	5	20	resolving	resolve	VERB
ejpam-6438	5	21	set	set	NOUN
ejpam-6438	5	22	,	,	PUNCT
ejpam-6438	5	23	metric	metric	ADJ
ejpam-6438	5	24	dimensions	dimension	NOUN
ejpam-6438	5	25	,	,	PUNCT
ejpam-6438	5	26	connected	connect	VERB
ejpam-6438	5	27	metric	metric	ADJ
ejpam-6438	5	28	dimensions	dimension	NOUN
ejpam-6438	5	29	,	,	PUNCT
ejpam-6438	5	30	algorithm	algorithm	NOUN
ejpam-6438	5	31	,	,	PUNCT
ejpam-6438	5	32	network	network	NOUN
ejpam-6438	5	33	security	security	NOUN
ejpam-6438	5	34	,	,	PUNCT
ejpam-6438	5	35	edge	edge	NOUN
ejpam-6438	5	36	computing	compute	VERB
ejpam-6438	5	37	1	1	NUM
ejpam-6438	5	38	.	.	PUNCT
ejpam-6438	6	1	introduction	introduction	NOUN
ejpam-6438	6	2	let	let	VERB
ejpam-6438	6	3	g	g	NOUN
ejpam-6438	6	4	be	be	AUX
ejpam-6438	6	5	a	a	DET
ejpam-6438	6	6	connected	connected	ADJ
ejpam-6438	6	7	graph	graph	NOUN
ejpam-6438	6	8	and	and	CCONJ
ejpam-6438	6	9	d	d	NOUN
ejpam-6438	6	10	(	(	PUNCT
ejpam-6438	6	11	x	x	NOUN
ejpam-6438	6	12	,	,	PUNCT
ejpam-6438	6	13	y	y	NOUN
ejpam-6438	6	14	)	)	PUNCT
ejpam-6438	6	15	be	be	VERB
ejpam-6438	6	16	the	the	DET
ejpam-6438	6	17	distance	distance	NOUN
ejpam-6438	6	18	between	between	ADP
ejpam-6438	6	19	the	the	DET
ejpam-6438	6	20	vertices	vertex	NOUN
ejpam-6438	6	21	x	x	PUNCT
ejpam-6438	6	22	and	and	CCONJ
ejpam-6438	6	23	y.	y.	PROPN
ejpam-6438	6	24	a	a	DET
ejpam-6438	6	25	subset	subset	NOUN
ejpam-6438	6	26	of	of	ADP
ejpam-6438	6	27	vertices	vertex	NOUN
ejpam-6438	6	28	w	w	NOUN
ejpam-6438	6	29	=	=	SYM
ejpam-6438	6	30	(	(	PUNCT
ejpam-6438	6	31	w1	w1	NOUN
ejpam-6438	6	32	,	,	PUNCT
ejpam-6438	6	33	.	.	PUNCT
ejpam-6438	6	34	.	.	PUNCT
ejpam-6438	7	1	.	.	PUNCT
ejpam-6438	8	1	,	,	PUNCT
ejpam-6438	8	2	wk	wk	X
ejpam-6438	8	3	)	)	PUNCT
ejpam-6438	8	4	is	be	AUX
ejpam-6438	8	5	called	call	VERB
ejpam-6438	8	6	a	a	DET
ejpam-6438	8	7	resolving	resolving	NOUN
ejpam-6438	8	8	set	set	VERB
ejpam-6438	8	9	for	for	ADP
ejpam-6438	8	10	g	g	PROPN
ejpam-6438	8	11	if	if	SCONJ
ejpam-6438	8	12	for	for	ADP
ejpam-6438	8	13	every	every	DET
ejpam-6438	8	14	two	two	NUM
ejpam-6438	8	15	distinct	distinct	ADJ
ejpam-6438	8	16	vertices	vertex	NOUN
ejpam-6438	8	17	x	x	X
ejpam-6438	8	18	,	,	PUNCT
ejpam-6438	8	19	y	y	PROPN
ejpam-6438	8	20	∈	∈	PROPN
ejpam-6438	8	21	v	v	ADP
ejpam-6438	8	22	(	(	PUNCT
ejpam-6438	8	23	g	g	NOUN
ejpam-6438	8	24	)	)	PUNCT
ejpam-6438	8	25	,	,	PUNCT
ejpam-6438	8	26	there	there	PRON
ejpam-6438	8	27	is	be	VERB
ejpam-6438	8	28	a	a	DET
ejpam-6438	8	29	vertex	vertex	NOUN
ejpam-6438	8	30	wi	wi	PROPN
ejpam-6438	8	31	∈	∈	PROPN
ejpam-6438	8	32	w	w	ADP
ejpam-6438	8	33	such	such	ADJ
ejpam-6438	8	34	that	that	DET
ejpam-6438	8	35	d(x	d(x	NOUN
ejpam-6438	8	36	,	,	PUNCT
ejpam-6438	9	1	[	[	X
ejpam-6438	9	2	wi	wi	PROPN
ejpam-6438	9	3	]	]	X
ejpam-6438	9	4	)	)	PUNCT
ejpam-6438	9	5	̸=	̸=	PROPN
ejpam-6438	9	6	d(y	d(y	PROPN
ejpam-6438	9	7	,	,	PUNCT
ejpam-6438	9	8	wi	wi	PROPN
ejpam-6438	9	9	,	,	PUNCT
ejpam-6438	9	10	)	)	PUNCT
ejpam-6438	9	11	.	.	PUNCT
ejpam-6438	10	1	the	the	DET
ejpam-6438	10	2	metric	metric	ADJ
ejpam-6438	10	3	dimension	dimension	NOUN
ejpam-6438	10	4	dim(g	dim(g	PROPN
ejpam-6438	10	5	)	)	PUNCT
ejpam-6438	10	6	of	of	ADP
ejpam-6438	10	7	g	g	PROPN
ejpam-6438	10	8	is	be	AUX
ejpam-6438	10	9	the	the	DET
ejpam-6438	10	10	minimum	minimum	ADJ
ejpam-6438	10	11	cardinality	cardinality	NOUN
ejpam-6438	10	12	of	of	ADP
ejpam-6438	10	13	a	a	DET
ejpam-6438	10	14	resolving	resolving	NOUN
ejpam-6438	10	15	set	set	VERB
ejpam-6438	10	16	for	for	ADP
ejpam-6438	10	17	g.	g.	PROPN
ejpam-6438	10	18	the	the	DET
ejpam-6438	10	19	concept	concept	NOUN
ejpam-6438	10	20	of	of	ADP
ejpam-6438	10	21	metric	metric	ADJ
ejpam-6438	10	22	dimension	dimension	NOUN
ejpam-6438	10	23	was	be	AUX
ejpam-6438	10	24	put	put	VERB
ejpam-6438	10	25	forward	forward	ADV
ejpam-6438	10	26	by	by	ADP
ejpam-6438	10	27	slater	slater	NOUN
ejpam-6438	11	1	[	[	X
ejpam-6438	11	2	1	1	NUM
ejpam-6438	11	3	]	]	PUNCT
ejpam-6438	11	4	,	,	PUNCT
ejpam-6438	11	5	where	where	SCONJ
ejpam-6438	11	6	it	it	PRON
ejpam-6438	11	7	was	be	AUX
ejpam-6438	11	8	expressed	express	VERB
ejpam-6438	11	9	as	as	ADP
ejpam-6438	11	10	locating	locate	VERB
ejpam-6438	11	11	sets	set	NOUN
ejpam-6438	11	12	,	,	PUNCT
ejpam-6438	11	13	and	and	CCONJ
ejpam-6438	11	14	later	later	ADV
ejpam-6438	11	15	by	by	ADP
ejpam-6438	11	16	harary	harary	NOUN
ejpam-6438	11	17	and	and	CCONJ
ejpam-6438	11	18	melter	melter	NOUN
ejpam-6438	11	19	[	[	X
ejpam-6438	11	20	2	2	NUM
ejpam-6438	11	21	]	]	PUNCT
ejpam-6438	11	22	called	call	VERB
ejpam-6438	11	23	it	it	PRON
ejpam-6438	11	24	as	as	ADP
ejpam-6438	11	25	a	a	DET
ejpam-6438	11	26	metric	metric	ADJ
ejpam-6438	11	27	dimension	dimension	NOUN
ejpam-6438	11	28	where	where	SCONJ
ejpam-6438	11	29	the	the	DET
ejpam-6438	11	30	associate	associate	ADJ
ejpam-6438	11	31	editor	editor	NOUN
ejpam-6438	11	32	coordinating	coordinate	VERB
ejpam-6438	11	33	the	the	DET
ejpam-6438	11	34	review	review	NOUN
ejpam-6438	11	35	of	of	ADP
ejpam-6438	11	36	this	this	DET
ejpam-6438	11	37	manuscript	manuscript	NOUN
ejpam-6438	11	38	and	and	CCONJ
ejpam-6438	11	39	approving	approve	VERB
ejpam-6438	11	40	it	it	PRON
ejpam-6438	11	41	for	for	ADP
ejpam-6438	11	42	publication	publication	NOUN
ejpam-6438	11	43	was	be	AUX
ejpam-6438	11	44	yilun	yilun	PROPN
ejpam-6438	11	45	shang	shang	PROPN
ejpam-6438	11	46	.	.	PUNCT
ejpam-6438	12	1	the	the	DET
ejpam-6438	12	2	metric	metric	ADJ
ejpam-6438	12	3	generators	generator	NOUN
ejpam-6438	12	4	were	be	AUX
ejpam-6438	12	5	termed	term	VERB
ejpam-6438	12	6	as	as	ADP
ejpam-6438	12	7	resolving	resolve	VERB
ejpam-6438	12	8	sets	set	NOUN
ejpam-6438	12	9	.	.	PUNCT
ejpam-6438	13	1	there	there	PRON
ejpam-6438	13	2	are	be	VERB
ejpam-6438	13	3	numerous	numerous	ADJ
ejpam-6438	13	4	metric	metric	ADJ
ejpam-6438	13	5	dimension	dimension	NOUN
ejpam-6438	13	6	applications	application	NOUN
ejpam-6438	13	7	,	,	PUNCT
ejpam-6438	13	8	such	such	ADJ
ejpam-6438	13	9	as	as	ADP
ejpam-6438	13	10	identifying	identify	VERB
ejpam-6438	13	11	an	an	DET
ejpam-6438	13	12	intruder	intruder	NOUN
ejpam-6438	13	13	in	in	ADP
ejpam-6438	13	14	a	a	DET
ejpam-6438	13	15	network	network	NOUN
ejpam-6438	13	16	,	,	PUNCT
ejpam-6438	13	17	robotics	robotic	NOUN
ejpam-6438	13	18	navigation	navigation	NOUN
ejpam-6438	13	19	,	,	PUNCT
ejpam-6438	13	20	chemistry	chemistry	NOUN
ejpam-6438	13	21	,	,	PUNCT
ejpam-6438	13	22	and	and	CCONJ
ejpam-6438	13	23	pattern	pattern	NOUN
ejpam-6438	13	24	recognition	recognition	NOUN
ejpam-6438	13	25	or	or	CCONJ
ejpam-6438	13	26	image	image	NOUN
ejpam-6438	13	27	processing	processing	NOUN
ejpam-6438	13	28	;	;	PUNCT
ejpam-6438	13	29	for	for	ADP
ejpam-6438	13	30	further	further	ADJ
ejpam-6438	13	31	studies	study	NOUN
ejpam-6438	13	32	related	relate	VERB
ejpam-6438	13	33	to	to	ADP
ejpam-6438	13	34	this	this	DET
ejpam-6438	13	35	invariant	invariant	ADJ
ejpam-6438	13	36	,	,	PUNCT
ejpam-6438	13	37	some	some	PRON
ejpam-6438	13	38	of	of	ADP
ejpam-6438	13	39	the	the	DET
ejpam-6438	13	40	references	reference	NOUN
ejpam-6438	13	41	are	be	AUX
ejpam-6438	13	42	,	,	PUNCT
ejpam-6438	13	43	see	see	VERB
ejpam-6438	13	44	,	,	PUNCT
ejpam-6438	13	45	for	for	ADP
ejpam-6438	13	46	instance	instance	NOUN
ejpam-6438	13	47	,	,	PUNCT
ejpam-6438	13	48	[	[	X
ejpam-6438	13	49	3–5	3–5	NOUN
ejpam-6438	13	50	]	]	PUNCT
ejpam-6438	13	51	.	.	PUNCT
ejpam-6438	14	1	some	some	DET
ejpam-6438	14	2	∗corresponding	∗corresponde	VERB
ejpam-6438	14	3	author	author	NOUN
ejpam-6438	14	4	.	.	PUNCT
ejpam-6438	15	1	doi	doi	NOUN
ejpam-6438	15	2	:	:	PUNCT
ejpam-6438	15	3	https://doi.org/10.29020/nybg.ejpam.v18i3.6438	https://doi.org/10.29020/nybg.ejpam.v18i3.6438	PRON
ejpam-6438	15	4	email	email	NOUN
ejpam-6438	15	5	addresses	address	NOUN
ejpam-6438	15	6	:	:	PUNCT
ejpam-6438	15	7	ashraf.hefnawy68@yahoo.com	ashraf.hefnawy68@yahoo.com	X
ejpam-6438	15	8	(	(	PUNCT
ejpam-6438	15	9	ashraf	ashraf	PROPN
ejpam-6438	15	10	elrokh	elrokh	VERB
ejpam-6438	15	11	)	)	PUNCT
ejpam-6438	15	12	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-6438	16	1	1	1	NUM
ejpam-6438	16	2	copyright	copyright	NOUN
ejpam-6438	16	3	:	:	PUNCT
ejpam-6438	16	4	©	©	PROPN
ejpam-6438	16	5	2025	2025	NUM
ejpam-6438	16	6	the	the	DET
ejpam-6438	16	7	author(s	author(s	NOUN
ejpam-6438	16	8	)	)	PUNCT
ejpam-6438	16	9	.	.	PUNCT
ejpam-6438	17	1	(	(	PUNCT
ejpam-6438	17	2	cc	cc	NOUN
ejpam-6438	17	3	by	by	ADP
ejpam-6438	17	4	-	-	PUNCT
ejpam-6438	17	5	nc	nc	PROPN
ejpam-6438	17	6	4.0	4.0	NUM
ejpam-6438	17	7	)	)	PUNCT
ejpam-6438	17	8	a.	a.	NOUN
ejpam-6438	17	9	elrokh	elrokh	NOUN
ejpam-6438	17	10	,	,	PUNCT
ejpam-6438	17	11	eman	eman	PROPN
ejpam-6438	17	12	s.	s.	PROPN
ejpam-6438	17	13	almotairi	almotairi	PROPN
ejpam-6438	17	14	,	,	PUNCT
ejpam-6438	17	15	h.	h.	PROPN
ejpam-6438	17	16	mostafa	mostafa	PROPN
ejpam-6438	17	17	/	/	SYM
ejpam-6438	17	18	eur	eur	PROPN
ejpam-6438	17	19	.	.	PUNCT
ejpam-6438	18	1	j.	j.	PROPN
ejpam-6438	18	2	pure	pure	PROPN
ejpam-6438	18	3	appl	appl	PROPN
ejpam-6438	18	4	.	.	PROPN
ejpam-6438	18	5	math	math	PROPN
ejpam-6438	18	6	,	,	PUNCT
ejpam-6438	18	7	18	18	NUM
ejpam-6438	18	8	(	(	PUNCT
ejpam-6438	18	9	3	3	NUM
ejpam-6438	18	10	)	)	PUNCT
ejpam-6438	18	11	(	(	PUNCT
ejpam-6438	18	12	2025	2025	NUM
ejpam-6438	18	13	)	)	PUNCT
ejpam-6438	18	14	,	,	PUNCT
ejpam-6438	18	15	6438	6438	NUM
ejpam-6438	18	16	2	2	NUM
ejpam-6438	18	17	of	of	ADP
ejpam-6438	18	18	18	18	NUM
ejpam-6438	18	19	of	of	ADP
ejpam-6438	18	20	the	the	DET
ejpam-6438	18	21	recent	recent	ADJ
ejpam-6438	18	22	studies	study	NOUN
ejpam-6438	18	23	on	on	ADP
ejpam-6438	18	24	the	the	DET
ejpam-6438	18	25	metric	metric	ADJ
ejpam-6438	18	26	dimension	dimension	NOUN
ejpam-6438	18	27	are	be	AUX
ejpam-6438	18	28	in	in	ADP
ejpam-6438	18	29	[	[	X
ejpam-6438	18	30	6–8	6–8	NOUN
ejpam-6438	18	31	]	]	X
ejpam-6438	18	32	.	.	PUNCT
ejpam-6438	19	1	the	the	DET
ejpam-6438	19	2	metric	metric	ADJ
ejpam-6438	19	3	dimension	dimension	NOUN
ejpam-6438	19	4	dim(g	dim(g	PROPN
ejpam-6438	19	5	)	)	PUNCT
ejpam-6438	19	6	of	of	ADP
ejpam-6438	19	7	g	g	PROPN
ejpam-6438	19	8	is	be	AUX
ejpam-6438	19	9	the	the	DET
ejpam-6438	19	10	minimum	minimum	ADJ
ejpam-6438	19	11	cardinality	cardinality	NOUN
ejpam-6438	19	12	of	of	ADP
ejpam-6438	19	13	a	a	DET
ejpam-6438	19	14	resolving	resolving	NOUN
ejpam-6438	19	15	set	set	VERB
ejpam-6438	19	16	for	for	ADP
ejpam-6438	19	17	g.	g.	PROPN
ejpam-6438	19	18	slater	slater	PROPN
ejpam-6438	20	1	[	[	X
ejpam-6438	20	2	9	9	NUM
ejpam-6438	20	3	,	,	PUNCT
ejpam-6438	20	4	10	10	NUM
ejpam-6438	20	5	]	]	PUNCT
ejpam-6438	20	6	introduced	introduce	VERB
ejpam-6438	20	7	the	the	DET
ejpam-6438	20	8	concept	concept	NOUN
ejpam-6438	20	9	of	of	ADP
ejpam-6438	20	10	a	a	DET
ejpam-6438	20	11	resolving	resolving	NOUN
ejpam-6438	20	12	set	set	VERB
ejpam-6438	20	13	for	for	ADP
ejpam-6438	20	14	a	a	DET
ejpam-6438	20	15	connected	connected	ADJ
ejpam-6438	20	16	graph	graph	NOUN
ejpam-6438	20	17	under	under	ADP
ejpam-6438	20	18	the	the	DET
ejpam-6438	20	19	term	term	NOUN
ejpam-6438	20	20	locating	locate	VERB
ejpam-6438	20	21	set	set	NOUN
ejpam-6438	20	22	.	.	PUNCT
ejpam-6438	21	1	he	he	PRON
ejpam-6438	21	2	referred	refer	VERB
ejpam-6438	21	3	to	to	ADP
ejpam-6438	21	4	a	a	DET
ejpam-6438	21	5	minimum	minimum	ADJ
ejpam-6438	21	6	resolving	resolving	NOUN
ejpam-6438	21	7	set	set	VERB
ejpam-6438	21	8	as	as	ADP
ejpam-6438	21	9	a	a	DET
ejpam-6438	21	10	reference	reference	NOUN
ejpam-6438	21	11	set	set	NOUN
ejpam-6438	21	12	,	,	PUNCT
ejpam-6438	21	13	and	and	CCONJ
ejpam-6438	21	14	the	the	DET
ejpam-6438	21	15	cardinality	cardinality	NOUN
ejpam-6438	21	16	of	of	ADP
ejpam-6438	21	17	a	a	DET
ejpam-6438	21	18	minimum	minimum	ADJ
ejpam-6438	21	19	resolving	resolving	NOUN
ejpam-6438	21	20	set	set	VERB
ejpam-6438	21	21	as	as	ADP
ejpam-6438	21	22	the	the	DET
ejpam-6438	21	23	location	location	NOUN
ejpam-6438	21	24	number	number	NOUN
ejpam-6438	21	25	of	of	ADP
ejpam-6438	21	26	a	a	DET
ejpam-6438	21	27	graph	graph	NOUN
ejpam-6438	21	28	.	.	PUNCT
ejpam-6438	22	1	independently	independently	ADV
ejpam-6438	22	2	,	,	PUNCT
ejpam-6438	22	3	harary	harary	NOUN
ejpam-6438	22	4	and	and	CCONJ
ejpam-6438	22	5	melter	melter	NOUN
ejpam-6438	22	6	[	[	X
ejpam-6438	22	7	11	11	NUM
ejpam-6438	22	8	]	]	PUNCT
ejpam-6438	22	9	studied	study	VERB
ejpam-6438	22	10	these	these	DET
ejpam-6438	22	11	concepts	concept	NOUN
ejpam-6438	22	12	under	under	ADP
ejpam-6438	22	13	the	the	DET
ejpam-6438	22	14	term	term	NOUN
ejpam-6438	22	15	metric	metric	ADJ
ejpam-6438	22	16	dimension	dimension	NOUN
ejpam-6438	22	17	.	.	PUNCT
ejpam-6438	23	1	a	a	DET
ejpam-6438	23	2	resolving	resolving	NOUN
ejpam-6438	23	3	set	set	NOUN
ejpam-6438	23	4	s	s	PRON
ejpam-6438	23	5	of	of	ADP
ejpam-6438	23	6	g	g	PROPN
ejpam-6438	23	7	is	be	AUX
ejpam-6438	23	8	called	call	VERB
ejpam-6438	23	9	a	a	DET
ejpam-6438	23	10	connected	connected	ADJ
ejpam-6438	23	11	resolving	resolving	NOUN
ejpam-6438	23	12	set	set	NOUN
ejpam-6438	23	13	of	of	ADP
ejpam-6438	23	14	g	g	PROPN
ejpam-6438	23	15	if	if	SCONJ
ejpam-6438	23	16	g[s	g[	NOUN
ejpam-6438	23	17	]	]	PUNCT
ejpam-6438	23	18	is	be	AUX
ejpam-6438	23	19	connected	connect	VERB
ejpam-6438	23	20	,	,	PUNCT
ejpam-6438	23	21	and	and	CCONJ
ejpam-6438	23	22	the	the	DET
ejpam-6438	23	23	connected	connected	ADJ
ejpam-6438	23	24	metric	metric	ADJ
ejpam-6438	23	25	dimension	dimension	NOUN
ejpam-6438	23	26	of	of	ADP
ejpam-6438	23	27	g	g	NOUN
ejpam-6438	23	28	,	,	PUNCT
ejpam-6438	23	29	denoted	denote	VERB
ejpam-6438	23	30	by	by	ADP
ejpam-6438	23	31	cdim(g	cdim(g	NOUN
ejpam-6438	23	32	)	)	PUNCT
ejpam-6438	23	33	,	,	PUNCT
ejpam-6438	23	34	is	be	AUX
ejpam-6438	23	35	the	the	DET
ejpam-6438	23	36	minimum	minimum	ADJ
ejpam-6438	23	37	cardinality	cardinality	NOUN
ejpam-6438	23	38	of	of	ADP
ejpam-6438	23	39	s	s	NOUN
ejpam-6438	23	40	over	over	ADP
ejpam-6438	23	41	all	all	DET
ejpam-6438	23	42	connected	connected	ADJ
ejpam-6438	23	43	resolving	resolve	VERB
ejpam-6438	23	44	sets	set	NOUN
ejpam-6438	23	45	of	of	ADP
ejpam-6438	23	46	g.	g.	NOUN
ejpam-6438	23	47	for	for	ADP
ejpam-6438	23	48	v	v	NOUN
ejpam-6438	23	49	∈	∈	PROPN
ejpam-6438	23	50	v	v	NOUN
ejpam-6438	23	51	(	(	PUNCT
ejpam-6438	23	52	g	g	NOUN
ejpam-6438	23	53	)	)	PUNCT
ejpam-6438	23	54	,	,	PUNCT
ejpam-6438	23	55	we	we	PRON
ejpam-6438	23	56	define	define	VERB
ejpam-6438	23	57	the	the	DET
ejpam-6438	23	58	connected	connected	ADJ
ejpam-6438	23	59	metric	metric	ADJ
ejpam-6438	23	60	dimension	dimension	NOUN
ejpam-6438	23	61	at	at	ADP
ejpam-6438	23	62	v	v	NUM
ejpam-6438	23	63	of	of	ADP
ejpam-6438	23	64	g	g	NOUN
ejpam-6438	23	65	,	,	PUNCT
ejpam-6438	23	66	denoted	denote	VERB
ejpam-6438	23	67	by	by	ADP
ejpam-6438	23	68	cdim(v	cdim(v	NOUN
ejpam-6438	23	69	)	)	PUNCT
ejpam-6438	23	70	,	,	PUNCT
ejpam-6438	23	71	to	to	PART
ejpam-6438	23	72	be	be	AUX
ejpam-6438	23	73	the	the	DET
ejpam-6438	23	74	minimum	minimum	ADJ
ejpam-6438	23	75	cardinality	cardinality	NOUN
ejpam-6438	23	76	of	of	ADP
ejpam-6438	23	77	a	a	DET
ejpam-6438	23	78	resolving	resolving	NOUN
ejpam-6438	23	79	set	set	NOUN
ejpam-6438	23	80	of	of	ADP
ejpam-6438	23	81	g	g	NOUN
ejpam-6438	23	82	which	which	PRON
ejpam-6438	23	83	contains	contain	VERB
ejpam-6438	23	84	v	v	ADP
ejpam-6438	23	85	and	and	CCONJ
ejpam-6438	23	86	induces	induce	VERB
ejpam-6438	23	87	a	a	DET
ejpam-6438	23	88	connected	connected	ADJ
ejpam-6438	23	89	sub	sub	NOUN
ejpam-6438	23	90	graph	graph	NOUN
ejpam-6438	23	91	of	of	ADP
ejpam-6438	23	92	g	g	NOUN
ejpam-6438	23	93	;	;	PUNCT
ejpam-6438	23	94	then	then	ADV
ejpam-6438	23	95	cdim(g	cdim(g	ADJ
ejpam-6438	23	96	)	)	PUNCT
ejpam-6438	23	97	=	=	PUNCT
ejpam-6438	24	1	minv	minv	NOUN
ejpam-6438	24	2	∈	∈	PROPN
ejpam-6438	24	3	v	v	ADP
ejpam-6438	24	4	(	(	PUNCT
ejpam-6438	24	5	g){cdimg(v	g){cdimg(v	NOUN
ejpam-6438	24	6	)	)	PUNCT
ejpam-6438	24	7	}	}	PUNCT
ejpam-6438	24	8	for	for	ADP
ejpam-6438	24	9	any	any	DET
ejpam-6438	24	10	vertex	vertex	NOUN
ejpam-6438	24	11	v	v	ADP
ejpam-6438	24	12	∈	∈	NOUN
ejpam-6438	24	13	v	v	NOUN
ejpam-6438	24	14	(	(	PUNCT
ejpam-6438	24	15	g	g	NOUN
ejpam-6438	24	16	)	)	PUNCT
ejpam-6438	24	17	.	.	PUNCT
ejpam-6438	25	1	moreover	moreover	ADV
ejpam-6438	25	2	,	,	PUNCT
ejpam-6438	25	3	connected	connected	ADJ
ejpam-6438	25	4	metric	metric	ADJ
ejpam-6438	25	5	dimension	dimension	NOUN
ejpam-6438	25	6	theory	theory	NOUN
ejpam-6438	25	7	is	be	AUX
ejpam-6438	25	8	used	use	VERB
ejpam-6438	25	9	by	by	ADP
ejpam-6438	25	10	wireless	wireless	ADJ
ejpam-6438	25	11	communication	communication	NOUN
ejpam-6438	25	12	networks	network	NOUN
ejpam-6438	25	13	,	,	PUNCT
ejpam-6438	25	14	electrical	electrical	ADJ
ejpam-6438	25	15	networks	network	NOUN
ejpam-6438	25	16	,	,	PUNCT
ejpam-6438	25	17	chemical	chemical	NOUN
ejpam-6438	25	18	structures	structure	NOUN
ejpam-6438	25	19	,	,	PUNCT
ejpam-6438	25	20	and	and	CCONJ
ejpam-6438	25	21	commercial	commercial	ADJ
ejpam-6438	25	22	networks	network	NOUN
ejpam-6438	25	23	[	[	X
ejpam-6438	25	24	12–28	12–28	NUM
ejpam-6438	25	25	]	]	PUNCT
ejpam-6438	25	26	.	.	PUNCT
ejpam-6438	26	1	this	this	DET
ejpam-6438	26	2	paper	paper	NOUN
ejpam-6438	26	3	is	be	AUX
ejpam-6438	26	4	organized	organize	VERB
ejpam-6438	26	5	as	as	SCONJ
ejpam-6438	26	6	follows	follow	VERB
ejpam-6438	26	7	:	:	PUNCT
ejpam-6438	26	8	the	the	DET
ejpam-6438	26	9	metric	metric	ADJ
ejpam-6438	26	10	and	and	CCONJ
ejpam-6438	26	11	connected	connected	ADJ
ejpam-6438	26	12	metric	metric	ADJ
ejpam-6438	26	13	dimension	dimension	NOUN
ejpam-6438	26	14	introduced	introduce	VERB
ejpam-6438	26	15	in	in	ADP
ejpam-6438	26	16	sect	sect	NOUN
ejpam-6438	26	17	.	.	PUNCT
ejpam-6438	27	1	2	2	NUM
ejpam-6438	27	2	the	the	DET
ejpam-6438	27	3	theorems	theorem	NOUN
ejpam-6438	27	4	that	that	PRON
ejpam-6438	27	5	determine	determine	VERB
ejpam-6438	27	6	the	the	DET
ejpam-6438	27	7	metric	metric	ADJ
ejpam-6438	27	8	and	and	CCONJ
ejpam-6438	27	9	connected	connected	ADJ
ejpam-6438	27	10	metric	metric	ADJ
ejpam-6438	27	11	dimension	dimension	NOUN
ejpam-6438	27	12	of	of	ADP
ejpam-6438	27	13	some	some	DET
ejpam-6438	27	14	graphs	graph	NOUN
ejpam-6438	27	15	along	along	ADP
ejpam-6438	27	16	with	with	ADP
ejpam-6438	27	17	examples	example	NOUN
ejpam-6438	27	18	in	in	ADP
ejpam-6438	27	19	section	section	NOUN
ejpam-6438	27	20	3	3	NUM
ejpam-6438	27	21	.	.	PUNCT
ejpam-6438	27	22	in	in	ADP
ejpam-6438	27	23	sect	sect	NOUN
ejpam-6438	27	24	.	.	PUNCT
ejpam-6438	28	1	4	4	NUM
ejpam-6438	28	2	an	an	DET
ejpam-6438	28	3	approximate	approximate	ADJ
ejpam-6438	28	4	algorithm	algorithm	NOUN
ejpam-6438	28	5	which	which	PRON
ejpam-6438	28	6	finds	find	VERB
ejpam-6438	28	7	the	the	DET
ejpam-6438	28	8	minimum	minimum	ADJ
ejpam-6438	28	9	connected	connect	VERB
ejpam-6438	28	10	metric	metric	ADJ
ejpam-6438	28	11	dimension	dimension	NOUN
ejpam-6438	28	12	finally	finally	ADV
ejpam-6438	28	13	,	,	PUNCT
ejpam-6438	28	14	conclusions	conclusion	NOUN
ejpam-6438	28	15	are	be	AUX
ejpam-6438	28	16	drawn	draw	VERB
ejpam-6438	28	17	in	in	ADP
ejpam-6438	28	18	sect	sect	NOUN
ejpam-6438	28	19	.	.	PUNCT
ejpam-6438	29	1	5	5	X
ejpam-6438	29	2	.	.	X
ejpam-6438	29	3	definition	definition	NOUN
ejpam-6438	29	4	1	1	NUM
ejpam-6438	30	1	[	[	X
ejpam-6438	30	2	21–23	21–23	NUM
ejpam-6438	30	3	,	,	PUNCT
ejpam-6438	30	4	29	29	NUM
ejpam-6438	30	5	]	]	PUNCT
ejpam-6438	30	6	:	:	PUNCT
ejpam-6438	30	7	the	the	DET
ejpam-6438	30	8	corona	corona	NOUN
ejpam-6438	30	9	g1	g1	PROPN
ejpam-6438	30	10	⊙	⊙	PROPN
ejpam-6438	30	11	g2	g2	PROPN
ejpam-6438	30	12	of	of	ADP
ejpam-6438	30	13	two	two	NUM
ejpam-6438	30	14	graphs	graph	NOUN
ejpam-6438	30	15	g1	g1	PROPN
ejpam-6438	30	16	(	(	PUNCT
ejpam-6438	30	17	with	with	ADP
ejpam-6438	30	18	n1	n1	ADJ
ejpam-6438	30	19	vertices	vertex	NOUN
ejpam-6438	30	20	and	and	CCONJ
ejpam-6438	30	21	m1	m1	PROPN
ejpam-6438	30	22	edges)and	edges)and	PROPN
ejpam-6438	30	23	g2	g2	PROPN
ejpam-6438	30	24	(	(	PUNCT
ejpam-6438	30	25	with	with	ADP
ejpam-6438	30	26	n2	n2	ADJ
ejpam-6438	30	27	vertices	vertex	NOUN
ejpam-6438	30	28	and	and	CCONJ
ejpam-6438	30	29	m2	m2	PROPN
ejpam-6438	30	30	edges	edge	NOUN
ejpam-6438	30	31	)	)	PUNCT
ejpam-6438	30	32	is	be	AUX
ejpam-6438	30	33	defined	define	VERB
ejpam-6438	30	34	as	as	ADP
ejpam-6438	30	35	the	the	DET
ejpam-6438	30	36	graph	graph	NOUN
ejpam-6438	30	37	obtained	obtain	VERB
ejpam-6438	30	38	by	by	ADP
ejpam-6438	30	39	taking	take	VERB
ejpam-6438	30	40	one	one	NUM
ejpam-6438	30	41	copy	copy	NOUN
ejpam-6438	30	42	of	of	ADP
ejpam-6438	30	43	g1	g1	NOUN
ejpam-6438	30	44	and	and	CCONJ
ejpam-6438	30	45	n1	n1	ADJ
ejpam-6438	30	46	copies	copy	NOUN
ejpam-6438	30	47	of	of	ADP
ejpam-6438	30	48	g2	g2	PROPN
ejpam-6438	30	49	,	,	PUNCT
ejpam-6438	30	50	and	and	CCONJ
ejpam-6438	30	51	then	then	ADV
ejpam-6438	30	52	joining	join	VERB
ejpam-6438	30	53	the	the	DET
ejpam-6438	30	54	ithvertex	ithvertex	NOUN
ejpam-6438	30	55	of	of	ADP
ejpam-6438	30	56	g1with	g1with	ADP
ejpam-6438	30	57	an	an	DET
ejpam-6438	30	58	edge	edge	NOUN
ejpam-6438	30	59	to	to	ADP
ejpam-6438	30	60	every	every	DET
ejpam-6438	30	61	vertex	vertex	NOUN
ejpam-6438	30	62	in	in	ADP
ejpam-6438	30	63	the	the	DET
ejpam-6438	30	64	ith	ith	PROPN
ejpam-6438	30	65	copy	copy	NOUN
ejpam-6438	30	66	of	of	ADP
ejpam-6438	30	67	g2	g2	PROPN
ejpam-6438	30	68	.	.	PUNCT
ejpam-6438	31	1	it	it	PRON
ejpam-6438	31	2	follows	follow	VERB
ejpam-6438	31	3	from	from	ADP
ejpam-6438	31	4	the	the	DET
ejpam-6438	31	5	definition	definition	NOUN
ejpam-6438	31	6	of	of	ADP
ejpam-6438	31	7	the	the	DET
ejpam-6438	31	8	corona	corona	NOUN
ejpam-6438	31	9	that	that	PRON
ejpam-6438	31	10	g1	g1	PROPN
ejpam-6438	31	11	⊙	⊙	PROPN
ejpam-6438	31	12	g2	g2	PROPN
ejpam-6438	31	13	has	have	VERB
ejpam-6438	31	14	n1	n1	PROPN
ejpam-6438	31	15	+	+	CCONJ
ejpam-6438	31	16	n1n2	n1n2	NUM
ejpam-6438	31	17	vertices	vertex	NOUN
ejpam-6438	31	18	and	and	CCONJ
ejpam-6438	31	19	m1n1m2	m1n1m2	PROPN
ejpam-6438	31	20	+	+	CCONJ
ejpam-6438	31	21	n1n2	n1n2	NUM
ejpam-6438	31	22	edges	edge	NOUN
ejpam-6438	31	23	.	.	PUNCT
ejpam-6438	32	1	as	as	SCONJ
ejpam-6438	32	2	show	show	NOUN
ejpam-6438	32	3	in	in	ADP
ejpam-6438	32	4	figure	figure	NOUN
ejpam-6438	32	5	1	1	NUM
ejpam-6438	32	6	.	.	PUNCT
ejpam-6438	32	7	figure	figure	NOUN
ejpam-6438	32	8	1	1	NUM
ejpam-6438	32	9	.	.	PUNCT
ejpam-6438	33	1	the	the	DET
ejpam-6438	33	2	corona	corona	NOUN
ejpam-6438	33	3	product	product	NOUN
ejpam-6438	33	4	between	between	ADP
ejpam-6438	33	5	two	two	NUM
ejpam-6438	33	6	graphs	graph	NOUN
ejpam-6438	33	7	g1	g1	NOUN
ejpam-6438	33	8	and	and	CCONJ
ejpam-6438	33	9	g2	g2	PROPN
ejpam-6438	33	10	.	.	PUNCT
ejpam-6438	34	1	definition	definition	NOUN
ejpam-6438	34	2	2	2	NUM
ejpam-6438	35	1	[	[	X
ejpam-6438	35	2	12	12	NUM
ejpam-6438	35	3	]	]	X
ejpam-6438	35	4	:	:	PUNCT
ejpam-6438	35	5	for	for	ADP
ejpam-6438	35	6	a	a	DET
ejpam-6438	35	7	connected	connected	ADJ
ejpam-6438	35	8	graph	graph	NOUN
ejpam-6438	35	9	g	g	PROPN
ejpam-6438	35	10	=	=	PUNCT
ejpam-6438	35	11	(	(	PUNCT
ejpam-6438	35	12	v	v	NOUN
ejpam-6438	35	13	,	,	PUNCT
ejpam-6438	35	14	e	e	NOUN
ejpam-6438	35	15	)	)	PUNCT
ejpam-6438	35	16	,	,	PUNCT
ejpam-6438	35	17	a	a	DET
ejpam-6438	35	18	set	set	NOUN
ejpam-6438	35	19	of	of	ADP
ejpam-6438	35	20	vertices	vertex	NOUN
ejpam-6438	35	21	b	b	PROPN
ejpam-6438	35	22	⊆	⊆	NUM
ejpam-6438	35	23	v	v	NOUN
ejpam-6438	35	24	(	(	PUNCT
ejpam-6438	35	25	g	g	NOUN
ejpam-6438	35	26	)	)	PUNCT
ejpam-6438	35	27	resolves	resolve	VERB
ejpam-6438	35	28	g	g	PROPN
ejpam-6438	35	29	if	if	SCONJ
ejpam-6438	35	30	every	every	DET
ejpam-6438	35	31	vertex	vertex	NOUN
ejpam-6438	35	32	of	of	ADP
ejpam-6438	35	33	g	g	PROPN
ejpam-6438	35	34	is	be	AUX
ejpam-6438	35	35	uniquely	uniquely	ADV
ejpam-6438	35	36	determined	determine	VERB
ejpam-6438	35	37	by	by	ADP
ejpam-6438	35	38	its	its	PRON
ejpam-6438	35	39	vector	vector	NOUN
ejpam-6438	35	40	of	of	ADP
ejpam-6438	35	41	distances	distance	NOUN
ejpam-6438	35	42	to	to	ADP
ejpam-6438	35	43	the	the	DET
ejpam-6438	35	44	vertices	vertex	NOUN
ejpam-6438	35	45	in	in	ADP
ejpam-6438	35	46	b.	b.	PROPN
ejpam-6438	35	47	mathematically	mathematically	ADV
ejpam-6438	35	48	:	:	PUNCT
ejpam-6438	35	49	r(v|	r(v|	DET
ejpam-6438	35	50	b	b	X
ejpam-6438	35	51	)	)	PUNCT
ejpam-6438	36	1	=	=	SYM
ejpam-6438	36	2	(	(	PUNCT
ejpam-6438	36	3	d(v	d(v	PROPN
ejpam-6438	36	4	,	,	PUNCT
ejpam-6438	36	5	x1	x1	PROPN
ejpam-6438	36	6	)	)	PUNCT
ejpam-6438	36	7	,	,	PUNCT
ejpam-6438	36	8	d(v	d(v	PROPN
ejpam-6438	36	9	,	,	PUNCT
ejpam-6438	36	10	x2	x2	PROPN
ejpam-6438	36	11	)	)	PUNCT
ejpam-6438	36	12	,	,	PUNCT
ejpam-6438	36	13	....	....	PUNCT
ejpam-6438	36	14	,	,	PUNCT
ejpam-6438	36	15	d(v	d(v	PROPN
ejpam-6438	36	16	,	,	PUNCT
ejpam-6438	36	17	xk	xk	NOUN
ejpam-6438	36	18	)	)	PUNCT
ejpam-6438	36	19	)	)	PUNCT
ejpam-6438	36	20	is	be	AUX
ejpam-6438	36	21	unique	unique	ADJ
ejpam-6438	36	22	for	for	ADP
ejpam-6438	36	23	every	every	DET
ejpam-6438	36	24	v	v	NUM
ejpam-6438	36	25	∈	∈	NOUN
ejpam-6438	36	26	v	v	NOUN
ejpam-6438	36	27	(	(	PUNCT
ejpam-6438	36	28	g	g	NOUN
ejpam-6438	36	29	)	)	PUNCT
ejpam-6438	36	30	.	.	PUNCT
ejpam-6438	37	1	definition	definition	NOUN
ejpam-6438	37	2	3	3	NUM
ejpam-6438	37	3	(	(	PUNCT
ejpam-6438	37	4	metric	metric	ADJ
ejpam-6438	37	5	basis	basis	NOUN
ejpam-6438	37	6	):	):	PUNCT
ejpam-6438	37	7	the	the	DET
ejpam-6438	37	8	minimum	minimum	NOUN
ejpam-6438	37	9	resolving	resolving	NOUN
ejpam-6438	37	10	set	set	NOUN
ejpam-6438	37	11	is	be	AUX
ejpam-6438	37	12	called	call	VERB
ejpam-6438	37	13	the	the	DET
ejpam-6438	37	14	metric	metric	ADJ
ejpam-6438	37	15	basis	basis	NOUN
ejpam-6438	37	16	.	.	PUNCT
ejpam-6438	38	1	definition	definition	NOUN
ejpam-6438	38	2	4	4	NUM
ejpam-6438	38	3	(	(	PUNCT
ejpam-6438	38	4	metric	metric	ADJ
ejpam-6438	38	5	dimension	dimension	NOUN
ejpam-6438	38	6	)	)	PUNCT
ejpam-6438	39	1	[	[	X
ejpam-6438	39	2	13	13	NUM
ejpam-6438	39	3	]	]	PUNCT
ejpam-6438	39	4	:	:	PUNCT
ejpam-6438	39	5	the	the	DET
ejpam-6438	39	6	cardinality	cardinality	NOUN
ejpam-6438	39	7	of	of	ADP
ejpam-6438	39	8	the	the	DET
ejpam-6438	39	9	basis	basis	NOUN
ejpam-6438	39	10	is	be	AUX
ejpam-6438	39	11	called	call	VERB
ejpam-6438	39	12	the	the	DET
ejpam-6438	39	13	metric	metric	ADJ
ejpam-6438	39	14	dimension	dimension	NOUN
ejpam-6438	39	15	of	of	ADP
ejpam-6438	39	16	g	g	PROPN
ejpam-6438	39	17	denoted	denote	VERB
ejpam-6438	39	18	by	by	ADP
ejpam-6438	39	19	dim(g	dim(g	PROPN
ejpam-6438	39	20	)	)	PUNCT
ejpam-6438	39	21	.	.	PUNCT
ejpam-6438	40	1	as	as	SCONJ
ejpam-6438	40	2	show	show	NOUN
ejpam-6438	40	3	in	in	ADP
ejpam-6438	40	4	figures	figure	NOUN
ejpam-6438	40	5	2	2	NUM
ejpam-6438	40	6	,	,	PUNCT
ejpam-6438	40	7	3	3	NUM
ejpam-6438	40	8	.	.	PUNCT
ejpam-6438	40	9	a.	a.	NOUN
ejpam-6438	40	10	elrokh	elrokh	PROPN
ejpam-6438	40	11	,	,	PUNCT
ejpam-6438	40	12	eman	eman	PROPN
ejpam-6438	40	13	s.	s.	PROPN
ejpam-6438	40	14	almotairi	almotairi	PROPN
ejpam-6438	40	15	,	,	PUNCT
ejpam-6438	40	16	h.	h.	PROPN
ejpam-6438	40	17	mostafa	mostafa	PROPN
ejpam-6438	40	18	/	/	SYM
ejpam-6438	40	19	eur	eur	PROPN
ejpam-6438	40	20	.	.	PUNCT
ejpam-6438	41	1	j.	j.	PROPN
ejpam-6438	41	2	pure	pure	PROPN
ejpam-6438	41	3	appl	appl	PROPN
ejpam-6438	41	4	.	.	PROPN
ejpam-6438	41	5	math	math	PROPN
ejpam-6438	41	6	,	,	PUNCT
ejpam-6438	41	7	18	18	NUM
ejpam-6438	41	8	(	(	PUNCT
ejpam-6438	41	9	3	3	NUM
ejpam-6438	41	10	)	)	PUNCT
ejpam-6438	41	11	(	(	PUNCT
ejpam-6438	41	12	2025	2025	NUM
ejpam-6438	41	13	)	)	PUNCT
ejpam-6438	41	14	,	,	PUNCT
ejpam-6438	41	15	6438	6438	NUM
ejpam-6438	41	16	3	3	NUM
ejpam-6438	41	17	of	of	ADP
ejpam-6438	41	18	18	18	NUM
ejpam-6438	41	19	figure	figure	NOUN
ejpam-6438	41	20	2	2	NUM
ejpam-6438	41	21	.	.	PUNCT
ejpam-6438	41	22	metric	metric	ADJ
ejpam-6438	41	23	dimension	dimension	NOUN
ejpam-6438	41	24	of	of	ADP
ejpam-6438	41	25	p2	p2	PROPN
ejpam-6438	41	26	⊙	⊙	PROPN
ejpam-6438	41	27	c5	c5	PROPN
ejpam-6438	41	28	.	.	PUNCT
ejpam-6438	42	1	figure	figure	VERB
ejpam-6438	42	2	3	3	NUM
ejpam-6438	42	3	.	.	PUNCT
ejpam-6438	43	1	metric	metric	ADJ
ejpam-6438	43	2	dimension	dimension	NOUN
ejpam-6438	43	3	of	of	ADP
ejpam-6438	43	4	c4	c4	PROPN
ejpam-6438	43	5	⊙	⊙	PROPN
ejpam-6438	43	6	c5	c5	PROPN
ejpam-6438	43	7	.	.	PUNCT
ejpam-6438	44	1	definition	definition	NOUN
ejpam-6438	44	2	5	5	NUM
ejpam-6438	44	3	[	[	X
ejpam-6438	44	4	11	11	NUM
ejpam-6438	44	5	]	]	X
ejpam-6438	44	6	:	:	PUNCT
ejpam-6438	44	7	a	a	DET
ejpam-6438	44	8	metric	metric	ADJ
ejpam-6438	44	9	basis	basis	NOUN
ejpam-6438	44	10	b	b	NOUN
ejpam-6438	44	11	of	of	ADP
ejpam-6438	44	12	g	g	PROPN
ejpam-6438	44	13	is	be	AUX
ejpam-6438	44	14	connected	connect	VERB
ejpam-6438	44	15	if	if	SCONJ
ejpam-6438	44	16	the	the	DET
ejpam-6438	44	17	sub	sub	NOUN
ejpam-6438	44	18	graph	graph	NOUN
ejpam-6438	44	19	induced	induce	VERB
ejpam-6438	44	20	by	by	ADP
ejpam-6438	44	21	b	b	PROPN
ejpam-6438	44	22	is	be	AUX
ejpam-6438	44	23	a	a	DET
ejpam-6438	44	24	nontrivial	nontrivial	ADJ
ejpam-6438	44	25	connected	connect	VERB
ejpam-6438	44	26	sub	sub	NOUN
ejpam-6438	44	27	graph	graph	NOUN
ejpam-6438	44	28	of	of	ADP
ejpam-6438	44	29	g.	g.	PROPN
ejpam-6438	44	30	the	the	DET
ejpam-6438	44	31	cardinality	cardinality	NOUN
ejpam-6438	44	32	number	number	NOUN
ejpam-6438	44	33	of	of	ADP
ejpam-6438	44	34	the	the	DET
ejpam-6438	44	35	connected	connect	VERB
ejpam-6438	44	36	metric	metric	ADJ
ejpam-6438	44	37	basis	basis	NOUN
ejpam-6438	44	38	is	be	AUX
ejpam-6438	44	39	the	the	DET
ejpam-6438	44	40	connected	connected	ADJ
ejpam-6438	44	41	metric	metric	ADJ
ejpam-6438	44	42	dimension	dimension	NOUN
ejpam-6438	44	43	of	of	ADP
ejpam-6438	44	44	g	g	NOUN
ejpam-6438	44	45	and	and	CCONJ
ejpam-6438	44	46	is	be	AUX
ejpam-6438	44	47	denoted	denote	VERB
ejpam-6438	44	48	cdim(g	cdim(g	NOUN
ejpam-6438	44	49	)	)	PUNCT
ejpam-6438	44	50	.	.	PUNCT
ejpam-6438	45	1	as	as	SCONJ
ejpam-6438	45	2	show	show	NOUN
ejpam-6438	45	3	in	in	ADP
ejpam-6438	45	4	figure	figure	NOUN
ejpam-6438	45	5	4	4	NUM
ejpam-6438	45	6	.	.	PUNCT
ejpam-6438	45	7	figure	figure	VERB
ejpam-6438	45	8	4	4	NUM
ejpam-6438	45	9	.	.	PUNCT
ejpam-6438	45	10	connected	connect	VERB
ejpam-6438	45	11	metric	metric	ADJ
ejpam-6438	45	12	dimension	dimension	NOUN
ejpam-6438	45	13	of	of	ADP
ejpam-6438	45	14	c4	c4	PROPN
ejpam-6438	45	15	⊙	⊙	PROPN
ejpam-6438	45	16	c5	c5	PROPN
ejpam-6438	45	17	.	.	PUNCT
ejpam-6438	46	1	the	the	DET
ejpam-6438	46	2	remaining	remain	VERB
ejpam-6438	46	3	of	of	ADP
ejpam-6438	46	4	this	this	DET
ejpam-6438	46	5	paper	paper	NOUN
ejpam-6438	46	6	is	be	AUX
ejpam-6438	46	7	organized	organize	VERB
ejpam-6438	46	8	as	as	SCONJ
ejpam-6438	46	9	follows	follow	VERB
ejpam-6438	46	10	:	:	PUNCT
ejpam-6438	46	11	the	the	DET
ejpam-6438	46	12	metric	metric	ADJ
ejpam-6438	46	13	and	and	CCONJ
ejpam-6438	46	14	connected	connected	ADJ
ejpam-6438	46	15	metric	metric	ADJ
ejpam-6438	46	16	dimension	dimension	NOUN
ejpam-6438	46	17	introduced	introduce	VERB
ejpam-6438	46	18	in	in	ADP
ejpam-6438	46	19	sect	sect	NOUN
ejpam-6438	46	20	.	.	PUNCT
ejpam-6438	47	1	2	2	NUM
ejpam-6438	47	2	the	the	DET
ejpam-6438	47	3	theorems	theorem	NOUN
ejpam-6438	47	4	that	that	PRON
ejpam-6438	47	5	determine	determine	VERB
ejpam-6438	47	6	the	the	DET
ejpam-6438	47	7	metric	metric	ADJ
ejpam-6438	47	8	and	and	CCONJ
ejpam-6438	47	9	connected	connected	ADJ
ejpam-6438	47	10	metric	metric	ADJ
ejpam-6438	47	11	dimension	dimension	NOUN
ejpam-6438	47	12	of	of	ADP
ejpam-6438	47	13	some	some	DET
ejpam-6438	47	14	graphs	graph	NOUN
ejpam-6438	47	15	.	.	PUNCT
ejpam-6438	48	1	with	with	ADP
ejpam-6438	48	2	an	an	DET
ejpam-6438	48	3	example	example	NOUN
ejpam-6438	48	4	in	in	ADP
ejpam-6438	48	5	section	section	NOUN
ejpam-6438	48	6	3	3	NUM
ejpam-6438	48	7	.	.	PUNCT
ejpam-6438	49	1	in	in	ADP
ejpam-6438	49	2	sect	sect	NOUN
ejpam-6438	49	3	.	.	PUNCT
ejpam-6438	50	1	4	4	NUM
ejpam-6438	50	2	an	an	DET
ejpam-6438	50	3	approximate	approximate	ADJ
ejpam-6438	50	4	algorithm	algorithm	NOUN
ejpam-6438	50	5	which	which	PRON
ejpam-6438	50	6	finds	find	VERB
ejpam-6438	50	7	the	the	DET
ejpam-6438	50	8	minimum	minimum	ADJ
ejpam-6438	50	9	connected	connect	VERB
ejpam-6438	50	10	metric	metric	ADJ
ejpam-6438	50	11	dimension	dimension	NOUN
ejpam-6438	50	12	finally	finally	ADV
ejpam-6438	50	13	,	,	PUNCT
ejpam-6438	50	14	conclusions	conclusion	NOUN
ejpam-6438	50	15	are	be	AUX
ejpam-6438	50	16	drawn	draw	VERB
ejpam-6438	50	17	in	in	ADP
ejpam-6438	50	18	sect	sect	NOUN
ejpam-6438	50	19	.	.	PUNCT
ejpam-6438	51	1	5	5	X
ejpam-6438	51	2	.	.	X
ejpam-6438	51	3	a.	a.	NOUN
ejpam-6438	51	4	elrokh	elrokh	PROPN
ejpam-6438	51	5	,	,	PUNCT
ejpam-6438	51	6	eman	eman	PROPN
ejpam-6438	51	7	s.	s.	PROPN
ejpam-6438	51	8	almotairi	almotairi	PROPN
ejpam-6438	51	9	,	,	PUNCT
ejpam-6438	51	10	h.	h.	PROPN
ejpam-6438	51	11	mostafa	mostafa	PROPN
ejpam-6438	51	12	/	/	SYM
ejpam-6438	51	13	eur	eur	PROPN
ejpam-6438	51	14	.	.	PUNCT
ejpam-6438	52	1	j.	j.	PROPN
ejpam-6438	52	2	pure	pure	PROPN
ejpam-6438	52	3	appl	appl	PROPN
ejpam-6438	52	4	.	.	PROPN
ejpam-6438	52	5	math	math	PROPN
ejpam-6438	52	6	,	,	PUNCT
ejpam-6438	52	7	18	18	NUM
ejpam-6438	52	8	(	(	PUNCT
ejpam-6438	52	9	3	3	NUM
ejpam-6438	52	10	)	)	PUNCT
ejpam-6438	52	11	(	(	PUNCT
ejpam-6438	52	12	2025	2025	NUM
ejpam-6438	52	13	)	)	PUNCT
ejpam-6438	52	14	,	,	PUNCT
ejpam-6438	52	15	6438	6438	NUM
ejpam-6438	52	16	4	4	NUM
ejpam-6438	52	17	of	of	ADP
ejpam-6438	52	18	18	18	NUM
ejpam-6438	52	19	2	2	NUM
ejpam-6438	52	20	.	.	PUNCT
ejpam-6438	52	21	main	main	ADJ
ejpam-6438	52	22	result	result	NOUN
ejpam-6438	52	23	in	in	ADP
ejpam-6438	52	24	this	this	DET
ejpam-6438	52	25	section	section	NOUN
ejpam-6438	52	26	,	,	PUNCT
ejpam-6438	52	27	we	we	PRON
ejpam-6438	52	28	prove	prove	VERB
ejpam-6438	52	29	the	the	DET
ejpam-6438	52	30	theorems	theorem	NOUN
ejpam-6438	52	31	that	that	PRON
ejpam-6438	52	32	determine	determine	VERB
ejpam-6438	52	33	the	the	DET
ejpam-6438	52	34	metric	metric	ADJ
ejpam-6438	52	35	and	and	CCONJ
ejpam-6438	52	36	connected	connected	ADJ
ejpam-6438	52	37	metric	metric	ADJ
ejpam-6438	52	38	dimension	dimension	NOUN
ejpam-6438	52	39	of	of	ADP
ejpam-6438	52	40	some	some	DET
ejpam-6438	52	41	graphs	graph	NOUN
ejpam-6438	52	42	.	.	PUNCT
ejpam-6438	53	1	theorem	theorem	NOUN
ejpam-6438	53	2	1	1	NUM
ejpam-6438	53	3	:	:	PUNCT
ejpam-6438	53	4	let	let	VERB
ejpam-6438	53	5	g	g	NOUN
ejpam-6438	53	6	be	be	AUX
ejpam-6438	53	7	pn	pn	PROPN
ejpam-6438	53	8	⊙	⊙	PROPN
ejpam-6438	53	9	p3	p3	PROPN
ejpam-6438	53	10	graphs	graph	NOUN
ejpam-6438	53	11	,	,	PUNCT
ejpam-6438	53	12	then	then	ADV
ejpam-6438	53	13	c.m.d	c.m.d	X
ejpam-6438	53	14	(	(	PUNCT
ejpam-6438	53	15	pn	pn	PROPN
ejpam-6438	53	16	⊙	⊙	PROPN
ejpam-6438	53	17	p3	p3	PROPN
ejpam-6438	53	18	)	)	PUNCT
ejpam-6438	53	19	equal	equal	ADJ
ejpam-6438	53	20	2n	2n	NUM
ejpam-6438	53	21	,	,	PUNCT
ejpam-6438	53	22	n	n	PRON
ejpam-6438	53	23	≥	≥	NOUN
ejpam-6438	53	24	1	1	NUM
ejpam-6438	53	25	.	.	PUNCT
ejpam-6438	54	1	proof	proof	NOUN
ejpam-6438	54	2	.	.	PUNCT
ejpam-6438	55	1	let	let	VERB
ejpam-6438	55	2	pn	pn	PART
ejpam-6438	55	3	be	be	AUX
ejpam-6438	55	4	the	the	DET
ejpam-6438	55	5	path	path	NOUN
ejpam-6438	55	6	graph	graph	NOUN
ejpam-6438	55	7	with	with	ADP
ejpam-6438	55	8	vertex	vertex	NOUN
ejpam-6438	55	9	set	set	NOUN
ejpam-6438	55	10	{	{	PUNCT
ejpam-6438	55	11	v1	v1	NOUN
ejpam-6438	55	12	,	,	PUNCT
ejpam-6438	55	13	v2	v2	PROPN
ejpam-6438	55	14	,	,	PUNCT
ejpam-6438	55	15	.	.	PUNCT
ejpam-6438	55	16	.	.	PUNCT
ejpam-6438	56	1	.	.	PUNCT
ejpam-6438	57	1	,	,	PUNCT
ejpam-6438	57	2	vn	vn	NOUN
ejpam-6438	57	3	}	}	PUNCT
ejpam-6438	57	4	and	and	CCONJ
ejpam-6438	57	5	edges	edge	VERB
ejpam-6438	57	6	vi	vi	NOUN
ejpam-6438	57	7	∼	∼	NOUN
ejpam-6438	57	8	vi+1	vi+1	NOUN
ejpam-6438	57	9	for	for	ADP
ejpam-6438	57	10	1	1	NUM
ejpam-6438	57	11	≤	≤	NUM
ejpam-6438	58	1	i	i	PRON
ejpam-6438	58	2	<	<	X
ejpam-6438	58	3	n.	n.	NOUN
ejpam-6438	58	4	in	in	ADP
ejpam-6438	58	5	the	the	DET
ejpam-6438	58	6	corona	corona	NOUN
ejpam-6438	58	7	product	product	NOUN
ejpam-6438	58	8	pn	pn	PROPN
ejpam-6438	58	9	⊙	⊙	PROPN
ejpam-6438	58	10	p3	p3	PROPN
ejpam-6438	58	11	,	,	PUNCT
ejpam-6438	58	12	for	for	ADP
ejpam-6438	58	13	each	each	DET
ejpam-6438	58	14	vertex	vertex	NOUN
ejpam-6438	58	15	vi	vi	PROPN
ejpam-6438	58	16	of	of	ADP
ejpam-6438	58	17	pn	pn	PROPN
ejpam-6438	58	18	,	,	PUNCT
ejpam-6438	58	19	we	we	PRON
ejpam-6438	58	20	attach	attach	VERB
ejpam-6438	58	21	a	a	DET
ejpam-6438	58	22	copy	copy	NOUN
ejpam-6438	58	23	of	of	ADP
ejpam-6438	58	24	p3	p3	PROPN
ejpam-6438	58	25	denoted	denote	VERB
ejpam-6438	58	26	by	by	ADP
ejpam-6438	58	27	ui1	ui1	PROPN
ejpam-6438	58	28	,	,	PUNCT
ejpam-6438	58	29	ui2	ui2	PROPN
ejpam-6438	58	30	,	,	PUNCT
ejpam-6438	58	31	ui3	ui3	VERB
ejpam-6438	58	32	and	and	CCONJ
ejpam-6438	58	33	connect	connect	VERB
ejpam-6438	58	34	each	each	DET
ejpam-6438	58	35	uij	uij	PRON
ejpam-6438	58	36	to	to	ADP
ejpam-6438	58	37	vi	vi	PROPN
ejpam-6438	58	38	,	,	PUNCT
ejpam-6438	58	39	as	as	SCONJ
ejpam-6438	58	40	show	show	NOUN
ejpam-6438	58	41	in	in	ADP
ejpam-6438	58	42	figure	figure	NOUN
ejpam-6438	58	43	5	5	NUM
ejpam-6438	58	44	.	.	PUNCT
ejpam-6438	58	45	define	define	VERB
ejpam-6438	58	46	the	the	DET
ejpam-6438	58	47	set	set	NOUN
ejpam-6438	58	48	r	r	NOUN
ejpam-6438	58	49	=	=	PUNCT
ejpam-6438	58	50	{	{	PUNCT
ejpam-6438	58	51	v1	v1	NOUN
ejpam-6438	58	52	,	,	PUNCT
ejpam-6438	58	53	v2	v2	PROPN
ejpam-6438	58	54	,	,	PUNCT
ejpam-6438	58	55	.	.	PUNCT
ejpam-6438	58	56	.	.	PUNCT
ejpam-6438	59	1	.	.	PUNCT
ejpam-6438	60	1	,	,	PUNCT
ejpam-6438	60	2	vn	vn	VERB
ejpam-6438	60	3	}	}	PUNCT
ejpam-6438	60	4	∪	∪	X
ejpam-6438	60	5	{	{	PUNCT
ejpam-6438	60	6	ui1	ui1	NOUN
ejpam-6438	60	7	|	|	ADV
ejpam-6438	60	8	1	1	NUM
ejpam-6438	60	9	≤	≤	NUM
ejpam-6438	60	10	i	i	PRON
ejpam-6438	60	11	≤	≤	NOUN
ejpam-6438	60	12	n	n	CCONJ
ejpam-6438	60	13	}	}	PUNCT
ejpam-6438	60	14	.	.	PUNCT
ejpam-6438	61	1	clearly	clearly	ADV
ejpam-6438	61	2	,	,	PUNCT
ejpam-6438	61	3	|r|	|r|	NOUN
ejpam-6438	61	4	=	=	SYM
ejpam-6438	61	5	2n	2n	NUM
ejpam-6438	61	6	.	.	PUNCT
ejpam-6438	62	1	we	we	PRON
ejpam-6438	62	2	will	will	AUX
ejpam-6438	62	3	show	show	VERB
ejpam-6438	62	4	that	that	SCONJ
ejpam-6438	62	5	r	r	NOUN
ejpam-6438	62	6	is	be	AUX
ejpam-6438	62	7	a	a	DET
ejpam-6438	62	8	connected	connected	ADJ
ejpam-6438	62	9	resolving	resolving	NOUN
ejpam-6438	62	10	set	set	VERB
ejpam-6438	62	11	and	and	CCONJ
ejpam-6438	62	12	that	that	SCONJ
ejpam-6438	62	13	no	no	PRON
ejpam-6438	62	14	smaller	small	ADJ
ejpam-6438	62	15	such	such	ADJ
ejpam-6438	62	16	set	set	NOUN
ejpam-6438	62	17	exists	exist	VERB
ejpam-6438	62	18	.	.	PUNCT
ejpam-6438	63	1	(	(	PUNCT
ejpam-6438	63	2	i	i	NOUN
ejpam-6438	63	3	)	)	PUNCT
ejpam-6438	63	4	r	r	NOUN
ejpam-6438	63	5	is	be	AUX
ejpam-6438	63	6	a	a	DET
ejpam-6438	63	7	resolving	resolving	NOUN
ejpam-6438	63	8	set	set	NOUN
ejpam-6438	63	9	:	:	PUNCT
ejpam-6438	63	10	we	we	PRON
ejpam-6438	63	11	must	must	AUX
ejpam-6438	63	12	show	show	VERB
ejpam-6438	63	13	that	that	SCONJ
ejpam-6438	63	14	for	for	ADP
ejpam-6438	63	15	any	any	DET
ejpam-6438	63	16	two	two	NUM
ejpam-6438	63	17	distinct	distinct	ADJ
ejpam-6438	63	18	vertices	vertex	NOUN
ejpam-6438	63	19	x	x	X
ejpam-6438	63	20	,	,	PUNCT
ejpam-6438	63	21	y	y	PROPN
ejpam-6438	63	22	∈	∈	PROPN
ejpam-6438	63	23	v	v	NOUN
ejpam-6438	63	24	(	(	PUNCT
ejpam-6438	63	25	g	g	NOUN
ejpam-6438	63	26	)	)	PUNCT
ejpam-6438	63	27	,	,	PUNCT
ejpam-6438	63	28	the	the	DET
ejpam-6438	63	29	distance	distance	NOUN
ejpam-6438	63	30	vectors	vector	VERB
ejpam-6438	63	31	r(x|r	r(x|r	NOUN
ejpam-6438	63	32	)	)	PUNCT
ejpam-6438	63	33	and	and	CCONJ
ejpam-6438	63	34	r(y|r	r(y|r	NUM
ejpam-6438	63	35	)	)	PUNCT
ejpam-6438	63	36	are	be	AUX
ejpam-6438	63	37	distinct	distinct	ADJ
ejpam-6438	63	38	.	.	PUNCT
ejpam-6438	63	39	•	•	NUM
ejpam-6438	63	40	for	for	ADP
ejpam-6438	63	41	vertices	vertex	NOUN
ejpam-6438	63	42	in	in	ADP
ejpam-6438	63	43	different	different	ADJ
ejpam-6438	63	44	p3	p3	PROPN
ejpam-6438	63	45	copies	copy	NOUN
ejpam-6438	63	46	,	,	PUNCT
ejpam-6438	63	47	the	the	DET
ejpam-6438	63	48	distances	distance	NOUN
ejpam-6438	63	49	to	to	ADP
ejpam-6438	63	50	the	the	DET
ejpam-6438	63	51	corresponding	corresponding	ADJ
ejpam-6438	63	52	vi	vi	PROPN
ejpam-6438	63	53	and	and	CCONJ
ejpam-6438	63	54	ui1	ui1	NOUN
ejpam-6438	63	55	in	in	ADP
ejpam-6438	63	56	r	r	NOUN
ejpam-6438	63	57	distinguish	distinguish	VERB
ejpam-6438	63	58	them	they	PRON
ejpam-6438	63	59	.	.	PUNCT
ejpam-6438	64	1	•	•	NOUN
ejpam-6438	64	2	within	within	ADP
ejpam-6438	64	3	each	each	DET
ejpam-6438	64	4	p3	p3	PROPN
ejpam-6438	64	5	copy	copy	NOUN
ejpam-6438	64	6	,	,	PUNCT
ejpam-6438	64	7	the	the	DET
ejpam-6438	64	8	inclusion	inclusion	NOUN
ejpam-6438	64	9	of	of	ADP
ejpam-6438	64	10	ui1	ui1	PROPN
ejpam-6438	64	11	and	and	CCONJ
ejpam-6438	64	12	vi	vi	VERB
ejpam-6438	64	13	in	in	ADP
ejpam-6438	64	14	r	r	NOUN
ejpam-6438	64	15	ensures	ensure	VERB
ejpam-6438	64	16	that	that	SCONJ
ejpam-6438	64	17	the	the	DET
ejpam-6438	64	18	other	other	ADJ
ejpam-6438	64	19	two	two	NUM
ejpam-6438	64	20	vertices	vertex	NOUN
ejpam-6438	64	21	ui2	ui2	PROPN
ejpam-6438	64	22	,	,	PUNCT
ejpam-6438	64	23	ui3	ui3	X
ejpam-6438	64	24	are	be	AUX
ejpam-6438	64	25	distinguishable	distinguishable	ADJ
ejpam-6438	64	26	by	by	ADP
ejpam-6438	64	27	their	their	PRON
ejpam-6438	64	28	distances	distance	NOUN
ejpam-6438	64	29	to	to	ADP
ejpam-6438	64	30	ui1	ui1	PROPN
ejpam-6438	64	31	and	and	CCONJ
ejpam-6438	64	32	vi	vi	NOUN
ejpam-6438	64	33	.	.	NOUN
ejpam-6438	64	34	•	•	NUM
ejpam-6438	64	35	vertices	vertex	NOUN
ejpam-6438	64	36	vi	vi	NOUN
ejpam-6438	64	37	are	be	AUX
ejpam-6438	64	38	all	all	ADV
ejpam-6438	64	39	in	in	ADP
ejpam-6438	64	40	r	r	NOUN
ejpam-6438	64	41	,	,	PUNCT
ejpam-6438	64	42	so	so	SCONJ
ejpam-6438	64	43	they	they	PRON
ejpam-6438	64	44	are	be	AUX
ejpam-6438	64	45	trivially	trivially	ADV
ejpam-6438	64	46	distinguished	distinguish	VERB
ejpam-6438	64	47	.	.	PUNCT
ejpam-6438	65	1	•	•	NUM
ejpam-6438	65	2	any	any	DET
ejpam-6438	65	3	vertex	vertex	NOUN
ejpam-6438	65	4	in	in	ADP
ejpam-6438	65	5	pn	pn	PROPN
ejpam-6438	65	6	and	and	CCONJ
ejpam-6438	65	7	any	any	DET
ejpam-6438	65	8	vertex	vertex	NOUN
ejpam-6438	65	9	in	in	ADP
ejpam-6438	65	10	a	a	DET
ejpam-6438	65	11	p3	p3	PROPN
ejpam-6438	65	12	copy	copy	NOUN
ejpam-6438	65	13	are	be	AUX
ejpam-6438	65	14	distinguished	distinguish	VERB
ejpam-6438	65	15	by	by	ADP
ejpam-6438	65	16	their	their	PRON
ejpam-6438	65	17	distances	distance	NOUN
ejpam-6438	65	18	to	to	ADP
ejpam-6438	65	19	r.	r.	PROPN
ejpam-6438	65	20	figure	figure	NOUN
ejpam-6438	65	21	5	5	NUM
ejpam-6438	65	22	.	.	PUNCT
ejpam-6438	65	23	pn	pn	PROPN
ejpam-6438	65	24	⊙	⊙	PROPN
ejpam-6438	65	25	p3	p3	PROPN
ejpam-6438	65	26	graph	graph	NOUN
ejpam-6438	65	27	.	.	PUNCT
ejpam-6438	66	1	w	w	PROPN
ejpam-6438	66	2	(	(	PUNCT
ejpam-6438	66	3	vi	vi	PROPN
ejpam-6438	66	4	,	,	PUNCT
ejpam-6438	66	5	r	r	NOUN
ejpam-6438	66	6	)	)	PUNCT
ejpam-6438	66	7	=	=	SYM
ejpam-6438	66	8			PROPN
ejpam-6438	66	9	{	{	PUNCT
ejpam-6438	66	10	0	0	NUM
ejpam-6438	66	11	,	,	PUNCT
ejpam-6438	66	12	1	1	NUM
ejpam-6438	66	13	,	,	PUNCT
ejpam-6438	66	14	2	2	NUM
ejpam-6438	66	15	,	,	PUNCT
ejpam-6438	66	16	.	.	PUNCT
ejpam-6438	66	17	.	.	PUNCT
ejpam-6438	66	18	.	.	PUNCT
ejpam-6438	67	1	,	,	PUNCT
ejpam-6438	67	2	n−	n−	NOUN
ejpam-6438	67	3	1	1	NUM
ejpam-6438	67	4	,	,	PUNCT
ejpam-6438	67	5	1	1	NUM
ejpam-6438	67	6	,	,	PUNCT
ejpam-6438	67	7	2	2	NUM
ejpam-6438	67	8	,	,	PUNCT
ejpam-6438	67	9	3	3	NUM
ejpam-6438	67	10	,	,	PUNCT
ejpam-6438	67	11	.	.	PUNCT
ejpam-6438	67	12	.	.	PUNCT
ejpam-6438	68	1	.	.	PUNCT
ejpam-6438	69	1	,	,	PUNCT
ejpam-6438	69	2	n	n	CCONJ
ejpam-6438	69	3	}	}	PUNCT
ejpam-6438	69	4	,	,	PUNCT
ejpam-6438	69	5	i	i	PRON
ejpam-6438	69	6	=	=	NOUN
ejpam-6438	69	7	1	1	NUM
ejpam-6438	69	8	{	{	PUNCT
ejpam-6438	69	9	1	1	NUM
ejpam-6438	69	10	,	,	PUNCT
ejpam-6438	69	11	0	0	NUM
ejpam-6438	69	12	,	,	PUNCT
ejpam-6438	69	13	1	1	NUM
ejpam-6438	69	14	,	,	PUNCT
ejpam-6438	69	15	.	.	PUNCT
ejpam-6438	69	16	.	.	PUNCT
ejpam-6438	69	17	.	.	PUNCT
ejpam-6438	70	1	,	,	PUNCT
ejpam-6438	70	2	n−	n−	NOUN
ejpam-6438	70	3	2	2	NUM
ejpam-6438	70	4	,	,	PUNCT
ejpam-6438	70	5	2	2	NUM
ejpam-6438	70	6	,	,	PUNCT
ejpam-6438	70	7	1	1	NUM
ejpam-6438	70	8	,	,	PUNCT
ejpam-6438	70	9	2	2	NUM
ejpam-6438	70	10	,	,	PUNCT
ejpam-6438	70	11	.	.	PUNCT
ejpam-6438	70	12	.	.	PUNCT
ejpam-6438	71	1	.	.	PUNCT
ejpam-6438	72	1	,	,	PUNCT
ejpam-6438	72	2	n−	n−	NOUN
ejpam-6438	72	3	1	1	NUM
ejpam-6438	72	4	}	}	PUNCT
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ejpam-6438	106	19	,	,	PUNCT
ejpam-6438	106	20	n−	n−	NOUN
ejpam-6438	106	21	1	1	NUM
ejpam-6438	106	22	,	,	PUNCT
ejpam-6438	106	23	n−	n−	NOUN
ejpam-6438	106	24	2	2	NUM
ejpam-6438	106	25	,	,	PUNCT
ejpam-6438	106	26	.	.	PUNCT
ejpam-6438	106	27	.	.	PUNCT
ejpam-6438	107	1	.	.	PUNCT
ejpam-6438	108	1	,	,	PUNCT
ejpam-6438	108	2	1	1	NUM
ejpam-6438	108	3	,	,	PUNCT
ejpam-6438	108	4	n+	n+	ADP
ejpam-6438	108	5	1	1	NUM
ejpam-6438	108	6	,	,	PUNCT
ejpam-6438	108	7	n	n	CCONJ
ejpam-6438	108	8	,	,	PUNCT
ejpam-6438	108	9	.	.	PUNCT
ejpam-6438	108	10	.	.	PUNCT
ejpam-6438	108	11	.	.	PUNCT
ejpam-6438	109	1	,	,	PUNCT
ejpam-6438	109	2	4	4	NUM
ejpam-6438	109	3	,	,	PUNCT
ejpam-6438	109	4	3	3	NUM
ejpam-6438	109	5	,	,	PUNCT
ejpam-6438	109	6	j	j	PROPN
ejpam-6438	109	7	−	−	PROPN
ejpam-6438	109	8	1	1	NUM
ejpam-6438	109	9	}	}	PUNCT
ejpam-6438	109	10	.i	.i	PUNCT
ejpam-6438	110	1	=	=	SYM
ejpam-6438	110	2	n	n	PROPN
ejpam-6438	110	3	(	(	PUNCT
ejpam-6438	110	4	ii	ii	NOUN
ejpam-6438	110	5	)	)	PUNCT
ejpam-6438	110	6	r	r	NOUN
ejpam-6438	110	7	is	be	AUX
ejpam-6438	110	8	connected	connect	VERB
ejpam-6438	110	9	:	:	PUNCT
ejpam-6438	110	10	the	the	DET
ejpam-6438	110	11	subgraph	subgraph	NOUN
ejpam-6438	110	12	induced	induce	VERB
ejpam-6438	110	13	by	by	ADP
ejpam-6438	110	14	{	{	PUNCT
ejpam-6438	110	15	v1	v1	NOUN
ejpam-6438	110	16	,	,	PUNCT
ejpam-6438	110	17	.	.	PUNCT
ejpam-6438	110	18	.	.	PUNCT
ejpam-6438	110	19	.	.	PUNCT
ejpam-6438	111	1	,	,	PUNCT
ejpam-6438	111	2	vn	vn	PROPN
ejpam-6438	111	3	}	}	PUNCT
ejpam-6438	111	4	is	be	AUX
ejpam-6438	111	5	a	a	DET
ejpam-6438	111	6	path	path	NOUN
ejpam-6438	111	7	and	and	CCONJ
ejpam-6438	111	8	hence	hence	ADV
ejpam-6438	111	9	connected	connect	VERB
ejpam-6438	111	10	.	.	PUNCT
ejpam-6438	112	1	each	each	DET
ejpam-6438	112	2	ui1	ui1	PROPN
ejpam-6438	112	3	is	be	AUX
ejpam-6438	112	4	adjacent	adjacent	ADJ
ejpam-6438	112	5	to	to	ADP
ejpam-6438	112	6	vi	vi	PROPN
ejpam-6438	112	7	,	,	PUNCT
ejpam-6438	112	8	so	so	SCONJ
ejpam-6438	112	9	the	the	DET
ejpam-6438	112	10	full	full	ADJ
ejpam-6438	112	11	induced	induced	ADJ
ejpam-6438	112	12	subgraph	subgraph	NOUN
ejpam-6438	112	13	on	on	ADP
ejpam-6438	112	14	r	r	NOUN
ejpam-6438	112	15	is	be	AUX
ejpam-6438	112	16	connected	connect	VERB
ejpam-6438	112	17	.	.	PUNCT
ejpam-6438	113	1	(	(	PUNCT
ejpam-6438	113	2	iii	iii	X
ejpam-6438	113	3	)	)	PUNCT
ejpam-6438	113	4	minimality	minimality	NOUN
ejpam-6438	113	5	:	:	PUNCT
ejpam-6438	113	6	suppose	suppose	VERB
ejpam-6438	113	7	there	there	PRON
ejpam-6438	113	8	exists	exist	VERB
ejpam-6438	113	9	a	a	DET
ejpam-6438	113	10	connected	connected	ADJ
ejpam-6438	113	11	resolving	resolving	NOUN
ejpam-6438	113	12	set	set	VERB
ejpam-6438	113	13	r′	r′	PROPN
ejpam-6438	113	14	with	with	ADP
ejpam-6438	113	15	|r′|	|r′|	PROPN
ejpam-6438	113	16	<	<	X
ejpam-6438	113	17	2n	2n	NUM
ejpam-6438	113	18	.	.	PUNCT
ejpam-6438	114	1	then	then	ADV
ejpam-6438	114	2	at	at	ADV
ejpam-6438	114	3	least	least	ADV
ejpam-6438	114	4	one	one	NUM
ejpam-6438	114	5	vi	vi	NOUN
ejpam-6438	114	6	or	or	CCONJ
ejpam-6438	114	7	ui1	ui1	NOUN
ejpam-6438	114	8	is	be	AUX
ejpam-6438	114	9	missing	miss	VERB
ejpam-6438	114	10	from	from	ADP
ejpam-6438	114	11	r′.	r′.	PROPN
ejpam-6438	114	12	if	if	SCONJ
ejpam-6438	114	13	vi	vi	PROPN
ejpam-6438	114	14	/∈	/∈	PUNCT
ejpam-6438	115	1	r′	r′	PROPN
ejpam-6438	115	2	,	,	PUNCT
ejpam-6438	115	3	then	then	ADV
ejpam-6438	115	4	ui1	ui1	PROPN
ejpam-6438	115	5	may	may	AUX
ejpam-6438	115	6	be	be	AUX
ejpam-6438	115	7	disconnected	disconnect	VERB
ejpam-6438	115	8	from	from	ADP
ejpam-6438	115	9	the	the	DET
ejpam-6438	115	10	rest	rest	NOUN
ejpam-6438	115	11	of	of	ADP
ejpam-6438	115	12	r′	r′	PROPN
ejpam-6438	115	13	,	,	PUNCT
ejpam-6438	115	14	violating	violate	VERB
ejpam-6438	115	15	connectivity	connectivity	NOUN
ejpam-6438	115	16	.	.	PUNCT
ejpam-6438	116	1	if	if	SCONJ
ejpam-6438	116	2	ui1	ui1	PROPN
ejpam-6438	116	3	/∈	/∈	PUNCT
ejpam-6438	117	1	r′	r′	PROPN
ejpam-6438	117	2	,	,	PUNCT
ejpam-6438	117	3	then	then	ADV
ejpam-6438	117	4	ui2	ui2	PROPN
ejpam-6438	117	5	and	and	CCONJ
ejpam-6438	117	6	ui3	ui3	PROPN
ejpam-6438	117	7	may	may	AUX
ejpam-6438	117	8	not	not	PART
ejpam-6438	117	9	be	be	AUX
ejpam-6438	117	10	distinguishable	distinguishable	ADJ
ejpam-6438	117	11	.	.	PUNCT
ejpam-6438	118	1	thus	thus	ADV
ejpam-6438	118	2	,	,	PUNCT
ejpam-6438	118	3	removing	remove	VERB
ejpam-6438	118	4	any	any	DET
ejpam-6438	118	5	vertex	vertex	NOUN
ejpam-6438	118	6	from	from	ADP
ejpam-6438	118	7	r	r	NOUN
ejpam-6438	118	8	breaks	break	NOUN
ejpam-6438	118	9	either	either	CCONJ
ejpam-6438	118	10	the	the	DET
ejpam-6438	118	11	resolving	resolve	VERB
ejpam-6438	118	12	property	property	NOUN
ejpam-6438	118	13	or	or	CCONJ
ejpam-6438	118	14	connectivity	connectivity	NOUN
ejpam-6438	118	15	.	.	PUNCT
ejpam-6438	119	1	therefore	therefore	ADV
ejpam-6438	119	2	,	,	PUNCT
ejpam-6438	119	3	r	r	NOUN
ejpam-6438	119	4	is	be	AUX
ejpam-6438	119	5	a	a	DET
ejpam-6438	119	6	minimum	minimum	ADJ
ejpam-6438	119	7	connected	connected	ADJ
ejpam-6438	119	8	resolving	resolving	NOUN
ejpam-6438	119	9	set	set	NOUN
ejpam-6438	119	10	,	,	PUNCT
ejpam-6438	119	11	and	and	CCONJ
ejpam-6438	119	12	cdim(pn	cdim(pn	PROPN
ejpam-6438	119	13	⊙	⊙	PROPN
ejpam-6438	119	14	p3	p3	PROPN
ejpam-6438	119	15	)	)	PUNCT
ejpam-6438	120	1	=	=	PUNCT
ejpam-6438	120	2	2n	2n	X
ejpam-6438	120	3	.	.	PUNCT
ejpam-6438	121	1	theorem	theorem	NOUN
ejpam-6438	121	2	2	2	NUM
ejpam-6438	121	3	:	:	PUNCT
ejpam-6438	121	4	let	let	VERB
ejpam-6438	121	5	g	g	NOUN
ejpam-6438	121	6	be	be	AUX
ejpam-6438	121	7	pn	pn	PROPN
ejpam-6438	121	8	⊙	⊙	PROPN
ejpam-6438	121	9	c3	c3	PROPN
ejpam-6438	121	10	graphs	graphs	PROPN
ejpam-6438	121	11	,	,	PUNCT
ejpam-6438	121	12	then	then	ADV
ejpam-6438	121	13	the	the	DET
ejpam-6438	121	14	connected	connected	ADJ
ejpam-6438	121	15	metric	metric	ADJ
ejpam-6438	121	16	dimension	dimension	NOUN
ejpam-6438	121	17	of	of	ADP
ejpam-6438	121	18	pn	pn	PROPN
ejpam-6438	121	19	⊙	⊙	PROPN
ejpam-6438	121	20	c3	c3	PROPN
ejpam-6438	121	21	equal	equal	ADJ
ejpam-6438	121	22	to	to	ADP
ejpam-6438	121	23	3n	3n	NUM
ejpam-6438	121	24	,	,	PUNCT
ejpam-6438	121	25	n	n	PRON
ejpam-6438	121	26	≥	≥	NOUN
ejpam-6438	121	27	1	1	NUM
ejpam-6438	121	28	.	.	PUNCT
ejpam-6438	122	1	proof	proof	NOUN
ejpam-6438	122	2	.	.	PUNCT
ejpam-6438	123	1	let	let	VERB
ejpam-6438	123	2	pn	pn	PART
ejpam-6438	123	3	be	be	AUX
ejpam-6438	123	4	a	a	DET
ejpam-6438	123	5	path	path	NOUN
ejpam-6438	123	6	graph	graph	NOUN
ejpam-6438	123	7	with	with	ADP
ejpam-6438	123	8	vertices	vertex	NOUN
ejpam-6438	123	9	v1	v1	NOUN
ejpam-6438	123	10	,	,	PUNCT
ejpam-6438	123	11	v2	v2	NOUN
ejpam-6438	123	12	,	,	PUNCT
ejpam-6438	123	13	.	.	PUNCT
ejpam-6438	123	14	.	.	PUNCT
ejpam-6438	124	1	.	.	PUNCT
ejpam-6438	125	1	,	,	PUNCT
ejpam-6438	125	2	vn	vn	PROPN
ejpam-6438	125	3	.	.	PUNCT
ejpam-6438	126	1	for	for	ADP
ejpam-6438	126	2	each	each	DET
ejpam-6438	126	3	vertex	vertex	NOUN
ejpam-6438	126	4	vi	vi	PROPN
ejpam-6438	126	5	in	in	ADP
ejpam-6438	126	6	pn	pn	PROPN
ejpam-6438	126	7	,	,	PUNCT
ejpam-6438	126	8	attach	attach	VERB
ejpam-6438	126	9	a	a	DET
ejpam-6438	126	10	copy	copy	NOUN
ejpam-6438	126	11	of	of	ADP
ejpam-6438	126	12	the	the	DET
ejpam-6438	126	13	cycle	cycle	NOUN
ejpam-6438	126	14	c3	c3	NOUN
ejpam-6438	126	15	with	with	ADP
ejpam-6438	126	16	vertices	vertex	NOUN
ejpam-6438	126	17	ui1	ui1	PROPN
ejpam-6438	126	18	,	,	PUNCT
ejpam-6438	126	19	ui2	ui2	PROPN
ejpam-6438	126	20	,	,	PUNCT
ejpam-6438	126	21	ui3	ui3	PROPN
ejpam-6438	126	22	,	,	PUNCT
ejpam-6438	126	23	and	and	CCONJ
ejpam-6438	126	24	connect	connect	VERB
ejpam-6438	126	25	each	each	DET
ejpam-6438	126	26	uij	uij	PRON
ejpam-6438	126	27	to	to	ADP
ejpam-6438	126	28	vi	vi	VERB
ejpam-6438	126	29	,	,	PUNCT
ejpam-6438	126	30	as	as	SCONJ
ejpam-6438	126	31	show	show	NOUN
ejpam-6438	126	32	in	in	ADP
ejpam-6438	126	33	figure	figure	NOUN
ejpam-6438	126	34	6	6	NUM
ejpam-6438	126	35	.	.	PUNCT
ejpam-6438	127	1	the	the	DET
ejpam-6438	127	2	resulting	result	VERB
ejpam-6438	127	3	graph	graph	NOUN
ejpam-6438	127	4	g	g	PROPN
ejpam-6438	127	5	=	=	PUNCT
ejpam-6438	127	6	pn	pn	PROPN
ejpam-6438	127	7	⊙	⊙	PROPN
ejpam-6438	127	8	c3	c3	PROPN
ejpam-6438	127	9	has	have	VERB
ejpam-6438	127	10	n	n	NUM
ejpam-6438	127	11	central	central	ADJ
ejpam-6438	127	12	vertices	vertex	NOUN
ejpam-6438	127	13	and	and	CCONJ
ejpam-6438	127	14	3n	3n	NUM
ejpam-6438	127	15	peripheral	peripheral	ADJ
ejpam-6438	127	16	vertices	vertex	NOUN
ejpam-6438	127	17	,	,	PUNCT
ejpam-6438	127	18	totaling	total	VERB
ejpam-6438	127	19	4n	4n	NOUN
ejpam-6438	127	20	vertices	vertex	NOUN
ejpam-6438	127	21	.	.	PUNCT
ejpam-6438	128	1	we	we	PRON
ejpam-6438	128	2	define	define	VERB
ejpam-6438	128	3	the	the	DET
ejpam-6438	128	4	set	set	NOUN
ejpam-6438	128	5	r	r	NOUN
ejpam-6438	128	6	=	=	PUNCT
ejpam-6438	128	7	{	{	PUNCT
ejpam-6438	128	8	v1	v1	NOUN
ejpam-6438	128	9	,	,	PUNCT
ejpam-6438	128	10	v2	v2	PROPN
ejpam-6438	128	11	,	,	PUNCT
ejpam-6438	128	12	.	.	PUNCT
ejpam-6438	128	13	.	.	PUNCT
ejpam-6438	128	14	.	.	PUNCT
ejpam-6438	129	1	,	,	PUNCT
ejpam-6438	129	2	vn	vn	VERB
ejpam-6438	129	3	}	}	PUNCT
ejpam-6438	129	4	∪	∪	X
ejpam-6438	129	5	{	{	PUNCT
ejpam-6438	129	6	ui1	ui1	ADJ
ejpam-6438	129	7	,	,	PUNCT
ejpam-6438	129	8	ui2	ui2	PUNCT
ejpam-6438	130	1	|	|	ADV
ejpam-6438	130	2	1	1	NUM
ejpam-6438	130	3	≤	≤	NUM
ejpam-6438	130	4	i	i	PRON
ejpam-6438	130	5	≤	≤	NOUN
ejpam-6438	130	6	n	n	CCONJ
ejpam-6438	130	7	}	}	PUNCT
ejpam-6438	130	8	,	,	PUNCT
ejpam-6438	130	9	which	which	PRON
ejpam-6438	130	10	includes	include	VERB
ejpam-6438	130	11	all	all	PRON
ejpam-6438	130	12	n	n	DET
ejpam-6438	130	13	central	central	ADJ
ejpam-6438	130	14	vertices	vertex	NOUN
ejpam-6438	130	15	and	and	CCONJ
ejpam-6438	130	16	two	two	NUM
ejpam-6438	130	17	vertices	vertex	NOUN
ejpam-6438	130	18	from	from	ADP
ejpam-6438	130	19	each	each	DET
ejpam-6438	130	20	c3	c3	PROPN
ejpam-6438	130	21	copy	copy	NOUN
ejpam-6438	130	22	.	.	PUNCT
ejpam-6438	131	1	thus	thus	ADV
ejpam-6438	131	2	,	,	PUNCT
ejpam-6438	131	3	|r|	|r|	PROPN
ejpam-6438	131	4	=	=	SYM
ejpam-6438	131	5	n+	n+	X
ejpam-6438	131	6	2n	2n	NUM
ejpam-6438	131	7	=	=	SYM
ejpam-6438	131	8	3n	3n	NUM
ejpam-6438	131	9	.	.	PUNCT
ejpam-6438	132	1	(	(	PUNCT
ejpam-6438	132	2	i	i	NOUN
ejpam-6438	132	3	)	)	PUNCT
ejpam-6438	132	4	r	r	NOUN
ejpam-6438	132	5	is	be	AUX
ejpam-6438	132	6	a	a	DET
ejpam-6438	132	7	resolving	resolving	NOUN
ejpam-6438	132	8	set	set	NOUN
ejpam-6438	132	9	.	.	PUNCT
ejpam-6438	133	1	consider	consider	VERB
ejpam-6438	133	2	any	any	DET
ejpam-6438	133	3	two	two	NUM
ejpam-6438	133	4	distinct	distinct	ADJ
ejpam-6438	133	5	vertices	vertex	NOUN
ejpam-6438	133	6	x	x	X
ejpam-6438	133	7	,	,	PUNCT
ejpam-6438	133	8	y	y	PROPN
ejpam-6438	133	9	∈	∈	PROPN
ejpam-6438	133	10	v	v	NOUN
ejpam-6438	133	11	(	(	PUNCT
ejpam-6438	133	12	g	g	NOUN
ejpam-6438	133	13	)	)	PUNCT
ejpam-6438	133	14	.	.	PUNCT
ejpam-6438	134	1	we	we	PRON
ejpam-6438	134	2	analyze	analyze	VERB
ejpam-6438	134	3	the	the	DET
ejpam-6438	134	4	following	follow	VERB
ejpam-6438	134	5	cases	case	NOUN
ejpam-6438	134	6	:	:	PUNCT
ejpam-6438	134	7	•	•	NUM
ejpam-6438	134	8	case	case	NOUN
ejpam-6438	134	9	1	1	NUM
ejpam-6438	134	10	:	:	PUNCT
ejpam-6438	134	11	x	x	X
ejpam-6438	134	12	and	and	CCONJ
ejpam-6438	134	13	y	y	PROPN
ejpam-6438	134	14	belong	belong	VERB
ejpam-6438	134	15	to	to	ADP
ejpam-6438	134	16	different	different	ADJ
ejpam-6438	134	17	c3	c3	PROPN
ejpam-6438	134	18	copies	copy	NOUN
ejpam-6438	134	19	.	.	PUNCT
ejpam-6438	135	1	since	since	SCONJ
ejpam-6438	135	2	each	each	DET
ejpam-6438	135	3	vi	vi	NOUN
ejpam-6438	135	4	is	be	AUX
ejpam-6438	135	5	in	in	ADP
ejpam-6438	135	6	r	r	NOUN
ejpam-6438	135	7	,	,	PUNCT
ejpam-6438	135	8	and	and	CCONJ
ejpam-6438	135	9	each	each	DET
ejpam-6438	135	10	uij	uij	PRON
ejpam-6438	135	11	is	be	AUX
ejpam-6438	135	12	connected	connect	VERB
ejpam-6438	135	13	to	to	ADP
ejpam-6438	135	14	vi	vi	PROPN
ejpam-6438	135	15	,	,	PUNCT
ejpam-6438	135	16	the	the	DET
ejpam-6438	135	17	distances	distance	NOUN
ejpam-6438	135	18	to	to	ADP
ejpam-6438	135	19	vi	vi	PROPN
ejpam-6438	135	20	and	and	CCONJ
ejpam-6438	135	21	the	the	DET
ejpam-6438	135	22	included	include	VERB
ejpam-6438	135	23	ui1	ui1	PROPN
ejpam-6438	135	24	,	,	PUNCT
ejpam-6438	135	25	ui2	ui2	PRON
ejpam-6438	135	26	uniquely	uniquely	ADV
ejpam-6438	135	27	identify	identify	VERB
ejpam-6438	135	28	vertices	vertex	NOUN
ejpam-6438	135	29	in	in	ADP
ejpam-6438	135	30	each	each	DET
ejpam-6438	135	31	c3	c3	NOUN
ejpam-6438	135	32	copy	copy	NOUN
ejpam-6438	135	33	.	.	PUNCT
ejpam-6438	136	1	•	•	NUM
ejpam-6438	136	2	case	case	NOUN
ejpam-6438	136	3	2	2	NUM
ejpam-6438	136	4	:	:	PUNCT
ejpam-6438	136	5	x	x	X
ejpam-6438	136	6	and	and	CCONJ
ejpam-6438	136	7	y	y	PROPN
ejpam-6438	136	8	belong	belong	VERB
ejpam-6438	136	9	to	to	ADP
ejpam-6438	136	10	the	the	DET
ejpam-6438	136	11	same	same	ADJ
ejpam-6438	136	12	c3	c3	PROPN
ejpam-6438	136	13	copy	copy	NOUN
ejpam-6438	136	14	.	.	PUNCT
ejpam-6438	137	1	the	the	DET
ejpam-6438	137	2	inclusion	inclusion	NOUN
ejpam-6438	137	3	of	of	ADP
ejpam-6438	137	4	two	two	NUM
ejpam-6438	137	5	vertices	vertex	NOUN
ejpam-6438	137	6	from	from	ADP
ejpam-6438	137	7	each	each	DET
ejpam-6438	137	8	c3	c3	NOUN
ejpam-6438	137	9	ensures	ensure	VERB
ejpam-6438	137	10	that	that	SCONJ
ejpam-6438	137	11	all	all	DET
ejpam-6438	137	12	three	three	NUM
ejpam-6438	137	13	vertices	vertex	NOUN
ejpam-6438	137	14	in	in	ADP
ejpam-6438	137	15	the	the	DET
ejpam-6438	137	16	cycle	cycle	NOUN
ejpam-6438	137	17	are	be	AUX
ejpam-6438	137	18	distinguishable	distinguishable	ADJ
ejpam-6438	137	19	by	by	ADP
ejpam-6438	137	20	their	their	PRON
ejpam-6438	137	21	distances	distance	NOUN
ejpam-6438	137	22	to	to	ADP
ejpam-6438	137	23	the	the	DET
ejpam-6438	137	24	two	two	NUM
ejpam-6438	137	25	included	include	VERB
ejpam-6438	137	26	vertices	vertex	NOUN
ejpam-6438	137	27	.	.	PUNCT
ejpam-6438	138	1	•	•	NUM
ejpam-6438	138	2	case	case	NOUN
ejpam-6438	138	3	3	3	NUM
ejpam-6438	138	4	:	:	PUNCT
ejpam-6438	138	5	one	one	NUM
ejpam-6438	138	6	of	of	ADP
ejpam-6438	138	7	x	x	PUNCT
ejpam-6438	138	8	or	or	CCONJ
ejpam-6438	138	9	y	y	PROPN
ejpam-6438	138	10	is	be	AUX
ejpam-6438	138	11	a	a	DET
ejpam-6438	138	12	central	central	ADJ
ejpam-6438	138	13	vertex	vertex	NOUN
ejpam-6438	138	14	vi	vi	NOUN
ejpam-6438	138	15	,	,	PUNCT
ejpam-6438	138	16	and	and	CCONJ
ejpam-6438	138	17	the	the	DET
ejpam-6438	138	18	other	other	ADJ
ejpam-6438	138	19	is	be	AUX
ejpam-6438	138	20	a	a	DET
ejpam-6438	138	21	peripheral	peripheral	ADJ
ejpam-6438	138	22	vertex	vertex	NOUN
ejpam-6438	138	23	uij	uij	PRON
ejpam-6438	138	24	.	.	PUNCT
ejpam-6438	139	1	since	since	SCONJ
ejpam-6438	139	2	vi	vi	PROPN
ejpam-6438	139	3	is	be	AUX
ejpam-6438	139	4	in	in	ADP
ejpam-6438	139	5	r	r	NOUN
ejpam-6438	139	6	and	and	CCONJ
ejpam-6438	139	7	ui1	ui1	ADV
ejpam-6438	139	8	,	,	PUNCT
ejpam-6438	139	9	ui2	ui2	PROPN
ejpam-6438	139	10	are	be	AUX
ejpam-6438	139	11	also	also	ADV
ejpam-6438	139	12	in	in	ADP
ejpam-6438	139	13	r	r	NOUN
ejpam-6438	139	14	,	,	PUNCT
ejpam-6438	139	15	the	the	DET
ejpam-6438	139	16	distance	distance	NOUN
ejpam-6438	139	17	vectors	vector	NOUN
ejpam-6438	139	18	to	to	ADP
ejpam-6438	139	19	r	r	NOUN
ejpam-6438	139	20	will	will	AUX
ejpam-6438	139	21	differ	differ	VERB
ejpam-6438	139	22	.	.	PUNCT
ejpam-6438	140	1	a.	a.	PROPN
ejpam-6438	140	2	elrokh	elrokh	PROPN
ejpam-6438	140	3	,	,	PUNCT
ejpam-6438	140	4	eman	eman	PROPN
ejpam-6438	140	5	s.	s.	PROPN
ejpam-6438	140	6	almotairi	almotairi	PROPN
ejpam-6438	140	7	,	,	PUNCT
ejpam-6438	140	8	h.	h.	PROPN
ejpam-6438	140	9	mostafa	mostafa	PROPN
ejpam-6438	140	10	/	/	SYM
ejpam-6438	140	11	eur	eur	PROPN
ejpam-6438	140	12	.	.	PUNCT
ejpam-6438	141	1	j.	j.	PROPN
ejpam-6438	141	2	pure	pure	PROPN
ejpam-6438	141	3	appl	appl	PROPN
ejpam-6438	141	4	.	.	PROPN
ejpam-6438	141	5	math	math	PROPN
ejpam-6438	141	6	,	,	PUNCT
ejpam-6438	141	7	18	18	NUM
ejpam-6438	141	8	(	(	PUNCT
ejpam-6438	141	9	3	3	NUM
ejpam-6438	141	10	)	)	PUNCT
ejpam-6438	141	11	(	(	PUNCT
ejpam-6438	141	12	2025	2025	NUM
ejpam-6438	141	13	)	)	PUNCT
ejpam-6438	141	14	,	,	PUNCT
ejpam-6438	141	15	6438	6438	NUM
ejpam-6438	141	16	6	6	NUM
ejpam-6438	141	17	of	of	ADP
ejpam-6438	141	18	18	18	NUM
ejpam-6438	141	19	•	•	NOUN
ejpam-6438	141	20	case	case	NOUN
ejpam-6438	141	21	4	4	NUM
ejpam-6438	141	22	:	:	PUNCT
ejpam-6438	141	23	x	x	X
ejpam-6438	141	24	and	and	CCONJ
ejpam-6438	141	25	y	y	PROPN
ejpam-6438	141	26	are	be	AUX
ejpam-6438	141	27	distinct	distinct	ADJ
ejpam-6438	141	28	central	central	ADJ
ejpam-6438	141	29	vertices	vertex	NOUN
ejpam-6438	141	30	.	.	PUNCT
ejpam-6438	142	1	since	since	SCONJ
ejpam-6438	142	2	all	all	DET
ejpam-6438	142	3	vi	vi	NOUN
ejpam-6438	142	4	are	be	AUX
ejpam-6438	142	5	in	in	ADP
ejpam-6438	142	6	r	r	NOUN
ejpam-6438	142	7	,	,	PUNCT
ejpam-6438	142	8	they	they	PRON
ejpam-6438	142	9	are	be	AUX
ejpam-6438	142	10	trivially	trivially	ADV
ejpam-6438	142	11	resolved	resolve	VERB
ejpam-6438	142	12	.	.	PUNCT
ejpam-6438	143	1	figure	figure	VERB
ejpam-6438	143	2	6	6	NUM
ejpam-6438	143	3	.	.	PUNCT
ejpam-6438	144	1	pn	pn	PROPN
ejpam-6438	144	2	⊙	⊙	PROPN
ejpam-6438	144	3	c3	c3	PROPN
ejpam-6438	144	4	graph	graph	PROPN
ejpam-6438	144	5	.	.	PUNCT
ejpam-6438	145	1	w	w	PROPN
ejpam-6438	145	2	(	(	PUNCT
ejpam-6438	145	3	vi	vi	PROPN
ejpam-6438	145	4	,	,	PUNCT
ejpam-6438	145	5	r	r	NOUN
ejpam-6438	145	6	)	)	PUNCT
ejpam-6438	145	7	=	=	SYM
ejpam-6438	145	8			PROPN
ejpam-6438	145	9	{	{	PUNCT
ejpam-6438	145	10	0	0	NUM
ejpam-6438	145	11	,	,	PUNCT
ejpam-6438	145	12	1	1	NUM
ejpam-6438	145	13	,	,	PUNCT
ejpam-6438	145	14	2	2	NUM
ejpam-6438	145	15	,	,	PUNCT
ejpam-6438	145	16	.	.	PUNCT
ejpam-6438	145	17	.	.	PUNCT
ejpam-6438	145	18	.	.	PUNCT
ejpam-6438	146	1	,	,	PUNCT
ejpam-6438	146	2	n−	n−	NOUN
ejpam-6438	146	3	1	1	NUM
ejpam-6438	146	4	,	,	PUNCT
ejpam-6438	146	5	1	1	NUM
ejpam-6438	146	6	,	,	PUNCT
ejpam-6438	146	7	1	1	NUM
ejpam-6438	146	8	,	,	PUNCT
ejpam-6438	146	9	2	2	NUM
ejpam-6438	146	10	,	,	PUNCT
ejpam-6438	146	11	2	2	NUM
ejpam-6438	146	12	,	,	PUNCT
ejpam-6438	146	13	3	3	NUM
ejpam-6438	146	14	,	,	PUNCT
ejpam-6438	146	15	3	3	NUM
ejpam-6438	146	16	,	,	PUNCT
ejpam-6438	146	17	.	.	PUNCT
ejpam-6438	146	18	.	.	PUNCT
ejpam-6438	147	1	.	.	PUNCT
ejpam-6438	148	1	,	,	PUNCT
ejpam-6438	148	2	n	n	CCONJ
ejpam-6438	148	3	,	,	PUNCT
ejpam-6438	148	4	n	n	CCONJ
ejpam-6438	148	5	}	}	PUNCT
ejpam-6438	148	6	,	,	PUNCT
ejpam-6438	148	7	i	i	PRON
ejpam-6438	148	8	=	=	NOUN
ejpam-6438	148	9	1	1	NUM
ejpam-6438	148	10	{	{	PUNCT
ejpam-6438	148	11	1	1	NUM
ejpam-6438	148	12	,	,	PUNCT
ejpam-6438	148	13	0	0	NUM
ejpam-6438	148	14	,	,	PUNCT
ejpam-6438	148	15	1	1	NUM
ejpam-6438	148	16	,	,	PUNCT
ejpam-6438	148	17	.	.	PUNCT
ejpam-6438	148	18	.	.	PUNCT
ejpam-6438	148	19	.	.	PUNCT
ejpam-6438	149	1	,	,	PUNCT
ejpam-6438	149	2	n−	n−	NOUN
ejpam-6438	149	3	2	2	NUM
ejpam-6438	149	4	,	,	PUNCT
ejpam-6438	149	5	2	2	NUM
ejpam-6438	149	6	,	,	PUNCT
ejpam-6438	149	7	2	2	NUM
ejpam-6438	149	8	,	,	PUNCT
ejpam-6438	149	9	1	1	NUM
ejpam-6438	149	10	,	,	PUNCT
ejpam-6438	149	11	1	1	NUM
ejpam-6438	149	12	,	,	PUNCT
ejpam-6438	149	13	2	2	NUM
ejpam-6438	149	14	,	,	PUNCT
ejpam-6438	149	15	2	2	NUM
ejpam-6438	149	16	.	.	PUNCT
ejpam-6438	149	17	.	.	PUNCT
ejpam-6438	150	1	.	.	PUNCT
ejpam-6438	151	1	,	,	PUNCT
ejpam-6438	151	2	n−	n−	NOUN
ejpam-6438	151	3	1	1	NUM
ejpam-6438	151	4	,	,	PUNCT
ejpam-6438	151	5	n−	n−	NOUN
ejpam-6438	151	6	1	1	NUM
ejpam-6438	151	7	}	}	PUNCT
ejpam-6438	151	8	,	,	PUNCT
ejpam-6438	151	9	i	i	PRON
ejpam-6438	151	10	=	=	NOUN
ejpam-6438	151	11	2	2	NUM
ejpam-6438	151	12	{	{	PUNCT
ejpam-6438	151	13	2	2	NUM
ejpam-6438	151	14	,	,	PUNCT
ejpam-6438	151	15	1	1	NUM
ejpam-6438	151	16	,	,	PUNCT
ejpam-6438	151	17	0	0	NUM
ejpam-6438	151	18	,	,	PUNCT
ejpam-6438	151	19	1	1	NUM
ejpam-6438	151	20	,	,	PUNCT
ejpam-6438	151	21	.	.	PUNCT
ejpam-6438	151	22	.	.	PUNCT
ejpam-6438	152	1	.	.	PUNCT
ejpam-6438	153	1	,	,	PUNCT
ejpam-6438	153	2	n−	n−	NOUN
ejpam-6438	153	3	3	3	NUM
ejpam-6438	153	4	,	,	PUNCT
ejpam-6438	153	5	3	3	NUM
ejpam-6438	153	6	,	,	PUNCT
ejpam-6438	153	7	3	3	NUM
ejpam-6438	153	8	,	,	PUNCT
ejpam-6438	153	9	2	2	NUM
ejpam-6438	153	10	,	,	PUNCT
ejpam-6438	153	11	2	2	NUM
ejpam-6438	153	12	,	,	PUNCT
ejpam-6438	153	13	1	1	NUM
ejpam-6438	153	14	,	,	PUNCT
ejpam-6438	153	15	1	1	NUM
ejpam-6438	153	16	,	,	PUNCT
ejpam-6438	153	17	.	.	PUNCT
ejpam-6438	153	18	.	.	PUNCT
ejpam-6438	154	1	.	.	PUNCT
ejpam-6438	155	1	,	,	PUNCT
ejpam-6438	155	2	n−	n−	NOUN
ejpam-6438	155	3	2	2	NUM
ejpam-6438	155	4	,	,	PUNCT
ejpam-6438	155	5	n−	n−	NOUN
ejpam-6438	155	6	2	2	NUM
ejpam-6438	155	7	}	}	PUNCT
ejpam-6438	155	8	,	,	PUNCT
ejpam-6438	155	9	i	i	PRON
ejpam-6438	155	10	=	=	NOUN
ejpam-6438	155	11	3	3	NUM
ejpam-6438	155	12	:	:	PUNCT
ejpam-6438	155	13	:	:	PUNCT
ejpam-6438	155	14	:	:	PUNCT
ejpam-6438	155	15	:	:	PUNCT
ejpam-6438	155	16	:	:	PUNCT
ejpam-6438	155	17	{	{	PUNCT
ejpam-6438	155	18	n−	n−	NOUN
ejpam-6438	155	19	1	1	NUM
ejpam-6438	155	20	,	,	PUNCT
ejpam-6438	155	21	n−	n−	NOUN
ejpam-6438	155	22	2	2	NUM
ejpam-6438	155	23	,	,	PUNCT
ejpam-6438	155	24	n−	n−	NOUN
ejpam-6438	155	25	3	3	NUM
ejpam-6438	155	26	,	,	PUNCT
ejpam-6438	155	27	.	.	PUNCT
ejpam-6438	155	28	.	.	PUNCT
ejpam-6438	156	1	.	.	PUNCT
ejpam-6438	157	1	,	,	PUNCT
ejpam-6438	157	2	0	0	NUM
ejpam-6438	157	3	,	,	PUNCT
ejpam-6438	157	4	n	n	CCONJ
ejpam-6438	157	5	,	,	PUNCT
ejpam-6438	157	6	n.n−	n.n−	X
ejpam-6438	157	7	1	1	NUM
ejpam-6438	157	8	,	,	PUNCT
ejpam-6438	157	9	n−	n−	NOUN
ejpam-6438	157	10	1	1	NUM
ejpam-6438	157	11	,	,	PUNCT
ejpam-6438	157	12	.	.	PUNCT
ejpam-6438	157	13	.	.	PUNCT
ejpam-6438	158	1	.	.	PUNCT
ejpam-6438	159	1	,	,	PUNCT
ejpam-6438	159	2	1	1	NUM
ejpam-6438	159	3	,	,	PUNCT
ejpam-6438	159	4	1	1	NUM
ejpam-6438	159	5	}	}	PUNCT
ejpam-6438	159	6	.i	.i	PUNCT
ejpam-6438	160	1	=	=	PUNCT
ejpam-6438	160	2	n	n	PROPN
ejpam-6438	160	3	w	w	NOUN
ejpam-6438	160	4	(	(	PUNCT
ejpam-6438	160	5	uij	uij	PRON
ejpam-6438	160	6	,	,	PUNCT
ejpam-6438	160	7	r	r	NOUN
ejpam-6438	160	8	)	)	PUNCT
ejpam-6438	160	9	=	=	SYM
ejpam-6438	160	10			NOUN
ejpam-6438	160	11	{	{	PUNCT
ejpam-6438	160	12	1	1	NUM
ejpam-6438	160	13	,	,	PUNCT
ejpam-6438	160	14	2	2	NUM
ejpam-6438	160	15	,	,	PUNCT
ejpam-6438	160	16	3	3	NUM
ejpam-6438	160	17	,	,	PUNCT
ejpam-6438	160	18	.	.	PUNCT
ejpam-6438	160	19	.	.	PUNCT
ejpam-6438	161	1	.	.	PUNCT
ejpam-6438	162	1	,	,	PUNCT
ejpam-6438	162	2	n	n	CCONJ
ejpam-6438	162	3	,	,	PUNCT
ejpam-6438	162	4	n	n	CCONJ
ejpam-6438	162	5	,	,	PUNCT
ejpam-6438	162	6	j	j	PROPN
ejpam-6438	162	7	−	−	PROPN
ejpam-6438	162	8	1	1	NUM
ejpam-6438	162	9	,	,	PUNCT
ejpam-6438	162	10	j	j	PROPN
ejpam-6438	162	11	,	,	PUNCT
ejpam-6438	162	12	3	3	NUM
ejpam-6438	162	13	,	,	PUNCT
ejpam-6438	162	14	3	3	NUM
ejpam-6438	162	15	,	,	PUNCT
ejpam-6438	162	16	4	4	NUM
ejpam-6438	162	17	,	,	PUNCT
ejpam-6438	162	18	4	4	NUM
ejpam-6438	162	19	,	,	PUNCT
ejpam-6438	162	20	.	.	PUNCT
ejpam-6438	162	21	.	.	PUNCT
ejpam-6438	163	1	.	.	PUNCT
ejpam-6438	163	2	,	,	PUNCT
ejpam-6438	163	3	n	n	CCONJ
ejpam-6438	163	4	,	,	PUNCT
ejpam-6438	163	5	n	n	CCONJ
ejpam-6438	163	6	,	,	PUNCT
ejpam-6438	163	7	n+	n+	ADP
ejpam-6438	163	8	1	1	NUM
ejpam-6438	163	9	,	,	PUNCT
ejpam-6438	163	10	n+	n+	ADP
ejpam-6438	163	11	1	1	NUM
ejpam-6438	163	12	}	}	PUNCT
ejpam-6438	163	13	,	,	PUNCT
ejpam-6438	163	14	i	i	PRON
ejpam-6438	163	15	=	=	NOUN
ejpam-6438	163	16	1	1	NUM
ejpam-6438	163	17	,	,	PUNCT
ejpam-6438	163	18	j	j	PROPN
ejpam-6438	164	1	=	=	SYM
ejpam-6438	164	2	1	1	NUM
ejpam-6438	164	3	{	{	PUNCT
ejpam-6438	164	4	1	1	NUM
ejpam-6438	164	5	,	,	PUNCT
ejpam-6438	164	6	2	2	NUM
ejpam-6438	164	7	,	,	PUNCT
ejpam-6438	164	8	3	3	NUM
ejpam-6438	164	9	,	,	PUNCT
ejpam-6438	164	10	.	.	PUNCT
ejpam-6438	164	11	.	.	PUNCT
ejpam-6438	164	12	.	.	PUNCT
ejpam-6438	164	13	,	,	PUNCT
ejpam-6438	164	14	n	n	CCONJ
ejpam-6438	164	15	,	,	PUNCT
ejpam-6438	164	16	n	n	CCONJ
ejpam-6438	164	17	,	,	PUNCT
ejpam-6438	164	18	j	j	PROPN
ejpam-6438	164	19	−	−	PROPN
ejpam-6438	164	20	1	1	NUM
ejpam-6438	164	21	,	,	PUNCT
ejpam-6438	164	22	j	j	PROPN
ejpam-6438	164	23	−	−	PROPN
ejpam-6438	164	24	2	2	NUM
ejpam-6438	164	25	,	,	PUNCT
ejpam-6438	164	26	3	3	NUM
ejpam-6438	164	27	,	,	PUNCT
ejpam-6438	164	28	3	3	NUM
ejpam-6438	164	29	,	,	PUNCT
ejpam-6438	164	30	4	4	NUM
ejpam-6438	164	31	,	,	PUNCT
ejpam-6438	164	32	4	4	NUM
ejpam-6438	164	33	,	,	PUNCT
ejpam-6438	164	34	.	.	PUNCT
ejpam-6438	164	35	.	.	PUNCT
ejpam-6438	164	36	.	.	PUNCT
ejpam-6438	164	37	,	,	PUNCT
ejpam-6438	164	38	n	n	CCONJ
ejpam-6438	164	39	,	,	PUNCT
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ejpam-6438	164	41	,	,	PUNCT
ejpam-6438	164	42	n+	n+	ADP
ejpam-6438	164	43	1	1	NUM
ejpam-6438	164	44	,	,	PUNCT
ejpam-6438	164	45	n+	n+	ADP
ejpam-6438	164	46	1	1	NUM
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ejpam-6438	164	48	,	,	PUNCT
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ejpam-6438	164	50	=	=	NOUN
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ejpam-6438	164	57	1	1	NUM
ejpam-6438	164	58	,	,	PUNCT
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ejpam-6438	164	60	,	,	PUNCT
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ejpam-6438	164	62	,	,	PUNCT
ejpam-6438	164	63	.	.	PUNCT
ejpam-6438	164	64	.	.	PUNCT
ejpam-6438	165	1	.	.	PUNCT
ejpam-6438	166	1	,	,	PUNCT
ejpam-6438	166	2	n	n	CCONJ
ejpam-6438	166	3	,	,	PUNCT
ejpam-6438	166	4	n	n	CCONJ
ejpam-6438	166	5	,	,	PUNCT
ejpam-6438	166	6	j	j	PROPN
ejpam-6438	167	1	−	−	PROPN
ejpam-6438	167	2	2	2	NUM
ejpam-6438	167	3	,	,	PUNCT
ejpam-6438	167	4	j	j	PROPN
ejpam-6438	167	5	−	−	PROPN
ejpam-6438	167	6	2	2	NUM
ejpam-6438	167	7	,	,	PUNCT
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ejpam-6438	167	9	,	,	PUNCT
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ejpam-6438	167	13	,	,	PUNCT
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ejpam-6438	167	15	,	,	PUNCT
ejpam-6438	167	16	.	.	PUNCT
ejpam-6438	167	17	.	.	PUNCT
ejpam-6438	168	1	.	.	PUNCT
ejpam-6438	168	2	,	,	PUNCT
ejpam-6438	168	3	n	n	CCONJ
ejpam-6438	168	4	,	,	PUNCT
ejpam-6438	168	5	n	n	CCONJ
ejpam-6438	168	6	,	,	PUNCT
ejpam-6438	168	7	n+	n+	ADP
ejpam-6438	168	8	1	1	NUM
ejpam-6438	168	9	,	,	PUNCT
ejpam-6438	168	10	n+	n+	ADP
ejpam-6438	168	11	1	1	NUM
ejpam-6438	168	12	}	}	PUNCT
ejpam-6438	168	13	,	,	PUNCT
ejpam-6438	168	14	i	i	PRON
ejpam-6438	168	15	=	=	NOUN
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ejpam-6438	168	17	,	,	PUNCT
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ejpam-6438	169	1	=	=	SYM
ejpam-6438	169	2	3	3	NUM
ejpam-6438	169	3	{	{	PUNCT
ejpam-6438	169	4	2	2	NUM
ejpam-6438	169	5	,	,	PUNCT
ejpam-6438	169	6	1	1	NUM
ejpam-6438	169	7	,	,	PUNCT
ejpam-6438	169	8	2	2	NUM
ejpam-6438	169	9	,	,	PUNCT
ejpam-6438	169	10	3	3	NUM
ejpam-6438	169	11	,	,	PUNCT
ejpam-6438	169	12	4	4	NUM
ejpam-6438	169	13	.	.	PUNCT
ejpam-6438	169	14	.	.	PUNCT
ejpam-6438	169	15	.	.	PUNCT
ejpam-6438	170	1	,	,	PUNCT
ejpam-6438	170	2	n−	n−	NOUN
ejpam-6438	170	3	1	1	NUM
ejpam-6438	170	4	,	,	PUNCT
ejpam-6438	170	5	3	3	NUM
ejpam-6438	170	6	,	,	PUNCT
ejpam-6438	170	7	3	3	NUM
ejpam-6438	170	8	,	,	PUNCT
ejpam-6438	170	9	j	j	PROPN
ejpam-6438	170	10	−	−	PROPN
ejpam-6438	170	11	1	1	NUM
ejpam-6438	170	12	,	,	PUNCT
ejpam-6438	170	13	j	j	PROPN
ejpam-6438	170	14	,	,	PUNCT
ejpam-6438	170	15	3	3	NUM
ejpam-6438	170	16	,	,	PUNCT
ejpam-6438	170	17	3	3	NUM
ejpam-6438	170	18	,	,	PUNCT
ejpam-6438	170	19	4	4	NUM
ejpam-6438	170	20	,	,	PUNCT
ejpam-6438	170	21	4	4	NUM
ejpam-6438	170	22	,	,	PUNCT
ejpam-6438	170	23	.	.	PUNCT
ejpam-6438	170	24	.	.	PUNCT
ejpam-6438	171	1	.	.	PUNCT
ejpam-6438	172	1	,	,	PUNCT
ejpam-6438	172	2	n	n	CCONJ
ejpam-6438	172	3	,	,	PUNCT
ejpam-6438	172	4	n	n	CCONJ
ejpam-6438	172	5	}	}	PUNCT
ejpam-6438	172	6	,	,	PUNCT
ejpam-6438	172	7	i	i	PRON
ejpam-6438	172	8	=	=	NOUN
ejpam-6438	172	9	2	2	NUM
ejpam-6438	172	10	,	,	PUNCT
ejpam-6438	172	11	j	j	NOUN
ejpam-6438	172	12	=	=	SYM
ejpam-6438	172	13	1	1	NUM
ejpam-6438	172	14	{	{	PUNCT
ejpam-6438	172	15	2	2	NUM
ejpam-6438	172	16	,	,	PUNCT
ejpam-6438	172	17	1	1	NUM
ejpam-6438	172	18	,	,	PUNCT
ejpam-6438	172	19	2	2	NUM
ejpam-6438	172	20	,	,	PUNCT
ejpam-6438	172	21	3	3	NUM
ejpam-6438	172	22	,	,	PUNCT
ejpam-6438	172	23	4	4	NUM
ejpam-6438	172	24	.	.	PUNCT
ejpam-6438	172	25	.	.	PUNCT
ejpam-6438	172	26	.	.	PUNCT
ejpam-6438	173	1	,	,	PUNCT
ejpam-6438	173	2	n−	n−	NOUN
ejpam-6438	173	3	1	1	NUM
ejpam-6438	173	4	,	,	PUNCT
ejpam-6438	173	5	3	3	NUM
ejpam-6438	173	6	,	,	PUNCT
ejpam-6438	173	7	3	3	NUM
ejpam-6438	173	8	,	,	PUNCT
ejpam-6438	173	9	j	j	PROPN
ejpam-6438	173	10	−	−	PROPN
ejpam-6438	173	11	1	1	NUM
ejpam-6438	173	12	,	,	PUNCT
ejpam-6438	173	13	j	j	PROPN
ejpam-6438	173	14	−	−	PROPN
ejpam-6438	173	15	2	2	NUM
ejpam-6438	173	16	,	,	PUNCT
ejpam-6438	173	17	3	3	NUM
ejpam-6438	173	18	,	,	PUNCT
ejpam-6438	173	19	3	3	NUM
ejpam-6438	173	20	,	,	PUNCT
ejpam-6438	173	21	4	4	NUM
ejpam-6438	173	22	,	,	PUNCT
ejpam-6438	173	23	4	4	NUM
ejpam-6438	173	24	,	,	PUNCT
ejpam-6438	173	25	.	.	PUNCT
ejpam-6438	173	26	.	.	PUNCT
ejpam-6438	174	1	.	.	PUNCT
ejpam-6438	175	1	,	,	PUNCT
ejpam-6438	175	2	n	n	CCONJ
ejpam-6438	175	3	,	,	PUNCT
ejpam-6438	175	4	n	n	CCONJ
ejpam-6438	175	5	}	}	PUNCT
ejpam-6438	175	6	,	,	PUNCT
ejpam-6438	175	7	i	i	PRON
ejpam-6438	175	8	=	=	NOUN
ejpam-6438	175	9	2	2	NUM
ejpam-6438	175	10	,	,	PUNCT
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ejpam-6438	175	12	=	=	SYM
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ejpam-6438	175	14	{	{	PUNCT
ejpam-6438	175	15	2	2	NUM
ejpam-6438	175	16	,	,	PUNCT
ejpam-6438	175	17	1	1	NUM
ejpam-6438	175	18	,	,	PUNCT
ejpam-6438	175	19	2	2	NUM
ejpam-6438	175	20	,	,	PUNCT
ejpam-6438	175	21	3	3	NUM
ejpam-6438	175	22	,	,	PUNCT
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ejpam-6438	175	24	.	.	PUNCT
ejpam-6438	175	25	.	.	PUNCT
ejpam-6438	175	26	.	.	PUNCT
ejpam-6438	176	1	,	,	PUNCT
ejpam-6438	176	2	n−	n−	NOUN
ejpam-6438	176	3	1	1	NUM
ejpam-6438	176	4	,	,	PUNCT
ejpam-6438	176	5	3	3	NUM
ejpam-6438	176	6	,	,	PUNCT
ejpam-6438	176	7	3	3	NUM
ejpam-6438	176	8	,	,	PUNCT
ejpam-6438	176	9	j	j	PROPN
ejpam-6438	176	10	−	−	PROPN
ejpam-6438	176	11	2	2	NUM
ejpam-6438	176	12	,	,	PUNCT
ejpam-6438	176	13	j	j	PROPN
ejpam-6438	176	14	−	−	PROPN
ejpam-6438	176	15	2	2	NUM
ejpam-6438	176	16	,	,	PUNCT
ejpam-6438	176	17	3	3	NUM
ejpam-6438	176	18	,	,	PUNCT
ejpam-6438	176	19	3	3	NUM
ejpam-6438	176	20	,	,	PUNCT
ejpam-6438	176	21	4	4	NUM
ejpam-6438	176	22	,	,	PUNCT
ejpam-6438	176	23	4	4	NUM
ejpam-6438	176	24	,	,	PUNCT
ejpam-6438	176	25	.	.	PUNCT
ejpam-6438	176	26	.	.	PUNCT
ejpam-6438	177	1	.	.	PUNCT
ejpam-6438	178	1	,	,	PUNCT
ejpam-6438	178	2	n	n	CCONJ
ejpam-6438	178	3	,	,	PUNCT
ejpam-6438	178	4	n	n	CCONJ
ejpam-6438	178	5	}	}	PUNCT
ejpam-6438	178	6	,	,	PUNCT
ejpam-6438	178	7	i	i	PRON
ejpam-6438	178	8	=	=	NOUN
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ejpam-6438	178	10	,	,	PUNCT
ejpam-6438	178	11	j	j	NOUN
ejpam-6438	178	12	=	=	SYM
ejpam-6438	178	13	3	3	NUM
ejpam-6438	178	14	:	:	PUNCT
ejpam-6438	178	15	:	:	PUNCT
ejpam-6438	178	16	:	:	PUNCT
ejpam-6438	178	17	{	{	PUNCT
ejpam-6438	178	18	n−	n−	NOUN
ejpam-6438	178	19	1	1	NUM
ejpam-6438	178	20	,	,	PUNCT
ejpam-6438	178	21	n−	n−	NOUN
ejpam-6438	178	22	2	2	NUM
ejpam-6438	178	23	,	,	PUNCT
ejpam-6438	178	24	.	.	PUNCT
ejpam-6438	178	25	.	.	PUNCT
ejpam-6438	178	26	.	.	PUNCT
ejpam-6438	179	1	.	.	PUNCT
ejpam-6438	180	1	,	,	PUNCT
ejpam-6438	180	2	1	1	NUM
ejpam-6438	180	3	,	,	PUNCT
ejpam-6438	180	4	n+	n+	NUM
ejpam-6438	180	5	1	1	NUM
ejpam-6438	180	6	,	,	PUNCT
ejpam-6438	180	7	n+	n+	ADP
ejpam-6438	180	8	1	1	NUM
ejpam-6438	180	9	,	,	PUNCT
ejpam-6438	180	10	n	n	CCONJ
ejpam-6438	180	11	,	,	PUNCT
ejpam-6438	180	12	n	n	CCONJ
ejpam-6438	180	13	,	,	PUNCT
ejpam-6438	180	14	n−	n−	NOUN
ejpam-6438	180	15	1	1	NUM
ejpam-6438	180	16	,	,	PUNCT
ejpam-6438	180	17	n−	n−	NOUN
ejpam-6438	180	18	1	1	NUM
ejpam-6438	180	19	,	,	PUNCT
ejpam-6438	180	20	j	j	PROPN
ejpam-6438	180	21	−	−	PROPN
ejpam-6438	180	22	1	1	NUM
ejpam-6438	180	23	,	,	PUNCT
ejpam-6438	180	24	j	j	PROPN
ejpam-6438	180	25	}	}	PUNCT
ejpam-6438	180	26	,	,	PUNCT
ejpam-6438	180	27	i	i	PRON
ejpam-6438	180	28	=	=	SYM
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ejpam-6438	180	30	,	,	PUNCT
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ejpam-6438	180	32	=	=	SYM
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ejpam-6438	180	35	n−	n−	NOUN
ejpam-6438	180	36	1	1	NUM
ejpam-6438	180	37	,	,	PUNCT
ejpam-6438	180	38	n−	n−	NOUN
ejpam-6438	180	39	2	2	NUM
ejpam-6438	180	40	,	,	PUNCT
ejpam-6438	180	41	.	.	PUNCT
ejpam-6438	180	42	.	.	PUNCT
ejpam-6438	180	43	.	.	PUNCT
ejpam-6438	181	1	.	.	PUNCT
ejpam-6438	182	1	,	,	PUNCT
ejpam-6438	182	2	1	1	NUM
ejpam-6438	182	3	,	,	PUNCT
ejpam-6438	182	4	n+	n+	NUM
ejpam-6438	182	5	1	1	NUM
ejpam-6438	182	6	,	,	PUNCT
ejpam-6438	182	7	n+	n+	ADP
ejpam-6438	182	8	1	1	NUM
ejpam-6438	182	9	,	,	PUNCT
ejpam-6438	182	10	n	n	CCONJ
ejpam-6438	182	11	,	,	PUNCT
ejpam-6438	182	12	n	n	CCONJ
ejpam-6438	182	13	,	,	PUNCT
ejpam-6438	182	14	n−	n−	NOUN
ejpam-6438	182	15	1	1	NUM
ejpam-6438	182	16	,	,	PUNCT
ejpam-6438	182	17	n−	n−	NOUN
ejpam-6438	182	18	1	1	NUM
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ejpam-6438	182	20	j	j	PROPN
ejpam-6438	182	21	−	−	PROPN
ejpam-6438	182	22	1	1	NUM
ejpam-6438	182	23	,	,	PUNCT
ejpam-6438	182	24	j	j	PROPN
ejpam-6438	182	25	−	−	PROPN
ejpam-6438	182	26	2	2	NUM
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ejpam-6438	182	28	,	,	PUNCT
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ejpam-6438	182	30	=	=	SYM
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ejpam-6438	182	32	,	,	PUNCT
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ejpam-6438	182	34	=	=	SYM
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ejpam-6438	182	36	{	{	PUNCT
ejpam-6438	182	37	n−	n−	NOUN
ejpam-6438	182	38	1	1	NUM
ejpam-6438	182	39	,	,	PUNCT
ejpam-6438	182	40	n−	n−	NOUN
ejpam-6438	182	41	2	2	NUM
ejpam-6438	182	42	,	,	PUNCT
ejpam-6438	182	43	.	.	PUNCT
ejpam-6438	182	44	.	.	PUNCT
ejpam-6438	182	45	.	.	PUNCT
ejpam-6438	183	1	.	.	PUNCT
ejpam-6438	184	1	,	,	PUNCT
ejpam-6438	184	2	1	1	NUM
ejpam-6438	184	3	,	,	PUNCT
ejpam-6438	184	4	n+	n+	NUM
ejpam-6438	184	5	1	1	NUM
ejpam-6438	184	6	,	,	PUNCT
ejpam-6438	184	7	n+	n+	ADP
ejpam-6438	184	8	1	1	NUM
ejpam-6438	184	9	,	,	PUNCT
ejpam-6438	184	10	n	n	CCONJ
ejpam-6438	184	11	,	,	PUNCT
ejpam-6438	184	12	n	n	CCONJ
ejpam-6438	184	13	,	,	PUNCT
ejpam-6438	184	14	n−	n−	NOUN
ejpam-6438	184	15	1	1	NUM
ejpam-6438	184	16	,	,	PUNCT
ejpam-6438	184	17	n−	n−	NOUN
ejpam-6438	184	18	1	1	NUM
ejpam-6438	184	19	,	,	PUNCT
ejpam-6438	184	20	j	j	PROPN
ejpam-6438	185	1	−	−	PROPN
ejpam-6438	185	2	2	2	NUM
ejpam-6438	185	3	,	,	PUNCT
ejpam-6438	185	4	j	j	PROPN
ejpam-6438	185	5	−	−	PROPN
ejpam-6438	185	6	2	2	NUM
ejpam-6438	185	7	}	}	PUNCT
ejpam-6438	185	8	,	,	PUNCT
ejpam-6438	185	9	i	i	PRON
ejpam-6438	185	10	=	=	SYM
ejpam-6438	185	11	n	n	PROPN
ejpam-6438	185	12	,	,	PUNCT
ejpam-6438	185	13	j	j	PROPN
ejpam-6438	185	14	=	=	NOUN
ejpam-6438	185	15	3	3	NUM
ejpam-6438	185	16	hence	hence	ADV
ejpam-6438	185	17	,	,	PUNCT
ejpam-6438	185	18	r	r	NOUN
ejpam-6438	185	19	is	be	AUX
ejpam-6438	185	20	a	a	DET
ejpam-6438	185	21	resolving	resolving	NOUN
ejpam-6438	185	22	set	set	NOUN
ejpam-6438	185	23	.	.	PUNCT
ejpam-6438	186	1	(	(	PUNCT
ejpam-6438	186	2	ii	ii	NOUN
ejpam-6438	186	3	)	)	PUNCT
ejpam-6438	186	4	r	r	NOUN
ejpam-6438	186	5	induces	induce	VERB
ejpam-6438	186	6	a	a	DET
ejpam-6438	186	7	connected	connected	ADJ
ejpam-6438	186	8	subgraph	subgraph	NOUN
ejpam-6438	186	9	.	.	PUNCT
ejpam-6438	187	1	the	the	DET
ejpam-6438	187	2	subgraph	subgraph	NOUN
ejpam-6438	187	3	induced	induce	VERB
ejpam-6438	187	4	by	by	ADP
ejpam-6438	187	5	{	{	PUNCT
ejpam-6438	187	6	v1	v1	NOUN
ejpam-6438	187	7	,	,	PUNCT
ejpam-6438	187	8	.	.	PUNCT
ejpam-6438	187	9	.	.	PUNCT
ejpam-6438	187	10	.	.	PUNCT
ejpam-6438	188	1	,	,	PUNCT
ejpam-6438	188	2	vn	vn	PROPN
ejpam-6438	188	3	}	}	PUNCT
ejpam-6438	188	4	is	be	AUX
ejpam-6438	188	5	a	a	DET
ejpam-6438	188	6	path	path	NOUN
ejpam-6438	188	7	and	and	CCONJ
ejpam-6438	188	8	hence	hence	ADV
ejpam-6438	188	9	connected	connect	VERB
ejpam-6438	188	10	.	.	PUNCT
ejpam-6438	189	1	each	each	DET
ejpam-6438	189	2	ui1	ui1	NOUN
ejpam-6438	189	3	and	and	CCONJ
ejpam-6438	189	4	ui2	ui2	PRON
ejpam-6438	189	5	is	be	AUX
ejpam-6438	189	6	adjacent	adjacent	ADJ
ejpam-6438	189	7	to	to	ADP
ejpam-6438	189	8	vi	vi	PROPN
ejpam-6438	189	9	,	,	PUNCT
ejpam-6438	189	10	so	so	SCONJ
ejpam-6438	189	11	the	the	DET
ejpam-6438	189	12	full	full	ADJ
ejpam-6438	189	13	induced	induced	ADJ
ejpam-6438	189	14	subgraph	subgraph	NOUN
ejpam-6438	189	15	is	be	AUX
ejpam-6438	189	16	connected	connect	VERB
ejpam-6438	189	17	.	.	PUNCT
ejpam-6438	190	1	(	(	PUNCT
ejpam-6438	190	2	iii	iii	X
ejpam-6438	190	3	)	)	PUNCT
ejpam-6438	190	4	r	r	NOUN
ejpam-6438	190	5	is	be	AUX
ejpam-6438	190	6	minimal	minimal	ADJ
ejpam-6438	190	7	.	.	PUNCT
ejpam-6438	191	1	a.	a.	PROPN
ejpam-6438	191	2	elrokh	elrokh	PROPN
ejpam-6438	191	3	,	,	PUNCT
ejpam-6438	191	4	eman	eman	PROPN
ejpam-6438	191	5	s.	s.	PROPN
ejpam-6438	191	6	almotairi	almotairi	PROPN
ejpam-6438	191	7	,	,	PUNCT
ejpam-6438	191	8	h.	h.	PROPN
ejpam-6438	191	9	mostafa	mostafa	PROPN
ejpam-6438	191	10	/	/	SYM
ejpam-6438	191	11	eur	eur	PROPN
ejpam-6438	191	12	.	.	PUNCT
ejpam-6438	192	1	j.	j.	PROPN
ejpam-6438	192	2	pure	pure	PROPN
ejpam-6438	192	3	appl	appl	PROPN
ejpam-6438	192	4	.	.	PROPN
ejpam-6438	192	5	math	math	PROPN
ejpam-6438	192	6	,	,	PUNCT
ejpam-6438	192	7	18	18	NUM
ejpam-6438	192	8	(	(	PUNCT
ejpam-6438	192	9	3	3	NUM
ejpam-6438	192	10	)	)	PUNCT
ejpam-6438	192	11	(	(	PUNCT
ejpam-6438	192	12	2025	2025	NUM
ejpam-6438	192	13	)	)	PUNCT
ejpam-6438	192	14	,	,	PUNCT
ejpam-6438	192	15	6438	6438	NUM
ejpam-6438	192	16	7	7	NUM
ejpam-6438	192	17	of	of	ADP
ejpam-6438	192	18	18	18	NUM
ejpam-6438	192	19	suppose	suppose	VERB
ejpam-6438	192	20	there	there	PRON
ejpam-6438	192	21	exists	exist	VERB
ejpam-6438	192	22	a	a	DET
ejpam-6438	192	23	connected	connected	ADJ
ejpam-6438	192	24	resolving	resolving	NOUN
ejpam-6438	192	25	set	set	VERB
ejpam-6438	192	26	r′	r′	PROPN
ejpam-6438	192	27	with	with	ADP
ejpam-6438	192	28	|r′|	|r′|	NOUN
ejpam-6438	192	29	<	<	X
ejpam-6438	192	30	3n	3n	NUM
ejpam-6438	192	31	.	.	PUNCT
ejpam-6438	193	1	then	then	ADV
ejpam-6438	193	2	for	for	ADP
ejpam-6438	193	3	some	some	DET
ejpam-6438	193	4	i	i	PROPN
ejpam-6438	193	5	,	,	PUNCT
ejpam-6438	193	6	at	at	ADP
ejpam-6438	193	7	most	most	ADJ
ejpam-6438	193	8	one	one	NUM
ejpam-6438	193	9	of	of	ADP
ejpam-6438	193	10	ui1	ui1	PROPN
ejpam-6438	193	11	,	,	PUNCT
ejpam-6438	193	12	ui2	ui2	PROPN
ejpam-6438	193	13	is	be	AUX
ejpam-6438	193	14	in	in	ADP
ejpam-6438	193	15	r′.	r′.	PROPN
ejpam-6438	193	16	but	but	CCONJ
ejpam-6438	193	17	in	in	ADP
ejpam-6438	193	18	a	a	DET
ejpam-6438	193	19	c3	c3	NOUN
ejpam-6438	193	20	cycle	cycle	NOUN
ejpam-6438	193	21	,	,	PUNCT
ejpam-6438	193	22	at	at	ADP
ejpam-6438	193	23	least	least	ADV
ejpam-6438	193	24	two	two	NUM
ejpam-6438	193	25	vertices	vertex	NOUN
ejpam-6438	193	26	are	be	AUX
ejpam-6438	193	27	needed	need	VERB
ejpam-6438	193	28	to	to	PART
ejpam-6438	193	29	resolve	resolve	VERB
ejpam-6438	193	30	all	all	DET
ejpam-6438	193	31	three	three	NUM
ejpam-6438	193	32	vertices	vertex	NOUN
ejpam-6438	193	33	.	.	PUNCT
ejpam-6438	194	1	removing	remove	VERB
ejpam-6438	194	2	any	any	DET
ejpam-6438	194	3	vi	vi	NOUN
ejpam-6438	194	4	would	would	AUX
ejpam-6438	194	5	disconnect	disconnect	VERB
ejpam-6438	194	6	the	the	DET
ejpam-6438	194	7	corresponding	corresponding	PROPN
ejpam-6438	194	8	c3	c3	PROPN
ejpam-6438	194	9	copy	copy	NOUN
ejpam-6438	194	10	from	from	ADP
ejpam-6438	194	11	the	the	DET
ejpam-6438	194	12	rest	rest	NOUN
ejpam-6438	194	13	of	of	ADP
ejpam-6438	194	14	the	the	DET
ejpam-6438	194	15	graph	graph	NOUN
ejpam-6438	194	16	.	.	PUNCT
ejpam-6438	195	1	thus	thus	ADV
ejpam-6438	195	2	,	,	PUNCT
ejpam-6438	195	3	r′	r′	PROPN
ejpam-6438	195	4	can	can	AUX
ejpam-6438	195	5	not	not	PART
ejpam-6438	195	6	be	be	AUX
ejpam-6438	195	7	both	both	PRON
ejpam-6438	195	8	resolving	resolve	VERB
ejpam-6438	195	9	and	and	CCONJ
ejpam-6438	195	10	connected	connect	VERB
ejpam-6438	195	11	.	.	PUNCT
ejpam-6438	196	1	therefore	therefore	ADV
ejpam-6438	196	2	,	,	PUNCT
ejpam-6438	196	3	r	r	NOUN
ejpam-6438	196	4	is	be	AUX
ejpam-6438	196	5	a	a	DET
ejpam-6438	196	6	minimal	minimal	ADJ
ejpam-6438	196	7	connected	connected	ADJ
ejpam-6438	196	8	resolving	resolving	NOUN
ejpam-6438	196	9	set	set	VERB
ejpam-6438	196	10	of	of	ADP
ejpam-6438	196	11	size	size	NOUN
ejpam-6438	196	12	3n	3n	NUM
ejpam-6438	196	13	.	.	PUNCT
ejpam-6438	197	1	theorem	theorem	VERB
ejpam-6438	197	2	3	3	NUM
ejpam-6438	197	3	:	:	PUNCT
ejpam-6438	197	4	the	the	DET
ejpam-6438	197	5	connected	connected	ADJ
ejpam-6438	197	6	metric	metric	ADJ
ejpam-6438	197	7	dimension	dimension	NOUN
ejpam-6438	197	8	of	of	ADP
ejpam-6438	197	9	cn	cn	PROPN
ejpam-6438	197	10	⊙	⊙	PROPN
ejpam-6438	197	11	p3	p3	PROPN
ejpam-6438	197	12	equal	equal	ADJ
ejpam-6438	197	13	to	to	ADP
ejpam-6438	197	14	2n	2n	NUM
ejpam-6438	197	15	,	,	PUNCT
ejpam-6438	197	16	if	if	SCONJ
ejpam-6438	197	17	n	n	PRON
ejpam-6438	197	18	≥	≥	NOUN
ejpam-6438	197	19	3	3	NUM
ejpam-6438	197	20	.	.	PUNCT
ejpam-6438	198	1	proof	proof	NOUN
ejpam-6438	198	2	.	.	PUNCT
ejpam-6438	199	1	the	the	DET
ejpam-6438	199	2	corona	corona	NOUN
ejpam-6438	199	3	product	product	NOUN
ejpam-6438	199	4	cn	cn	PROPN
ejpam-6438	199	5	⊙	⊙	PROPN
ejpam-6438	199	6	p3	p3	PROPN
ejpam-6438	199	7	is	be	AUX
ejpam-6438	199	8	formed	form	VERB
ejpam-6438	199	9	by	by	ADP
ejpam-6438	199	10	taking	take	VERB
ejpam-6438	199	11	a	a	DET
ejpam-6438	199	12	cycle	cycle	NOUN
ejpam-6438	199	13	cn	cn	NOUN
ejpam-6438	199	14	with	with	ADP
ejpam-6438	199	15	vertices	vertex	NOUN
ejpam-6438	199	16	v1	v1	NOUN
ejpam-6438	199	17	,	,	PUNCT
ejpam-6438	199	18	v2	v2	NOUN
ejpam-6438	199	19	,	,	PUNCT
ejpam-6438	199	20	.	.	PUNCT
ejpam-6438	199	21	.	.	PUNCT
ejpam-6438	199	22	.	.	PUNCT
ejpam-6438	200	1	,	,	PUNCT
ejpam-6438	200	2	vn	vn	PROPN
ejpam-6438	200	3	and	and	CCONJ
ejpam-6438	200	4	attaching	attach	VERB
ejpam-6438	200	5	to	to	ADP
ejpam-6438	200	6	each	each	DET
ejpam-6438	200	7	vi	vi	NOUN
ejpam-6438	200	8	a	a	DET
ejpam-6438	200	9	copy	copy	NOUN
ejpam-6438	200	10	of	of	ADP
ejpam-6438	200	11	p3	p3	PROPN
ejpam-6438	200	12	with	with	ADP
ejpam-6438	200	13	vertices	vertex	NOUN
ejpam-6438	200	14	ui1	ui1	ADV
ejpam-6438	200	15	,	,	PUNCT
ejpam-6438	200	16	ui2	ui2	PROPN
ejpam-6438	200	17	,	,	PUNCT
ejpam-6438	200	18	ui3	ui3	PROPN
ejpam-6438	200	19	,	,	PUNCT
ejpam-6438	200	20	where	where	SCONJ
ejpam-6438	200	21	each	each	DET
ejpam-6438	200	22	uij	uij	PRON
ejpam-6438	200	23	is	be	AUX
ejpam-6438	200	24	connected	connect	VERB
ejpam-6438	200	25	to	to	ADP
ejpam-6438	200	26	vi	vi	PROPN
ejpam-6438	200	27	,	,	PUNCT
ejpam-6438	200	28	as	as	SCONJ
ejpam-6438	200	29	show	show	NOUN
ejpam-6438	200	30	in	in	ADP
ejpam-6438	200	31	figure	figure	NOUN
ejpam-6438	200	32	7	7	NUM
ejpam-6438	200	33	.	.	PUNCT
ejpam-6438	201	1	we	we	PRON
ejpam-6438	201	2	construct	construct	VERB
ejpam-6438	201	3	a	a	DET
ejpam-6438	201	4	set	set	NOUN
ejpam-6438	201	5	r	r	NOUN
ejpam-6438	201	6	consisting	consist	VERB
ejpam-6438	201	7	of	of	ADP
ejpam-6438	201	8	:	:	PUNCT
ejpam-6438	201	9	r	r	NOUN
ejpam-6438	201	10	=	=	SYM
ejpam-6438	201	11	{	{	PUNCT
ejpam-6438	201	12	v1	v1	NOUN
ejpam-6438	201	13	,	,	PUNCT
ejpam-6438	201	14	v2	v2	PROPN
ejpam-6438	201	15	,	,	PUNCT
ejpam-6438	201	16	.	.	PUNCT
ejpam-6438	201	17	.	.	PUNCT
ejpam-6438	201	18	.	.	PUNCT
ejpam-6438	202	1	,	,	PUNCT
ejpam-6438	202	2	vn	vn	VERB
ejpam-6438	202	3	}	}	PUNCT
ejpam-6438	202	4	∪	∪	X
ejpam-6438	202	5	{	{	PUNCT
ejpam-6438	202	6	ui1	ui1	NOUN
ejpam-6438	202	7	|	|	ADV
ejpam-6438	202	8	1	1	NUM
ejpam-6438	202	9	≤	≤	NUM
ejpam-6438	202	10	i	i	PRON
ejpam-6438	202	11	≤	≤	NOUN
ejpam-6438	202	12	n	n	CCONJ
ejpam-6438	202	13	}	}	PUNCT
ejpam-6438	202	14	thus	thus	ADV
ejpam-6438	202	15	,	,	PUNCT
ejpam-6438	202	16	|r|	|r|	NOUN
ejpam-6438	202	17	=	=	SYM
ejpam-6438	202	18	2n	2n	NUM
ejpam-6438	202	19	.	.	PUNCT
ejpam-6438	203	1	resolving	resolve	VERB
ejpam-6438	203	2	property	property	NOUN
ejpam-6438	203	3	:	:	PUNCT
ejpam-6438	203	4	•	•	ADP
ejpam-6438	203	5	each	each	DET
ejpam-6438	203	6	vi	vi	NOUN
ejpam-6438	203	7	is	be	AUX
ejpam-6438	203	8	in	in	ADP
ejpam-6438	203	9	r	r	NOUN
ejpam-6438	203	10	,	,	PUNCT
ejpam-6438	203	11	so	so	ADV
ejpam-6438	203	12	any	any	DET
ejpam-6438	203	13	pair	pair	NOUN
ejpam-6438	203	14	of	of	ADP
ejpam-6438	203	15	vi	vi	PROPN
ejpam-6438	203	16	,	,	PUNCT
ejpam-6438	203	17	vj	vj	PROPN
ejpam-6438	203	18	is	be	AUX
ejpam-6438	203	19	trivially	trivially	ADV
ejpam-6438	203	20	resolved	resolve	VERB
ejpam-6438	203	21	.	.	PUNCT
ejpam-6438	204	1	•	•	NUM
ejpam-6438	204	2	for	for	ADP
ejpam-6438	204	3	each	each	DET
ejpam-6438	204	4	p3	p3	PROPN
ejpam-6438	204	5	copy	copy	NOUN
ejpam-6438	204	6	,	,	PUNCT
ejpam-6438	204	7	the	the	DET
ejpam-6438	204	8	inclusion	inclusion	NOUN
ejpam-6438	204	9	of	of	ADP
ejpam-6438	204	10	ui1	ui1	PROPN
ejpam-6438	204	11	and	and	CCONJ
ejpam-6438	204	12	vi	vi	NOUN
ejpam-6438	204	13	ensures	ensure	VERB
ejpam-6438	204	14	that	that	SCONJ
ejpam-6438	204	15	the	the	DET
ejpam-6438	204	16	other	other	ADJ
ejpam-6438	204	17	two	two	NUM
ejpam-6438	204	18	vertices	vertex	NOUN
ejpam-6438	204	19	ui2	ui2	PROPN
ejpam-6438	204	20	,	,	PUNCT
ejpam-6438	204	21	ui3	ui3	PROPN
ejpam-6438	204	22	are	be	AUX
ejpam-6438	204	23	uniquely	uniquely	ADV
ejpam-6438	204	24	identified	identify	VERB
ejpam-6438	204	25	by	by	ADP
ejpam-6438	204	26	their	their	PRON
ejpam-6438	204	27	distances	distance	NOUN
ejpam-6438	204	28	to	to	ADP
ejpam-6438	204	29	ui1	ui1	PROPN
ejpam-6438	204	30	and	and	CCONJ
ejpam-6438	204	31	vi	vi	NOUN
ejpam-6438	204	32	.	.	NOUN
ejpam-6438	205	1	•	•	NUM
ejpam-6438	205	2	vertices	vertex	NOUN
ejpam-6438	205	3	from	from	ADP
ejpam-6438	205	4	different	different	ADJ
ejpam-6438	205	5	p3	p3	PROPN
ejpam-6438	205	6	copies	copy	NOUN
ejpam-6438	205	7	are	be	AUX
ejpam-6438	205	8	distinguished	distinguish	VERB
ejpam-6438	205	9	by	by	ADP
ejpam-6438	205	10	their	their	PRON
ejpam-6438	205	11	distances	distance	NOUN
ejpam-6438	205	12	to	to	ADP
ejpam-6438	205	13	the	the	DET
ejpam-6438	205	14	corresponding	corresponding	ADJ
ejpam-6438	205	15	vi	vi	PROPN
ejpam-6438	205	16	and	and	CCONJ
ejpam-6438	205	17	ui1	ui1	PROPN
ejpam-6438	205	18	.	.	PUNCT
ejpam-6438	206	1	figure	figure	VERB
ejpam-6438	206	2	7	7	NUM
ejpam-6438	206	3	.	.	PUNCT
ejpam-6438	207	1	the	the	DET
ejpam-6438	207	2	cn	cn	PROPN
ejpam-6438	207	3	⊙	⊙	PROPN
ejpam-6438	207	4	p3	p3	PROPN
ejpam-6438	207	5	graph	graph	NOUN
ejpam-6438	207	6	.	.	PUNCT
ejpam-6438	208	1	w	w	PROPN
ejpam-6438	208	2	(	(	PUNCT
ejpam-6438	208	3	vi	vi	PROPN
ejpam-6438	208	4	,	,	PUNCT
ejpam-6438	208	5	r	r	NOUN
ejpam-6438	208	6	)	)	PUNCT
ejpam-6438	208	7	=	=	SYM
ejpam-6438	208	8			X
ejpam-6438	208	9	{	{	PUNCT
ejpam-6438	208	10	0	0	NUM
ejpam-6438	208	11	,	,	PUNCT
ejpam-6438	208	12	1	1	NUM
ejpam-6438	208	13	,	,	PUNCT
ejpam-6438	208	14	2	2	NUM
ejpam-6438	208	15	,	,	PUNCT
ejpam-6438	208	16	.	.	PUNCT
ejpam-6438	208	17	.	.	PUNCT
ejpam-6438	208	18	.	.	PUNCT
ejpam-6438	209	1	,	,	PUNCT
ejpam-6438	209	2	1	1	NUM
ejpam-6438	209	3	,	,	PUNCT
ejpam-6438	209	4	1	1	NUM
ejpam-6438	209	5	,	,	PUNCT
ejpam-6438	209	6	2	2	NUM
ejpam-6438	209	7	,	,	PUNCT
ejpam-6438	209	8	.	.	PUNCT
ejpam-6438	209	9	.	.	PUNCT
ejpam-6438	209	10	.	.	PUNCT
ejpam-6438	210	1	,	,	PUNCT
ejpam-6438	210	2	2	2	X
ejpam-6438	210	3	}	}	PUNCT
ejpam-6438	210	4	,	,	PUNCT
ejpam-6438	210	5	i	i	PRON
ejpam-6438	210	6	=	=	NOUN
ejpam-6438	210	7	1	1	NUM
ejpam-6438	210	8	{	{	PUNCT
ejpam-6438	210	9	1	1	NUM
ejpam-6438	210	10	,	,	PUNCT
ejpam-6438	210	11	0	0	NUM
ejpam-6438	210	12	,	,	PUNCT
ejpam-6438	210	13	1	1	NUM
ejpam-6438	210	14	,	,	PUNCT
ejpam-6438	210	15	.	.	PUNCT
ejpam-6438	210	16	.	.	PUNCT
ejpam-6438	210	17	.	.	PUNCT
ejpam-6438	211	1	,	,	PUNCT
ejpam-6438	211	2	2	2	NUM
ejpam-6438	211	3	,	,	PUNCT
ejpam-6438	211	4	2	2	NUM
ejpam-6438	211	5	,	,	PUNCT
ejpam-6438	211	6	1	1	NUM
ejpam-6438	211	7	,	,	PUNCT
ejpam-6438	211	8	2	2	NUM
ejpam-6438	211	9	,	,	PUNCT
ejpam-6438	211	10	.	.	PUNCT
ejpam-6438	211	11	.	.	PUNCT
ejpam-6438	211	12	.	.	PUNCT
ejpam-6438	212	1	,	,	PUNCT
ejpam-6438	212	2	2	2	X
ejpam-6438	212	3	}	}	PUNCT
ejpam-6438	212	4	,	,	PUNCT
ejpam-6438	212	5	i	i	PRON
ejpam-6438	212	6	=	=	NOUN
ejpam-6438	212	7	2	2	NUM
ejpam-6438	212	8	{	{	PUNCT
ejpam-6438	212	9	2	2	NUM
ejpam-6438	212	10	,	,	PUNCT
ejpam-6438	212	11	1	1	NUM
ejpam-6438	212	12	,	,	PUNCT
ejpam-6438	212	13	0	0	NUM
ejpam-6438	212	14	,	,	PUNCT
ejpam-6438	212	15	1	1	NUM
ejpam-6438	212	16	,	,	PUNCT
ejpam-6438	212	17	.	.	PUNCT
ejpam-6438	212	18	.	.	PUNCT
ejpam-6438	212	19	.	.	PUNCT
ejpam-6438	213	1	,	,	PUNCT
ejpam-6438	213	2	2	2	NUM
ejpam-6438	213	3	,	,	PUNCT
ejpam-6438	213	4	3	3	NUM
ejpam-6438	213	5	,	,	PUNCT
ejpam-6438	213	6	2	2	NUM
ejpam-6438	213	7	,	,	PUNCT
ejpam-6438	213	8	1	1	NUM
ejpam-6438	213	9	,	,	PUNCT
ejpam-6438	213	10	.	.	PUNCT
ejpam-6438	213	11	.	.	PUNCT
ejpam-6438	213	12	.	.	PUNCT
ejpam-6438	214	1	,	,	PUNCT
ejpam-6438	214	2	3	3	X
ejpam-6438	214	3	}	}	PUNCT
ejpam-6438	214	4	,	,	PUNCT
ejpam-6438	214	5	i	i	PRON
ejpam-6438	214	6	=	=	NOUN
ejpam-6438	214	7	3	3	NUM
ejpam-6438	214	8	:	:	PUNCT
ejpam-6438	214	9	:	:	PUNCT
ejpam-6438	214	10	:	:	PUNCT
ejpam-6438	214	11	:	:	PUNCT
ejpam-6438	214	12	{	{	PUNCT
ejpam-6438	214	13	1	1	NUM
ejpam-6438	214	14	,	,	PUNCT
ejpam-6438	214	15	2	2	NUM
ejpam-6438	214	16	,	,	PUNCT
ejpam-6438	214	17	3	3	NUM
ejpam-6438	214	18	,	,	PUNCT
ejpam-6438	214	19	.	.	PUNCT
ejpam-6438	214	20	.	.	PUNCT
ejpam-6438	214	21	.	.	PUNCT
ejpam-6438	215	1	,	,	PUNCT
ejpam-6438	215	2	0	0	NUM
ejpam-6438	215	3	,	,	PUNCT
ejpam-6438	215	4	2	2	NUM
ejpam-6438	215	5	,	,	PUNCT
ejpam-6438	215	6	3	3	NUM
ejpam-6438	215	7	,	,	PUNCT
ejpam-6438	215	8	n−	n−	NOUN
ejpam-6438	215	9	2	2	NUM
ejpam-6438	215	10	,	,	PUNCT
ejpam-6438	215	11	.	.	PUNCT
ejpam-6438	215	12	.	.	PUNCT
ejpam-6438	216	1	.	.	PUNCT
ejpam-6438	217	1	,	,	PUNCT
ejpam-6438	217	2	2	2	NUM
ejpam-6438	217	3	,	,	PUNCT
ejpam-6438	217	4	1	1	NUM
ejpam-6438	217	5	}	}	PUNCT
ejpam-6438	217	6	.i	.i	PUNCT
ejpam-6438	218	1	=	=	SYM
ejpam-6438	218	2	n	n	NOUN
ejpam-6438	218	3	a.	a.	NOUN
ejpam-6438	218	4	elrokh	elrokh	NOUN
ejpam-6438	218	5	,	,	PUNCT
ejpam-6438	218	6	eman	eman	PROPN
ejpam-6438	218	7	s.	s.	PROPN
ejpam-6438	218	8	almotairi	almotairi	PROPN
ejpam-6438	218	9	,	,	PUNCT
ejpam-6438	218	10	h.	h.	PROPN
ejpam-6438	218	11	mostafa	mostafa	PROPN
ejpam-6438	218	12	/	/	SYM
ejpam-6438	218	13	eur	eur	PROPN
ejpam-6438	218	14	.	.	PUNCT
ejpam-6438	219	1	j.	j.	PROPN
ejpam-6438	219	2	pure	pure	PROPN
ejpam-6438	219	3	appl	appl	PROPN
ejpam-6438	219	4	.	.	PROPN
ejpam-6438	219	5	math	math	PROPN
ejpam-6438	219	6	,	,	PUNCT
ejpam-6438	219	7	18	18	NUM
ejpam-6438	219	8	(	(	PUNCT
ejpam-6438	219	9	3	3	NUM
ejpam-6438	219	10	)	)	PUNCT
ejpam-6438	219	11	(	(	PUNCT
ejpam-6438	219	12	2025	2025	NUM
ejpam-6438	219	13	)	)	PUNCT
ejpam-6438	219	14	,	,	PUNCT
ejpam-6438	219	15	6438	6438	NUM
ejpam-6438	219	16	8	8	NUM
ejpam-6438	219	17	of	of	ADP
ejpam-6438	219	18	18	18	NUM
ejpam-6438	219	19	w	w	NOUN
ejpam-6438	219	20	(	(	PUNCT
ejpam-6438	219	21	uij	uij	PRON
ejpam-6438	219	22	,	,	PUNCT
ejpam-6438	219	23	r	r	NOUN
ejpam-6438	219	24	)	)	PUNCT
ejpam-6438	219	25	=	=	SYM
ejpam-6438	219	26			X
ejpam-6438	219	27	{	{	PUNCT
ejpam-6438	219	28	1	1	NUM
ejpam-6438	219	29	,	,	PUNCT
ejpam-6438	219	30	2	2	NUM
ejpam-6438	219	31	,	,	PUNCT
ejpam-6438	219	32	3	3	NUM
ejpam-6438	219	33	,	,	PUNCT
ejpam-6438	219	34	.	.	PUNCT
ejpam-6438	219	35	.	.	PUNCT
ejpam-6438	220	1	.	.	PUNCT
ejpam-6438	221	1	,	,	PUNCT
ejpam-6438	221	2	2	2	X
ejpam-6438	221	3	,	,	PUNCT
ejpam-6438	221	4	j	j	PROPN
ejpam-6438	221	5	−	−	PROPN
ejpam-6438	221	6	1	1	NUM
ejpam-6438	221	7	,	,	PUNCT
ejpam-6438	221	8	3	3	NUM
ejpam-6438	221	9	,	,	PUNCT
ejpam-6438	221	10	4	4	NUM
ejpam-6438	221	11	,	,	PUNCT
ejpam-6438	221	12	.	.	PUNCT
ejpam-6438	221	13	.	.	PUNCT
ejpam-6438	221	14	.	.	PUNCT
ejpam-6438	222	1	,	,	PUNCT
ejpam-6438	222	2	3	3	X
ejpam-6438	222	3	}	}	PUNCT
ejpam-6438	222	4	,	,	PUNCT
ejpam-6438	222	5	i	i	PRON
ejpam-6438	222	6	=	=	NOUN
ejpam-6438	222	7	1	1	NUM
ejpam-6438	222	8	{	{	PUNCT
ejpam-6438	222	9	2	2	NUM
ejpam-6438	222	10	,	,	PUNCT
ejpam-6438	222	11	1	1	NUM
ejpam-6438	222	12	,	,	PUNCT
ejpam-6438	222	13	2	2	NUM
ejpam-6438	222	14	,	,	PUNCT
ejpam-6438	222	15	.	.	PUNCT
ejpam-6438	222	16	.	.	PUNCT
ejpam-6438	222	17	.	.	PUNCT
ejpam-6438	223	1	,	,	PUNCT
ejpam-6438	223	2	3	3	NUM
ejpam-6438	223	3	,	,	PUNCT
ejpam-6438	223	4	3	3	NUM
ejpam-6438	223	5	,	,	PUNCT
ejpam-6438	223	6	j	j	PROPN
ejpam-6438	223	7	−	−	PROPN
ejpam-6438	223	8	1	1	NUM
ejpam-6438	223	9	,	,	PUNCT
ejpam-6438	223	10	3	3	NUM
ejpam-6438	223	11	,	,	PUNCT
ejpam-6438	223	12	.	.	PUNCT
ejpam-6438	223	13	.	.	PUNCT
ejpam-6438	223	14	.	.	PUNCT
ejpam-6438	224	1	,	,	PUNCT
ejpam-6438	224	2	n−	n−	NOUN
ejpam-6438	224	3	2	2	NUM
ejpam-6438	224	4	,	,	PUNCT
ejpam-6438	224	5	n−	n−	NOUN
ejpam-6438	224	6	1	1	NUM
ejpam-6438	224	7	,	,	PUNCT
ejpam-6438	224	8	4	4	NUM
ejpam-6438	224	9	}	}	PUNCT
ejpam-6438	224	10	,	,	PUNCT
ejpam-6438	224	11	i	i	PRON
ejpam-6438	224	12	=	=	NOUN
ejpam-6438	224	13	2	2	NUM
ejpam-6438	224	14	{	{	PUNCT
ejpam-6438	224	15	3	3	NUM
ejpam-6438	224	16	,	,	PUNCT
ejpam-6438	224	17	2	2	NUM
ejpam-6438	224	18	,	,	PUNCT
ejpam-6438	224	19	1	1	NUM
ejpam-6438	224	20	,	,	PUNCT
ejpam-6438	224	21	2	2	NUM
ejpam-6438	224	22	,	,	PUNCT
ejpam-6438	224	23	.	.	PUNCT
ejpam-6438	224	24	.	.	PUNCT
ejpam-6438	225	1	.	.	PUNCT
ejpam-6438	226	1	,	,	PUNCT
ejpam-6438	226	2	n−	n−	NOUN
ejpam-6438	226	3	2	2	NUM
ejpam-6438	226	4	,	,	PUNCT
ejpam-6438	226	5	4	4	NUM
ejpam-6438	226	6	,	,	PUNCT
ejpam-6438	226	7	3	3	NUM
ejpam-6438	226	8	,	,	PUNCT
ejpam-6438	226	9	j	j	PROPN
ejpam-6438	226	10	−	−	PROPN
ejpam-6438	226	11	1	1	NUM
ejpam-6438	226	12	,	,	PUNCT
ejpam-6438	226	13	3	3	NUM
ejpam-6438	226	14	,	,	PUNCT
ejpam-6438	226	15	4	4	NUM
ejpam-6438	226	16	,	,	PUNCT
ejpam-6438	226	17	.	.	PUNCT
ejpam-6438	226	18	.	.	PUNCT
ejpam-6438	227	1	.	.	PUNCT
ejpam-6438	228	1	,	,	PUNCT
ejpam-6438	228	2	n−	n−	NOUN
ejpam-6438	228	3	2	2	NUM
ejpam-6438	228	4	,	,	PUNCT
ejpam-6438	228	5	n−	n−	NOUN
ejpam-6438	228	6	1	1	NUM
ejpam-6438	228	7	}	}	PUNCT
ejpam-6438	228	8	,	,	PUNCT
ejpam-6438	228	9	i	i	PRON
ejpam-6438	228	10	=	=	NOUN
ejpam-6438	228	11	3	3	NUM
ejpam-6438	228	12	:	:	PUNCT
ejpam-6438	228	13	:	:	PUNCT
ejpam-6438	228	14	:	:	PUNCT
ejpam-6438	228	15	:	:	PUNCT
ejpam-6438	228	16	{	{	PUNCT
ejpam-6438	228	17	1	1	NUM
ejpam-6438	228	18	,	,	PUNCT
ejpam-6438	228	19	2	2	NUM
ejpam-6438	228	20	,	,	PUNCT
ejpam-6438	228	21	3	3	NUM
ejpam-6438	228	22	,	,	PUNCT
ejpam-6438	228	23	4	4	NUM
ejpam-6438	228	24	.	.	PUNCT
ejpam-6438	228	25	.	.	PUNCT
ejpam-6438	229	1	.	.	PUNCT
ejpam-6438	230	1	,	,	PUNCT
ejpam-6438	230	2	1	1	NUM
ejpam-6438	230	3	,	,	PUNCT
ejpam-6438	230	4	3	3	NUM
ejpam-6438	230	5	,	,	PUNCT
ejpam-6438	230	6	4	4	NUM
ejpam-6438	230	7	,	,	PUNCT
ejpam-6438	230	8	.	.	PUNCT
ejpam-6438	230	9	.	.	PUNCT
ejpam-6438	230	10	.	.	PUNCT
ejpam-6438	231	1	,	,	PUNCT
ejpam-6438	231	2	4	4	NUM
ejpam-6438	231	3	,	,	PUNCT
ejpam-6438	231	4	3	3	NUM
ejpam-6438	231	5	,	,	PUNCT
ejpam-6438	231	6	j	j	PROPN
ejpam-6438	231	7	−	−	PROPN
ejpam-6438	231	8	1	1	NUM
ejpam-6438	231	9	}	}	PUNCT
ejpam-6438	231	10	.i	.i	PUNCT
ejpam-6438	232	1	=	=	PUNCT
ejpam-6438	232	2	n	n	PRON
ejpam-6438	232	3	connectivity	connectivity	NOUN
ejpam-6438	232	4	:	:	PUNCT
ejpam-6438	232	5	the	the	DET
ejpam-6438	232	6	subgraph	subgraph	NOUN
ejpam-6438	232	7	induced	induce	VERB
ejpam-6438	232	8	by	by	ADP
ejpam-6438	232	9	r	r	NOUN
ejpam-6438	232	10	includes	include	VERB
ejpam-6438	232	11	the	the	DET
ejpam-6438	232	12	cycle	cycle	NOUN
ejpam-6438	232	13	cn	cn	PROPN
ejpam-6438	232	14	(	(	PUNCT
ejpam-6438	232	15	which	which	PRON
ejpam-6438	232	16	is	be	AUX
ejpam-6438	232	17	connected	connect	VERB
ejpam-6438	232	18	)	)	PUNCT
ejpam-6438	232	19	and	and	CCONJ
ejpam-6438	232	20	each	each	DET
ejpam-6438	232	21	ui1	ui1	NOUN
ejpam-6438	232	22	is	be	AUX
ejpam-6438	232	23	connected	connect	VERB
ejpam-6438	232	24	to	to	ADP
ejpam-6438	232	25	vi	vi	PROPN
ejpam-6438	232	26	,	,	PUNCT
ejpam-6438	232	27	forming	form	VERB
ejpam-6438	232	28	a	a	DET
ejpam-6438	232	29	connected	connected	ADJ
ejpam-6438	232	30	tree	tree	NOUN
ejpam-6438	232	31	-	-	PUNCT
ejpam-6438	232	32	like	like	ADJ
ejpam-6438	232	33	structure	structure	NOUN
ejpam-6438	232	34	rooted	root	VERB
ejpam-6438	232	35	at	at	ADP
ejpam-6438	232	36	the	the	DET
ejpam-6438	232	37	cycle	cycle	NOUN
ejpam-6438	232	38	.	.	PUNCT
ejpam-6438	233	1	minimality	minimality	NOUN
ejpam-6438	233	2	:	:	PUNCT
ejpam-6438	233	3	suppose	suppose	VERB
ejpam-6438	233	4	a	a	DET
ejpam-6438	233	5	smaller	small	ADJ
ejpam-6438	233	6	connected	connected	ADJ
ejpam-6438	233	7	resolving	resolving	NOUN
ejpam-6438	233	8	set	set	VERB
ejpam-6438	233	9	r′	r′	NOUN
ejpam-6438	233	10	exists	exist	NOUN
ejpam-6438	233	11	with	with	ADP
ejpam-6438	233	12	|r′|	|r′|	PROPN
ejpam-6438	233	13	<	<	X
ejpam-6438	233	14	2n	2n	NUM
ejpam-6438	233	15	.	.	PUNCT
ejpam-6438	234	1	then	then	ADV
ejpam-6438	234	2	at	at	ADV
ejpam-6438	234	3	least	least	ADV
ejpam-6438	234	4	one	one	NUM
ejpam-6438	234	5	vi	vi	NOUN
ejpam-6438	234	6	or	or	CCONJ
ejpam-6438	234	7	ui1	ui1	NOUN
ejpam-6438	234	8	is	be	AUX
ejpam-6438	234	9	missing	missing	ADJ
ejpam-6438	234	10	.	.	PUNCT
ejpam-6438	235	1	if	if	SCONJ
ejpam-6438	235	2	vi	vi	PROPN
ejpam-6438	235	3	/∈	/∈	PUNCT
ejpam-6438	236	1	r′	r′	PROPN
ejpam-6438	236	2	,	,	PUNCT
ejpam-6438	236	3	then	then	ADV
ejpam-6438	236	4	ui1	ui1	PROPN
ejpam-6438	236	5	may	may	AUX
ejpam-6438	236	6	become	become	VERB
ejpam-6438	236	7	disconnected	disconnected	ADJ
ejpam-6438	236	8	or	or	CCONJ
ejpam-6438	236	9	fail	fail	VERB
ejpam-6438	236	10	to	to	PART
ejpam-6438	236	11	resolve	resolve	VERB
ejpam-6438	236	12	its	its	PRON
ejpam-6438	236	13	p3	p3	PROPN
ejpam-6438	236	14	copy	copy	NOUN
ejpam-6438	236	15	.	.	PUNCT
ejpam-6438	237	1	if	if	SCONJ
ejpam-6438	237	2	ui1	ui1	PROPN
ejpam-6438	237	3	/∈	/∈	PUNCT
ejpam-6438	238	1	r′	r′	PROPN
ejpam-6438	238	2	,	,	PUNCT
ejpam-6438	238	3	then	then	ADV
ejpam-6438	238	4	ui2	ui2	PROPN
ejpam-6438	238	5	,	,	PUNCT
ejpam-6438	238	6	ui3	ui3	PROPN
ejpam-6438	238	7	may	may	AUX
ejpam-6438	238	8	not	not	PART
ejpam-6438	238	9	be	be	AUX
ejpam-6438	238	10	distinguishable	distinguishable	ADJ
ejpam-6438	238	11	.	.	PUNCT
ejpam-6438	239	1	hence	hence	ADV
ejpam-6438	239	2	,	,	PUNCT
ejpam-6438	239	3	r	r	NOUN
ejpam-6438	239	4	is	be	AUX
ejpam-6438	239	5	minimal	minimal	ADJ
ejpam-6438	239	6	.	.	PUNCT
ejpam-6438	240	1	therefore	therefore	ADV
ejpam-6438	240	2	,	,	PUNCT
ejpam-6438	240	3	cdim(cn	cdim(cn	PROPN
ejpam-6438	240	4	⊙	⊙	PROPN
ejpam-6438	240	5	p3	p3	PROPN
ejpam-6438	240	6	)	)	PUNCT
ejpam-6438	240	7	=	=	PUNCT
ejpam-6438	240	8	2n	2n	X
ejpam-6438	240	9	.	.	PUNCT
ejpam-6438	240	10	theorem	theorem	VERB
ejpam-6438	240	11	4	4	NUM
ejpam-6438	240	12	:	:	PUNCT
ejpam-6438	240	13	if	if	SCONJ
ejpam-6438	240	14	n	n	PRON
ejpam-6438	240	15	≥	≥	NOUN
ejpam-6438	240	16	3	3	NUM
ejpam-6438	240	17	,	,	PUNCT
ejpam-6438	240	18	then	then	ADV
ejpam-6438	240	19	connected	connect	VERB
ejpam-6438	240	20	metric	metric	ADJ
ejpam-6438	240	21	dimension	dimension	NOUN
ejpam-6438	240	22	of	of	ADP
ejpam-6438	240	23	cn	cn	PROPN
ejpam-6438	240	24	⊙	⊙	PROPN
ejpam-6438	240	25	c3	c3	PROPN
ejpam-6438	240	26	graphs	graph	NOUN
ejpam-6438	240	27	are	be	AUX
ejpam-6438	240	28	equal	equal	ADJ
ejpam-6438	240	29	3n	3n	NOUN
ejpam-6438	240	30	.	.	PUNCT
ejpam-6438	241	1	proof	proof	NOUN
ejpam-6438	241	2	.	.	PUNCT
ejpam-6438	242	1	the	the	DET
ejpam-6438	242	2	corona	corona	NOUN
ejpam-6438	242	3	product	product	NOUN
ejpam-6438	242	4	cn	cn	PROPN
ejpam-6438	242	5	⊙	⊙	PROPN
ejpam-6438	242	6	c3	c3	PROPN
ejpam-6438	242	7	is	be	AUX
ejpam-6438	242	8	formed	form	VERB
ejpam-6438	242	9	by	by	ADP
ejpam-6438	242	10	taking	take	VERB
ejpam-6438	242	11	a	a	DET
ejpam-6438	242	12	cycle	cycle	NOUN
ejpam-6438	242	13	cn	cn	NOUN
ejpam-6438	242	14	with	with	ADP
ejpam-6438	242	15	vertices	vertex	NOUN
ejpam-6438	242	16	v1	v1	NOUN
ejpam-6438	242	17	,	,	PUNCT
ejpam-6438	242	18	v2	v2	NOUN
ejpam-6438	242	19	,	,	PUNCT
ejpam-6438	242	20	.	.	PUNCT
ejpam-6438	242	21	.	.	PUNCT
ejpam-6438	242	22	.	.	PUNCT
ejpam-6438	243	1	,	,	PUNCT
ejpam-6438	243	2	vn	vn	PROPN
ejpam-6438	243	3	and	and	CCONJ
ejpam-6438	243	4	attaching	attach	VERB
ejpam-6438	243	5	to	to	ADP
ejpam-6438	243	6	each	each	DET
ejpam-6438	243	7	vi	vi	NOUN
ejpam-6438	243	8	a	a	DET
ejpam-6438	243	9	copy	copy	NOUN
ejpam-6438	243	10	of	of	ADP
ejpam-6438	243	11	c3	c3	PROPN
ejpam-6438	243	12	with	with	ADP
ejpam-6438	243	13	vertices	vertex	NOUN
ejpam-6438	243	14	ui1	ui1	PROPN
ejpam-6438	243	15	,	,	PUNCT
ejpam-6438	243	16	ui2	ui2	PROPN
ejpam-6438	243	17	,	,	PUNCT
ejpam-6438	243	18	ui3	ui3	PROPN
ejpam-6438	243	19	,	,	PUNCT
ejpam-6438	243	20	where	where	SCONJ
ejpam-6438	243	21	each	each	DET
ejpam-6438	243	22	uij	uij	PRON
ejpam-6438	243	23	is	be	AUX
ejpam-6438	243	24	connected	connect	VERB
ejpam-6438	243	25	to	to	ADP
ejpam-6438	243	26	vi	vi	PROPN
ejpam-6438	243	27	,	,	PUNCT
ejpam-6438	243	28	as	as	SCONJ
ejpam-6438	243	29	show	show	NOUN
ejpam-6438	243	30	in	in	ADP
ejpam-6438	243	31	figure	figure	NOUN
ejpam-6438	243	32	8	8	NUM
ejpam-6438	243	33	.	.	PUNCT
ejpam-6438	244	1	we	we	PRON
ejpam-6438	244	2	construct	construct	VERB
ejpam-6438	244	3	a	a	DET
ejpam-6438	244	4	set	set	NOUN
ejpam-6438	244	5	r	r	NOUN
ejpam-6438	244	6	consisting	consist	VERB
ejpam-6438	244	7	of	of	ADP
ejpam-6438	244	8	:	:	PUNCT
ejpam-6438	244	9	r	r	NOUN
ejpam-6438	244	10	=	=	SYM
ejpam-6438	244	11	{	{	PUNCT
ejpam-6438	244	12	v1	v1	NOUN
ejpam-6438	244	13	,	,	PUNCT
ejpam-6438	244	14	v2	v2	PROPN
ejpam-6438	244	15	,	,	PUNCT
ejpam-6438	244	16	.	.	PUNCT
ejpam-6438	244	17	.	.	PUNCT
ejpam-6438	244	18	.	.	PUNCT
ejpam-6438	245	1	,	,	PUNCT
ejpam-6438	245	2	vn	vn	VERB
ejpam-6438	245	3	}	}	PUNCT
ejpam-6438	245	4	∪	∪	X
ejpam-6438	245	5	{	{	PUNCT
ejpam-6438	245	6	ui1	ui1	ADJ
ejpam-6438	245	7	,	,	PUNCT
ejpam-6438	245	8	ui2	ui2	PUNCT
ejpam-6438	246	1	|	|	ADV
ejpam-6438	246	2	1	1	NUM
ejpam-6438	246	3	≤	≤	NUM
ejpam-6438	246	4	i	i	PRON
ejpam-6438	246	5	≤	≤	NOUN
ejpam-6438	246	6	n	n	CCONJ
ejpam-6438	246	7	}	}	PUNCT
ejpam-6438	246	8	thus	thus	ADV
ejpam-6438	246	9	,	,	PUNCT
ejpam-6438	246	10	|r|	|r|	NOUN
ejpam-6438	246	11	=	=	SYM
ejpam-6438	246	12	3n	3n	NOUN
ejpam-6438	246	13	.	.	PUNCT
ejpam-6438	247	1	resolving	resolve	VERB
ejpam-6438	247	2	property	property	NOUN
ejpam-6438	247	3	:	:	PUNCT
ejpam-6438	247	4	•	•	ADP
ejpam-6438	247	5	each	each	DET
ejpam-6438	247	6	vi	vi	NOUN
ejpam-6438	247	7	is	be	AUX
ejpam-6438	247	8	in	in	ADP
ejpam-6438	247	9	r	r	NOUN
ejpam-6438	247	10	,	,	PUNCT
ejpam-6438	247	11	so	so	ADV
ejpam-6438	247	12	all	all	DET
ejpam-6438	247	13	cycle	cycle	NOUN
ejpam-6438	247	14	vertices	vertex	NOUN
ejpam-6438	247	15	are	be	AUX
ejpam-6438	247	16	resolved	resolve	VERB
ejpam-6438	247	17	.	.	PUNCT
ejpam-6438	248	1	•	•	NUM
ejpam-6438	248	2	including	include	VERB
ejpam-6438	248	3	two	two	NUM
ejpam-6438	248	4	vertices	vertex	NOUN
ejpam-6438	248	5	from	from	ADP
ejpam-6438	248	6	each	each	DET
ejpam-6438	248	7	c3	c3	NOUN
ejpam-6438	248	8	copy	copy	NOUN
ejpam-6438	248	9	ensures	ensure	VERB
ejpam-6438	248	10	that	that	SCONJ
ejpam-6438	248	11	all	all	DET
ejpam-6438	248	12	three	three	NUM
ejpam-6438	248	13	vertices	vertex	NOUN
ejpam-6438	248	14	in	in	ADP
ejpam-6438	248	15	the	the	DET
ejpam-6438	248	16	triangle	triangle	NOUN
ejpam-6438	248	17	are	be	AUX
ejpam-6438	248	18	distinguishable	distinguishable	ADJ
ejpam-6438	248	19	.	.	PUNCT
ejpam-6438	249	1	•	•	NUM
ejpam-6438	249	2	vertices	vertex	NOUN
ejpam-6438	249	3	from	from	ADP
ejpam-6438	249	4	different	different	ADJ
ejpam-6438	249	5	c3	c3	NOUN
ejpam-6438	249	6	copies	copy	NOUN
ejpam-6438	249	7	are	be	AUX
ejpam-6438	249	8	resolved	resolve	VERB
ejpam-6438	249	9	by	by	ADP
ejpam-6438	249	10	their	their	PRON
ejpam-6438	249	11	distances	distance	NOUN
ejpam-6438	249	12	to	to	ADP
ejpam-6438	249	13	the	the	DET
ejpam-6438	249	14	corresponding	corresponding	ADJ
ejpam-6438	249	15	vi	vi	PROPN
ejpam-6438	249	16	,	,	PUNCT
ejpam-6438	249	17	ui1	ui1	ADV
ejpam-6438	249	18	,	,	PUNCT
ejpam-6438	249	19	and	and	CCONJ
ejpam-6438	249	20	ui2	ui2	PROPN
ejpam-6438	249	21	.	.	PUNCT
ejpam-6438	250	1	a.	a.	PROPN
ejpam-6438	250	2	elrokh	elrokh	PROPN
ejpam-6438	250	3	,	,	PUNCT
ejpam-6438	250	4	eman	eman	PROPN
ejpam-6438	250	5	s.	s.	PROPN
ejpam-6438	250	6	almotairi	almotairi	PROPN
ejpam-6438	250	7	,	,	PUNCT
ejpam-6438	250	8	h.	h.	PROPN
ejpam-6438	250	9	mostafa	mostafa	PROPN
ejpam-6438	250	10	/	/	SYM
ejpam-6438	250	11	eur	eur	PROPN
ejpam-6438	250	12	.	.	PUNCT
ejpam-6438	251	1	j.	j.	PROPN
ejpam-6438	251	2	pure	pure	PROPN
ejpam-6438	251	3	appl	appl	PROPN
ejpam-6438	251	4	.	.	PROPN
ejpam-6438	251	5	math	math	PROPN
ejpam-6438	251	6	,	,	PUNCT
ejpam-6438	251	7	18	18	NUM
ejpam-6438	251	8	(	(	PUNCT
ejpam-6438	251	9	3	3	NUM
ejpam-6438	251	10	)	)	PUNCT
ejpam-6438	251	11	(	(	PUNCT
ejpam-6438	251	12	2025	2025	NUM
ejpam-6438	251	13	)	)	PUNCT
ejpam-6438	251	14	,	,	PUNCT
ejpam-6438	251	15	6438	6438	NUM
ejpam-6438	251	16	9	9	NUM
ejpam-6438	251	17	of	of	ADP
ejpam-6438	251	18	18	18	NUM
ejpam-6438	251	19	figure	figure	NOUN
ejpam-6438	251	20	8	8	NUM
ejpam-6438	251	21	.	.	PUNCT
ejpam-6438	252	1	the	the	DET
ejpam-6438	252	2	cn	cn	PROPN
ejpam-6438	252	3	⊙	⊙	PROPN
ejpam-6438	252	4	c3	c3	PROPN
ejpam-6438	252	5	graph	graph	PROPN
ejpam-6438	252	6	.	.	PUNCT
ejpam-6438	253	1	w	w	PROPN
ejpam-6438	253	2	(	(	PUNCT
ejpam-6438	253	3	vi	vi	PROPN
ejpam-6438	253	4	,	,	PUNCT
ejpam-6438	253	5	r	r	NOUN
ejpam-6438	253	6	)	)	PUNCT
ejpam-6438	253	7	=	=	SYM
ejpam-6438	253	8			X
ejpam-6438	253	9	{	{	PUNCT
ejpam-6438	253	10	0	0	NUM
ejpam-6438	253	11	,	,	PUNCT
ejpam-6438	253	12	1	1	NUM
ejpam-6438	253	13	,	,	PUNCT
ejpam-6438	253	14	2	2	NUM
ejpam-6438	253	15	,	,	PUNCT
ejpam-6438	253	16	.	.	PUNCT
ejpam-6438	253	17	.	.	PUNCT
ejpam-6438	253	18	.	.	PUNCT
ejpam-6438	254	1	,	,	PUNCT
ejpam-6438	254	2	n−	n−	NOUN
ejpam-6438	254	3	1	1	NUM
ejpam-6438	254	4	,	,	PUNCT
ejpam-6438	254	5	1	1	NUM
ejpam-6438	254	6	,	,	PUNCT
ejpam-6438	254	7	1	1	NUM
ejpam-6438	254	8	,	,	PUNCT
ejpam-6438	254	9	2	2	NUM
ejpam-6438	254	10	,	,	PUNCT
ejpam-6438	254	11	2	2	NUM
ejpam-6438	254	12	,	,	PUNCT
ejpam-6438	254	13	3	3	NUM
ejpam-6438	254	14	,	,	PUNCT
ejpam-6438	254	15	3	3	NUM
ejpam-6438	254	16	,	,	PUNCT
ejpam-6438	254	17	.	.	PUNCT
ejpam-6438	254	18	.	.	PUNCT
ejpam-6438	255	1	.	.	PUNCT
ejpam-6438	256	1	,	,	PUNCT
ejpam-6438	256	2	n	n	CCONJ
ejpam-6438	256	3	,	,	PUNCT
ejpam-6438	256	4	n	n	CCONJ
ejpam-6438	256	5	}	}	PUNCT
ejpam-6438	256	6	,	,	PUNCT
ejpam-6438	256	7	i	i	PRON
ejpam-6438	256	8	=	=	NOUN
ejpam-6438	256	9	1	1	NUM
ejpam-6438	256	10	{	{	PUNCT
ejpam-6438	256	11	1	1	NUM
ejpam-6438	256	12	,	,	PUNCT
ejpam-6438	256	13	0	0	NUM
ejpam-6438	256	14	,	,	PUNCT
ejpam-6438	256	15	1	1	NUM
ejpam-6438	256	16	,	,	PUNCT
ejpam-6438	256	17	.	.	PUNCT
ejpam-6438	256	18	.	.	PUNCT
ejpam-6438	256	19	.	.	PUNCT
ejpam-6438	257	1	,	,	PUNCT
ejpam-6438	257	2	n−	n−	NOUN
ejpam-6438	257	3	2	2	NUM
ejpam-6438	257	4	,	,	PUNCT
ejpam-6438	257	5	2	2	NUM
ejpam-6438	257	6	,	,	PUNCT
ejpam-6438	257	7	2	2	NUM
ejpam-6438	257	8	,	,	PUNCT
ejpam-6438	257	9	1	1	NUM
ejpam-6438	257	10	,	,	PUNCT
ejpam-6438	257	11	1	1	NUM
ejpam-6438	257	12	,	,	PUNCT
ejpam-6438	257	13	2	2	NUM
ejpam-6438	257	14	,	,	PUNCT
ejpam-6438	257	15	2	2	NUM
ejpam-6438	257	16	.	.	PUNCT
ejpam-6438	257	17	.	.	PUNCT
ejpam-6438	258	1	.	.	PUNCT
ejpam-6438	259	1	,	,	PUNCT
ejpam-6438	259	2	n−	n−	NOUN
ejpam-6438	259	3	1	1	NUM
ejpam-6438	259	4	,	,	PUNCT
ejpam-6438	259	5	n−	n−	NOUN
ejpam-6438	259	6	1	1	NUM
ejpam-6438	259	7	}	}	PUNCT
ejpam-6438	259	8	,	,	PUNCT
ejpam-6438	259	9	i	i	PRON
ejpam-6438	259	10	=	=	NOUN
ejpam-6438	259	11	2	2	NUM
ejpam-6438	259	12	{	{	PUNCT
ejpam-6438	259	13	2	2	NUM
ejpam-6438	259	14	,	,	PUNCT
ejpam-6438	259	15	1	1	NUM
ejpam-6438	259	16	,	,	PUNCT
ejpam-6438	259	17	0	0	NUM
ejpam-6438	259	18	,	,	PUNCT
ejpam-6438	259	19	1	1	NUM
ejpam-6438	259	20	,	,	PUNCT
ejpam-6438	259	21	.	.	PUNCT
ejpam-6438	259	22	.	.	PUNCT
ejpam-6438	260	1	.	.	PUNCT
ejpam-6438	261	1	,	,	PUNCT
ejpam-6438	261	2	n−	n−	NOUN
ejpam-6438	261	3	3	3	NUM
ejpam-6438	261	4	,	,	PUNCT
ejpam-6438	261	5	3	3	NUM
ejpam-6438	261	6	,	,	PUNCT
ejpam-6438	261	7	3	3	NUM
ejpam-6438	261	8	,	,	PUNCT
ejpam-6438	261	9	2	2	NUM
ejpam-6438	261	10	,	,	PUNCT
ejpam-6438	261	11	2	2	NUM
ejpam-6438	261	12	,	,	PUNCT
ejpam-6438	261	13	1	1	NUM
ejpam-6438	261	14	,	,	PUNCT
ejpam-6438	261	15	1	1	NUM
ejpam-6438	261	16	,	,	PUNCT
ejpam-6438	261	17	.	.	PUNCT
ejpam-6438	261	18	.	.	PUNCT
ejpam-6438	262	1	.	.	PUNCT
ejpam-6438	263	1	,	,	PUNCT
ejpam-6438	263	2	n−	n−	NOUN
ejpam-6438	263	3	2	2	NUM
ejpam-6438	263	4	,	,	PUNCT
ejpam-6438	263	5	n−	n−	NOUN
ejpam-6438	263	6	2	2	NUM
ejpam-6438	263	7	}	}	PUNCT
ejpam-6438	263	8	,	,	PUNCT
ejpam-6438	263	9	i	i	PRON
ejpam-6438	263	10	=	=	NOUN
ejpam-6438	263	11	3	3	NUM
ejpam-6438	263	12	:	:	PUNCT
ejpam-6438	263	13	:	:	PUNCT
ejpam-6438	263	14	:	:	PUNCT
ejpam-6438	263	15	:	:	PUNCT
ejpam-6438	263	16	{	{	PUNCT
ejpam-6438	263	17	n−	n−	NOUN
ejpam-6438	263	18	1	1	NUM
ejpam-6438	263	19	,	,	PUNCT
ejpam-6438	263	20	n−	n−	NOUN
ejpam-6438	263	21	2	2	NUM
ejpam-6438	263	22	,	,	PUNCT
ejpam-6438	263	23	n−	n−	NOUN
ejpam-6438	263	24	3	3	NUM
ejpam-6438	263	25	,	,	PUNCT
ejpam-6438	263	26	.	.	PUNCT
ejpam-6438	263	27	.	.	PUNCT
ejpam-6438	264	1	.	.	PUNCT
ejpam-6438	265	1	,	,	PUNCT
ejpam-6438	265	2	0	0	NUM
ejpam-6438	265	3	,	,	PUNCT
ejpam-6438	265	4	n	n	CCONJ
ejpam-6438	265	5	,	,	PUNCT
ejpam-6438	265	6	n.n−	n.n−	X
ejpam-6438	265	7	1	1	NUM
ejpam-6438	265	8	,	,	PUNCT
ejpam-6438	265	9	n−	n−	NOUN
ejpam-6438	265	10	1	1	NUM
ejpam-6438	265	11	,	,	PUNCT
ejpam-6438	265	12	.	.	PUNCT
ejpam-6438	265	13	.	.	PUNCT
ejpam-6438	266	1	.	.	PUNCT
ejpam-6438	267	1	,	,	PUNCT
ejpam-6438	267	2	1	1	NUM
ejpam-6438	267	3	,	,	PUNCT
ejpam-6438	267	4	1	1	NUM
ejpam-6438	267	5	}	}	PUNCT
ejpam-6438	267	6	.i	.i	PUNCT
ejpam-6438	268	1	=	=	PUNCT
ejpam-6438	268	2	n	n	PROPN
ejpam-6438	268	3	w	w	NOUN
ejpam-6438	268	4	(	(	PUNCT
ejpam-6438	268	5	uij	uij	PRON
ejpam-6438	268	6	,	,	PUNCT
ejpam-6438	268	7	r	r	NOUN
ejpam-6438	268	8	)	)	PUNCT
ejpam-6438	268	9	=	=	SYM
ejpam-6438	268	10			NOUN
ejpam-6438	268	11	{	{	PUNCT
ejpam-6438	268	12	1	1	NUM
ejpam-6438	268	13	,	,	PUNCT
ejpam-6438	268	14	2	2	NUM
ejpam-6438	268	15	,	,	PUNCT
ejpam-6438	268	16	3	3	NUM
ejpam-6438	268	17	,	,	PUNCT
ejpam-6438	268	18	.	.	PUNCT
ejpam-6438	268	19	.	.	PUNCT
ejpam-6438	269	1	.	.	PUNCT
ejpam-6438	270	1	,	,	PUNCT
ejpam-6438	270	2	n	n	CCONJ
ejpam-6438	270	3	,	,	PUNCT
ejpam-6438	270	4	0	0	NUM
ejpam-6438	270	5	,	,	PUNCT
ejpam-6438	270	6	1	1	NUM
ejpam-6438	270	7	,	,	PUNCT
ejpam-6438	270	8	.	.	PUNCT
ejpam-6438	271	1	.	.	PUNCT
ejpam-6438	272	1	.	.	PUNCT
ejpam-6438	273	1	,	,	PUNCT
ejpam-6438	273	2	n	n	CCONJ
ejpam-6438	273	3	,	,	PUNCT
ejpam-6438	273	4	n	n	CCONJ
ejpam-6438	273	5	,	,	PUNCT
ejpam-6438	273	6	n+	n+	ADP
ejpam-6438	273	7	1	1	NUM
ejpam-6438	273	8	,	,	PUNCT
ejpam-6438	273	9	n+	n+	ADP
ejpam-6438	273	10	1	1	NUM
ejpam-6438	273	11	}	}	PUNCT
ejpam-6438	273	12	,	,	PUNCT
ejpam-6438	274	1	i	i	PRON
ejpam-6438	274	2	=	=	NOUN
ejpam-6438	274	3	1	1	NUM
ejpam-6438	274	4	,	,	PUNCT
ejpam-6438	274	5	j	j	PROPN
ejpam-6438	274	6	=	=	SYM
ejpam-6438	274	7	1	1	NUM
ejpam-6438	274	8	{	{	PUNCT
ejpam-6438	274	9	1	1	NUM
ejpam-6438	274	10	,	,	PUNCT
ejpam-6438	274	11	2	2	NUM
ejpam-6438	274	12	,	,	PUNCT
ejpam-6438	274	13	3	3	NUM
ejpam-6438	274	14	,	,	PUNCT
ejpam-6438	274	15	.	.	PUNCT
ejpam-6438	274	16	.	.	PUNCT
ejpam-6438	275	1	.	.	PUNCT
ejpam-6438	276	1	,	,	PUNCT
ejpam-6438	276	2	n	n	CCONJ
ejpam-6438	276	3	,	,	PUNCT
ejpam-6438	276	4	1	1	NUM
ejpam-6438	276	5	,	,	PUNCT
ejpam-6438	276	6	0	0	NUM
ejpam-6438	276	7	,	,	PUNCT
ejpam-6438	276	8	.	.	PUNCT
ejpam-6438	277	1	.	.	PUNCT
ejpam-6438	278	1	.	.	PUNCT
ejpam-6438	279	1	,	,	PUNCT
ejpam-6438	279	2	n	n	CCONJ
ejpam-6438	279	3	,	,	PUNCT
ejpam-6438	279	4	n	n	CCONJ
ejpam-6438	279	5	,	,	PUNCT
ejpam-6438	279	6	n+	n+	ADP
ejpam-6438	279	7	1	1	NUM
ejpam-6438	279	8	,	,	PUNCT
ejpam-6438	279	9	n+	n+	ADP
ejpam-6438	279	10	1	1	NUM
ejpam-6438	279	11	}	}	PUNCT
ejpam-6438	279	12	,	,	PUNCT
ejpam-6438	280	1	i	i	PRON
ejpam-6438	280	2	=	=	NOUN
ejpam-6438	280	3	1	1	NUM
ejpam-6438	280	4	,	,	PUNCT
ejpam-6438	280	5	j	j	PROPN
ejpam-6438	280	6	=	=	SYM
ejpam-6438	280	7	2	2	NUM
ejpam-6438	280	8	{	{	PUNCT
ejpam-6438	280	9	1	1	NUM
ejpam-6438	280	10	,	,	PUNCT
ejpam-6438	280	11	2	2	NUM
ejpam-6438	280	12	,	,	PUNCT
ejpam-6438	280	13	3	3	NUM
ejpam-6438	280	14	,	,	PUNCT
ejpam-6438	280	15	.	.	PUNCT
ejpam-6438	280	16	.	.	PUNCT
ejpam-6438	281	1	.	.	PUNCT
ejpam-6438	282	1	,	,	PUNCT
ejpam-6438	282	2	n	n	CCONJ
ejpam-6438	282	3	,	,	PUNCT
ejpam-6438	282	4	1	1	NUM
ejpam-6438	282	5	,	,	PUNCT
ejpam-6438	282	6	1	1	NUM
ejpam-6438	282	7	,	,	PUNCT
ejpam-6438	282	8	.	.	PUNCT
ejpam-6438	283	1	.	.	PUNCT
ejpam-6438	284	1	.	.	PUNCT
ejpam-6438	285	1	,	,	PUNCT
ejpam-6438	285	2	n	n	CCONJ
ejpam-6438	285	3	,	,	PUNCT
ejpam-6438	285	4	n	n	CCONJ
ejpam-6438	285	5	,	,	PUNCT
ejpam-6438	285	6	n+	n+	ADP
ejpam-6438	285	7	1	1	NUM
ejpam-6438	285	8	,	,	PUNCT
ejpam-6438	285	9	n+	n+	ADP
ejpam-6438	285	10	1	1	NUM
ejpam-6438	285	11	}	}	PUNCT
ejpam-6438	285	12	,	,	PUNCT
ejpam-6438	286	1	i	i	PRON
ejpam-6438	286	2	=	=	NOUN
ejpam-6438	286	3	1	1	NUM
ejpam-6438	286	4	,	,	PUNCT
ejpam-6438	286	5	j	j	PROPN
ejpam-6438	286	6	=	=	SYM
ejpam-6438	286	7	3	3	NUM
ejpam-6438	286	8	{	{	PUNCT
ejpam-6438	286	9	2	2	NUM
ejpam-6438	286	10	,	,	PUNCT
ejpam-6438	286	11	1	1	NUM
ejpam-6438	286	12	,	,	PUNCT
ejpam-6438	286	13	2	2	NUM
ejpam-6438	286	14	,	,	PUNCT
ejpam-6438	286	15	3	3	NUM
ejpam-6438	286	16	.	.	PUNCT
ejpam-6438	286	17	.	.	PUNCT
ejpam-6438	286	18	.	.	PUNCT
ejpam-6438	287	1	,	,	PUNCT
ejpam-6438	287	2	n−	n−	NOUN
ejpam-6438	287	3	1	1	NUM
ejpam-6438	287	4	,	,	PUNCT
ejpam-6438	287	5	3	3	NUM
ejpam-6438	287	6	,	,	PUNCT
ejpam-6438	287	7	3	3	NUM
ejpam-6438	287	8	,	,	PUNCT
ejpam-6438	287	9	j	j	PROPN
ejpam-6438	287	10	−	−	PROPN
ejpam-6438	287	11	1	1	NUM
ejpam-6438	287	12	,	,	PUNCT
ejpam-6438	287	13	j	j	PROPN
ejpam-6438	287	14	,	,	PUNCT
ejpam-6438	287	15	3	3	NUM
ejpam-6438	287	16	,	,	PUNCT
ejpam-6438	287	17	3	3	NUM
ejpam-6438	287	18	,	,	PUNCT
ejpam-6438	287	19	4	4	NUM
ejpam-6438	287	20	,	,	PUNCT
ejpam-6438	287	21	4	4	NUM
ejpam-6438	287	22	,	,	PUNCT
ejpam-6438	287	23	.	.	PUNCT
ejpam-6438	287	24	.	.	PUNCT
ejpam-6438	288	1	.	.	PUNCT
ejpam-6438	289	1	,	,	PUNCT
ejpam-6438	289	2	n	n	CCONJ
ejpam-6438	289	3	,	,	PUNCT
ejpam-6438	289	4	n	n	CCONJ
ejpam-6438	289	5	}	}	PUNCT
ejpam-6438	289	6	,	,	PUNCT
ejpam-6438	289	7	i	i	PRON
ejpam-6438	289	8	=	=	NOUN
ejpam-6438	289	9	2	2	NUM
ejpam-6438	289	10	,	,	PUNCT
ejpam-6438	289	11	j	j	NOUN
ejpam-6438	289	12	=	=	SYM
ejpam-6438	289	13	1	1	NUM
ejpam-6438	289	14	{	{	PUNCT
ejpam-6438	289	15	2	2	NUM
ejpam-6438	289	16	,	,	PUNCT
ejpam-6438	289	17	1	1	NUM
ejpam-6438	289	18	,	,	PUNCT
ejpam-6438	289	19	2	2	NUM
ejpam-6438	289	20	,	,	PUNCT
ejpam-6438	289	21	3	3	NUM
ejpam-6438	289	22	.	.	PUNCT
ejpam-6438	289	23	.	.	PUNCT
ejpam-6438	289	24	.	.	PUNCT
ejpam-6438	290	1	,	,	PUNCT
ejpam-6438	290	2	n−	n−	NOUN
ejpam-6438	290	3	1	1	NUM
ejpam-6438	290	4	,	,	PUNCT
ejpam-6438	290	5	3	3	NUM
ejpam-6438	290	6	,	,	PUNCT
ejpam-6438	290	7	3	3	NUM
ejpam-6438	290	8	,	,	PUNCT
ejpam-6438	290	9	j	j	PROPN
ejpam-6438	290	10	−	−	PROPN
ejpam-6438	290	11	1	1	NUM
ejpam-6438	290	12	,	,	PUNCT
ejpam-6438	290	13	j	j	PROPN
ejpam-6438	290	14	−	−	PROPN
ejpam-6438	290	15	2	2	NUM
ejpam-6438	290	16	,	,	PUNCT
ejpam-6438	290	17	3	3	NUM
ejpam-6438	290	18	,	,	PUNCT
ejpam-6438	290	19	3	3	NUM
ejpam-6438	290	20	,	,	PUNCT
ejpam-6438	290	21	4	4	NUM
ejpam-6438	290	22	,	,	PUNCT
ejpam-6438	290	23	4	4	NUM
ejpam-6438	290	24	,	,	PUNCT
ejpam-6438	290	25	.	.	PUNCT
ejpam-6438	290	26	.	.	PUNCT
ejpam-6438	291	1	.	.	PUNCT
ejpam-6438	292	1	,	,	PUNCT
ejpam-6438	292	2	n	n	CCONJ
ejpam-6438	292	3	,	,	PUNCT
ejpam-6438	292	4	n	n	CCONJ
ejpam-6438	292	5	}	}	PUNCT
ejpam-6438	292	6	,	,	PUNCT
ejpam-6438	292	7	i	i	PRON
ejpam-6438	292	8	=	=	NOUN
ejpam-6438	292	9	2	2	NUM
ejpam-6438	292	10	,	,	PUNCT
ejpam-6438	292	11	j	j	PROPN
ejpam-6438	292	12	=	=	SYM
ejpam-6438	292	13	2	2	NUM
ejpam-6438	292	14	{	{	PUNCT
ejpam-6438	292	15	2	2	NUM
ejpam-6438	292	16	,	,	PUNCT
ejpam-6438	292	17	1	1	NUM
ejpam-6438	292	18	,	,	PUNCT
ejpam-6438	292	19	2	2	NUM
ejpam-6438	292	20	,	,	PUNCT
ejpam-6438	292	21	3	3	NUM
ejpam-6438	292	22	.	.	PUNCT
ejpam-6438	292	23	.	.	PUNCT
ejpam-6438	292	24	.	.	PUNCT
ejpam-6438	293	1	,	,	PUNCT
ejpam-6438	293	2	n−	n−	NOUN
ejpam-6438	293	3	1	1	NUM
ejpam-6438	293	4	,	,	PUNCT
ejpam-6438	293	5	3	3	NUM
ejpam-6438	293	6	,	,	PUNCT
ejpam-6438	293	7	3	3	NUM
ejpam-6438	293	8	,	,	PUNCT
ejpam-6438	293	9	j	j	PROPN
ejpam-6438	293	10	−	−	PROPN
ejpam-6438	293	11	2	2	NUM
ejpam-6438	293	12	,	,	PUNCT
ejpam-6438	293	13	j	j	PROPN
ejpam-6438	293	14	−	−	PROPN
ejpam-6438	293	15	2	2	NUM
ejpam-6438	293	16	,	,	PUNCT
ejpam-6438	293	17	3	3	NUM
ejpam-6438	293	18	,	,	PUNCT
ejpam-6438	293	19	3	3	NUM
ejpam-6438	293	20	,	,	PUNCT
ejpam-6438	293	21	4	4	NUM
ejpam-6438	293	22	,	,	PUNCT
ejpam-6438	293	23	4	4	NUM
ejpam-6438	293	24	,	,	PUNCT
ejpam-6438	293	25	.	.	PUNCT
ejpam-6438	293	26	.	.	PUNCT
ejpam-6438	294	1	.	.	PUNCT
ejpam-6438	295	1	,	,	PUNCT
ejpam-6438	295	2	n	n	CCONJ
ejpam-6438	295	3	,	,	PUNCT
ejpam-6438	295	4	n	n	CCONJ
ejpam-6438	295	5	}	}	PUNCT
ejpam-6438	295	6	,	,	PUNCT
ejpam-6438	295	7	i	i	PRON
ejpam-6438	295	8	=	=	NOUN
ejpam-6438	295	9	2	2	NUM
ejpam-6438	295	10	,	,	PUNCT
ejpam-6438	295	11	j	j	NOUN
ejpam-6438	295	12	=	=	SYM
ejpam-6438	295	13	3	3	NUM
ejpam-6438	295	14	:	:	PUNCT
ejpam-6438	295	15	:	:	PUNCT
ejpam-6438	295	16	:	:	PUNCT
ejpam-6438	295	17	{	{	PUNCT
ejpam-6438	295	18	n	n	X
ejpam-6438	295	19	,	,	PUNCT
ejpam-6438	295	20	n−	n−	NOUN
ejpam-6438	295	21	1	1	NUM
ejpam-6438	295	22	,	,	PUNCT
ejpam-6438	295	23	.	.	PUNCT
ejpam-6438	295	24	.	.	PUNCT
ejpam-6438	295	25	.	.	PUNCT
ejpam-6438	296	1	.	.	PUNCT
ejpam-6438	297	1	,	,	PUNCT
ejpam-6438	297	2	1	1	NUM
ejpam-6438	297	3	,	,	PUNCT
ejpam-6438	297	4	n+	n+	NUM
ejpam-6438	297	5	1	1	NUM
ejpam-6438	297	6	,	,	PUNCT
ejpam-6438	297	7	n+	n+	ADP
ejpam-6438	297	8	1	1	NUM
ejpam-6438	297	9	,	,	PUNCT
ejpam-6438	297	10	n	n	CCONJ
ejpam-6438	297	11	,	,	PUNCT
ejpam-6438	297	12	n	n	CCONJ
ejpam-6438	297	13	,	,	PUNCT
ejpam-6438	297	14	n−	n−	NOUN
ejpam-6438	297	15	1	1	NUM
ejpam-6438	297	16	,	,	PUNCT
ejpam-6438	297	17	n−	n−	NOUN
ejpam-6438	297	18	1	1	NUM
ejpam-6438	297	19	,	,	PUNCT
ejpam-6438	297	20	.	.	PUNCT
ejpam-6438	297	21	.	.	PUNCT
ejpam-6438	297	22	.	.	PUNCT
ejpam-6438	298	1	.	.	PUNCT
ejpam-6438	299	1	,	,	PUNCT
ejpam-6438	300	1	j	j	PROPN
ejpam-6438	301	1	−	−	PROPN
ejpam-6438	301	2	1	1	NUM
ejpam-6438	301	3	,	,	PUNCT
ejpam-6438	301	4	j	j	PROPN
ejpam-6438	301	5	}	}	PUNCT
ejpam-6438	301	6	,	,	PUNCT
ejpam-6438	301	7	i	i	PRON
ejpam-6438	301	8	=	=	SYM
ejpam-6438	301	9	n	n	PROPN
ejpam-6438	301	10	,	,	PUNCT
ejpam-6438	301	11	j	j	PROPN
ejpam-6438	301	12	=	=	SYM
ejpam-6438	301	13	1	1	NUM
ejpam-6438	301	14	{	{	PUNCT
ejpam-6438	301	15	n	n	CCONJ
ejpam-6438	301	16	,	,	PUNCT
ejpam-6438	301	17	n−	n−	NOUN
ejpam-6438	301	18	1	1	NUM
ejpam-6438	301	19	,	,	PUNCT
ejpam-6438	301	20	.	.	PUNCT
ejpam-6438	301	21	.	.	PUNCT
ejpam-6438	301	22	.	.	PUNCT
ejpam-6438	302	1	.	.	PUNCT
ejpam-6438	303	1	,	,	PUNCT
ejpam-6438	303	2	1	1	NUM
ejpam-6438	303	3	,	,	PUNCT
ejpam-6438	303	4	n+	n+	NUM
ejpam-6438	303	5	1	1	NUM
ejpam-6438	303	6	,	,	PUNCT
ejpam-6438	303	7	n+	n+	ADP
ejpam-6438	303	8	1	1	NUM
ejpam-6438	303	9	,	,	PUNCT
ejpam-6438	303	10	n	n	CCONJ
ejpam-6438	303	11	,	,	PUNCT
ejpam-6438	303	12	n	n	CCONJ
ejpam-6438	303	13	,	,	PUNCT
ejpam-6438	303	14	n−	n−	NOUN
ejpam-6438	303	15	1	1	NUM
ejpam-6438	303	16	,	,	PUNCT
ejpam-6438	303	17	n−	n−	NOUN
ejpam-6438	303	18	1	1	NUM
ejpam-6438	303	19	,	,	PUNCT
ejpam-6438	303	20	.	.	PUNCT
ejpam-6438	303	21	.	.	PUNCT
ejpam-6438	303	22	.	.	PUNCT
ejpam-6438	304	1	.	.	PUNCT
ejpam-6438	305	1	,	,	PUNCT
ejpam-6438	306	1	j	j	PROPN
ejpam-6438	307	1	−	−	PROPN
ejpam-6438	307	2	1	1	NUM
ejpam-6438	307	3	,	,	PUNCT
ejpam-6438	307	4	j	j	PROPN
ejpam-6438	307	5	−	−	PROPN
ejpam-6438	307	6	2	2	NUM
ejpam-6438	307	7	}	}	PUNCT
ejpam-6438	307	8	,	,	PUNCT
ejpam-6438	307	9	i	i	PRON
ejpam-6438	307	10	=	=	SYM
ejpam-6438	307	11	n	n	PROPN
ejpam-6438	307	12	,	,	PUNCT
ejpam-6438	307	13	j	j	PROPN
ejpam-6438	307	14	=	=	SYM
ejpam-6438	307	15	2	2	NUM
ejpam-6438	307	16	{	{	PUNCT
ejpam-6438	307	17	n	n	CCONJ
ejpam-6438	307	18	,	,	PUNCT
ejpam-6438	307	19	n−	n−	NOUN
ejpam-6438	307	20	1	1	NUM
ejpam-6438	307	21	,	,	PUNCT
ejpam-6438	307	22	.	.	PUNCT
ejpam-6438	307	23	.	.	PUNCT
ejpam-6438	307	24	.	.	PUNCT
ejpam-6438	308	1	.	.	PUNCT
ejpam-6438	309	1	,	,	PUNCT
ejpam-6438	309	2	1	1	NUM
ejpam-6438	309	3	,	,	PUNCT
ejpam-6438	309	4	n+	n+	NUM
ejpam-6438	309	5	1	1	NUM
ejpam-6438	309	6	,	,	PUNCT
ejpam-6438	309	7	n+	n+	ADP
ejpam-6438	309	8	1	1	NUM
ejpam-6438	309	9	,	,	PUNCT
ejpam-6438	309	10	n	n	CCONJ
ejpam-6438	309	11	,	,	PUNCT
ejpam-6438	309	12	n	n	CCONJ
ejpam-6438	309	13	,	,	PUNCT
ejpam-6438	309	14	n−	n−	NOUN
ejpam-6438	309	15	1	1	NUM
ejpam-6438	309	16	,	,	PUNCT
ejpam-6438	309	17	n−	n−	NOUN
ejpam-6438	309	18	1	1	NUM
ejpam-6438	309	19	,	,	PUNCT
ejpam-6438	309	20	.	.	PUNCT
ejpam-6438	309	21	.	.	PUNCT
ejpam-6438	309	22	.	.	PUNCT
ejpam-6438	310	1	.	.	PUNCT
ejpam-6438	311	1	,	,	PUNCT
ejpam-6438	312	1	j	j	PROPN
ejpam-6438	313	1	−	−	PROPN
ejpam-6438	313	2	2	2	NUM
ejpam-6438	313	3	,	,	PUNCT
ejpam-6438	313	4	j	j	PROPN
ejpam-6438	313	5	−	−	PROPN
ejpam-6438	313	6	2	2	NUM
ejpam-6438	313	7	}	}	PUNCT
ejpam-6438	313	8	,	,	PUNCT
ejpam-6438	313	9	i	i	PRON
ejpam-6438	313	10	=	=	SYM
ejpam-6438	313	11	n	n	PROPN
ejpam-6438	313	12	,	,	PUNCT
ejpam-6438	313	13	j	j	PROPN
ejpam-6438	313	14	=	=	SYM
ejpam-6438	313	15	3	3	NUM
ejpam-6438	313	16	connectivity	connectivity	NOUN
ejpam-6438	313	17	:	:	PUNCT
ejpam-6438	313	18	the	the	DET
ejpam-6438	313	19	subgraph	subgraph	NOUN
ejpam-6438	313	20	induced	induce	VERB
ejpam-6438	313	21	by	by	ADP
ejpam-6438	313	22	r	r	NOUN
ejpam-6438	313	23	includes	include	VERB
ejpam-6438	313	24	the	the	DET
ejpam-6438	313	25	cycle	cycle	NOUN
ejpam-6438	313	26	cn	cn	PROPN
ejpam-6438	313	27	and	and	CCONJ
ejpam-6438	313	28	two	two	NUM
ejpam-6438	313	29	vertices	vertex	NOUN
ejpam-6438	313	30	from	from	ADP
ejpam-6438	313	31	each	each	DET
ejpam-6438	313	32	triangle	triangle	NOUN
ejpam-6438	313	33	connected	connect	VERB
ejpam-6438	313	34	to	to	ADP
ejpam-6438	313	35	vi	vi	PROPN
ejpam-6438	313	36	.	.	PUNCT
ejpam-6438	314	1	since	since	SCONJ
ejpam-6438	314	2	each	each	DET
ejpam-6438	314	3	ui1	ui1	NOUN
ejpam-6438	314	4	,	,	PUNCT
ejpam-6438	314	5	ui2	ui2	PROPN
ejpam-6438	314	6	is	be	AUX
ejpam-6438	314	7	adjacent	adjacent	ADJ
ejpam-6438	314	8	to	to	ADP
ejpam-6438	314	9	vi	vi	PROPN
ejpam-6438	314	10	,	,	PUNCT
ejpam-6438	314	11	the	the	DET
ejpam-6438	314	12	induced	induced	ADJ
ejpam-6438	314	13	subgraph	subgraph	NOUN
ejpam-6438	314	14	is	be	AUX
ejpam-6438	314	15	connected	connect	VERB
ejpam-6438	314	16	.	.	PUNCT
ejpam-6438	315	1	minimality	minimality	NOUN
ejpam-6438	315	2	:	:	PUNCT
ejpam-6438	315	3	suppose	suppose	VERB
ejpam-6438	315	4	a	a	DET
ejpam-6438	315	5	smaller	small	ADJ
ejpam-6438	315	6	connected	connected	ADJ
ejpam-6438	315	7	resolving	resolving	NOUN
ejpam-6438	315	8	set	set	VERB
ejpam-6438	315	9	r′	r′	NOUN
ejpam-6438	315	10	exists	exist	NOUN
ejpam-6438	315	11	with	with	ADP
ejpam-6438	315	12	|r′|	|r′|	NOUN
ejpam-6438	315	13	<	<	X
ejpam-6438	315	14	3n	3n	NUM
ejpam-6438	315	15	.	.	PUNCT
ejpam-6438	316	1	then	then	ADV
ejpam-6438	316	2	at	at	ADV
ejpam-6438	316	3	least	least	ADV
ejpam-6438	316	4	one	one	NUM
ejpam-6438	316	5	vi	vi	NOUN
ejpam-6438	316	6	,	,	PUNCT
ejpam-6438	316	7	ui1	ui1	ADV
ejpam-6438	316	8	,	,	PUNCT
ejpam-6438	316	9	or	or	CCONJ
ejpam-6438	316	10	ui2	ui2	NOUN
ejpam-6438	316	11	is	be	AUX
ejpam-6438	316	12	missing	miss	VERB
ejpam-6438	316	13	.	.	PUNCT
ejpam-6438	317	1	omitting	omit	VERB
ejpam-6438	317	2	any	any	PRON
ejpam-6438	317	3	of	of	ADP
ejpam-6438	317	4	these	these	PRON
ejpam-6438	317	5	may	may	AUX
ejpam-6438	317	6	cause	cause	VERB
ejpam-6438	317	7	failure	failure	NOUN
ejpam-6438	317	8	to	to	PART
ejpam-6438	317	9	resolve	resolve	VERB
ejpam-6438	317	10	the	the	DET
ejpam-6438	317	11	triangle	triangle	NOUN
ejpam-6438	317	12	or	or	CCONJ
ejpam-6438	317	13	disconnect	disconnect	VERB
ejpam-6438	317	14	the	the	DET
ejpam-6438	317	15	induced	induced	ADJ
ejpam-6438	317	16	subgraph	subgraph	NOUN
ejpam-6438	317	17	.	.	PUNCT
ejpam-6438	318	1	hence	hence	ADV
ejpam-6438	318	2	,	,	PUNCT
ejpam-6438	318	3	r	r	NOUN
ejpam-6438	318	4	is	be	AUX
ejpam-6438	318	5	minimal	minimal	ADJ
ejpam-6438	318	6	.	.	PUNCT
ejpam-6438	319	1	therefore	therefore	ADV
ejpam-6438	319	2	,	,	PUNCT
ejpam-6438	319	3	cdim(cn	cdim(cn	PROPN
ejpam-6438	319	4	⊙	⊙	PROPN
ejpam-6438	319	5	c3	c3	PROPN
ejpam-6438	319	6	)	)	PUNCT
ejpam-6438	320	1	=	=	SYM
ejpam-6438	320	2	3n	3n	NUM
ejpam-6438	320	3	.	.	PUNCT
ejpam-6438	321	1	in	in	ADP
ejpam-6438	321	2	the	the	DET
ejpam-6438	321	3	following	follow	VERB
ejpam-6438	321	4	theorems	theorem	NOUN
ejpam-6438	321	5	,	,	PUNCT
ejpam-6438	321	6	we	we	PRON
ejpam-6438	321	7	study	study	VERB
ejpam-6438	321	8	and	and	CCONJ
ejpam-6438	321	9	investigate	investigate	VERB
ejpam-6438	321	10	the	the	DET
ejpam-6438	321	11	metric	metric	ADJ
ejpam-6438	321	12	dimension	dimension	NOUN
ejpam-6438	321	13	of	of	ADP
ejpam-6438	321	14	pn	pn	PROPN
ejpam-6438	321	15	⊙	⊙	PROPN
ejpam-6438	321	16	p3	p3	PROPN
ejpam-6438	321	17	,	,	PUNCT
ejpam-6438	321	18	cn	cn	PROPN
ejpam-6438	321	19	⊙	⊙	PROPN
ejpam-6438	321	20	p3	p3	PROPN
ejpam-6438	321	21	,	,	PUNCT
ejpam-6438	321	22	pn	pn	PROPN
ejpam-6438	321	23	⊙	⊙	PROPN
ejpam-6438	321	24	c3	c3	PROPN
ejpam-6438	321	25	,	,	PUNCT
ejpam-6438	321	26	cn	cn	PROPN
ejpam-6438	321	27	⊙	⊙	PROPN
ejpam-6438	321	28	c3	c3	PROPN
ejpam-6438	321	29	and	and	CCONJ
ejpam-6438	321	30	kim	kim	PROPN
ejpam-6438	321	31	,	,	PUNCT
ejpam-6438	321	32	n.	n.	PROPN
ejpam-6438	321	33	theorem	theorem	VERB
ejpam-6438	321	34	5	5	NUM
ejpam-6438	321	35	:	:	PUNCT
ejpam-6438	321	36	let	let	VERB
ejpam-6438	321	37	g	g	NOUN
ejpam-6438	321	38	be	be	AUX
ejpam-6438	321	39	pn	pn	PROPN
ejpam-6438	321	40	⊙	⊙	PROPN
ejpam-6438	321	41	p3	p3	PROPN
ejpam-6438	321	42	graphs	graph	NOUN
ejpam-6438	321	43	,	,	PUNCT
ejpam-6438	321	44	then	then	ADV
ejpam-6438	321	45	m.d	m.d	PROPN
ejpam-6438	321	46	(	(	PUNCT
ejpam-6438	321	47	pn	pn	PROPN
ejpam-6438	321	48	⊙	⊙	PROPN
ejpam-6438	321	49	p3	p3	PROPN
ejpam-6438	321	50	)	)	PUNCT
ejpam-6438	322	1	=	=	SYM
ejpam-6438	322	2	n.	n.	NOUN
ejpam-6438	322	3	proof	proof	NOUN
ejpam-6438	322	4	.	.	PUNCT
ejpam-6438	323	1	label	label	VERB
ejpam-6438	323	2	the	the	DET
ejpam-6438	323	3	vertices	vertex	NOUN
ejpam-6438	323	4	of	of	ADP
ejpam-6438	323	5	pn	pn	PROPN
ejpam-6438	323	6	as	as	ADP
ejpam-6438	323	7	v1	v1	NOUN
ejpam-6438	323	8	,	,	PUNCT
ejpam-6438	323	9	v2	v2	NOUN
ejpam-6438	323	10	,	,	PUNCT
ejpam-6438	323	11	.	.	PUNCT
ejpam-6438	323	12	.	.	PUNCT
ejpam-6438	324	1	.	.	PUNCT
ejpam-6438	325	1	,	,	PUNCT
ejpam-6438	325	2	vn	vn	PROPN
ejpam-6438	325	3	.	.	PUNCT
ejpam-6438	326	1	for	for	ADP
ejpam-6438	326	2	each	each	DET
ejpam-6438	326	3	vi	vi	NOUN
ejpam-6438	326	4	,	,	PUNCT
ejpam-6438	326	5	attach	attach	VERB
ejpam-6438	326	6	a	a	DET
ejpam-6438	326	7	copy	copy	NOUN
ejpam-6438	326	8	of	of	ADP
ejpam-6438	326	9	p3	p3	PROPN
ejpam-6438	326	10	with	with	ADP
ejpam-6438	326	11	vertices	vertex	NOUN
ejpam-6438	326	12	ui1	ui1	ADV
ejpam-6438	326	13	,	,	PUNCT
ejpam-6438	326	14	ui2	ui2	PROPN
ejpam-6438	326	15	,	,	PUNCT
ejpam-6438	326	16	ui3	ui3	PROPN
ejpam-6438	326	17	,	,	PUNCT
ejpam-6438	326	18	where	where	SCONJ
ejpam-6438	326	19	each	each	DET
ejpam-6438	326	20	uij	uij	PRON
ejpam-6438	326	21	is	be	AUX
ejpam-6438	326	22	adjacent	adjacent	ADJ
ejpam-6438	326	23	to	to	ADP
ejpam-6438	326	24	vi	vi	NUM
ejpam-6438	326	25	,	,	PUNCT
ejpam-6438	326	26	as	as	SCONJ
ejpam-6438	326	27	show	show	NOUN
ejpam-6438	326	28	in	in	ADP
ejpam-6438	326	29	figure	figure	NOUN
ejpam-6438	326	30	9	9	NUM
ejpam-6438	326	31	.	.	PUNCT
ejpam-6438	327	1	let	let	VERB
ejpam-6438	327	2	r	r	NOUN
ejpam-6438	327	3	=	=	PRON
ejpam-6438	327	4	{	{	PUNCT
ejpam-6438	327	5	ui1	ui1	NOUN
ejpam-6438	327	6	|	|	ADV
ejpam-6438	327	7	1	1	NUM
ejpam-6438	327	8	≤	≤	NUM
ejpam-6438	327	9	i	i	PRON
ejpam-6438	327	10	≤	≤	NOUN
ejpam-6438	327	11	n	n	CCONJ
ejpam-6438	327	12	}	}	PUNCT
ejpam-6438	327	13	.	.	PUNCT
ejpam-6438	328	1	we	we	PRON
ejpam-6438	328	2	claim	claim	VERB
ejpam-6438	328	3	that	that	SCONJ
ejpam-6438	328	4	r	r	NOUN
ejpam-6438	328	5	is	be	AUX
ejpam-6438	328	6	a	a	DET
ejpam-6438	328	7	resolving	resolving	NOUN
ejpam-6438	328	8	set	set	NOUN
ejpam-6438	328	9	.	.	PUNCT
ejpam-6438	329	1	each	each	DET
ejpam-6438	329	2	vi	vi	PROPN
ejpam-6438	329	3	is	be	AUX
ejpam-6438	329	4	uniquely	uniquely	ADV
ejpam-6438	329	5	identified	identify	VERB
ejpam-6438	329	6	by	by	ADP
ejpam-6438	329	7	its	its	PRON
ejpam-6438	329	8	distance	distance	NOUN
ejpam-6438	329	9	to	to	ADP
ejpam-6438	329	10	ui1	ui1	PROPN
ejpam-6438	329	11	(	(	PUNCT
ejpam-6438	329	12	which	which	PRON
ejpam-6438	329	13	is	be	AUX
ejpam-6438	329	14	1	1	NUM
ejpam-6438	329	15	)	)	PUNCT
ejpam-6438	329	16	,	,	PUNCT
ejpam-6438	329	17	and	and	CCONJ
ejpam-6438	329	18	to	to	ADP
ejpam-6438	329	19	all	all	DET
ejpam-6438	329	20	other	other	ADJ
ejpam-6438	329	21	uj1	uj1	NOUN
ejpam-6438	329	22	(	(	PUNCT
ejpam-6438	329	23	which	which	PRON
ejpam-6438	329	24	are	be	AUX
ejpam-6438	329	25	at	at	ADV
ejpam-6438	329	26	least	least	ADJ
ejpam-6438	329	27	2	2	NUM
ejpam-6438	329	28	)	)	PUNCT
ejpam-6438	329	29	.	.	PUNCT
ejpam-6438	330	1	similarly	similarly	ADV
ejpam-6438	330	2	,	,	PUNCT
ejpam-6438	330	3	within	within	ADP
ejpam-6438	330	4	each	each	DET
ejpam-6438	330	5	p3	p3	PROPN
ejpam-6438	330	6	copy	copy	NOUN
ejpam-6438	330	7	,	,	PUNCT
ejpam-6438	330	8	the	the	DET
ejpam-6438	330	9	vertices	vertex	NOUN
ejpam-6438	330	10	ui2	ui2	VERB
ejpam-6438	330	11	and	and	CCONJ
ejpam-6438	330	12	ui3	ui3	PROPN
ejpam-6438	330	13	are	be	AUX
ejpam-6438	330	14	distinguishable	distinguishable	ADJ
ejpam-6438	330	15	by	by	ADP
ejpam-6438	330	16	their	their	PRON
ejpam-6438	330	17	distances	distance	NOUN
ejpam-6438	330	18	to	to	ADP
ejpam-6438	330	19	ui1	ui1	PROPN
ejpam-6438	330	20	(	(	PUNCT
ejpam-6438	330	21	which	which	PRON
ejpam-6438	330	22	are	be	AUX
ejpam-6438	330	23	2	2	NUM
ejpam-6438	330	24	)	)	PUNCT
ejpam-6438	330	25	,	,	PUNCT
ejpam-6438	330	26	while	while	SCONJ
ejpam-6438	330	27	ui1	ui1	ADV
ejpam-6438	330	28	is	be	AUX
ejpam-6438	330	29	in	in	ADP
ejpam-6438	330	30	r.	r.	PROPN
ejpam-6438	330	31	a.	a.	PROPN
ejpam-6438	330	32	elrokh	elrokh	PROPN
ejpam-6438	330	33	,	,	PUNCT
ejpam-6438	330	34	eman	eman	PROPN
ejpam-6438	330	35	s.	s.	PROPN
ejpam-6438	330	36	almotairi	almotairi	PROPN
ejpam-6438	330	37	,	,	PUNCT
ejpam-6438	330	38	h.	h.	PROPN
ejpam-6438	330	39	mostafa	mostafa	PROPN
ejpam-6438	330	40	/	/	SYM
ejpam-6438	330	41	eur	eur	PROPN
ejpam-6438	330	42	.	.	PUNCT
ejpam-6438	331	1	j.	j.	PROPN
ejpam-6438	331	2	pure	pure	PROPN
ejpam-6438	331	3	appl	appl	PROPN
ejpam-6438	331	4	.	.	PROPN
ejpam-6438	331	5	math	math	PROPN
ejpam-6438	331	6	,	,	PUNCT
ejpam-6438	331	7	18	18	NUM
ejpam-6438	331	8	(	(	PUNCT
ejpam-6438	331	9	3	3	NUM
ejpam-6438	331	10	)	)	PUNCT
ejpam-6438	331	11	(	(	PUNCT
ejpam-6438	331	12	2025	2025	NUM
ejpam-6438	331	13	)	)	PUNCT
ejpam-6438	331	14	,	,	PUNCT
ejpam-6438	331	15	6438	6438	NUM
ejpam-6438	331	16	10	10	NUM
ejpam-6438	331	17	of	of	ADP
ejpam-6438	331	18	18	18	NUM
ejpam-6438	331	19	figure	figure	NOUN
ejpam-6438	331	20	9	9	NUM
ejpam-6438	331	21	.	.	PUNCT
ejpam-6438	331	22	pn	pn	PROPN
ejpam-6438	331	23	⊙	⊙	PROPN
ejpam-6438	331	24	p3	p3	PROPN
ejpam-6438	331	25	graph	graph	NOUN
ejpam-6438	331	26	.	.	PUNCT
ejpam-6438	332	1	w	w	PROPN
ejpam-6438	332	2	(	(	PUNCT
ejpam-6438	332	3	vi	vi	PROPN
ejpam-6438	332	4	,	,	PUNCT
ejpam-6438	332	5	r	r	NOUN
ejpam-6438	332	6	)	)	PUNCT
ejpam-6438	332	7	=	=	SYM
ejpam-6438	332	8			NOUN
ejpam-6438	332	9	{	{	PUNCT
ejpam-6438	332	10	1	1	NUM
ejpam-6438	332	11	,	,	PUNCT
ejpam-6438	332	12	2	2	NUM
ejpam-6438	332	13	,	,	PUNCT
ejpam-6438	332	14	3	3	NUM
ejpam-6438	332	15	,	,	PUNCT
ejpam-6438	332	16	.	.	PUNCT
ejpam-6438	332	17	.	.	PUNCT
ejpam-6438	332	18	.	.	PUNCT
ejpam-6438	332	19	,	,	PUNCT
ejpam-6438	332	20	n	n	CCONJ
ejpam-6438	332	21	}	}	PUNCT
ejpam-6438	332	22	,	,	PUNCT
ejpam-6438	332	23	i	i	PRON
ejpam-6438	332	24	=	=	NOUN
ejpam-6438	332	25	1	1	NUM
ejpam-6438	332	26	{	{	PUNCT
ejpam-6438	332	27	2	2	NUM
ejpam-6438	332	28	,	,	PUNCT
ejpam-6438	332	29	1	1	NUM
ejpam-6438	332	30	,	,	PUNCT
ejpam-6438	332	31	2	2	NUM
ejpam-6438	332	32	,	,	PUNCT
ejpam-6438	332	33	.	.	PUNCT
ejpam-6438	332	34	.	.	PUNCT
ejpam-6438	332	35	.	.	PUNCT
ejpam-6438	333	1	,	,	PUNCT
ejpam-6438	333	2	n−	n−	NOUN
ejpam-6438	333	3	1	1	NUM
ejpam-6438	333	4	}	}	PUNCT
ejpam-6438	333	5	,	,	PUNCT
ejpam-6438	333	6	i	i	PRON
ejpam-6438	333	7	=	=	NOUN
ejpam-6438	333	8	2	2	NUM
ejpam-6438	333	9	{	{	PUNCT
ejpam-6438	333	10	3	3	NUM
ejpam-6438	333	11	,	,	PUNCT
ejpam-6438	333	12	2	2	NUM
ejpam-6438	333	13	,	,	PUNCT
ejpam-6438	333	14	1	1	NUM
ejpam-6438	333	15	,	,	PUNCT
ejpam-6438	333	16	2	2	NUM
ejpam-6438	333	17	,	,	PUNCT
ejpam-6438	333	18	.	.	PUNCT
ejpam-6438	333	19	.	.	PUNCT
ejpam-6438	334	1	.	.	PUNCT
ejpam-6438	335	1	,	,	PUNCT
ejpam-6438	335	2	n−	n−	NOUN
ejpam-6438	335	3	2	2	NUM
ejpam-6438	335	4	}	}	PUNCT
ejpam-6438	335	5	,	,	PUNCT
ejpam-6438	335	6	i	i	PRON
ejpam-6438	335	7	=	=	NOUN
ejpam-6438	335	8	3	3	NUM
ejpam-6438	335	9	:	:	PUNCT
ejpam-6438	335	10	:	:	PUNCT
ejpam-6438	335	11	:	:	PUNCT
ejpam-6438	335	12	{	{	PUNCT
ejpam-6438	335	13	n−	n−	NOUN
ejpam-6438	335	14	2	2	NUM
ejpam-6438	335	15	,	,	PUNCT
ejpam-6438	335	16	.	.	PUNCT
ejpam-6438	335	17	.	.	PUNCT
ejpam-6438	336	1	.	.	PUNCT
ejpam-6438	337	1	,	,	PUNCT
ejpam-6438	337	2	2	2	NUM
ejpam-6438	337	3	,	,	PUNCT
ejpam-6438	337	4	1	1	NUM
ejpam-6438	337	5	,	,	PUNCT
ejpam-6438	337	6	2	2	NUM
ejpam-6438	337	7	,	,	PUNCT
ejpam-6438	337	8	3	3	NUM
ejpam-6438	337	9	}	}	PUNCT
ejpam-6438	337	10	,	,	PUNCT
ejpam-6438	337	11	i	i	PRON
ejpam-6438	337	12	=	=	VERB
ejpam-6438	337	13	n−	n−	NOUN
ejpam-6438	337	14	2	2	NUM
ejpam-6438	337	15	{	{	PUNCT
ejpam-6438	337	16	n−	n−	NOUN
ejpam-6438	337	17	1	1	NUM
ejpam-6438	337	18	,	,	PUNCT
ejpam-6438	337	19	.	.	PUNCT
ejpam-6438	337	20	.	.	PUNCT
ejpam-6438	338	1	.	.	PUNCT
ejpam-6438	339	1	,	,	PUNCT
ejpam-6438	339	2	2	2	NUM
ejpam-6438	339	3	,	,	PUNCT
ejpam-6438	339	4	1	1	NUM
ejpam-6438	339	5	,	,	PUNCT
ejpam-6438	339	6	2	2	NUM
ejpam-6438	339	7	,	,	PUNCT
ejpam-6438	339	8	3	3	NUM
ejpam-6438	339	9	}	}	PUNCT
ejpam-6438	339	10	,	,	PUNCT
ejpam-6438	339	11	i	i	PRON
ejpam-6438	339	12	=	=	VERB
ejpam-6438	339	13	n−	n−	NOUN
ejpam-6438	339	14	1	1	NUM
ejpam-6438	339	15	{	{	PUNCT
ejpam-6438	339	16	n	n	CCONJ
ejpam-6438	339	17	,	,	PUNCT
ejpam-6438	339	18	.	.	PUNCT
ejpam-6438	339	19	.	.	PUNCT
ejpam-6438	340	1	.	.	PUNCT
ejpam-6438	341	1	,	,	PUNCT
ejpam-6438	341	2	3	3	NUM
ejpam-6438	341	3	,	,	PUNCT
ejpam-6438	341	4	2	2	NUM
ejpam-6438	341	5	,	,	PUNCT
ejpam-6438	341	6	1	1	NUM
ejpam-6438	341	7	}	}	PUNCT
ejpam-6438	341	8	.i	.i	PUNCT
ejpam-6438	342	1	=	=	PUNCT
ejpam-6438	342	2	n	n	PROPN
ejpam-6438	342	3	w	w	NOUN
ejpam-6438	342	4	(	(	PUNCT
ejpam-6438	342	5	uij	uij	PRON
ejpam-6438	342	6	,	,	PUNCT
ejpam-6438	342	7	r	r	NOUN
ejpam-6438	342	8	)	)	PUNCT
ejpam-6438	342	9	=	=	SYM
ejpam-6438	342	10			PROPN
ejpam-6438	342	11	{	{	PUNCT
ejpam-6438	342	12	j	j	PROPN
ejpam-6438	342	13	−	−	PROPN
ejpam-6438	343	1	1	1	NUM
ejpam-6438	343	2	,	,	PUNCT
ejpam-6438	343	3	3	3	NUM
ejpam-6438	343	4	,	,	PUNCT
ejpam-6438	343	5	4	4	NUM
ejpam-6438	343	6	,	,	PUNCT
ejpam-6438	343	7	.	.	PUNCT
ejpam-6438	343	8	.	.	PUNCT
ejpam-6438	344	1	.	.	PUNCT
ejpam-6438	345	1	,	,	PUNCT
ejpam-6438	345	2	n	n	CCONJ
ejpam-6438	345	3	,	,	PUNCT
ejpam-6438	345	4	n+	n+	ADP
ejpam-6438	345	5	1	1	NUM
ejpam-6438	345	6	}	}	PUNCT
ejpam-6438	345	7	,	,	PUNCT
ejpam-6438	345	8	i	i	PRON
ejpam-6438	345	9	=	=	NOUN
ejpam-6438	345	10	1	1	NUM
ejpam-6438	345	11	{	{	PUNCT
ejpam-6438	345	12	3	3	NUM
ejpam-6438	345	13	,	,	PUNCT
ejpam-6438	345	14	j	j	PROPN
ejpam-6438	345	15	−	−	PROPN
ejpam-6438	345	16	1	1	NUM
ejpam-6438	345	17	,	,	PUNCT
ejpam-6438	345	18	3	3	NUM
ejpam-6438	345	19	,	,	PUNCT
ejpam-6438	345	20	4	4	NUM
ejpam-6438	345	21	,	,	PUNCT
ejpam-6438	345	22	.	.	PUNCT
ejpam-6438	345	23	.	.	PUNCT
ejpam-6438	346	1	.	.	PUNCT
ejpam-6438	347	1	,	,	PUNCT
ejpam-6438	347	2	n−	n−	NOUN
ejpam-6438	347	3	1	1	NUM
ejpam-6438	347	4	,	,	PUNCT
ejpam-6438	347	5	n	n	CCONJ
ejpam-6438	347	6	}	}	PUNCT
ejpam-6438	347	7	,	,	PUNCT
ejpam-6438	347	8	i	i	PRON
ejpam-6438	347	9	=	=	NOUN
ejpam-6438	347	10	2	2	NUM
ejpam-6438	347	11	{	{	PUNCT
ejpam-6438	347	12	4	4	NUM
ejpam-6438	347	13	,	,	PUNCT
ejpam-6438	347	14	3	3	NUM
ejpam-6438	347	15	,	,	PUNCT
ejpam-6438	347	16	j	j	PROPN
ejpam-6438	347	17	−	−	PROPN
ejpam-6438	347	18	1	1	NUM
ejpam-6438	347	19	,	,	PUNCT
ejpam-6438	347	20	3	3	NUM
ejpam-6438	347	21	,	,	PUNCT
ejpam-6438	347	22	4	4	NUM
ejpam-6438	347	23	,	,	PUNCT
ejpam-6438	347	24	.	.	PUNCT
ejpam-6438	347	25	.	.	PUNCT
ejpam-6438	348	1	.	.	PUNCT
ejpam-6438	349	1	,	,	PUNCT
ejpam-6438	349	2	n−	n−	NOUN
ejpam-6438	349	3	2	2	NUM
ejpam-6438	349	4	,	,	PUNCT
ejpam-6438	349	5	n−	n−	NOUN
ejpam-6438	349	6	1	1	NUM
ejpam-6438	349	7	}	}	PUNCT
ejpam-6438	349	8	,	,	PUNCT
ejpam-6438	349	9	i	i	PRON
ejpam-6438	349	10	=	=	NOUN
ejpam-6438	349	11	3	3	NUM
ejpam-6438	349	12	:	:	PUNCT
ejpam-6438	349	13	:	:	PUNCT
ejpam-6438	349	14	:	:	PUNCT
ejpam-6438	349	15	{	{	PUNCT
ejpam-6438	349	16	n−	n−	NOUN
ejpam-6438	349	17	1	1	NUM
ejpam-6438	349	18	,	,	PUNCT
ejpam-6438	349	19	n−	n−	NOUN
ejpam-6438	349	20	2	2	NUM
ejpam-6438	349	21	,	,	PUNCT
ejpam-6438	349	22	4	4	NUM
ejpam-6438	349	23	,	,	PUNCT
ejpam-6438	349	24	3	3	NUM
ejpam-6438	349	25	,	,	PUNCT
ejpam-6438	349	26	j	j	PROPN
ejpam-6438	349	27	−	−	PROPN
ejpam-6438	349	28	1	1	NUM
ejpam-6438	349	29	,	,	PUNCT
ejpam-6438	349	30	3	3	NUM
ejpam-6438	349	31	,	,	PUNCT
ejpam-6438	349	32	4	4	NUM
ejpam-6438	349	33	}	}	PUNCT
ejpam-6438	349	34	,	,	PUNCT
ejpam-6438	349	35	i	i	PRON
ejpam-6438	349	36	=	=	VERB
ejpam-6438	349	37	n−	n−	NOUN
ejpam-6438	349	38	2	2	NUM
ejpam-6438	349	39	{	{	PUNCT
ejpam-6438	349	40	n	n	CCONJ
ejpam-6438	349	41	,	,	PUNCT
ejpam-6438	349	42	n−	n−	NOUN
ejpam-6438	349	43	1	1	NUM
ejpam-6438	349	44	,	,	PUNCT
ejpam-6438	349	45	.	.	PUNCT
ejpam-6438	349	46	.	.	PUNCT
ejpam-6438	350	1	.	.	PUNCT
ejpam-6438	351	1	,	,	PUNCT
ejpam-6438	351	2	4	4	NUM
ejpam-6438	351	3	,	,	PUNCT
ejpam-6438	351	4	3	3	NUM
ejpam-6438	351	5	,	,	PUNCT
ejpam-6438	351	6	j	j	PROPN
ejpam-6438	351	7	−	−	PROPN
ejpam-6438	351	8	1	1	NUM
ejpam-6438	351	9	,	,	PUNCT
ejpam-6438	351	10	3	3	NUM
ejpam-6438	351	11	}	}	PUNCT
ejpam-6438	351	12	,	,	PUNCT
ejpam-6438	351	13	i	i	PRON
ejpam-6438	351	14	=	=	VERB
ejpam-6438	351	15	n−	n−	NOUN
ejpam-6438	351	16	1	1	NUM
ejpam-6438	351	17	{	{	PUNCT
ejpam-6438	351	18	n+	n+	NOUN
ejpam-6438	351	19	1	1	NUM
ejpam-6438	351	20	,	,	PUNCT
ejpam-6438	351	21	n	n	CCONJ
ejpam-6438	351	22	,	,	PUNCT
ejpam-6438	351	23	.	.	PUNCT
ejpam-6438	351	24	.	.	PUNCT
ejpam-6438	351	25	.	.	PUNCT
ejpam-6438	352	1	,	,	PUNCT
ejpam-6438	352	2	4	4	NUM
ejpam-6438	352	3	,	,	PUNCT
ejpam-6438	352	4	3	3	NUM
ejpam-6438	352	5	,	,	PUNCT
ejpam-6438	352	6	j	j	PROPN
ejpam-6438	352	7	−	−	PROPN
ejpam-6438	352	8	1	1	NUM
ejpam-6438	352	9	}	}	PUNCT
ejpam-6438	352	10	.i	.i	PUNCT
ejpam-6438	353	1	=	=	PUNCT
ejpam-6438	353	2	n	n	CCONJ
ejpam-6438	353	3	thus	thus	ADV
ejpam-6438	353	4	,	,	PUNCT
ejpam-6438	353	5	all	all	DET
ejpam-6438	353	6	vertices	vertex	NOUN
ejpam-6438	353	7	are	be	AUX
ejpam-6438	353	8	uniquely	uniquely	ADV
ejpam-6438	353	9	identified	identify	VERB
ejpam-6438	353	10	by	by	ADP
ejpam-6438	353	11	their	their	PRON
ejpam-6438	353	12	distance	distance	NOUN
ejpam-6438	353	13	vectors	vector	NOUN
ejpam-6438	353	14	to	to	ADP
ejpam-6438	353	15	r	r	NOUN
ejpam-6438	353	16	,	,	PUNCT
ejpam-6438	353	17	and	and	CCONJ
ejpam-6438	353	18	|r|	|r|	NOUN
ejpam-6438	353	19	=	=	NOUN
ejpam-6438	353	20	n.	n.	NOUN
ejpam-6438	353	21	to	to	PART
ejpam-6438	353	22	show	show	VERB
ejpam-6438	353	23	minimality	minimality	NOUN
ejpam-6438	353	24	,	,	PUNCT
ejpam-6438	353	25	note	note	VERB
ejpam-6438	353	26	that	that	SCONJ
ejpam-6438	353	27	if	if	SCONJ
ejpam-6438	353	28	any	any	DET
ejpam-6438	353	29	ui1	ui1	NOUN
ejpam-6438	353	30	is	be	AUX
ejpam-6438	353	31	removed	remove	VERB
ejpam-6438	353	32	from	from	ADP
ejpam-6438	353	33	r	r	NOUN
ejpam-6438	353	34	,	,	PUNCT
ejpam-6438	353	35	then	then	ADV
ejpam-6438	353	36	the	the	DET
ejpam-6438	353	37	vertices	vertex	NOUN
ejpam-6438	353	38	in	in	ADP
ejpam-6438	353	39	the	the	DET
ejpam-6438	353	40	i	i	PROPN
ejpam-6438	353	41	-	-	PUNCT
ejpam-6438	353	42	th	th	VERB
ejpam-6438	353	43	p3	p3	NOUN
ejpam-6438	353	44	copy	copy	NOUN
ejpam-6438	353	45	are	be	AUX
ejpam-6438	353	46	no	no	ADV
ejpam-6438	353	47	longer	long	ADV
ejpam-6438	353	48	distinguishable	distinguishable	ADJ
ejpam-6438	353	49	.	.	PUNCT
ejpam-6438	354	1	hence	hence	ADV
ejpam-6438	354	2	,	,	PUNCT
ejpam-6438	354	3	dim(g	dim(g	PROPN
ejpam-6438	354	4	)	)	PUNCT
ejpam-6438	355	1	=	=	SYM
ejpam-6438	355	2	n.	n.	NOUN
ejpam-6438	355	3	theorem	theorem	VERB
ejpam-6438	355	4	6	6	NUM
ejpam-6438	355	5	:	:	PUNCT
ejpam-6438	355	6	let	let	VERB
ejpam-6438	355	7	g	g	PRON
ejpam-6438	355	8	be	be	AUX
ejpam-6438	355	9	cn	cn	PROPN
ejpam-6438	355	10	⊙	⊙	PROPN
ejpam-6438	355	11	p3	p3	PROPN
ejpam-6438	355	12	graph	graph	NOUN
ejpam-6438	355	13	,	,	PUNCT
ejpam-6438	355	14	then	then	ADV
ejpam-6438	355	15	m.d	m.d	PROPN
ejpam-6438	355	16	(	(	PUNCT
ejpam-6438	355	17	cn	cn	PROPN
ejpam-6438	355	18	⊙	⊙	PROPN
ejpam-6438	355	19	p3	p3	PROPN
ejpam-6438	355	20	)	)	PUNCT
ejpam-6438	355	21	=	=	SYM
ejpam-6438	355	22	n	n	CCONJ
ejpam-6438	355	23	,	,	PUNCT
ejpam-6438	355	24	n	n	PRON
ejpam-6438	355	25	≥	≥	NOUN
ejpam-6438	355	26	3	3	NUM
ejpam-6438	355	27	.	.	PUNCT
ejpam-6438	356	1	proof	proof	NOUN
ejpam-6438	356	2	.	.	PUNCT
ejpam-6438	357	1	label	label	VERB
ejpam-6438	357	2	the	the	DET
ejpam-6438	357	3	cycle	cycle	NOUN
ejpam-6438	357	4	cn	cn	PROPN
ejpam-6438	357	5	as	as	ADP
ejpam-6438	357	6	v1	v1	NOUN
ejpam-6438	357	7	,	,	PUNCT
ejpam-6438	357	8	v2	v2	NOUN
ejpam-6438	357	9	,	,	PUNCT
ejpam-6438	357	10	.	.	PUNCT
ejpam-6438	357	11	.	.	PUNCT
ejpam-6438	358	1	.	.	PUNCT
ejpam-6438	359	1	,	,	PUNCT
ejpam-6438	359	2	vn	vn	X
ejpam-6438	359	3	in	in	ADP
ejpam-6438	359	4	cyclic	cyclic	ADJ
ejpam-6438	359	5	order	order	NOUN
ejpam-6438	359	6	.	.	PUNCT
ejpam-6438	360	1	for	for	ADP
ejpam-6438	360	2	each	each	DET
ejpam-6438	360	3	vi	vi	NOUN
ejpam-6438	360	4	,	,	PUNCT
ejpam-6438	360	5	attach	attach	VERB
ejpam-6438	360	6	a	a	DET
ejpam-6438	360	7	copy	copy	NOUN
ejpam-6438	360	8	of	of	ADP
ejpam-6438	360	9	p3	p3	PROPN
ejpam-6438	360	10	with	with	ADP
ejpam-6438	360	11	vertices	vertex	NOUN
ejpam-6438	360	12	ui1	ui1	ADV
ejpam-6438	360	13	,	,	PUNCT
ejpam-6438	360	14	ui2	ui2	PROPN
ejpam-6438	360	15	,	,	PUNCT
ejpam-6438	360	16	ui3	ui3	PROPN
ejpam-6438	360	17	,	,	PUNCT
ejpam-6438	360	18	each	each	PRON
ejpam-6438	360	19	adjacent	adjacent	ADJ
ejpam-6438	360	20	to	to	ADP
ejpam-6438	360	21	vi	vi	NUM
ejpam-6438	360	22	,	,	PUNCT
ejpam-6438	360	23	as	as	SCONJ
ejpam-6438	360	24	show	show	NOUN
ejpam-6438	360	25	in	in	ADP
ejpam-6438	360	26	figure	figure	NOUN
ejpam-6438	360	27	10	10	NUM
ejpam-6438	360	28	.	.	PUNCT
ejpam-6438	361	1	let	let	VERB
ejpam-6438	361	2	r	r	NOUN
ejpam-6438	361	3	=	=	PRON
ejpam-6438	361	4	{	{	PUNCT
ejpam-6438	361	5	ui1	ui1	NOUN
ejpam-6438	361	6	|	|	ADV
ejpam-6438	361	7	1	1	NUM
ejpam-6438	361	8	≤	≤	NUM
ejpam-6438	361	9	i	i	PRON
ejpam-6438	361	10	≤	≤	NOUN
ejpam-6438	361	11	n	n	CCONJ
ejpam-6438	361	12	}	}	PUNCT
ejpam-6438	361	13	.	.	PUNCT
ejpam-6438	362	1	we	we	PRON
ejpam-6438	362	2	claim	claim	VERB
ejpam-6438	362	3	that	that	SCONJ
ejpam-6438	362	4	r	r	NOUN
ejpam-6438	362	5	is	be	AUX
ejpam-6438	362	6	a	a	DET
ejpam-6438	362	7	resolving	resolving	NOUN
ejpam-6438	362	8	set	set	NOUN
ejpam-6438	362	9	.	.	PUNCT
ejpam-6438	363	1	a.	a.	PROPN
ejpam-6438	363	2	elrokh	elrokh	PROPN
ejpam-6438	363	3	,	,	PUNCT
ejpam-6438	363	4	eman	eman	PROPN
ejpam-6438	363	5	s.	s.	PROPN
ejpam-6438	363	6	almotairi	almotairi	PROPN
ejpam-6438	363	7	,	,	PUNCT
ejpam-6438	363	8	h.	h.	PROPN
ejpam-6438	363	9	mostafa	mostafa	PROPN
ejpam-6438	363	10	/	/	SYM
ejpam-6438	363	11	eur	eur	PROPN
ejpam-6438	363	12	.	.	PUNCT
ejpam-6438	364	1	j.	j.	PROPN
ejpam-6438	364	2	pure	pure	PROPN
ejpam-6438	364	3	appl	appl	PROPN
ejpam-6438	364	4	.	.	PROPN
ejpam-6438	364	5	math	math	PROPN
ejpam-6438	364	6	,	,	PUNCT
ejpam-6438	364	7	18	18	NUM
ejpam-6438	364	8	(	(	PUNCT
ejpam-6438	364	9	3	3	NUM
ejpam-6438	364	10	)	)	PUNCT
ejpam-6438	364	11	(	(	PUNCT
ejpam-6438	364	12	2025	2025	NUM
ejpam-6438	364	13	)	)	PUNCT
ejpam-6438	364	14	,	,	PUNCT
ejpam-6438	364	15	6438	6438	NUM
ejpam-6438	364	16	11	11	NUM
ejpam-6438	364	17	of	of	ADP
ejpam-6438	364	18	18	18	NUM
ejpam-6438	364	19	figure	figure	NOUN
ejpam-6438	364	20	10	10	NUM
ejpam-6438	364	21	.	.	PUNCT
ejpam-6438	365	1	the	the	DET
ejpam-6438	365	2	cn	cn	PROPN
ejpam-6438	365	3	⊙	⊙	PROPN
ejpam-6438	365	4	p3	p3	PROPN
ejpam-6438	365	5	graph	graph	NOUN
ejpam-6438	365	6	.	.	PUNCT
ejpam-6438	366	1	w	w	PROPN
ejpam-6438	366	2	(	(	PUNCT
ejpam-6438	366	3	vi	vi	PROPN
ejpam-6438	366	4	,	,	PUNCT
ejpam-6438	366	5	r	r	NOUN
ejpam-6438	366	6	)	)	PUNCT
ejpam-6438	366	7	=	=	SYM
ejpam-6438	366	8			PROPN
ejpam-6438	366	9	{	{	PUNCT
ejpam-6438	366	10	1	1	NUM
ejpam-6438	366	11	,	,	PUNCT
ejpam-6438	366	12	2	2	NUM
ejpam-6438	366	13	,	,	PUNCT
ejpam-6438	366	14	.	.	PUNCT
ejpam-6438	366	15	.	.	PUNCT
ejpam-6438	366	16	.	.	PUNCT
ejpam-6438	367	1	,	,	PUNCT
ejpam-6438	367	2	2	2	X
ejpam-6438	367	3	}	}	PUNCT
ejpam-6438	367	4	,	,	PUNCT
ejpam-6438	367	5	i	i	PRON
ejpam-6438	367	6	=	=	NOUN
ejpam-6438	367	7	1	1	NUM
ejpam-6438	367	8	{	{	PUNCT
ejpam-6438	367	9	2	2	NUM
ejpam-6438	367	10	,	,	PUNCT
ejpam-6438	367	11	1	1	NUM
ejpam-6438	367	12	,	,	PUNCT
ejpam-6438	367	13	2	2	NUM
ejpam-6438	367	14	,	,	PUNCT
ejpam-6438	367	15	.	.	PUNCT
ejpam-6438	367	16	.	.	PUNCT
ejpam-6438	367	17	.	.	PUNCT
ejpam-6438	368	1	,	,	PUNCT
ejpam-6438	368	2	2	2	X
ejpam-6438	368	3	}	}	PUNCT
ejpam-6438	368	4	,	,	PUNCT
ejpam-6438	368	5	i	i	PRON
ejpam-6438	368	6	=	=	NOUN
ejpam-6438	368	7	2	2	NUM
ejpam-6438	368	8	{	{	PUNCT
ejpam-6438	368	9	3	3	NUM
ejpam-6438	368	10	,	,	PUNCT
ejpam-6438	368	11	2	2	NUM
ejpam-6438	368	12	,	,	PUNCT
ejpam-6438	368	13	1	1	NUM
ejpam-6438	368	14	,	,	PUNCT
ejpam-6438	368	15	.	.	PUNCT
ejpam-6438	368	16	.	.	PUNCT
ejpam-6438	368	17	.	.	PUNCT
ejpam-6438	369	1	,	,	PUNCT
ejpam-6438	369	2	3	3	X
ejpam-6438	369	3	}	}	PUNCT
ejpam-6438	369	4	,	,	PUNCT
ejpam-6438	369	5	i	i	PRON
ejpam-6438	369	6	=	=	NOUN
ejpam-6438	369	7	3	3	NUM
ejpam-6438	369	8	:	:	PUNCT
ejpam-6438	369	9	:	:	PUNCT
ejpam-6438	369	10	:	:	PUNCT
ejpam-6438	369	11	{	{	PUNCT
ejpam-6438	369	12	2	2	NUM
ejpam-6438	369	13	,	,	PUNCT
ejpam-6438	369	14	3	3	NUM
ejpam-6438	369	15	,	,	PUNCT
ejpam-6438	369	16	n−	n−	NOUN
ejpam-6438	369	17	2	2	NUM
ejpam-6438	369	18	,	,	PUNCT
ejpam-6438	369	19	.	.	PUNCT
ejpam-6438	369	20	.	.	PUNCT
ejpam-6438	369	21	.	.	PUNCT
ejpam-6438	370	1	,	,	PUNCT
ejpam-6438	370	2	2	2	NUM
ejpam-6438	370	3	,	,	PUNCT
ejpam-6438	370	4	1	1	NUM
ejpam-6438	370	5	}	}	PUNCT
ejpam-6438	370	6	.i	.i	PUNCT
ejpam-6438	371	1	=	=	PUNCT
ejpam-6438	371	2	n	n	PROPN
ejpam-6438	371	3	w	w	NOUN
ejpam-6438	371	4	(	(	PUNCT
ejpam-6438	371	5	uij	uij	PRON
ejpam-6438	371	6	,	,	PUNCT
ejpam-6438	371	7	r	r	NOUN
ejpam-6438	371	8	)	)	PUNCT
ejpam-6438	371	9	=	=	SYM
ejpam-6438	371	10			PROPN
ejpam-6438	371	11	{	{	PUNCT
ejpam-6438	371	12	j	j	PROPN
ejpam-6438	371	13	−	−	PROPN
ejpam-6438	372	1	1	1	NUM
ejpam-6438	372	2	,	,	PUNCT
ejpam-6438	372	3	3	3	NUM
ejpam-6438	372	4	,	,	PUNCT
ejpam-6438	372	5	4	4	NUM
ejpam-6438	372	6	,	,	PUNCT
ejpam-6438	372	7	.	.	PUNCT
ejpam-6438	372	8	.	.	PUNCT
ejpam-6438	373	1	.	.	PUNCT
ejpam-6438	374	1	,	,	PUNCT
ejpam-6438	374	2	3	3	X
ejpam-6438	374	3	}	}	PUNCT
ejpam-6438	374	4	,	,	PUNCT
ejpam-6438	374	5	i	i	PRON
ejpam-6438	374	6	=	=	NOUN
ejpam-6438	374	7	1	1	NUM
ejpam-6438	374	8	{	{	PUNCT
ejpam-6438	374	9	3	3	NUM
ejpam-6438	374	10	,	,	PUNCT
ejpam-6438	374	11	j	j	PROPN
ejpam-6438	374	12	−	−	PROPN
ejpam-6438	374	13	1	1	NUM
ejpam-6438	374	14	,	,	PUNCT
ejpam-6438	374	15	3	3	NUM
ejpam-6438	374	16	,	,	PUNCT
ejpam-6438	374	17	.	.	PUNCT
ejpam-6438	374	18	.	.	PUNCT
ejpam-6438	374	19	.	.	PUNCT
ejpam-6438	375	1	,	,	PUNCT
ejpam-6438	375	2	n−	n−	NOUN
ejpam-6438	375	3	2	2	NUM
ejpam-6438	375	4	,	,	PUNCT
ejpam-6438	375	5	n−	n−	NOUN
ejpam-6438	375	6	1	1	NUM
ejpam-6438	375	7	,	,	PUNCT
ejpam-6438	375	8	4	4	NUM
ejpam-6438	375	9	}	}	PUNCT
ejpam-6438	375	10	,	,	PUNCT
ejpam-6438	375	11	i	i	PRON
ejpam-6438	375	12	=	=	NOUN
ejpam-6438	375	13	2	2	NUM
ejpam-6438	375	14	{	{	PUNCT
ejpam-6438	375	15	4	4	NUM
ejpam-6438	375	16	,	,	PUNCT
ejpam-6438	375	17	3	3	NUM
ejpam-6438	375	18	,	,	PUNCT
ejpam-6438	375	19	j	j	PROPN
ejpam-6438	375	20	−	−	PROPN
ejpam-6438	375	21	1	1	NUM
ejpam-6438	375	22	,	,	PUNCT
ejpam-6438	375	23	3	3	NUM
ejpam-6438	375	24	,	,	PUNCT
ejpam-6438	375	25	4	4	NUM
ejpam-6438	375	26	,	,	PUNCT
ejpam-6438	375	27	.	.	PUNCT
ejpam-6438	375	28	.	.	PUNCT
ejpam-6438	376	1	.	.	PUNCT
ejpam-6438	377	1	,	,	PUNCT
ejpam-6438	377	2	n−	n−	NOUN
ejpam-6438	377	3	2	2	NUM
ejpam-6438	377	4	,	,	PUNCT
ejpam-6438	377	5	n−	n−	NOUN
ejpam-6438	377	6	1	1	NUM
ejpam-6438	377	7	}	}	PUNCT
ejpam-6438	377	8	,	,	PUNCT
ejpam-6438	377	9	i	i	PRON
ejpam-6438	377	10	=	=	NOUN
ejpam-6438	377	11	3	3	NUM
ejpam-6438	377	12	:	:	PUNCT
ejpam-6438	377	13	:	:	PUNCT
ejpam-6438	377	14	:	:	PUNCT
ejpam-6438	377	15	{	{	PUNCT
ejpam-6438	377	16	3	3	NUM
ejpam-6438	377	17	,	,	PUNCT
ejpam-6438	377	18	4	4	NUM
ejpam-6438	377	19	,	,	PUNCT
ejpam-6438	377	20	.	.	PUNCT
ejpam-6438	377	21	.	.	PUNCT
ejpam-6438	378	1	.	.	PUNCT
ejpam-6438	379	1	,	,	PUNCT
ejpam-6438	379	2	4	4	NUM
ejpam-6438	379	3	,	,	PUNCT
ejpam-6438	379	4	3	3	NUM
ejpam-6438	379	5	,	,	PUNCT
ejpam-6438	379	6	j	j	PROPN
ejpam-6438	379	7	−	−	PROPN
ejpam-6438	379	8	1	1	NUM
ejpam-6438	379	9	}	}	PUNCT
ejpam-6438	379	10	.i	.i	PUNCT
ejpam-6438	380	1	=	=	SYM
ejpam-6438	380	2	n	n	CCONJ
ejpam-6438	380	3	each	each	DET
ejpam-6438	380	4	vi	vi	NOUN
ejpam-6438	380	5	is	be	AUX
ejpam-6438	380	6	uniquely	uniquely	ADV
ejpam-6438	380	7	identified	identify	VERB
ejpam-6438	380	8	by	by	ADP
ejpam-6438	380	9	its	its	PRON
ejpam-6438	380	10	distance	distance	NOUN
ejpam-6438	380	11	to	to	ADP
ejpam-6438	380	12	ui1	ui1	PROPN
ejpam-6438	380	13	(	(	PUNCT
ejpam-6438	380	14	which	which	PRON
ejpam-6438	380	15	is	be	AUX
ejpam-6438	380	16	1	1	NUM
ejpam-6438	380	17	)	)	PUNCT
ejpam-6438	380	18	,	,	PUNCT
ejpam-6438	380	19	and	and	CCONJ
ejpam-6438	380	20	to	to	ADP
ejpam-6438	380	21	other	other	ADJ
ejpam-6438	380	22	uj1	uj1	NOUN
ejpam-6438	380	23	(	(	PUNCT
ejpam-6438	380	24	which	which	PRON
ejpam-6438	380	25	vary	vary	VERB
ejpam-6438	380	26	due	due	ADP
ejpam-6438	380	27	to	to	ADP
ejpam-6438	380	28	the	the	DET
ejpam-6438	380	29	cycle	cycle	NOUN
ejpam-6438	380	30	structure	structure	NOUN
ejpam-6438	380	31	)	)	PUNCT
ejpam-6438	380	32	.	.	PUNCT
ejpam-6438	381	1	each	each	DET
ejpam-6438	381	2	uij	uij	PRON
ejpam-6438	381	3	in	in	ADP
ejpam-6438	381	4	the	the	DET
ejpam-6438	381	5	i	i	PROPN
ejpam-6438	381	6	-	-	PUNCT
ejpam-6438	381	7	th	th	VERB
ejpam-6438	381	8	p3	p3	NOUN
ejpam-6438	381	9	copy	copy	NOUN
ejpam-6438	381	10	is	be	AUX
ejpam-6438	381	11	distinguishable	distinguishable	ADJ
ejpam-6438	381	12	by	by	ADP
ejpam-6438	381	13	its	its	PRON
ejpam-6438	381	14	distance	distance	NOUN
ejpam-6438	381	15	to	to	ADP
ejpam-6438	381	16	ui1	ui1	NOUN
ejpam-6438	381	17	.	.	PUNCT
ejpam-6438	382	1	if	if	SCONJ
ejpam-6438	382	2	any	any	DET
ejpam-6438	382	3	ui1	ui1	NOUN
ejpam-6438	382	4	is	be	AUX
ejpam-6438	382	5	removed	remove	VERB
ejpam-6438	382	6	,	,	PUNCT
ejpam-6438	382	7	then	then	ADV
ejpam-6438	382	8	the	the	DET
ejpam-6438	382	9	corresponding	correspond	VERB
ejpam-6438	382	10	p3	p3	PROPN
ejpam-6438	382	11	copy	copy	NOUN
ejpam-6438	382	12	can	can	AUX
ejpam-6438	382	13	not	not	PART
ejpam-6438	382	14	be	be	AUX
ejpam-6438	382	15	resolved	resolve	VERB
ejpam-6438	382	16	.	.	PUNCT
ejpam-6438	383	1	hence	hence	ADV
ejpam-6438	383	2	,	,	PUNCT
ejpam-6438	383	3	r	r	NOUN
ejpam-6438	383	4	is	be	AUX
ejpam-6438	383	5	minimal	minimal	ADJ
ejpam-6438	383	6	and	and	CCONJ
ejpam-6438	383	7	dim(g	dim(g	PROPN
ejpam-6438	383	8	)	)	PUNCT
ejpam-6438	383	9	=	=	SYM
ejpam-6438	383	10	n.	n.	NOUN
ejpam-6438	383	11	theorem	theorem	VERB
ejpam-6438	383	12	7	7	NUM
ejpam-6438	383	13	:	:	PUNCT
ejpam-6438	383	14	let	let	VERB
ejpam-6438	383	15	g	g	NOUN
ejpam-6438	383	16	be	be	AUX
ejpam-6438	383	17	pn	pn	PROPN
ejpam-6438	383	18	⊙	⊙	PROPN
ejpam-6438	383	19	c3	c3	PROPN
ejpam-6438	383	20	graph	graph	NOUN
ejpam-6438	383	21	,	,	PUNCT
ejpam-6438	383	22	then	then	ADV
ejpam-6438	383	23	m.d	m.d	PROPN
ejpam-6438	383	24	(	(	PUNCT
ejpam-6438	383	25	pn	pn	PROPN
ejpam-6438	383	26	⊙	⊙	PROPN
ejpam-6438	383	27	c3	c3	PROPN
ejpam-6438	383	28	)	)	PUNCT
ejpam-6438	383	29	=	=	SYM
ejpam-6438	383	30	2n	2n	NUM
ejpam-6438	383	31	,	,	PUNCT
ejpam-6438	383	32	n	n	PRON
ejpam-6438	383	33	≥	≥	NOUN
ejpam-6438	383	34	1	1	NUM
ejpam-6438	383	35	.	.	PUNCT
ejpam-6438	384	1	proof	proof	NOUN
ejpam-6438	384	2	.	.	PUNCT
ejpam-6438	385	1	label	label	VERB
ejpam-6438	385	2	the	the	DET
ejpam-6438	385	3	path	path	NOUN
ejpam-6438	385	4	pn	pn	PROPN
ejpam-6438	385	5	as	as	ADP
ejpam-6438	385	6	v1	v1	NOUN
ejpam-6438	385	7	,	,	PUNCT
ejpam-6438	385	8	v2	v2	NOUN
ejpam-6438	385	9	,	,	PUNCT
ejpam-6438	385	10	.	.	PUNCT
ejpam-6438	385	11	.	.	PUNCT
ejpam-6438	386	1	.	.	PUNCT
ejpam-6438	387	1	,	,	PUNCT
ejpam-6438	387	2	vn	vn	PROPN
ejpam-6438	387	3	.	.	PUNCT
ejpam-6438	388	1	for	for	ADP
ejpam-6438	388	2	each	each	DET
ejpam-6438	388	3	vi	vi	NOUN
ejpam-6438	388	4	,	,	PUNCT
ejpam-6438	388	5	attach	attach	VERB
ejpam-6438	388	6	a	a	DET
ejpam-6438	388	7	copy	copy	NOUN
ejpam-6438	388	8	of	of	ADP
ejpam-6438	388	9	c3	c3	PROPN
ejpam-6438	388	10	with	with	ADP
ejpam-6438	388	11	vertices	vertex	NOUN
ejpam-6438	388	12	ui1	ui1	PROPN
ejpam-6438	388	13	,	,	PUNCT
ejpam-6438	388	14	ui2	ui2	PRON
ejpam-6438	388	15	,	,	PUNCT
ejpam-6438	388	16	ui3	ui3	VERB
ejpam-6438	388	17	forming	form	VERB
ejpam-6438	388	18	a	a	DET
ejpam-6438	388	19	triangle	triangle	NOUN
ejpam-6438	388	20	,	,	PUNCT
ejpam-6438	388	21	and	and	CCONJ
ejpam-6438	388	22	connect	connect	VERB
ejpam-6438	388	23	each	each	PRON
ejpam-6438	388	24	to	to	ADP
ejpam-6438	388	25	vi	vi	NUM
ejpam-6438	388	26	,	,	PUNCT
ejpam-6438	388	27	as	as	SCONJ
ejpam-6438	388	28	show	show	NOUN
ejpam-6438	388	29	in	in	ADP
ejpam-6438	388	30	figure	figure	NOUN
ejpam-6438	388	31	11	11	NUM
ejpam-6438	388	32	.	.	PUNCT
ejpam-6438	389	1	let	let	VERB
ejpam-6438	389	2	r	r	NOUN
ejpam-6438	389	3	=	=	PUNCT
ejpam-6438	389	4	{	{	PUNCT
ejpam-6438	389	5	ui1	ui1	ADV
ejpam-6438	389	6	,	,	PUNCT
ejpam-6438	389	7	ui2	ui2	PUNCT
ejpam-6438	390	1	|	|	ADV
ejpam-6438	390	2	1	1	NUM
ejpam-6438	390	3	≤	≤	NUM
ejpam-6438	390	4	i	i	PRON
ejpam-6438	390	5	≤	≤	NOUN
ejpam-6438	390	6	n	n	CCONJ
ejpam-6438	390	7	}	}	PUNCT
ejpam-6438	390	8	.	.	PUNCT
ejpam-6438	391	1	we	we	PRON
ejpam-6438	391	2	claim	claim	VERB
ejpam-6438	391	3	that	that	SCONJ
ejpam-6438	391	4	r	r	NOUN
ejpam-6438	391	5	is	be	AUX
ejpam-6438	391	6	a	a	DET
ejpam-6438	391	7	resolving	resolving	NOUN
ejpam-6438	391	8	set	set	NOUN
ejpam-6438	391	9	.	.	PUNCT
ejpam-6438	392	1	figure	figure	NOUN
ejpam-6438	392	2	11	11	NUM
ejpam-6438	392	3	.	.	PUNCT
ejpam-6438	393	1	the	the	DET
ejpam-6438	393	2	pn	pn	PROPN
ejpam-6438	393	3	⊙	⊙	PROPN
ejpam-6438	393	4	c3	c3	PROPN
ejpam-6438	393	5	graph	graph	PROPN
ejpam-6438	393	6	.	.	PUNCT
ejpam-6438	393	7	a.	a.	PROPN
ejpam-6438	393	8	elrokh	elrokh	PROPN
ejpam-6438	393	9	,	,	PUNCT
ejpam-6438	393	10	eman	eman	PROPN
ejpam-6438	393	11	s.	s.	PROPN
ejpam-6438	393	12	almotairi	almotairi	PROPN
ejpam-6438	393	13	,	,	PUNCT
ejpam-6438	393	14	h.	h.	PROPN
ejpam-6438	393	15	mostafa	mostafa	PROPN
ejpam-6438	393	16	/	/	SYM
ejpam-6438	393	17	eur	eur	PROPN
ejpam-6438	393	18	.	.	PUNCT
ejpam-6438	394	1	j.	j.	PROPN
ejpam-6438	394	2	pure	pure	PROPN
ejpam-6438	394	3	appl	appl	PROPN
ejpam-6438	394	4	.	.	PROPN
ejpam-6438	394	5	math	math	PROPN
ejpam-6438	394	6	,	,	PUNCT
ejpam-6438	394	7	18	18	NUM
ejpam-6438	394	8	(	(	PUNCT
ejpam-6438	394	9	3	3	NUM
ejpam-6438	394	10	)	)	PUNCT
ejpam-6438	394	11	(	(	PUNCT
ejpam-6438	394	12	2025	2025	NUM
ejpam-6438	394	13	)	)	PUNCT
ejpam-6438	394	14	,	,	PUNCT
ejpam-6438	394	15	6438	6438	NUM
ejpam-6438	394	16	12	12	NUM
ejpam-6438	394	17	of	of	ADP
ejpam-6438	394	18	18	18	NUM
ejpam-6438	394	19	w	w	PROPN
ejpam-6438	394	20	(	(	PUNCT
ejpam-6438	394	21	vi	vi	PROPN
ejpam-6438	394	22	,	,	PUNCT
ejpam-6438	394	23	r	r	NOUN
ejpam-6438	394	24	)	)	PUNCT
ejpam-6438	394	25	=	=	SYM
ejpam-6438	394	26			PROPN
ejpam-6438	394	27	{	{	PUNCT
ejpam-6438	394	28	1	1	NUM
ejpam-6438	394	29	,	,	PUNCT
ejpam-6438	394	30	1	1	NUM
ejpam-6438	394	31	,	,	PUNCT
ejpam-6438	394	32	2	2	NUM
ejpam-6438	394	33	,	,	PUNCT
ejpam-6438	394	34	2	2	NUM
ejpam-6438	394	35	,	,	PUNCT
ejpam-6438	394	36	3	3	NUM
ejpam-6438	394	37	,	,	PUNCT
ejpam-6438	394	38	3	3	NUM
ejpam-6438	394	39	,	,	PUNCT
ejpam-6438	394	40	.	.	PUNCT
ejpam-6438	394	41	.	.	PUNCT
ejpam-6438	395	1	.	.	PUNCT
ejpam-6438	396	1	,	,	PUNCT
ejpam-6438	396	2	n	n	CCONJ
ejpam-6438	396	3	,	,	PUNCT
ejpam-6438	396	4	n	n	CCONJ
ejpam-6438	396	5	}	}	PUNCT
ejpam-6438	396	6	,	,	PUNCT
ejpam-6438	396	7	i	i	PRON
ejpam-6438	396	8	=	=	NOUN
ejpam-6438	396	9	1	1	NUM
ejpam-6438	396	10	{	{	PUNCT
ejpam-6438	396	11	2	2	NUM
ejpam-6438	396	12	,	,	PUNCT
ejpam-6438	396	13	2	2	NUM
ejpam-6438	396	14	,	,	PUNCT
ejpam-6438	396	15	1	1	NUM
ejpam-6438	396	16	,	,	PUNCT
ejpam-6438	396	17	1	1	NUM
ejpam-6438	396	18	,	,	PUNCT
ejpam-6438	396	19	2	2	NUM
ejpam-6438	396	20	,	,	PUNCT
ejpam-6438	396	21	2	2	NUM
ejpam-6438	396	22	.	.	PUNCT
ejpam-6438	396	23	.	.	PUNCT
ejpam-6438	396	24	.	.	PUNCT
ejpam-6438	397	1	,	,	PUNCT
ejpam-6438	397	2	n−	n−	NOUN
ejpam-6438	397	3	1	1	NUM
ejpam-6438	397	4	,	,	PUNCT
ejpam-6438	397	5	n−	n−	NOUN
ejpam-6438	397	6	1	1	NUM
ejpam-6438	397	7	}	}	PUNCT
ejpam-6438	397	8	,	,	PUNCT
ejpam-6438	397	9	i	i	PRON
ejpam-6438	397	10	=	=	NOUN
ejpam-6438	397	11	2	2	NUM
ejpam-6438	397	12	{	{	PUNCT
ejpam-6438	397	13	3	3	NUM
ejpam-6438	397	14	,	,	PUNCT
ejpam-6438	397	15	3	3	NUM
ejpam-6438	397	16	,	,	PUNCT
ejpam-6438	397	17	2	2	NUM
ejpam-6438	397	18	,	,	PUNCT
ejpam-6438	397	19	2	2	NUM
ejpam-6438	397	20	,	,	PUNCT
ejpam-6438	397	21	1	1	NUM
ejpam-6438	397	22	,	,	PUNCT
ejpam-6438	397	23	1	1	NUM
ejpam-6438	397	24	,	,	PUNCT
ejpam-6438	397	25	.	.	PUNCT
ejpam-6438	397	26	.	.	PUNCT
ejpam-6438	398	1	.	.	PUNCT
ejpam-6438	399	1	,	,	PUNCT
ejpam-6438	399	2	n−	n−	NOUN
ejpam-6438	399	3	2	2	NUM
ejpam-6438	399	4	,	,	PUNCT
ejpam-6438	399	5	n−	n−	NOUN
ejpam-6438	399	6	2	2	NUM
ejpam-6438	399	7	}	}	PUNCT
ejpam-6438	399	8	,	,	PUNCT
ejpam-6438	399	9	i	i	PRON
ejpam-6438	399	10	=	=	NOUN
ejpam-6438	399	11	3	3	NUM
ejpam-6438	399	12	:	:	PUNCT
ejpam-6438	399	13	:	:	PUNCT
ejpam-6438	399	14	:	:	PUNCT
ejpam-6438	399	15	{	{	PUNCT
ejpam-6438	399	16	n	n	CCONJ
ejpam-6438	399	17	,	,	PUNCT
ejpam-6438	399	18	n.n−	n.n−	X
ejpam-6438	399	19	1	1	NUM
ejpam-6438	399	20	,	,	PUNCT
ejpam-6438	399	21	n−	n−	NOUN
ejpam-6438	399	22	1	1	NUM
ejpam-6438	399	23	,	,	PUNCT
ejpam-6438	399	24	.	.	PUNCT
ejpam-6438	399	25	.	.	PUNCT
ejpam-6438	400	1	.	.	PUNCT
ejpam-6438	401	1	,	,	PUNCT
ejpam-6438	401	2	1	1	NUM
ejpam-6438	401	3	,	,	PUNCT
ejpam-6438	401	4	1	1	NUM
ejpam-6438	401	5	}	}	PUNCT
ejpam-6438	401	6	.i	.i	PUNCT
ejpam-6438	402	1	=	=	PUNCT
ejpam-6438	402	2	n	n	PROPN
ejpam-6438	402	3	w	w	NOUN
ejpam-6438	402	4	(	(	PUNCT
ejpam-6438	402	5	uij	uij	PRON
ejpam-6438	402	6	,	,	PUNCT
ejpam-6438	402	7	r	r	NOUN
ejpam-6438	402	8	)	)	PUNCT
ejpam-6438	402	9	=	=	SYM
ejpam-6438	402	10			NOUN
ejpam-6438	402	11	{	{	PUNCT
ejpam-6438	402	12	j	j	NOUN
ejpam-6438	402	13	−	−	PROPN
ejpam-6438	402	14	1	1	NUM
ejpam-6438	402	15	,	,	PUNCT
ejpam-6438	402	16	j	j	PROPN
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ejpam-6438	402	18	3	3	NUM
ejpam-6438	402	19	,	,	PUNCT
ejpam-6438	402	20	3	3	NUM
ejpam-6438	402	21	,	,	PUNCT
ejpam-6438	402	22	4	4	NUM
ejpam-6438	402	23	,	,	PUNCT
ejpam-6438	402	24	4	4	NUM
ejpam-6438	402	25	,	,	PUNCT
ejpam-6438	402	26	.	.	PUNCT
ejpam-6438	402	27	.	.	PUNCT
ejpam-6438	402	28	.	.	PUNCT
ejpam-6438	402	29	,	,	PUNCT
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ejpam-6438	402	36	,	,	PUNCT
ejpam-6438	402	37	n+	n+	ADP
ejpam-6438	402	38	1	1	NUM
ejpam-6438	402	39	}	}	PUNCT
ejpam-6438	402	40	,	,	PUNCT
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ejpam-6438	402	42	=	=	NOUN
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ejpam-6438	402	44	,	,	PUNCT
ejpam-6438	402	45	j	j	PROPN
ejpam-6438	402	46	=	=	SYM
ejpam-6438	402	47	1	1	NUM
ejpam-6438	402	48	{	{	PUNCT
ejpam-6438	402	49	j	j	NOUN
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ejpam-6438	402	51	1	1	NUM
ejpam-6438	402	52	,	,	PUNCT
ejpam-6438	402	53	j	j	PROPN
ejpam-6438	402	54	−	−	PROPN
ejpam-6438	402	55	2	2	NUM
ejpam-6438	402	56	,	,	PUNCT
ejpam-6438	402	57	3	3	NUM
ejpam-6438	402	58	,	,	PUNCT
ejpam-6438	402	59	3	3	NUM
ejpam-6438	402	60	,	,	PUNCT
ejpam-6438	402	61	4	4	NUM
ejpam-6438	402	62	,	,	PUNCT
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ejpam-6438	402	64	,	,	PUNCT
ejpam-6438	402	65	.	.	PUNCT
ejpam-6438	402	66	.	.	PUNCT
ejpam-6438	402	67	.	.	PUNCT
ejpam-6438	402	68	,	,	PUNCT
ejpam-6438	402	69	n	n	CCONJ
ejpam-6438	402	70	,	,	PUNCT
ejpam-6438	402	71	n	n	CCONJ
ejpam-6438	402	72	,	,	PUNCT
ejpam-6438	402	73	n+	n+	ADP
ejpam-6438	402	74	1	1	NUM
ejpam-6438	402	75	,	,	PUNCT
ejpam-6438	402	76	n+	n+	ADP
ejpam-6438	402	77	1	1	NUM
ejpam-6438	402	78	}	}	PUNCT
ejpam-6438	402	79	,	,	PUNCT
ejpam-6438	402	80	i	i	PRON
ejpam-6438	402	81	=	=	NOUN
ejpam-6438	402	82	1	1	NUM
ejpam-6438	402	83	,	,	PUNCT
ejpam-6438	402	84	j	j	PROPN
ejpam-6438	402	85	=	=	SYM
ejpam-6438	402	86	2	2	NUM
ejpam-6438	402	87	{	{	PUNCT
ejpam-6438	402	88	j	j	NOUN
ejpam-6438	403	1	−	−	PROPN
ejpam-6438	403	2	2	2	NUM
ejpam-6438	403	3	,	,	PUNCT
ejpam-6438	403	4	j	j	PROPN
ejpam-6438	403	5	−	−	PROPN
ejpam-6438	403	6	2	2	NUM
ejpam-6438	403	7	,	,	PUNCT
ejpam-6438	403	8	3	3	NUM
ejpam-6438	403	9	,	,	PUNCT
ejpam-6438	403	10	3	3	NUM
ejpam-6438	403	11	,	,	PUNCT
ejpam-6438	403	12	4	4	NUM
ejpam-6438	403	13	,	,	PUNCT
ejpam-6438	403	14	4	4	NUM
ejpam-6438	403	15	,	,	PUNCT
ejpam-6438	403	16	.	.	PUNCT
ejpam-6438	403	17	.	.	PUNCT
ejpam-6438	404	1	.	.	PUNCT
ejpam-6438	404	2	,	,	PUNCT
ejpam-6438	404	3	n	n	CCONJ
ejpam-6438	404	4	,	,	PUNCT
ejpam-6438	404	5	n	n	CCONJ
ejpam-6438	404	6	,	,	PUNCT
ejpam-6438	404	7	n+	n+	ADP
ejpam-6438	404	8	1	1	NUM
ejpam-6438	404	9	,	,	PUNCT
ejpam-6438	404	10	n+	n+	ADP
ejpam-6438	404	11	1	1	NUM
ejpam-6438	404	12	}	}	PUNCT
ejpam-6438	404	13	,	,	PUNCT
ejpam-6438	404	14	i	i	PRON
ejpam-6438	404	15	=	=	NOUN
ejpam-6438	404	16	1	1	NUM
ejpam-6438	404	17	,	,	PUNCT
ejpam-6438	404	18	j	j	PROPN
ejpam-6438	405	1	=	=	SYM
ejpam-6438	405	2	3	3	NUM
ejpam-6438	405	3	{	{	PUNCT
ejpam-6438	405	4	3	3	NUM
ejpam-6438	405	5	,	,	PUNCT
ejpam-6438	405	6	3	3	NUM
ejpam-6438	405	7	,	,	PUNCT
ejpam-6438	405	8	j	j	PROPN
ejpam-6438	405	9	−	−	PROPN
ejpam-6438	405	10	1	1	NUM
ejpam-6438	405	11	,	,	PUNCT
ejpam-6438	405	12	j	j	PROPN
ejpam-6438	405	13	,	,	PUNCT
ejpam-6438	405	14	3	3	NUM
ejpam-6438	405	15	,	,	PUNCT
ejpam-6438	405	16	3	3	NUM
ejpam-6438	405	17	,	,	PUNCT
ejpam-6438	405	18	4	4	NUM
ejpam-6438	405	19	,	,	PUNCT
ejpam-6438	405	20	4	4	NUM
ejpam-6438	405	21	,	,	PUNCT
ejpam-6438	405	22	.	.	PUNCT
ejpam-6438	405	23	.	.	PUNCT
ejpam-6438	405	24	.	.	PUNCT
ejpam-6438	405	25	,	,	PUNCT
ejpam-6438	405	26	n	n	CCONJ
ejpam-6438	405	27	,	,	PUNCT
ejpam-6438	405	28	n	n	CCONJ
ejpam-6438	405	29	}	}	PUNCT
ejpam-6438	405	30	,	,	PUNCT
ejpam-6438	405	31	i	i	PRON
ejpam-6438	405	32	=	=	NOUN
ejpam-6438	405	33	2	2	NUM
ejpam-6438	405	34	,	,	PUNCT
ejpam-6438	405	35	j	j	NOUN
ejpam-6438	405	36	=	=	SYM
ejpam-6438	405	37	1	1	NUM
ejpam-6438	405	38	{	{	PUNCT
ejpam-6438	405	39	3	3	NUM
ejpam-6438	405	40	,	,	PUNCT
ejpam-6438	405	41	3	3	NUM
ejpam-6438	405	42	,	,	PUNCT
ejpam-6438	405	43	j	j	PROPN
ejpam-6438	406	1	−	−	PROPN
ejpam-6438	406	2	1	1	NUM
ejpam-6438	406	3	,	,	PUNCT
ejpam-6438	406	4	j	j	PROPN
ejpam-6438	406	5	−	−	PROPN
ejpam-6438	406	6	2	2	NUM
ejpam-6438	406	7	,	,	PUNCT
ejpam-6438	406	8	3	3	NUM
ejpam-6438	406	9	,	,	PUNCT
ejpam-6438	406	10	3	3	NUM
ejpam-6438	406	11	,	,	PUNCT
ejpam-6438	406	12	4	4	NUM
ejpam-6438	406	13	,	,	PUNCT
ejpam-6438	406	14	4	4	NUM
ejpam-6438	406	15	,	,	PUNCT
ejpam-6438	406	16	.	.	PUNCT
ejpam-6438	406	17	.	.	PUNCT
ejpam-6438	407	1	.	.	PUNCT
ejpam-6438	408	1	,	,	PUNCT
ejpam-6438	408	2	n	n	CCONJ
ejpam-6438	408	3	,	,	PUNCT
ejpam-6438	408	4	n	n	CCONJ
ejpam-6438	408	5	}	}	PUNCT
ejpam-6438	408	6	,	,	PUNCT
ejpam-6438	408	7	i	i	PRON
ejpam-6438	408	8	=	=	NOUN
ejpam-6438	408	9	2	2	NUM
ejpam-6438	408	10	,	,	PUNCT
ejpam-6438	408	11	j	j	PROPN
ejpam-6438	408	12	=	=	SYM
ejpam-6438	408	13	2	2	NUM
ejpam-6438	408	14	{	{	PUNCT
ejpam-6438	408	15	3	3	NUM
ejpam-6438	408	16	,	,	PUNCT
ejpam-6438	408	17	3	3	NUM
ejpam-6438	408	18	,	,	PUNCT
ejpam-6438	408	19	j	j	PROPN
ejpam-6438	408	20	−	−	PROPN
ejpam-6438	408	21	2	2	NUM
ejpam-6438	408	22	,	,	PUNCT
ejpam-6438	408	23	j	j	PROPN
ejpam-6438	408	24	−	−	PROPN
ejpam-6438	408	25	2	2	NUM
ejpam-6438	408	26	,	,	PUNCT
ejpam-6438	408	27	3	3	NUM
ejpam-6438	408	28	,	,	PUNCT
ejpam-6438	408	29	3	3	NUM
ejpam-6438	408	30	,	,	PUNCT
ejpam-6438	408	31	4	4	NUM
ejpam-6438	408	32	,	,	PUNCT
ejpam-6438	408	33	4	4	NUM
ejpam-6438	408	34	,	,	PUNCT
ejpam-6438	408	35	.	.	PUNCT
ejpam-6438	408	36	.	.	PUNCT
ejpam-6438	409	1	.	.	PUNCT
ejpam-6438	410	1	,	,	PUNCT
ejpam-6438	410	2	n	n	CCONJ
ejpam-6438	410	3	,	,	PUNCT
ejpam-6438	410	4	n	n	CCONJ
ejpam-6438	410	5	}	}	PUNCT
ejpam-6438	410	6	,	,	PUNCT
ejpam-6438	410	7	i	i	PRON
ejpam-6438	410	8	=	=	NOUN
ejpam-6438	410	9	2	2	NUM
ejpam-6438	410	10	,	,	PUNCT
ejpam-6438	410	11	j	j	NOUN
ejpam-6438	410	12	=	=	SYM
ejpam-6438	410	13	3	3	NUM
ejpam-6438	410	14	:	:	PUNCT
ejpam-6438	410	15	:	:	PUNCT
ejpam-6438	410	16	:	:	PUNCT
ejpam-6438	410	17	{	{	PUNCT
ejpam-6438	410	18	n+	n+	NOUN
ejpam-6438	410	19	1	1	NUM
ejpam-6438	410	20	,	,	PUNCT
ejpam-6438	410	21	n+	n+	ADP
ejpam-6438	410	22	1	1	NUM
ejpam-6438	410	23	,	,	PUNCT
ejpam-6438	410	24	n	n	CCONJ
ejpam-6438	410	25	,	,	PUNCT
ejpam-6438	410	26	n	n	CCONJ
ejpam-6438	410	27	,	,	PUNCT
ejpam-6438	410	28	n−	n−	NOUN
ejpam-6438	410	29	1	1	NUM
ejpam-6438	410	30	,	,	PUNCT
ejpam-6438	410	31	n−	n−	NOUN
ejpam-6438	410	32	1	1	NUM
ejpam-6438	410	33	,	,	PUNCT
ejpam-6438	410	34	j	j	PROPN
ejpam-6438	411	1	−	−	PROPN
ejpam-6438	411	2	1	1	NUM
ejpam-6438	411	3	,	,	PUNCT
ejpam-6438	411	4	j	j	PROPN
ejpam-6438	411	5	}	}	PUNCT
ejpam-6438	411	6	,	,	PUNCT
ejpam-6438	411	7	i	i	PRON
ejpam-6438	411	8	=	=	SYM
ejpam-6438	411	9	n	n	PROPN
ejpam-6438	411	10	,	,	PUNCT
ejpam-6438	411	11	j	j	PROPN
ejpam-6438	411	12	=	=	SYM
ejpam-6438	411	13	1	1	NUM
ejpam-6438	411	14	{	{	PUNCT
ejpam-6438	411	15	n+	n+	NOUN
ejpam-6438	411	16	1	1	NUM
ejpam-6438	411	17	,	,	PUNCT
ejpam-6438	411	18	n+	n+	ADP
ejpam-6438	411	19	1	1	NUM
ejpam-6438	411	20	,	,	PUNCT
ejpam-6438	411	21	n	n	CCONJ
ejpam-6438	411	22	,	,	PUNCT
ejpam-6438	411	23	n	n	CCONJ
ejpam-6438	411	24	,	,	PUNCT
ejpam-6438	411	25	n−	n−	NOUN
ejpam-6438	411	26	1	1	NUM
ejpam-6438	411	27	,	,	PUNCT
ejpam-6438	411	28	n−	n−	NOUN
ejpam-6438	411	29	1	1	NUM
ejpam-6438	411	30	,	,	PUNCT
ejpam-6438	411	31	j	j	PROPN
ejpam-6438	411	32	−	−	PROPN
ejpam-6438	411	33	1	1	NUM
ejpam-6438	411	34	,	,	PUNCT
ejpam-6438	411	35	j	j	PROPN
ejpam-6438	411	36	−	−	PROPN
ejpam-6438	411	37	2	2	NUM
ejpam-6438	411	38	}	}	PUNCT
ejpam-6438	411	39	,	,	PUNCT
ejpam-6438	411	40	i	i	PRON
ejpam-6438	411	41	=	=	SYM
ejpam-6438	411	42	n	n	PROPN
ejpam-6438	411	43	,	,	PUNCT
ejpam-6438	411	44	j	j	PROPN
ejpam-6438	411	45	=	=	SYM
ejpam-6438	411	46	2	2	NUM
ejpam-6438	411	47	{	{	PUNCT
ejpam-6438	411	48	n+	n+	NOUN
ejpam-6438	411	49	1	1	NUM
ejpam-6438	411	50	,	,	PUNCT
ejpam-6438	411	51	n+	n+	ADP
ejpam-6438	411	52	1	1	NUM
ejpam-6438	411	53	,	,	PUNCT
ejpam-6438	411	54	n	n	CCONJ
ejpam-6438	411	55	,	,	PUNCT
ejpam-6438	411	56	n	n	CCONJ
ejpam-6438	411	57	,	,	PUNCT
ejpam-6438	411	58	n−	n−	NOUN
ejpam-6438	411	59	1	1	NUM
ejpam-6438	411	60	,	,	PUNCT
ejpam-6438	411	61	n−	n−	NOUN
ejpam-6438	411	62	1	1	NUM
ejpam-6438	411	63	,	,	PUNCT
ejpam-6438	411	64	j	j	PROPN
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ejpam-6438	411	66	2	2	NUM
ejpam-6438	411	67	,	,	PUNCT
ejpam-6438	411	68	j	j	PROPN
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ejpam-6438	411	70	2	2	NUM
ejpam-6438	411	71	}	}	PUNCT
ejpam-6438	411	72	,	,	PUNCT
ejpam-6438	411	73	i	i	PRON
ejpam-6438	411	74	=	=	SYM
ejpam-6438	411	75	n	n	PROPN
ejpam-6438	411	76	,	,	PUNCT
ejpam-6438	411	77	j	j	PROPN
ejpam-6438	411	78	=	=	SYM
ejpam-6438	411	79	3	3	NUM
ejpam-6438	411	80	each	each	DET
ejpam-6438	411	81	vi	vi	PROPN
ejpam-6438	411	82	is	be	AUX
ejpam-6438	411	83	uniquely	uniquely	ADV
ejpam-6438	411	84	identified	identify	VERB
ejpam-6438	411	85	by	by	ADP
ejpam-6438	411	86	its	its	PRON
ejpam-6438	411	87	distances	distance	NOUN
ejpam-6438	411	88	to	to	ADP
ejpam-6438	411	89	ui1	ui1	PROPN
ejpam-6438	411	90	and	and	CCONJ
ejpam-6438	411	91	ui2	ui2	INTJ
ejpam-6438	411	92	(	(	PUNCT
ejpam-6438	411	93	both	both	DET
ejpam-6438	411	94	1	1	NUM
ejpam-6438	411	95	)	)	PUNCT
ejpam-6438	411	96	,	,	PUNCT
ejpam-6438	411	97	and	and	CCONJ
ejpam-6438	411	98	to	to	ADP
ejpam-6438	411	99	other	other	ADJ
ejpam-6438	411	100	ujk	ujk	NOUN
ejpam-6438	411	101	(	(	PUNCT
ejpam-6438	411	102	which	which	PRON
ejpam-6438	411	103	are	be	AUX
ejpam-6438	411	104	at	at	ADV
ejpam-6438	411	105	least	least	ADJ
ejpam-6438	411	106	2	2	NUM
ejpam-6438	411	107	)	)	PUNCT
ejpam-6438	411	108	.	.	PUNCT
ejpam-6438	412	1	each	each	DET
ejpam-6438	412	2	ui3	ui3	PROPN
ejpam-6438	412	3	is	be	AUX
ejpam-6438	412	4	distinguishable	distinguishable	ADJ
ejpam-6438	412	5	from	from	ADP
ejpam-6438	412	6	ui1	ui1	PRON
ejpam-6438	412	7	and	and	CCONJ
ejpam-6438	412	8	ui2	ui2	ADP
ejpam-6438	412	9	by	by	ADP
ejpam-6438	412	10	its	its	PRON
ejpam-6438	412	11	distances	distance	NOUN
ejpam-6438	412	12	to	to	ADP
ejpam-6438	412	13	them	they	PRON
ejpam-6438	412	14	(	(	PUNCT
ejpam-6438	412	15	1	1	NUM
ejpam-6438	412	16	or	or	CCONJ
ejpam-6438	412	17	2	2	NUM
ejpam-6438	412	18	)	)	PUNCT
ejpam-6438	412	19	.	.	PUNCT
ejpam-6438	413	1	removing	remove	VERB
ejpam-6438	413	2	any	any	DET
ejpam-6438	413	3	ui1	ui1	NOUN
ejpam-6438	413	4	or	or	CCONJ
ejpam-6438	413	5	ui2	ui2	PRON
ejpam-6438	413	6	would	would	AUX
ejpam-6438	413	7	make	make	VERB
ejpam-6438	413	8	the	the	DET
ejpam-6438	413	9	i	i	PRON
ejpam-6438	413	10	-	-	PUNCT
ejpam-6438	413	11	th	th	X
ejpam-6438	413	12	c3	c3	PROPN
ejpam-6438	413	13	copy	copy	NOUN
ejpam-6438	413	14	unresolved	unresolved	ADJ
ejpam-6438	413	15	.	.	PUNCT
ejpam-6438	414	1	hence	hence	ADV
ejpam-6438	414	2	,	,	PUNCT
ejpam-6438	414	3	r	r	NOUN
ejpam-6438	414	4	is	be	AUX
ejpam-6438	414	5	minimal	minimal	ADJ
ejpam-6438	414	6	and	and	CCONJ
ejpam-6438	414	7	dim(g	dim(g	PROPN
ejpam-6438	414	8	)	)	PUNCT
ejpam-6438	414	9	=	=	PUNCT
ejpam-6438	414	10	2n	2n	X
ejpam-6438	414	11	.	.	PUNCT
ejpam-6438	415	1	theorem	theorem	ADJ
ejpam-6438	415	2	8	8	NUM
ejpam-6438	415	3	:	:	PUNCT
ejpam-6438	415	4	let	let	VERB
ejpam-6438	415	5	g	g	PRON
ejpam-6438	415	6	be	be	AUX
ejpam-6438	415	7	cn	cn	PROPN
ejpam-6438	415	8	⊙	⊙	PROPN
ejpam-6438	415	9	c3	c3	PROPN
ejpam-6438	415	10	graph	graph	NOUN
ejpam-6438	415	11	,	,	PUNCT
ejpam-6438	415	12	then	then	ADV
ejpam-6438	415	13	m.d	m.d	PROPN
ejpam-6438	415	14	(	(	PUNCT
ejpam-6438	415	15	cn	cn	PROPN
ejpam-6438	415	16	⊙	⊙	PROPN
ejpam-6438	415	17	c3	c3	PROPN
ejpam-6438	415	18	)	)	PUNCT
ejpam-6438	415	19	=	=	SYM
ejpam-6438	415	20	2n	2n	NUM
ejpam-6438	415	21	,	,	PUNCT
ejpam-6438	415	22	n	n	PRON
ejpam-6438	415	23	≥	≥	NOUN
ejpam-6438	415	24	3	3	NUM
ejpam-6438	415	25	.	.	PUNCT
ejpam-6438	416	1	proof	proof	NOUN
ejpam-6438	416	2	.	.	PUNCT
ejpam-6438	417	1	label	label	VERB
ejpam-6438	417	2	the	the	DET
ejpam-6438	417	3	cycle	cycle	NOUN
ejpam-6438	417	4	cn	cn	PROPN
ejpam-6438	417	5	as	as	ADP
ejpam-6438	417	6	v1	v1	NOUN
ejpam-6438	417	7	,	,	PUNCT
ejpam-6438	417	8	v2	v2	NOUN
ejpam-6438	417	9	,	,	PUNCT
ejpam-6438	417	10	.	.	PUNCT
ejpam-6438	417	11	.	.	PUNCT
ejpam-6438	418	1	.	.	PUNCT
ejpam-6438	419	1	,	,	PUNCT
ejpam-6438	419	2	vn	vn	PROPN
ejpam-6438	419	3	.	.	PUNCT
ejpam-6438	420	1	for	for	ADP
ejpam-6438	420	2	each	each	DET
ejpam-6438	420	3	vi	vi	NOUN
ejpam-6438	420	4	,	,	PUNCT
ejpam-6438	420	5	attach	attach	VERB
ejpam-6438	420	6	a	a	DET
ejpam-6438	420	7	copy	copy	NOUN
ejpam-6438	420	8	of	of	ADP
ejpam-6438	420	9	c3	c3	PROPN
ejpam-6438	420	10	with	with	ADP
ejpam-6438	420	11	vertices	vertex	NOUN
ejpam-6438	420	12	ui1	ui1	PROPN
ejpam-6438	420	13	,	,	PUNCT
ejpam-6438	420	14	ui2	ui2	PRON
ejpam-6438	420	15	,	,	PUNCT
ejpam-6438	420	16	ui3	ui3	VERB
ejpam-6438	420	17	forming	form	VERB
ejpam-6438	420	18	a	a	DET
ejpam-6438	420	19	triangle	triangle	NOUN
ejpam-6438	420	20	,	,	PUNCT
ejpam-6438	420	21	and	and	CCONJ
ejpam-6438	420	22	connect	connect	VERB
ejpam-6438	420	23	each	each	PRON
ejpam-6438	420	24	to	to	ADP
ejpam-6438	420	25	vi	vi	NUM
ejpam-6438	420	26	,	,	PUNCT
ejpam-6438	420	27	as	as	SCONJ
ejpam-6438	420	28	show	show	NOUN
ejpam-6438	420	29	in	in	ADP
ejpam-6438	420	30	figure	figure	NOUN
ejpam-6438	420	31	12	12	NUM
ejpam-6438	420	32	.	.	PUNCT
ejpam-6438	421	1	let	let	VERB
ejpam-6438	421	2	r	r	NOUN
ejpam-6438	421	3	=	=	PUNCT
ejpam-6438	421	4	{	{	PUNCT
ejpam-6438	421	5	ui1	ui1	ADV
ejpam-6438	421	6	,	,	PUNCT
ejpam-6438	421	7	ui2	ui2	PUNCT
ejpam-6438	422	1	|	|	ADV
ejpam-6438	422	2	1	1	NUM
ejpam-6438	422	3	≤	≤	NUM
ejpam-6438	422	4	i	i	PRON
ejpam-6438	422	5	≤	≤	NOUN
ejpam-6438	422	6	n	n	CCONJ
ejpam-6438	422	7	}	}	PUNCT
ejpam-6438	422	8	.	.	PUNCT
ejpam-6438	423	1	we	we	PRON
ejpam-6438	423	2	claim	claim	VERB
ejpam-6438	423	3	that	that	SCONJ
ejpam-6438	423	4	r	r	NOUN
ejpam-6438	423	5	is	be	AUX
ejpam-6438	423	6	a	a	DET
ejpam-6438	423	7	resolving	resolving	NOUN
ejpam-6438	423	8	set	set	NOUN
ejpam-6438	423	9	.	.	PUNCT
ejpam-6438	424	1	figure	figure	NOUN
ejpam-6438	424	2	12	12	NUM
ejpam-6438	424	3	.	.	PUNCT
ejpam-6438	425	1	the	the	DET
ejpam-6438	425	2	cn	cn	PROPN
ejpam-6438	425	3	⊙	⊙	PROPN
ejpam-6438	425	4	c3	c3	PROPN
ejpam-6438	425	5	graph	graph	PROPN
ejpam-6438	425	6	.	.	PUNCT
ejpam-6438	425	7	a.	a.	PROPN
ejpam-6438	425	8	elrokh	elrokh	PROPN
ejpam-6438	425	9	,	,	PUNCT
ejpam-6438	425	10	eman	eman	PROPN
ejpam-6438	425	11	s.	s.	PROPN
ejpam-6438	425	12	almotairi	almotairi	PROPN
ejpam-6438	425	13	,	,	PUNCT
ejpam-6438	425	14	h.	h.	PROPN
ejpam-6438	425	15	mostafa	mostafa	PROPN
ejpam-6438	425	16	/	/	SYM
ejpam-6438	425	17	eur	eur	PROPN
ejpam-6438	425	18	.	.	PUNCT
ejpam-6438	426	1	j.	j.	PROPN
ejpam-6438	426	2	pure	pure	PROPN
ejpam-6438	426	3	appl	appl	PROPN
ejpam-6438	426	4	.	.	PROPN
ejpam-6438	426	5	math	math	PROPN
ejpam-6438	426	6	,	,	PUNCT
ejpam-6438	426	7	18	18	NUM
ejpam-6438	426	8	(	(	PUNCT
ejpam-6438	426	9	3	3	NUM
ejpam-6438	426	10	)	)	PUNCT
ejpam-6438	426	11	(	(	PUNCT
ejpam-6438	426	12	2025	2025	NUM
ejpam-6438	426	13	)	)	PUNCT
ejpam-6438	426	14	,	,	PUNCT
ejpam-6438	426	15	6438	6438	NUM
ejpam-6438	426	16	13	13	NUM
ejpam-6438	426	17	of	of	ADP
ejpam-6438	426	18	18	18	NUM
ejpam-6438	426	19	w	w	PROPN
ejpam-6438	426	20	(	(	PUNCT
ejpam-6438	426	21	vi	vi	PROPN
ejpam-6438	426	22	,	,	PUNCT
ejpam-6438	426	23	r	r	NOUN
ejpam-6438	426	24	)	)	PUNCT
ejpam-6438	426	25	=	=	SYM
ejpam-6438	426	26			NOUN
ejpam-6438	426	27	{	{	PUNCT
ejpam-6438	426	28	1	1	NUM
ejpam-6438	426	29	,	,	PUNCT
ejpam-6438	426	30	1	1	NUM
ejpam-6438	426	31	,	,	PUNCT
ejpam-6438	426	32	2	2	NUM
ejpam-6438	426	33	,	,	PUNCT
ejpam-6438	426	34	2	2	NUM
ejpam-6438	426	35	,	,	PUNCT
ejpam-6438	426	36	3	3	NUM
ejpam-6438	426	37	,	,	PUNCT
ejpam-6438	426	38	3	3	NUM
ejpam-6438	426	39	,	,	PUNCT
ejpam-6438	426	40	.	.	PUNCT
ejpam-6438	426	41	.	.	PUNCT
ejpam-6438	427	1	.	.	PUNCT
ejpam-6438	428	1	,	,	PUNCT
ejpam-6438	428	2	n	n	CCONJ
ejpam-6438	428	3	,	,	PUNCT
ejpam-6438	428	4	n	n	CCONJ
ejpam-6438	428	5	}	}	PUNCT
ejpam-6438	428	6	,	,	PUNCT
ejpam-6438	428	7	i	i	PRON
ejpam-6438	428	8	=	=	NOUN
ejpam-6438	428	9	1	1	NUM
ejpam-6438	428	10	{	{	PUNCT
ejpam-6438	428	11	2	2	NUM
ejpam-6438	428	12	,	,	PUNCT
ejpam-6438	428	13	2	2	NUM
ejpam-6438	428	14	,	,	PUNCT
ejpam-6438	428	15	1	1	NUM
ejpam-6438	428	16	,	,	PUNCT
ejpam-6438	428	17	1	1	NUM
ejpam-6438	428	18	,	,	PUNCT
ejpam-6438	428	19	2	2	NUM
ejpam-6438	428	20	,	,	PUNCT
ejpam-6438	428	21	2	2	NUM
ejpam-6438	428	22	.	.	PUNCT
ejpam-6438	428	23	.	.	PUNCT
ejpam-6438	428	24	.	.	PUNCT
ejpam-6438	429	1	,	,	PUNCT
ejpam-6438	429	2	n−	n−	NOUN
ejpam-6438	429	3	1	1	NUM
ejpam-6438	429	4	,	,	PUNCT
ejpam-6438	429	5	n−	n−	NOUN
ejpam-6438	429	6	1	1	NUM
ejpam-6438	429	7	}	}	PUNCT
ejpam-6438	429	8	,	,	PUNCT
ejpam-6438	429	9	i	i	PRON
ejpam-6438	429	10	=	=	NOUN
ejpam-6438	429	11	2	2	NUM
ejpam-6438	429	12	{	{	PUNCT
ejpam-6438	429	13	3	3	NUM
ejpam-6438	429	14	,	,	PUNCT
ejpam-6438	429	15	3	3	NUM
ejpam-6438	429	16	,	,	PUNCT
ejpam-6438	429	17	2	2	NUM
ejpam-6438	429	18	,	,	PUNCT
ejpam-6438	429	19	2	2	NUM
ejpam-6438	429	20	,	,	PUNCT
ejpam-6438	429	21	1	1	NUM
ejpam-6438	429	22	,	,	PUNCT
ejpam-6438	429	23	1	1	NUM
ejpam-6438	429	24	,	,	PUNCT
ejpam-6438	429	25	.	.	PUNCT
ejpam-6438	429	26	.	.	PUNCT
ejpam-6438	430	1	.	.	PUNCT
ejpam-6438	431	1	,	,	PUNCT
ejpam-6438	431	2	n−	n−	NOUN
ejpam-6438	431	3	2	2	NUM
ejpam-6438	431	4	,	,	PUNCT
ejpam-6438	431	5	n−	n−	NOUN
ejpam-6438	431	6	2	2	NUM
ejpam-6438	431	7	}	}	PUNCT
ejpam-6438	431	8	,	,	PUNCT
ejpam-6438	431	9	i	i	PRON
ejpam-6438	431	10	=	=	NOUN
ejpam-6438	431	11	3	3	NUM
ejpam-6438	431	12	:	:	PUNCT
ejpam-6438	431	13	:	:	PUNCT
ejpam-6438	431	14	:	:	PUNCT
ejpam-6438	431	15	:	:	PUNCT
ejpam-6438	431	16	:	:	PUNCT
ejpam-6438	431	17	{	{	PUNCT
ejpam-6438	431	18	n	n	CCONJ
ejpam-6438	431	19	,	,	PUNCT
ejpam-6438	431	20	n	n	CCONJ
ejpam-6438	431	21	,	,	PUNCT
ejpam-6438	431	22	n−	n−	NOUN
ejpam-6438	431	23	1	1	NUM
ejpam-6438	431	24	,	,	PUNCT
ejpam-6438	431	25	n−	n−	NOUN
ejpam-6438	431	26	1	1	NUM
ejpam-6438	431	27	,	,	PUNCT
ejpam-6438	431	28	.	.	PUNCT
ejpam-6438	431	29	.	.	PUNCT
ejpam-6438	432	1	.	.	PUNCT
ejpam-6438	433	1	,	,	PUNCT
ejpam-6438	433	2	1	1	NUM
ejpam-6438	433	3	,	,	PUNCT
ejpam-6438	433	4	1	1	NUM
ejpam-6438	433	5	}	}	PUNCT
ejpam-6438	433	6	.i	.i	PUNCT
ejpam-6438	434	1	=	=	PUNCT
ejpam-6438	434	2	n	n	PROPN
ejpam-6438	434	3	w	w	NOUN
ejpam-6438	434	4	(	(	PUNCT
ejpam-6438	434	5	uij	uij	PRON
ejpam-6438	434	6	,	,	PUNCT
ejpam-6438	434	7	r	r	NOUN
ejpam-6438	434	8	)	)	PUNCT
ejpam-6438	434	9	=	=	SYM
ejpam-6438	434	10			NOUN
ejpam-6438	434	11	{	{	PUNCT
ejpam-6438	434	12	0	0	NUM
ejpam-6438	434	13	,	,	PUNCT
ejpam-6438	434	14	1	1	NUM
ejpam-6438	434	15	,	,	PUNCT
ejpam-6438	434	16	.	.	PUNCT
ejpam-6438	434	17	.	.	PUNCT
ejpam-6438	434	18	.	.	PUNCT
ejpam-6438	434	19	,	,	PUNCT
ejpam-6438	434	20	n	n	CCONJ
ejpam-6438	434	21	,	,	PUNCT
ejpam-6438	434	22	n	n	CCONJ
ejpam-6438	434	23	,	,	PUNCT
ejpam-6438	434	24	n+	n+	ADP
ejpam-6438	434	25	1	1	NUM
ejpam-6438	434	26	,	,	PUNCT
ejpam-6438	434	27	n+	n+	ADP
ejpam-6438	434	28	1	1	NUM
ejpam-6438	434	29	}	}	PUNCT
ejpam-6438	434	30	,	,	PUNCT
ejpam-6438	434	31	i	i	PRON
ejpam-6438	434	32	=	=	NOUN
ejpam-6438	434	33	1	1	NUM
ejpam-6438	434	34	,	,	PUNCT
ejpam-6438	434	35	j	j	PROPN
ejpam-6438	434	36	=	=	SYM
ejpam-6438	434	37	1	1	NUM
ejpam-6438	434	38	{	{	PUNCT
ejpam-6438	434	39	1	1	NUM
ejpam-6438	434	40	,	,	PUNCT
ejpam-6438	434	41	0	0	NUM
ejpam-6438	434	42	,	,	PUNCT
ejpam-6438	434	43	.	.	PUNCT
ejpam-6438	434	44	.	.	PUNCT
ejpam-6438	434	45	.	.	PUNCT
ejpam-6438	434	46	,	,	PUNCT
ejpam-6438	434	47	n	n	CCONJ
ejpam-6438	434	48	,	,	PUNCT
ejpam-6438	434	49	n	n	CCONJ
ejpam-6438	434	50	,	,	PUNCT
ejpam-6438	434	51	n+	n+	ADP
ejpam-6438	434	52	1	1	NUM
ejpam-6438	434	53	,	,	PUNCT
ejpam-6438	434	54	n+	n+	ADP
ejpam-6438	434	55	1	1	NUM
ejpam-6438	434	56	}	}	PUNCT
ejpam-6438	434	57	,	,	PUNCT
ejpam-6438	434	58	i	i	PRON
ejpam-6438	434	59	=	=	NOUN
ejpam-6438	434	60	1	1	NUM
ejpam-6438	434	61	,	,	PUNCT
ejpam-6438	434	62	j	j	PROPN
ejpam-6438	434	63	=	=	SYM
ejpam-6438	434	64	2	2	NUM
ejpam-6438	434	65	{	{	PUNCT
ejpam-6438	434	66	1	1	NUM
ejpam-6438	434	67	,	,	PUNCT
ejpam-6438	434	68	1	1	NUM
ejpam-6438	434	69	,	,	PUNCT
ejpam-6438	434	70	.	.	PUNCT
ejpam-6438	434	71	.	.	PUNCT
ejpam-6438	434	72	.	.	PUNCT
ejpam-6438	434	73	,	,	PUNCT
ejpam-6438	434	74	n	n	CCONJ
ejpam-6438	434	75	,	,	PUNCT
ejpam-6438	434	76	n	n	CCONJ
ejpam-6438	434	77	,	,	PUNCT
ejpam-6438	434	78	n+	n+	ADP
ejpam-6438	434	79	1	1	NUM
ejpam-6438	434	80	,	,	PUNCT
ejpam-6438	434	81	n+	n+	ADP
ejpam-6438	434	82	1	1	NUM
ejpam-6438	434	83	}	}	PUNCT
ejpam-6438	434	84	,	,	PUNCT
ejpam-6438	434	85	i	i	PRON
ejpam-6438	434	86	=	=	NOUN
ejpam-6438	434	87	1	1	NUM
ejpam-6438	434	88	,	,	PUNCT
ejpam-6438	434	89	j	j	PROPN
ejpam-6438	434	90	=	=	SYM
ejpam-6438	434	91	3	3	NUM
ejpam-6438	434	92	{	{	PUNCT
ejpam-6438	434	93	3	3	NUM
ejpam-6438	434	94	,	,	PUNCT
ejpam-6438	434	95	3	3	NUM
ejpam-6438	434	96	,	,	PUNCT
ejpam-6438	434	97	j	j	PROPN
ejpam-6438	434	98	−	−	PROPN
ejpam-6438	434	99	1	1	NUM
ejpam-6438	434	100	,	,	PUNCT
ejpam-6438	434	101	j	j	PROPN
ejpam-6438	434	102	,	,	PUNCT
ejpam-6438	434	103	3	3	NUM
ejpam-6438	434	104	,	,	PUNCT
ejpam-6438	434	105	3	3	NUM
ejpam-6438	434	106	,	,	PUNCT
ejpam-6438	434	107	4	4	NUM
ejpam-6438	434	108	,	,	PUNCT
ejpam-6438	434	109	4	4	NUM
ejpam-6438	434	110	,	,	PUNCT
ejpam-6438	434	111	.	.	PUNCT
ejpam-6438	434	112	.	.	PUNCT
ejpam-6438	434	113	.	.	PUNCT
ejpam-6438	434	114	,	,	PUNCT
ejpam-6438	434	115	n	n	CCONJ
ejpam-6438	434	116	,	,	PUNCT
ejpam-6438	434	117	n	n	CCONJ
ejpam-6438	434	118	}	}	PUNCT
ejpam-6438	434	119	,	,	PUNCT
ejpam-6438	434	120	i	i	PRON
ejpam-6438	434	121	=	=	NOUN
ejpam-6438	434	122	2	2	NUM
ejpam-6438	434	123	,	,	PUNCT
ejpam-6438	434	124	j	j	NOUN
ejpam-6438	435	1	=	=	SYM
ejpam-6438	435	2	1	1	NUM
ejpam-6438	435	3	{	{	PUNCT
ejpam-6438	435	4	3	3	NUM
ejpam-6438	435	5	,	,	PUNCT
ejpam-6438	435	6	3	3	NUM
ejpam-6438	435	7	,	,	PUNCT
ejpam-6438	435	8	j	j	PROPN
ejpam-6438	435	9	−	−	PROPN
ejpam-6438	435	10	1	1	NUM
ejpam-6438	435	11	,	,	PUNCT
ejpam-6438	435	12	j	j	PROPN
ejpam-6438	435	13	−	−	PROPN
ejpam-6438	435	14	2	2	NUM
ejpam-6438	435	15	,	,	PUNCT
ejpam-6438	435	16	3	3	NUM
ejpam-6438	435	17	,	,	PUNCT
ejpam-6438	435	18	3	3	NUM
ejpam-6438	435	19	,	,	PUNCT
ejpam-6438	435	20	4	4	NUM
ejpam-6438	435	21	,	,	PUNCT
ejpam-6438	435	22	4	4	NUM
ejpam-6438	435	23	,	,	PUNCT
ejpam-6438	435	24	.	.	PUNCT
ejpam-6438	435	25	.	.	PUNCT
ejpam-6438	435	26	.	.	PUNCT
ejpam-6438	435	27	,	,	PUNCT
ejpam-6438	435	28	n	n	CCONJ
ejpam-6438	435	29	,	,	PUNCT
ejpam-6438	435	30	n	n	CCONJ
ejpam-6438	435	31	}	}	PUNCT
ejpam-6438	435	32	,	,	PUNCT
ejpam-6438	435	33	i	i	PRON
ejpam-6438	435	34	=	=	NOUN
ejpam-6438	435	35	2	2	NUM
ejpam-6438	435	36	,	,	PUNCT
ejpam-6438	435	37	j	j	PROPN
ejpam-6438	435	38	=	=	SYM
ejpam-6438	435	39	2	2	NUM
ejpam-6438	435	40	{	{	PUNCT
ejpam-6438	435	41	3	3	NUM
ejpam-6438	435	42	,	,	PUNCT
ejpam-6438	435	43	3	3	NUM
ejpam-6438	435	44	,	,	PUNCT
ejpam-6438	435	45	j	j	PROPN
ejpam-6438	435	46	−	−	PROPN
ejpam-6438	435	47	2	2	NUM
ejpam-6438	435	48	,	,	PUNCT
ejpam-6438	435	49	j	j	PROPN
ejpam-6438	436	1	−	−	PROPN
ejpam-6438	436	2	2	2	NUM
ejpam-6438	436	3	,	,	PUNCT
ejpam-6438	436	4	3	3	NUM
ejpam-6438	436	5	,	,	PUNCT
ejpam-6438	436	6	3	3	NUM
ejpam-6438	436	7	,	,	PUNCT
ejpam-6438	436	8	4	4	NUM
ejpam-6438	436	9	,	,	PUNCT
ejpam-6438	436	10	4	4	NUM
ejpam-6438	436	11	,	,	PUNCT
ejpam-6438	436	12	.	.	PUNCT
ejpam-6438	436	13	.	.	PUNCT
ejpam-6438	437	1	.	.	PUNCT
ejpam-6438	438	1	,	,	PUNCT
ejpam-6438	438	2	n	n	CCONJ
ejpam-6438	438	3	,	,	PUNCT
ejpam-6438	438	4	n	n	CCONJ
ejpam-6438	438	5	}	}	PUNCT
ejpam-6438	438	6	,	,	PUNCT
ejpam-6438	438	7	i	i	PRON
ejpam-6438	438	8	=	=	NOUN
ejpam-6438	438	9	2	2	NUM
ejpam-6438	438	10	,	,	PUNCT
ejpam-6438	438	11	j	j	NOUN
ejpam-6438	438	12	=	=	SYM
ejpam-6438	438	13	3	3	NUM
ejpam-6438	438	14	:	:	PUNCT
ejpam-6438	438	15	:	:	PUNCT
ejpam-6438	438	16	:	:	PUNCT
ejpam-6438	438	17	{	{	PUNCT
ejpam-6438	438	18	n+	n+	NOUN
ejpam-6438	438	19	1	1	NUM
ejpam-6438	438	20	,	,	PUNCT
ejpam-6438	438	21	n+	n+	ADP
ejpam-6438	438	22	1	1	NUM
ejpam-6438	438	23	,	,	PUNCT
ejpam-6438	438	24	n	n	CCONJ
ejpam-6438	438	25	,	,	PUNCT
ejpam-6438	438	26	n	n	CCONJ
ejpam-6438	438	27	,	,	PUNCT
ejpam-6438	438	28	n−	n−	NOUN
ejpam-6438	438	29	1	1	NUM
ejpam-6438	438	30	,	,	PUNCT
ejpam-6438	438	31	n−	n−	NOUN
ejpam-6438	438	32	1	1	NUM
ejpam-6438	438	33	,	,	PUNCT
ejpam-6438	438	34	.	.	PUNCT
ejpam-6438	438	35	.	.	PUNCT
ejpam-6438	438	36	.	.	PUNCT
ejpam-6438	439	1	.	.	PUNCT
ejpam-6438	440	1	,	,	PUNCT
ejpam-6438	441	1	j	j	PROPN
ejpam-6438	442	1	−	−	PROPN
ejpam-6438	442	2	1	1	NUM
ejpam-6438	442	3	,	,	PUNCT
ejpam-6438	442	4	j	j	PROPN
ejpam-6438	442	5	}	}	PUNCT
ejpam-6438	442	6	,	,	PUNCT
ejpam-6438	442	7	i	i	PRON
ejpam-6438	442	8	=	=	SYM
ejpam-6438	442	9	n	n	PROPN
ejpam-6438	442	10	,	,	PUNCT
ejpam-6438	442	11	j	j	PROPN
ejpam-6438	442	12	=	=	SYM
ejpam-6438	442	13	1	1	NUM
ejpam-6438	442	14	{	{	PUNCT
ejpam-6438	442	15	n+	n+	NOUN
ejpam-6438	442	16	1	1	NUM
ejpam-6438	442	17	,	,	PUNCT
ejpam-6438	442	18	n+	n+	ADP
ejpam-6438	442	19	1	1	NUM
ejpam-6438	442	20	,	,	PUNCT
ejpam-6438	442	21	n	n	CCONJ
ejpam-6438	442	22	,	,	PUNCT
ejpam-6438	442	23	n	n	CCONJ
ejpam-6438	442	24	,	,	PUNCT
ejpam-6438	442	25	n−	n−	NOUN
ejpam-6438	442	26	1	1	NUM
ejpam-6438	442	27	,	,	PUNCT
ejpam-6438	442	28	n−	n−	NOUN
ejpam-6438	442	29	1	1	NUM
ejpam-6438	442	30	,	,	PUNCT
ejpam-6438	442	31	.	.	PUNCT
ejpam-6438	442	32	.	.	PUNCT
ejpam-6438	442	33	.	.	PUNCT
ejpam-6438	443	1	.	.	PUNCT
ejpam-6438	444	1	,	,	PUNCT
ejpam-6438	445	1	j	j	PROPN
ejpam-6438	446	1	−	−	PROPN
ejpam-6438	446	2	1	1	NUM
ejpam-6438	446	3	,	,	PUNCT
ejpam-6438	446	4	j	j	PROPN
ejpam-6438	446	5	−	−	PROPN
ejpam-6438	446	6	2	2	NUM
ejpam-6438	446	7	}	}	PUNCT
ejpam-6438	446	8	,	,	PUNCT
ejpam-6438	446	9	i	i	PRON
ejpam-6438	446	10	=	=	SYM
ejpam-6438	446	11	n	n	PROPN
ejpam-6438	446	12	,	,	PUNCT
ejpam-6438	446	13	j	j	PROPN
ejpam-6438	446	14	=	=	SYM
ejpam-6438	446	15	2	2	NUM
ejpam-6438	446	16	{	{	PUNCT
ejpam-6438	446	17	n+	n+	NOUN
ejpam-6438	446	18	1	1	NUM
ejpam-6438	446	19	,	,	PUNCT
ejpam-6438	446	20	n+	n+	ADP
ejpam-6438	446	21	1	1	NUM
ejpam-6438	446	22	,	,	PUNCT
ejpam-6438	446	23	n	n	CCONJ
ejpam-6438	446	24	,	,	PUNCT
ejpam-6438	446	25	n	n	CCONJ
ejpam-6438	446	26	,	,	PUNCT
ejpam-6438	446	27	n−	n−	NOUN
ejpam-6438	446	28	1	1	NUM
ejpam-6438	446	29	,	,	PUNCT
ejpam-6438	446	30	n−	n−	NOUN
ejpam-6438	446	31	1	1	NUM
ejpam-6438	446	32	,	,	PUNCT
ejpam-6438	446	33	.	.	PUNCT
ejpam-6438	446	34	.	.	PUNCT
ejpam-6438	446	35	.	.	PUNCT
ejpam-6438	447	1	.	.	PUNCT
ejpam-6438	448	1	,	,	PUNCT
ejpam-6438	449	1	j	j	PROPN
ejpam-6438	450	1	−	−	PROPN
ejpam-6438	450	2	2	2	NUM
ejpam-6438	450	3	,	,	PUNCT
ejpam-6438	450	4	j	j	PROPN
ejpam-6438	450	5	−	−	PROPN
ejpam-6438	450	6	2	2	NUM
ejpam-6438	450	7	}	}	PUNCT
ejpam-6438	450	8	,	,	PUNCT
ejpam-6438	450	9	i	i	PRON
ejpam-6438	450	10	=	=	SYM
ejpam-6438	450	11	n	n	PROPN
ejpam-6438	450	12	,	,	PUNCT
ejpam-6438	450	13	j	j	PROPN
ejpam-6438	450	14	=	=	SYM
ejpam-6438	450	15	3	3	NUM
ejpam-6438	450	16	each	each	DET
ejpam-6438	450	17	vi	vi	PROPN
ejpam-6438	450	18	is	be	AUX
ejpam-6438	450	19	uniquely	uniquely	ADV
ejpam-6438	450	20	identified	identify	VERB
ejpam-6438	450	21	by	by	ADP
ejpam-6438	450	22	its	its	PRON
ejpam-6438	450	23	distances	distance	NOUN
ejpam-6438	450	24	to	to	ADP
ejpam-6438	450	25	ui1	ui1	PROPN
ejpam-6438	450	26	and	and	CCONJ
ejpam-6438	450	27	ui2	ui2	INTJ
ejpam-6438	450	28	(	(	PUNCT
ejpam-6438	450	29	both	both	DET
ejpam-6438	450	30	1	1	NUM
ejpam-6438	450	31	)	)	PUNCT
ejpam-6438	450	32	,	,	PUNCT
ejpam-6438	450	33	and	and	CCONJ
ejpam-6438	450	34	to	to	ADP
ejpam-6438	450	35	other	other	ADJ
ejpam-6438	450	36	ujk	ujk	NOUN
ejpam-6438	450	37	(	(	PUNCT
ejpam-6438	450	38	which	which	PRON
ejpam-6438	450	39	vary	vary	VERB
ejpam-6438	450	40	due	due	ADP
ejpam-6438	450	41	to	to	ADP
ejpam-6438	450	42	the	the	DET
ejpam-6438	450	43	cycle	cycle	NOUN
ejpam-6438	450	44	)	)	PUNCT
ejpam-6438	450	45	.	.	PUNCT
ejpam-6438	451	1	each	each	DET
ejpam-6438	451	2	ui3	ui3	PROPN
ejpam-6438	451	3	is	be	AUX
ejpam-6438	451	4	distinguishable	distinguishable	ADJ
ejpam-6438	451	5	from	from	ADP
ejpam-6438	451	6	ui1	ui1	PRON
ejpam-6438	451	7	and	and	CCONJ
ejpam-6438	451	8	ui2	ui2	ADP
ejpam-6438	451	9	by	by	ADP
ejpam-6438	451	10	its	its	PRON
ejpam-6438	451	11	distances	distance	NOUN
ejpam-6438	451	12	to	to	ADP
ejpam-6438	451	13	them	they	PRON
ejpam-6438	451	14	.	.	PUNCT
ejpam-6438	452	1	removing	remove	VERB
ejpam-6438	452	2	any	any	DET
ejpam-6438	452	3	ui1	ui1	NOUN
ejpam-6438	452	4	or	or	CCONJ
ejpam-6438	452	5	ui2	ui2	PRON
ejpam-6438	452	6	would	would	AUX
ejpam-6438	452	7	make	make	VERB
ejpam-6438	452	8	the	the	DET
ejpam-6438	452	9	i	i	PRON
ejpam-6438	452	10	-	-	PUNCT
ejpam-6438	452	11	th	th	X
ejpam-6438	452	12	c3	c3	PROPN
ejpam-6438	452	13	copy	copy	NOUN
ejpam-6438	452	14	unresolved	unresolved	ADJ
ejpam-6438	452	15	.	.	PUNCT
ejpam-6438	453	1	hence	hence	ADV
ejpam-6438	453	2	,	,	PUNCT
ejpam-6438	453	3	r	r	NOUN
ejpam-6438	453	4	is	be	AUX
ejpam-6438	453	5	minimal	minimal	ADJ
ejpam-6438	453	6	and	and	CCONJ
ejpam-6438	453	7	dim(g	dim(g	PROPN
ejpam-6438	453	8	)	)	PUNCT
ejpam-6438	453	9	=	=	PUNCT
ejpam-6438	453	10	2n	2n	X
ejpam-6438	453	11	.	.	PUNCT
ejpam-6438	454	1	theorem	theorem	VERB
ejpam-6438	454	2	9	9	NUM
ejpam-6438	454	3	:	:	PUNCT
ejpam-6438	454	4	let	let	VERB
ejpam-6438	454	5	g	g	PROPN
ejpam-6438	454	6	be	be	AUX
ejpam-6438	454	7	kim	kim	PROPN
ejpam-6438	454	8	,	,	PUNCT
ejpam-6438	454	9	n	n	PRON
ejpam-6438	454	10	graph	graph	NOUN
ejpam-6438	454	11	,	,	PUNCT
ejpam-6438	454	12	then	then	ADV
ejpam-6438	454	13	m.d	m.d	PROPN
ejpam-6438	454	14	.	.	PUNCT
ejpam-6438	455	1	(	(	PUNCT
ejpam-6438	455	2	kim	kim	PROPN
ejpam-6438	455	3	,	,	PUNCT
ejpam-6438	455	4	n	n	CCONJ
ejpam-6438	455	5	)	)	PUNCT
ejpam-6438	455	6	=	=	SYM
ejpam-6438	455	7	2	2	X
ejpam-6438	455	8	,	,	PUNCT
ejpam-6438	455	9	if	if	SCONJ
ejpam-6438	455	10	m	m	PROPN
ejpam-6438	455	11	is	be	AUX
ejpam-6438	455	12	odd	odd	ADJ
ejpam-6438	455	13	.	.	PUNCT
ejpam-6438	456	1	proof	proof	NOUN
ejpam-6438	456	2	.	.	PUNCT
ejpam-6438	457	1	we	we	PRON
ejpam-6438	457	2	labelling	label	VERB
ejpam-6438	457	3	kim	kim	PROPN
ejpam-6438	457	4	,	,	PUNCT
ejpam-6438	457	5	n	n	CCONJ
ejpam-6438	457	6	,	,	PUNCT
ejpam-6438	457	7	as	as	SCONJ
ejpam-6438	457	8	show	show	NOUN
ejpam-6438	457	9	in	in	ADP
ejpam-6438	457	10	figure	figure	NOUN
ejpam-6438	457	11	13	13	NUM
ejpam-6438	457	12	.	.	PUNCT
ejpam-6438	458	1	it	it	PRON
ejpam-6438	458	2	is	be	AUX
ejpam-6438	458	3	clear	clear	ADJ
ejpam-6438	458	4	that	that	SCONJ
ejpam-6438	458	5	the	the	DET
ejpam-6438	458	6	number	number	NOUN
ejpam-6438	458	7	of	of	ADP
ejpam-6438	458	8	vertices	vertex	NOUN
ejpam-6438	458	9	is	be	AUX
ejpam-6438	458	10	n+m	n+m	NUM
ejpam-6438	458	11	.	.	PUNCT
ejpam-6438	459	1	let	let	VERB
ejpam-6438	459	2	r	r	NOUN
ejpam-6438	459	3	=	=	PRON
ejpam-6438	459	4	{	{	PUNCT
ejpam-6438	459	5	v1,vn+2	v1,vn+2	PROPN
ejpam-6438	459	6	}	}	PUNCT
ejpam-6438	459	7	be	be	AUX
ejpam-6438	459	8	any	any	DET
ejpam-6438	459	9	resolving	resolving	NOUN
ejpam-6438	459	10	set	set	NOUN
ejpam-6438	459	11	of	of	ADP
ejpam-6438	459	12	kim	kim	PROPN
ejpam-6438	459	13	,	,	PUNCT
ejpam-6438	459	14	n.	n.	PROPN
ejpam-6438	459	15	figure	figure	NOUN
ejpam-6438	459	16	13	13	NUM
ejpam-6438	459	17	.	.	PUNCT
ejpam-6438	460	1	the	the	DET
ejpam-6438	460	2	kim	kim	PROPN
ejpam-6438	460	3	,	,	PUNCT
ejpam-6438	460	4	n	n	PRON
ejpam-6438	460	5	graph	graph	NOUN
ejpam-6438	460	6	.	.	PUNCT
ejpam-6438	460	7	a.	a.	PROPN
ejpam-6438	460	8	elrokh	elrokh	PROPN
ejpam-6438	460	9	,	,	PUNCT
ejpam-6438	460	10	eman	eman	PROPN
ejpam-6438	460	11	s.	s.	PROPN
ejpam-6438	460	12	almotairi	almotairi	PROPN
ejpam-6438	460	13	,	,	PUNCT
ejpam-6438	460	14	h.	h.	PROPN
ejpam-6438	460	15	mostafa	mostafa	PROPN
ejpam-6438	460	16	/	/	SYM
ejpam-6438	460	17	eur	eur	PROPN
ejpam-6438	460	18	.	.	PUNCT
ejpam-6438	461	1	j.	j.	PROPN
ejpam-6438	461	2	pure	pure	PROPN
ejpam-6438	461	3	appl	appl	PROPN
ejpam-6438	461	4	.	.	PROPN
ejpam-6438	461	5	math	math	PROPN
ejpam-6438	461	6	,	,	PUNCT
ejpam-6438	461	7	18	18	NUM
ejpam-6438	461	8	(	(	PUNCT
ejpam-6438	461	9	3	3	NUM
ejpam-6438	461	10	)	)	PUNCT
ejpam-6438	461	11	(	(	PUNCT
ejpam-6438	461	12	2025	2025	NUM
ejpam-6438	461	13	)	)	PUNCT
ejpam-6438	461	14	,	,	PUNCT
ejpam-6438	461	15	6438	6438	NUM
ejpam-6438	461	16	14	14	NUM
ejpam-6438	461	17	of	of	ADP
ejpam-6438	461	18	18	18	NUM
ejpam-6438	461	19	being	be	AUX
ejpam-6438	461	20	for	for	ADP
ejpam-6438	461	21	(	(	PUNCT
ejpam-6438	461	22	i	i	NOUN
ejpam-6438	461	23	=	=	NOUN
ejpam-6438	461	24	1	1	NUM
ejpam-6438	461	25	;	;	PUNCT
ejpam-6438	461	26	i	i	PRON
ejpam-6438	461	27	≤	≤	ADV
ejpam-6438	461	28	2	2	NUM
ejpam-6438	461	29	;	;	PUNCT
ejpam-6438	462	1	i	i	PRON
ejpam-6438	462	2	=	=	PUNCT
ejpam-6438	462	3	i+	i+	NUM
ejpam-6438	462	4	1	1	X
ejpam-6438	462	5	)	)	PUNCT
ejpam-6438	462	6	do	do	VERB
ejpam-6438	462	7	r	r	NOUN
ejpam-6438	462	8	(	(	PUNCT
ejpam-6438	462	9	vi	vi	NOUN
ejpam-6438	462	10	,	,	PUNCT
ejpam-6438	462	11	r	r	NOUN
ejpam-6438	462	12	)	)	PUNCT
ejpam-6438	462	13	=	=	SYM
ejpam-6438	462	14	{	{	PUNCT
ejpam-6438	462	15	i−	i−	PROPN
ejpam-6438	462	16	1	1	NUM
ejpam-6438	462	17	,	,	PUNCT
ejpam-6438	462	18	n	n	CCONJ
ejpam-6438	462	19	}	}	PUNCT
ejpam-6438	462	20	end	end	VERB
ejpam-6438	462	21	for	for	ADP
ejpam-6438	462	22	(	(	PUNCT
ejpam-6438	462	23	i	i	NOUN
ejpam-6438	462	24	=	=	NOUN
ejpam-6438	462	25	3	3	NUM
ejpam-6438	462	26	;	;	PUNCT
ejpam-6438	462	27	i	i	PROPN
ejpam-6438	462	28	≤	≤	PROPN
ejpam-6438	462	29	n+m	n+m	NUM
ejpam-6438	462	30	;	;	PUNCT
ejpam-6438	462	31	i	i	PRON
ejpam-6438	462	32	=	=	PUNCT
ejpam-6438	462	33	i+	i+	NUM
ejpam-6438	462	34	1	1	X
ejpam-6438	462	35	)	)	PUNCT
ejpam-6438	462	36	do	do	VERB
ejpam-6438	462	37	r	r	NOUN
ejpam-6438	462	38	(	(	PUNCT
ejpam-6438	462	39	vi	vi	NOUN
ejpam-6438	462	40	,	,	PUNCT
ejpam-6438	462	41	r	r	NOUN
ejpam-6438	462	42	)	)	PUNCT
ejpam-6438	462	43	=	=	SYM
ejpam-6438	462	44	{	{	PUNCT
ejpam-6438	462	45	i−	i−	PROPN
ejpam-6438	462	46	2	2	NUM
ejpam-6438	462	47	,	,	PUNCT
ejpam-6438	462	48	|n+	|n+	PROPN
ejpam-6438	462	49	2−	2−	NUM
ejpam-6438	462	50	i|	i|	NOUN
ejpam-6438	462	51	}	}	PUNCT
ejpam-6438	462	52	end	end	NOUN
ejpam-6438	462	53	we	we	PRON
ejpam-6438	462	54	aim	aim	VERB
ejpam-6438	462	55	to	to	PART
ejpam-6438	462	56	show	show	VERB
ejpam-6438	462	57	that	that	SCONJ
ejpam-6438	462	58	the	the	DET
ejpam-6438	462	59	metric	metric	ADJ
ejpam-6438	462	60	dimension	dimension	NOUN
ejpam-6438	462	61	of	of	ADP
ejpam-6438	462	62	g	g	PROPN
ejpam-6438	462	63	is	be	AUX
ejpam-6438	462	64	2	2	NUM
ejpam-6438	462	65	.	.	PUNCT
ejpam-6438	463	1	that	that	PRON
ejpam-6438	463	2	is	is	ADV
ejpam-6438	463	3	,	,	PUNCT
ejpam-6438	463	4	there	there	PRON
ejpam-6438	463	5	exists	exist	VERB
ejpam-6438	463	6	a	a	DET
ejpam-6438	463	7	resolving	resolving	NOUN
ejpam-6438	463	8	set	set	VERB
ejpam-6438	463	9	r	r	NOUN
ejpam-6438	463	10	⊆	⊆	NUM
ejpam-6438	463	11	v	v	NOUN
ejpam-6438	463	12	(	(	PUNCT
ejpam-6438	463	13	g	g	NOUN
ejpam-6438	463	14	)	)	PUNCT
ejpam-6438	463	15	with	with	ADP
ejpam-6438	463	16	|r|	|r|	NOUN
ejpam-6438	463	17	=	=	SYM
ejpam-6438	463	18	2	2	NUM
ejpam-6438	463	19	such	such	ADJ
ejpam-6438	463	20	that	that	PRON
ejpam-6438	463	21	for	for	ADP
ejpam-6438	463	22	every	every	DET
ejpam-6438	463	23	pair	pair	NOUN
ejpam-6438	463	24	of	of	ADP
ejpam-6438	463	25	distinct	distinct	ADJ
ejpam-6438	463	26	vertices	vertex	NOUN
ejpam-6438	463	27	x	x	X
ejpam-6438	463	28	,	,	PUNCT
ejpam-6438	463	29	y	y	PROPN
ejpam-6438	463	30	∈	∈	PROPN
ejpam-6438	463	31	v	v	NOUN
ejpam-6438	463	32	(	(	PUNCT
ejpam-6438	463	33	g	g	NOUN
ejpam-6438	463	34	)	)	PUNCT
ejpam-6438	463	35	,	,	PUNCT
ejpam-6438	463	36	the	the	DET
ejpam-6438	463	37	distance	distance	NOUN
ejpam-6438	463	38	vectors	vector	VERB
ejpam-6438	463	39	r(x|r	r(x|r	NOUN
ejpam-6438	463	40	)	)	PUNCT
ejpam-6438	463	41	and	and	CCONJ
ejpam-6438	463	42	r(y|r	r(y|r	NUM
ejpam-6438	463	43	)	)	PUNCT
ejpam-6438	463	44	are	be	AUX
ejpam-6438	463	45	distinct	distinct	ADJ
ejpam-6438	463	46	.	.	PUNCT
ejpam-6438	464	1	let	let	VERB
ejpam-6438	464	2	us	we	PRON
ejpam-6438	464	3	choose	choose	VERB
ejpam-6438	464	4	r	r	NOUN
ejpam-6438	464	5	=	=	SYM
ejpam-6438	464	6	{	{	PUNCT
ejpam-6438	464	7	u1	u1	NOUN
ejpam-6438	464	8	,	,	PUNCT
ejpam-6438	464	9	v1	v1	PROPN
ejpam-6438	464	10	}	}	PUNCT
ejpam-6438	464	11	,	,	PUNCT
ejpam-6438	464	12	where	where	SCONJ
ejpam-6438	464	13	u1	u1	PROPN
ejpam-6438	464	14	∈	∈	PROPN
ejpam-6438	464	15	u	u	NOUN
ejpam-6438	464	16	and	and	CCONJ
ejpam-6438	464	17	v1	v1	PROPN
ejpam-6438	464	18	∈	∈	PROPN
ejpam-6438	464	19	v	v	NOUN
ejpam-6438	464	20	.	.	PUNCT
ejpam-6438	465	1	we	we	PRON
ejpam-6438	465	2	will	will	AUX
ejpam-6438	465	3	show	show	VERB
ejpam-6438	465	4	that	that	SCONJ
ejpam-6438	465	5	r	r	NOUN
ejpam-6438	465	6	resolves	resolve	NOUN
ejpam-6438	465	7	all	all	DET
ejpam-6438	465	8	vertices	vertex	NOUN
ejpam-6438	465	9	in	in	ADP
ejpam-6438	465	10	g.	g.	PROPN
ejpam-6438	465	11	case	case	NOUN
ejpam-6438	465	12	1	1	NUM
ejpam-6438	465	13	:	:	PUNCT
ejpam-6438	465	14	x	x	X
ejpam-6438	465	15	,	,	PUNCT
ejpam-6438	465	16	y	y	PROPN
ejpam-6438	465	17	∈	∈	PROPN
ejpam-6438	465	18	u	u	PROPN
ejpam-6438	465	19	,	,	PUNCT
ejpam-6438	465	20	x	x	PROPN
ejpam-6438	465	21	̸=	̸=	PROPN
ejpam-6438	465	22	y.	y.	NOUN
ejpam-6438	465	23	then	then	ADV
ejpam-6438	465	24	d(x	d(x	PROPN
ejpam-6438	465	25	,	,	PUNCT
ejpam-6438	465	26	u1	u1	NOUN
ejpam-6438	465	27	)	)	PUNCT
ejpam-6438	465	28	=	=	SYM
ejpam-6438	465	29	0	0	PUNCT
ejpam-6438	466	1	if	if	SCONJ
ejpam-6438	466	2	x	x	X
ejpam-6438	466	3	=	=	SYM
ejpam-6438	466	4	u1	u1	NOUN
ejpam-6438	466	5	,	,	PUNCT
ejpam-6438	466	6	and	and	CCONJ
ejpam-6438	466	7	2	2	NUM
ejpam-6438	466	8	otherwise	otherwise	ADV
ejpam-6438	466	9	(	(	PUNCT
ejpam-6438	466	10	since	since	SCONJ
ejpam-6438	466	11	x	x	PRON
ejpam-6438	466	12	and	and	CCONJ
ejpam-6438	466	13	u1	u1	NOUN
ejpam-6438	466	14	are	be	AUX
ejpam-6438	466	15	in	in	ADP
ejpam-6438	466	16	the	the	DET
ejpam-6438	466	17	same	same	ADJ
ejpam-6438	466	18	partite	partite	ADJ
ejpam-6438	466	19	set	set	NOUN
ejpam-6438	466	20	and	and	CCONJ
ejpam-6438	466	21	not	not	PART
ejpam-6438	466	22	adjacent	adjacent	ADJ
ejpam-6438	466	23	,	,	PUNCT
ejpam-6438	466	24	but	but	CCONJ
ejpam-6438	466	25	both	both	PRON
ejpam-6438	466	26	are	be	AUX
ejpam-6438	466	27	adjacent	adjacent	ADJ
ejpam-6438	466	28	to	to	ADP
ejpam-6438	466	29	all	all	DET
ejpam-6438	466	30	vertices	vertex	NOUN
ejpam-6438	466	31	in	in	ADP
ejpam-6438	466	32	v	v	NOUN
ejpam-6438	466	33	)	)	PUNCT
ejpam-6438	466	34	.	.	PUNCT
ejpam-6438	467	1	also	also	ADV
ejpam-6438	467	2	,	,	PUNCT
ejpam-6438	467	3	d(x	d(x	PROPN
ejpam-6438	467	4	,	,	PUNCT
ejpam-6438	467	5	v1	v1	NOUN
ejpam-6438	467	6	)	)	PUNCT
ejpam-6438	467	7	=	=	SYM
ejpam-6438	467	8	1	1	NUM
ejpam-6438	467	9	for	for	ADP
ejpam-6438	467	10	all	all	DET
ejpam-6438	467	11	x	x	SYM
ejpam-6438	467	12	∈	∈	PROPN
ejpam-6438	467	13	u	u	NOUN
ejpam-6438	467	14	since	since	SCONJ
ejpam-6438	467	15	each	each	PRON
ejpam-6438	467	16	x	x	VERB
ejpam-6438	467	17	is	be	AUX
ejpam-6438	467	18	adjacent	adjacent	ADJ
ejpam-6438	467	19	to	to	PART
ejpam-6438	467	20	v1	v1	VERB
ejpam-6438	467	21	.	.	PUNCT
ejpam-6438	468	1	thus	thus	ADV
ejpam-6438	468	2	,	,	PUNCT
ejpam-6438	468	3	the	the	DET
ejpam-6438	468	4	distance	distance	NOUN
ejpam-6438	468	5	vectors	vector	NOUN
ejpam-6438	468	6	differ	differ	VERB
ejpam-6438	468	7	at	at	ADP
ejpam-6438	468	8	the	the	DET
ejpam-6438	468	9	first	first	ADJ
ejpam-6438	468	10	coordinate	coordinate	NOUN
ejpam-6438	468	11	if	if	SCONJ
ejpam-6438	468	12	x	x	NOUN
ejpam-6438	468	13	=	=	SYM
ejpam-6438	468	14	u1	u1	NOUN
ejpam-6438	468	15	,	,	PUNCT
ejpam-6438	468	16	and	and	CCONJ
ejpam-6438	468	17	otherwise	otherwise	ADV
ejpam-6438	468	18	they	they	PRON
ejpam-6438	468	19	differ	differ	VERB
ejpam-6438	468	20	due	due	ADJ
ejpam-6438	468	21	to	to	ADP
ejpam-6438	468	22	symmetry	symmetry	NOUN
ejpam-6438	468	23	and	and	CCONJ
ejpam-6438	468	24	the	the	DET
ejpam-6438	468	25	odd	odd	ADJ
ejpam-6438	468	26	cardinality	cardinality	NOUN
ejpam-6438	468	27	of	of	ADP
ejpam-6438	468	28	u	u	PROPN
ejpam-6438	468	29	.	.	PUNCT
ejpam-6438	469	1	case	case	NOUN
ejpam-6438	469	2	2	2	NUM
ejpam-6438	469	3	:	:	PUNCT
ejpam-6438	469	4	x	x	X
ejpam-6438	469	5	,	,	PUNCT
ejpam-6438	469	6	y	y	PROPN
ejpam-6438	469	7	∈	∈	PROPN
ejpam-6438	469	8	v	v	NOUN
ejpam-6438	469	9	,	,	PUNCT
ejpam-6438	469	10	x	x	PROPN
ejpam-6438	469	11	̸=	̸=	PROPN
ejpam-6438	469	12	y.	y.	NOUN
ejpam-6438	469	13	similarly	similarly	ADV
ejpam-6438	469	14	,	,	PUNCT
ejpam-6438	469	15	d(x	d(x	PROPN
ejpam-6438	469	16	,	,	PUNCT
ejpam-6438	469	17	v1	v1	NOUN
ejpam-6438	469	18	)	)	PUNCT
ejpam-6438	470	1	=	=	SYM
ejpam-6438	470	2	0	0	PUNCT
ejpam-6438	471	1	if	if	SCONJ
ejpam-6438	471	2	x	x	X
ejpam-6438	471	3	=	=	SYM
ejpam-6438	471	4	v1	v1	NOUN
ejpam-6438	471	5	,	,	PUNCT
ejpam-6438	471	6	and	and	CCONJ
ejpam-6438	471	7	2	2	NUM
ejpam-6438	471	8	otherwise	otherwise	ADV
ejpam-6438	471	9	.	.	PUNCT
ejpam-6438	472	1	also	also	ADV
ejpam-6438	472	2	,	,	PUNCT
ejpam-6438	472	3	d(x	d(x	PROPN
ejpam-6438	472	4	,	,	PUNCT
ejpam-6438	472	5	u1	u1	NOUN
ejpam-6438	472	6	)	)	PUNCT
ejpam-6438	472	7	=	=	SYM
ejpam-6438	472	8	1	1	NUM
ejpam-6438	472	9	for	for	ADP
ejpam-6438	472	10	all	all	DET
ejpam-6438	472	11	x	x	SYM
ejpam-6438	472	12	∈	∈	PROPN
ejpam-6438	472	13	v	v	NOUN
ejpam-6438	472	14	.	.	PUNCT
ejpam-6438	473	1	hence	hence	ADV
ejpam-6438	473	2	,	,	PUNCT
ejpam-6438	473	3	the	the	DET
ejpam-6438	473	4	distance	distance	NOUN
ejpam-6438	473	5	vectors	vector	NOUN
ejpam-6438	473	6	differ	differ	VERB
ejpam-6438	473	7	at	at	ADP
ejpam-6438	473	8	the	the	DET
ejpam-6438	473	9	second	second	ADJ
ejpam-6438	473	10	coordinate	coordinate	NOUN
ejpam-6438	473	11	if	if	SCONJ
ejpam-6438	473	12	x	x	NOUN
ejpam-6438	473	13	=	=	SYM
ejpam-6438	473	14	v1	v1	NOUN
ejpam-6438	473	15	,	,	PUNCT
ejpam-6438	473	16	and	and	CCONJ
ejpam-6438	473	17	otherwise	otherwise	ADV
ejpam-6438	473	18	they	they	PRON
ejpam-6438	473	19	are	be	AUX
ejpam-6438	473	20	distinguishable	distinguishable	ADJ
ejpam-6438	473	21	.	.	PUNCT
ejpam-6438	474	1	case	case	NOUN
ejpam-6438	474	2	3	3	NUM
ejpam-6438	474	3	:	:	PUNCT
ejpam-6438	474	4	x	x	SYM
ejpam-6438	474	5	∈	∈	PROPN
ejpam-6438	474	6	u	u	NOUN
ejpam-6438	474	7	,	,	PUNCT
ejpam-6438	474	8	y	y	PROPN
ejpam-6438	474	9	∈	∈	PROPN
ejpam-6438	474	10	v	v	NOUN
ejpam-6438	474	11	.	.	PUNCT
ejpam-6438	475	1	then	then	ADV
ejpam-6438	475	2	d(x	d(x	PROPN
ejpam-6438	475	3	,	,	PUNCT
ejpam-6438	475	4	u1	u1	NOUN
ejpam-6438	475	5	)	)	PUNCT
ejpam-6438	475	6	∈	∈	PROPN
ejpam-6438	475	7	{	{	PUNCT
ejpam-6438	475	8	0	0	NUM
ejpam-6438	475	9	,	,	PUNCT
ejpam-6438	475	10	2	2	NUM
ejpam-6438	475	11	}	}	PUNCT
ejpam-6438	475	12	and	and	CCONJ
ejpam-6438	475	13	d(y	d(y	NOUN
ejpam-6438	475	14	,	,	PUNCT
ejpam-6438	475	15	u1	u1	NOUN
ejpam-6438	475	16	)	)	PUNCT
ejpam-6438	475	17	=	=	SYM
ejpam-6438	475	18	1	1	NUM
ejpam-6438	475	19	,	,	PUNCT
ejpam-6438	475	20	so	so	ADV
ejpam-6438	475	21	the	the	DET
ejpam-6438	475	22	first	first	ADJ
ejpam-6438	475	23	coordinates	coordinate	NOUN
ejpam-6438	475	24	differ	differ	VERB
ejpam-6438	475	25	.	.	PUNCT
ejpam-6438	476	1	hence	hence	ADV
ejpam-6438	476	2	,	,	PUNCT
ejpam-6438	476	3	r(x|r	r(x|r	NOUN
ejpam-6438	476	4	)	)	PUNCT
ejpam-6438	476	5	̸=	̸=	PROPN
ejpam-6438	476	6	r(y|r	r(y|r	NUM
ejpam-6438	476	7	)	)	PUNCT
ejpam-6438	476	8	.	.	PUNCT
ejpam-6438	477	1	therefore	therefore	ADV
ejpam-6438	477	2	,	,	PUNCT
ejpam-6438	477	3	r	r	NOUN
ejpam-6438	477	4	=	=	SYM
ejpam-6438	477	5	{	{	PUNCT
ejpam-6438	477	6	u1	u1	NOUN
ejpam-6438	477	7	,	,	PUNCT
ejpam-6438	477	8	v1	v1	PROPN
ejpam-6438	477	9	}	}	PUNCT
ejpam-6438	477	10	is	be	AUX
ejpam-6438	477	11	a	a	DET
ejpam-6438	477	12	resolving	resolving	NOUN
ejpam-6438	477	13	set	set	NOUN
ejpam-6438	477	14	,	,	PUNCT
ejpam-6438	477	15	and	and	CCONJ
ejpam-6438	477	16	dim(g	dim(g	PROPN
ejpam-6438	477	17	)	)	PUNCT
ejpam-6438	477	18	≤	≤	NOUN
ejpam-6438	477	19	2	2	NUM
ejpam-6438	477	20	.	.	PUNCT
ejpam-6438	477	21	to	to	PART
ejpam-6438	477	22	prove	prove	VERB
ejpam-6438	477	23	minimality	minimality	NOUN
ejpam-6438	477	24	,	,	PUNCT
ejpam-6438	477	25	suppose	suppose	VERB
ejpam-6438	477	26	there	there	PRON
ejpam-6438	477	27	exists	exist	VERB
ejpam-6438	477	28	a	a	DET
ejpam-6438	477	29	resolving	resolving	NOUN
ejpam-6438	477	30	set	set	VERB
ejpam-6438	477	31	r′	r′	PROPN
ejpam-6438	477	32	with	with	ADP
ejpam-6438	477	33	|r′|	|r′|	NOUN
ejpam-6438	477	34	=	=	SYM
ejpam-6438	478	1	1	1	X
ejpam-6438	478	2	.	.	PUNCT
ejpam-6438	478	3	then	then	ADV
ejpam-6438	478	4	all	all	DET
ejpam-6438	478	5	vertices	vertex	NOUN
ejpam-6438	478	6	in	in	ADP
ejpam-6438	478	7	one	one	NUM
ejpam-6438	478	8	partite	partite	ADJ
ejpam-6438	478	9	set	set	NOUN
ejpam-6438	478	10	are	be	AUX
ejpam-6438	478	11	equidistant	equidistant	ADJ
ejpam-6438	478	12	from	from	ADP
ejpam-6438	478	13	the	the	DET
ejpam-6438	478	14	single	single	ADJ
ejpam-6438	478	15	vertex	vertex	NOUN
ejpam-6438	478	16	in	in	ADP
ejpam-6438	478	17	r′	r′	PROPN
ejpam-6438	478	18	,	,	PUNCT
ejpam-6438	478	19	and	and	CCONJ
ejpam-6438	478	20	hence	hence	ADV
ejpam-6438	478	21	can	can	AUX
ejpam-6438	478	22	not	not	PART
ejpam-6438	478	23	be	be	AUX
ejpam-6438	478	24	distinguished	distinguish	VERB
ejpam-6438	478	25	.	.	PUNCT
ejpam-6438	479	1	therefore	therefore	ADV
ejpam-6438	479	2	,	,	PUNCT
ejpam-6438	479	3	no	no	DET
ejpam-6438	479	4	single	single	ADJ
ejpam-6438	479	5	vertex	vertex	NOUN
ejpam-6438	479	6	can	can	AUX
ejpam-6438	479	7	resolve	resolve	VERB
ejpam-6438	479	8	g	g	NOUN
ejpam-6438	479	9	,	,	PUNCT
ejpam-6438	479	10	and	and	CCONJ
ejpam-6438	479	11	dim(g	dim(g	PROPN
ejpam-6438	479	12	)	)	PUNCT
ejpam-6438	479	13	≥	≥	NOUN
ejpam-6438	479	14	2	2	NUM
ejpam-6438	479	15	.	.	PUNCT
ejpam-6438	480	1	thus	thus	ADV
ejpam-6438	480	2	,	,	PUNCT
ejpam-6438	480	3	dim(g	dim(g	PROPN
ejpam-6438	480	4	)	)	PUNCT
ejpam-6438	480	5	=	=	SYM
ejpam-6438	481	1	2	2	NUM
ejpam-6438	481	2	.	.	NOUN
ejpam-6438	481	3	3	3	NUM
ejpam-6438	481	4	.	.	X
ejpam-6438	481	5	algorithm	algorithm	NOUN
ejpam-6438	481	6	for	for	ADP
ejpam-6438	481	7	connected	connect	VERB
ejpam-6438	481	8	metric	metric	ADJ
ejpam-6438	481	9	dimension	dimension	NOUN
ejpam-6438	481	10	in	in	ADP
ejpam-6438	481	11	this	this	DET
ejpam-6438	481	12	section	section	NOUN
ejpam-6438	481	13	,	,	PUNCT
ejpam-6438	481	14	we	we	PRON
ejpam-6438	481	15	propose	propose	VERB
ejpam-6438	481	16	an	an	DET
ejpam-6438	481	17	algorithm	algorithm	NOUN
ejpam-6438	481	18	that	that	PRON
ejpam-6438	481	19	determines	determine	VERB
ejpam-6438	481	20	a	a	DET
ejpam-6438	481	21	connected	connected	ADJ
ejpam-6438	481	22	metric	metric	ADJ
ejpam-6438	481	23	dimension	dimension	NOUN
ejpam-6438	481	24	for	for	ADP
ejpam-6438	481	25	an	an	DET
ejpam-6438	481	26	arbitrary	arbitrary	ADJ
ejpam-6438	481	27	graph	graph	NOUN
ejpam-6438	481	28	g.	g.	NOUN
ejpam-6438	482	1	this	this	DET
ejpam-6438	482	2	algorithm	algorithm	NOUN
ejpam-6438	482	3	provides	provide	VERB
ejpam-6438	482	4	a	a	DET
ejpam-6438	482	5	basic	basic	ADJ
ejpam-6438	482	6	framework	framework	NOUN
ejpam-6438	482	7	for	for	ADP
ejpam-6438	482	8	computing	compute	VERB
ejpam-6438	482	9	the	the	DET
ejpam-6438	482	10	connected	connected	ADJ
ejpam-6438	482	11	metric	metric	ADJ
ejpam-6438	482	12	dimension	dimension	NOUN
ejpam-6438	482	13	.	.	PUNCT
ejpam-6438	483	1	for	for	ADP
ejpam-6438	483	2	more	more	ADJ
ejpam-6438	483	3	complex	complex	ADJ
ejpam-6438	483	4	graphs	graph	NOUN
ejpam-6438	483	5	,	,	PUNCT
ejpam-6438	483	6	heuristic	heuristic	ADJ
ejpam-6438	483	7	or	or	CCONJ
ejpam-6438	483	8	metanephritic	metanephritic	ADJ
ejpam-6438	483	9	approaches	approach	NOUN
ejpam-6438	483	10	like	like	ADP
ejpam-6438	483	11	genetic	genetic	ADJ
ejpam-6438	483	12	algorithms	algorithm	NOUN
ejpam-6438	483	13	or	or	CCONJ
ejpam-6438	483	14	binary	binary	NOUN
ejpam-6438	483	15	equilibrium	equilibrium	NOUN
ejpam-6438	483	16	optimization	optimization	NOUN
ejpam-6438	483	17	algorithm	algorithm	NOUN
ejpam-6438	483	18	can	can	AUX
ejpam-6438	483	19	be	be	AUX
ejpam-6438	483	20	used	use	VERB
ejpam-6438	483	21	to	to	PART
ejpam-6438	483	22	find	find	VERB
ejpam-6438	483	23	optimal	optimal	ADJ
ejpam-6438	483	24	or	or	CCONJ
ejpam-6438	483	25	near	near	ADV
ejpam-6438	483	26	-	-	PUNCT
ejpam-6438	483	27	optimal	optimal	ADJ
ejpam-6438	483	28	solutions	solution	NOUN
ejpam-6438	483	29	efficiently	efficiently	ADV
ejpam-6438	483	30	.	.	PUNCT
ejpam-6438	484	1	algorithm	algorithm	NOUN
ejpam-6438	484	2	:	:	PUNCT
ejpam-6438	484	3	connected	connect	VERB
ejpam-6438	484	4	metric	metric	ADJ
ejpam-6438	484	5	dimension	dimension	NOUN
ejpam-6438	484	6	a.	a.	NOUN
ejpam-6438	484	7	elrokh	elrokh	PROPN
ejpam-6438	484	8	,	,	PUNCT
ejpam-6438	484	9	eman	eman	PROPN
ejpam-6438	484	10	s.	s.	PROPN
ejpam-6438	484	11	almotairi	almotairi	PROPN
ejpam-6438	484	12	,	,	PUNCT
ejpam-6438	484	13	h.	h.	PROPN
ejpam-6438	484	14	mostafa	mostafa	PROPN
ejpam-6438	484	15	/	/	SYM
ejpam-6438	484	16	eur	eur	PROPN
ejpam-6438	484	17	.	.	PUNCT
ejpam-6438	485	1	j.	j.	PROPN
ejpam-6438	485	2	pure	pure	PROPN
ejpam-6438	485	3	appl	appl	PROPN
ejpam-6438	485	4	.	.	PROPN
ejpam-6438	485	5	math	math	PROPN
ejpam-6438	485	6	,	,	PUNCT
ejpam-6438	485	7	18	18	NUM
ejpam-6438	485	8	(	(	PUNCT
ejpam-6438	485	9	3	3	NUM
ejpam-6438	485	10	)	)	PUNCT
ejpam-6438	485	11	(	(	PUNCT
ejpam-6438	485	12	2025	2025	NUM
ejpam-6438	485	13	)	)	PUNCT
ejpam-6438	485	14	,	,	PUNCT
ejpam-6438	485	15	6438	6438	NUM
ejpam-6438	485	16	15	15	NUM
ejpam-6438	485	17	of	of	ADP
ejpam-6438	485	18	18	18	NUM
ejpam-6438	485	19	input	input	NOUN
ejpam-6438	485	20	:	:	PUNCT
ejpam-6438	485	21	a	a	DET
ejpam-6438	485	22	connected	connected	ADJ
ejpam-6438	485	23	graph	graph	NOUN
ejpam-6438	485	24	g	g	PROPN
ejpam-6438	485	25	=	=	PUNCT
ejpam-6438	485	26	(	(	PUNCT
ejpam-6438	485	27	v	v	NOUN
ejpam-6438	485	28	,	,	PUNCT
ejpam-6438	485	29	e	e	NOUN
ejpam-6438	485	30	)	)	PUNCT
ejpam-6438	485	31	output	output	NOUN
ejpam-6438	485	32	:	:	PUNCT
ejpam-6438	485	33	a	a	DET
ejpam-6438	485	34	connected	connected	ADJ
ejpam-6438	485	35	resolving	resolving	NOUN
ejpam-6438	485	36	set	set	VERB
ejpam-6438	485	37	(	(	PUNCT
ejpam-6438	485	38	s	s	NOUN
ejpam-6438	485	39	)	)	PUNCT
ejpam-6438	485	40	with	with	ADP
ejpam-6438	485	41	the	the	DET
ejpam-6438	485	42	smallest	small	ADJ
ejpam-6438	485	43	possible	possible	ADJ
ejpam-6438	485	44	size	size	NOUN
ejpam-6438	485	45	initialization	initialization	NOUN
ejpam-6438	485	46	:	:	PUNCT
ejpam-6438	485	47	let	let	VERB
ejpam-6438	485	48	(	(	PUNCT
ejpam-6438	485	49	s	s	X
ejpam-6438	485	50	)	)	PUNCT
ejpam-6438	485	51	be	be	AUX
ejpam-6438	485	52	an	an	DET
ejpam-6438	485	53	empty	empty	ADJ
ejpam-6438	485	54	set	set	NOUN
ejpam-6438	485	55	.	.	PUNCT
ejpam-6438	486	1	let	let	VERB
ejpam-6438	486	2	(	(	PUNCT
ejpam-6438	486	3	u	u	NOUN
ejpam-6438	486	4	)	)	PUNCT
ejpam-6438	486	5	be	be	VERB
ejpam-6438	486	6	the	the	DET
ejpam-6438	486	7	set	set	NOUN
ejpam-6438	486	8	of	of	ADP
ejpam-6438	486	9	all	all	DET
ejpam-6438	486	10	vertices	vertex	NOUN
ejpam-6438	486	11	in	in	ADP
ejpam-6438	486	12	(	(	PUNCT
ejpam-6438	486	13	v	v	NOUN
ejpam-6438	486	14	)	)	PUNCT
ejpam-6438	486	15	.	.	PUNCT
ejpam-6438	487	1	step	step	NOUN
ejpam-6438	487	2	1	1	NUM
ejpam-6438	487	3	:	:	PUNCT
ejpam-6438	487	4	select	select	ADJ
ejpam-6438	487	5	initial	initial	ADJ
ejpam-6438	487	6	vertex	vertex	NOUN
ejpam-6438	487	7	:	:	PUNCT
ejpam-6438	487	8	choose	choose	VERB
ejpam-6438	487	9	an	an	DET
ejpam-6438	487	10	arbitrary	arbitrary	ADJ
ejpam-6438	487	11	vertex	vertex	NOUN
ejpam-6438	487	12	(	(	PUNCT
ejpam-6438	487	13	v	v	NOUN
ejpam-6438	487	14	∈	∈	PROPN
ejpam-6438	487	15	v	v	NOUN
ejpam-6438	487	16	)	)	PUNCT
ejpam-6438	487	17	and	and	CCONJ
ejpam-6438	487	18	add	add	VERB
ejpam-6438	487	19	it	it	PRON
ejpam-6438	487	20	to	to	ADP
ejpam-6438	487	21	(	(	PUNCT
ejpam-6438	487	22	s	s	NOUN
ejpam-6438	487	23	)	)	PUNCT
ejpam-6438	487	24	.	.	PUNCT
ejpam-6438	488	1	remove	remove	VERB
ejpam-6438	488	2	(	(	PUNCT
ejpam-6438	488	3	v	v	NOUN
ejpam-6438	488	4	)	)	PUNCT
ejpam-6438	488	5	from	from	ADP
ejpam-6438	488	6	(	(	PUNCT
ejpam-6438	488	7	u	u	NOUN
ejpam-6438	488	8	)	)	PUNCT
ejpam-6438	488	9	.	.	PUNCT
ejpam-6438	489	1	step	step	NOUN
ejpam-6438	489	2	2	2	NUM
ejpam-6438	489	3	:	:	PUNCT
ejpam-6438	489	4	iterative	iterative	NOUN
ejpam-6438	489	5	selection	selection	NOUN
ejpam-6438	489	6	:	:	PUNCT
ejpam-6438	489	7	while	while	SCONJ
ejpam-6438	489	8	(	(	PUNCT
ejpam-6438	489	9	u	u	NOUN
ejpam-6438	489	10	)	)	PUNCT
ejpam-6438	489	11	is	be	AUX
ejpam-6438	489	12	not	not	PART
ejpam-6438	489	13	empty	empty	ADJ
ejpam-6438	489	14	:	:	PUNCT
ejpam-6438	489	15	for	for	SCONJ
ejpam-6438	489	16	each	each	DET
ejpam-6438	489	17	vertex	vertex	NOUN
ejpam-6438	489	18	(	(	PUNCT
ejpam-6438	489	19	u	u	NOUN
ejpam-6438	489	20	∈	∈	PROPN
ejpam-6438	489	21	u	u	NOUN
ejpam-6438	489	22	):	):	PUNCT
ejpam-6438	489	23	calculate	calculate	VERB
ejpam-6438	489	24	the	the	DET
ejpam-6438	489	25	distance	distance	NOUN
ejpam-6438	489	26	from	from	ADP
ejpam-6438	489	27	u	u	PRON
ejpam-6438	489	28	to	to	ADP
ejpam-6438	489	29	all	all	DET
ejpam-6438	489	30	vertices	vertex	NOUN
ejpam-6438	489	31	in	in	ADP
ejpam-6438	489	32	s.	s.	PROPN
ejpam-6438	489	33	step	step	NOUN
ejpam-6438	489	34	3	3	NUM
ejpam-6438	489	35	:	:	PUNCT
ejpam-6438	489	36	select	select	VERB
ejpam-6438	489	37	the	the	DET
ejpam-6438	489	38	vertex	vertex	NOUN
ejpam-6438	489	39	(	(	PUNCT
ejpam-6438	489	40	u	u	NOUN
ejpam-6438	489	41	∈	∈	PROPN
ejpam-6438	489	42	u	u	NOUN
ejpam-6438	489	43	)	)	PUNCT
ejpam-6438	489	44	that	that	PRON
ejpam-6438	489	45	maximizes	maximize	VERB
ejpam-6438	489	46	the	the	DET
ejpam-6438	489	47	number	number	NOUN
ejpam-6438	489	48	of	of	ADP
ejpam-6438	489	49	vertices	vertex	NOUN
ejpam-6438	489	50	in	in	ADP
ejpam-6438	489	51	u	u	NOUN
ejpam-6438	489	52	that	that	PRON
ejpam-6438	489	53	can	can	AUX
ejpam-6438	489	54	be	be	AUX
ejpam-6438	489	55	uniquely	uniquely	ADV
ejpam-6438	489	56	identified	identify	VERB
ejpam-6438	489	57	by	by	ADP
ejpam-6438	489	58	their	their	PRON
ejpam-6438	489	59	distances	distance	NOUN
ejpam-6438	489	60	to	to	ADP
ejpam-6438	489	61	the	the	DET
ejpam-6438	489	62	vertices	vertex	NOUN
ejpam-6438	489	63	in	in	ADP
ejpam-6438	489	64	(	(	PUNCT
ejpam-6438	489	65	s	s	NOUN
ejpam-6438	489	66	)	)	PUNCT
ejpam-6438	489	67	.	.	PUNCT
ejpam-6438	490	1	add	add	VERB
ejpam-6438	490	2	(	(	PUNCT
ejpam-6438	490	3	u	u	NOUN
ejpam-6438	490	4	)	)	PUNCT
ejpam-6438	490	5	to	to	ADP
ejpam-6438	490	6	(	(	PUNCT
ejpam-6438	490	7	s	s	NOUN
ejpam-6438	490	8	)	)	PUNCT
ejpam-6438	490	9	.	.	PUNCT
ejpam-6438	491	1	remove	remove	VERB
ejpam-6438	491	2	(	(	PUNCT
ejpam-6438	491	3	u	u	NOUN
ejpam-6438	491	4	)	)	PUNCT
ejpam-6438	491	5	from	from	ADP
ejpam-6438	491	6	(	(	PUNCT
ejpam-6438	491	7	u	u	NOUN
ejpam-6438	491	8	)	)	PUNCT
ejpam-6438	491	9	.	.	PUNCT
ejpam-6438	492	1	step	step	NOUN
ejpam-6438	492	2	4	4	NUM
ejpam-6438	492	3	:	:	PUNCT
ejpam-6438	492	4	ensure	ensure	VERB
ejpam-6438	492	5	connectivity	connectivity	NOUN
ejpam-6438	492	6	:	:	PUNCT
ejpam-6438	492	7	check	check	VERB
ejpam-6438	492	8	if	if	SCONJ
ejpam-6438	492	9	the	the	DET
ejpam-6438	492	10	sub	sub	NOUN
ejpam-6438	492	11	graph	graph	NOUN
ejpam-6438	492	12	induced	induce	VERB
ejpam-6438	492	13	by	by	ADP
ejpam-6438	492	14	(	(	PUNCT
ejpam-6438	492	15	s	s	X
ejpam-6438	492	16	)	)	PUNCT
ejpam-6438	492	17	is	be	AUX
ejpam-6438	492	18	connected	connect	VERB
ejpam-6438	492	19	.	.	PUNCT
ejpam-6438	493	1	if	if	SCONJ
ejpam-6438	493	2	not	not	PART
ejpam-6438	493	3	,	,	PUNCT
ejpam-6438	493	4	add	add	VERB
ejpam-6438	493	5	the	the	DET
ejpam-6438	493	6	necessary	necessary	ADJ
ejpam-6438	493	7	vertices	vertex	NOUN
ejpam-6438	493	8	from	from	ADP
ejpam-6438	493	9	(	(	PUNCT
ejpam-6438	493	10	v⧹s	v⧹s	X
ejpam-6438	493	11	)	)	PUNCT
ejpam-6438	493	12	to	to	ADP
ejpam-6438	493	13	(	(	PUNCT
ejpam-6438	493	14	s	s	X
ejpam-6438	493	15	)	)	PUNCT
ejpam-6438	493	16	to	to	PART
ejpam-6438	493	17	make	make	VERB
ejpam-6438	493	18	it	it	PRON
ejpam-6438	493	19	connected	connect	VERB
ejpam-6438	493	20	.	.	PUNCT
ejpam-6438	494	1	step	step	NOUN
ejpam-6438	494	2	5	5	NUM
ejpam-6438	494	3	:	:	PUNCT
ejpam-6438	494	4	optimization	optimization	NOUN
ejpam-6438	494	5	:	:	PUNCT
ejpam-6438	494	6	attempt	attempt	VERB
ejpam-6438	494	7	to	to	PART
ejpam-6438	494	8	remove	remove	VERB
ejpam-6438	494	9	any	any	DET
ejpam-6438	494	10	redundant	redundant	ADJ
ejpam-6438	494	11	vertices	vertex	NOUN
ejpam-6438	494	12	from	from	ADP
ejpam-6438	494	13	(	(	PUNCT
ejpam-6438	494	14	s	s	X
ejpam-6438	494	15	)	)	PUNCT
ejpam-6438	494	16	while	while	SCONJ
ejpam-6438	494	17	maintaining	maintain	VERB
ejpam-6438	494	18	its	its	PRON
ejpam-6438	494	19	properties	property	NOUN
ejpam-6438	494	20	as	as	ADP
ejpam-6438	494	21	a	a	DET
ejpam-6438	494	22	connected	connected	ADJ
ejpam-6438	494	23	resolving	resolving	NOUN
ejpam-6438	494	24	set	set	NOUN
ejpam-6438	494	25	.	.	PUNCT
ejpam-6438	495	1	step	step	NOUN
ejpam-6438	495	2	6	6	NUM
ejpam-6438	495	3	:	:	PUNCT
ejpam-6438	495	4	output	output	NOUN
ejpam-6438	495	5	:	:	PUNCT
ejpam-6438	495	6	return	return	VERB
ejpam-6438	495	7	the	the	DET
ejpam-6438	495	8	set	set	NOUN
ejpam-6438	495	9	(	(	PUNCT
ejpam-6438	495	10	s	s	NOUN
ejpam-6438	495	11	)	)	PUNCT
ejpam-6438	495	12	.	.	PUNCT
ejpam-6438	496	1	example	example	NOUN
ejpam-6438	496	2	:	:	PUNCT
ejpam-6438	496	3	path	path	NOUN
ejpam-6438	496	4	with	with	ADP
ejpam-6438	496	5	4	4	NUM
ejpam-6438	496	6	vertices	vertex	NOUN
ejpam-6438	496	7	and	and	CCONJ
ejpam-6438	496	8	one	one	NUM
ejpam-6438	496	9	triangle	triangle	NOUN
ejpam-6438	496	10	let	let	VERB
ejpam-6438	496	11	g	g	NOUN
ejpam-6438	496	12	be	be	AUX
ejpam-6438	496	13	a	a	DET
ejpam-6438	496	14	path	path	NOUN
ejpam-6438	496	15	p4	p4	ADJ
ejpam-6438	496	16	with	with	ADP
ejpam-6438	496	17	vertices	vertex	NOUN
ejpam-6438	496	18	v1	v1	VERB
ejpam-6438	496	19	−	−	PROPN
ejpam-6438	496	20	v2	v2	PROPN
ejpam-6438	496	21	−	−	PROPN
ejpam-6438	496	22	v3	v3	PROPN
ejpam-6438	496	23	−	−	PROPN
ejpam-6438	496	24	v4	v4	PROPN
ejpam-6438	496	25	and	and	CCONJ
ejpam-6438	496	26	a	a	DET
ejpam-6438	496	27	triangle	triangle	NOUN
ejpam-6438	496	28	u1	u1	NOUN
ejpam-6438	496	29	,	,	PUNCT
ejpam-6438	496	30	u2	u2	NOUN
ejpam-6438	496	31	,	,	PUNCT
ejpam-6438	496	32	u3	u3	NOUN
ejpam-6438	496	33	attached	attach	VERB
ejpam-6438	496	34	to	to	ADP
ejpam-6438	496	35	v2	v2	PROPN
ejpam-6438	496	36	.	.	PUNCT
ejpam-6438	497	1	•	•	NUM
ejpam-6438	497	2	step	step	NOUN
ejpam-6438	497	3	1	1	NUM
ejpam-6438	497	4	:	:	PUNCT
ejpam-6438	497	5	choose	choose	VERB
ejpam-6438	497	6	v2	v2	PROPN
ejpam-6438	497	7	as	as	ADP
ejpam-6438	497	8	initial	initial	ADJ
ejpam-6438	497	9	vertex	vertex	NOUN
ejpam-6438	497	10	⇒	⇒	NOUN
ejpam-6438	497	11	s	s	PART
ejpam-6438	497	12	=	=	PUNCT
ejpam-6438	497	13	{	{	PUNCT
ejpam-6438	497	14	v2	v2	NOUN
ejpam-6438	497	15	}	}	PUNCT
ejpam-6438	497	16	•	•	NUM
ejpam-6438	497	17	step	step	NOUN
ejpam-6438	497	18	2	2	NUM
ejpam-6438	497	19	:	:	PUNCT
ejpam-6438	497	20	add	add	VERB
ejpam-6438	497	21	v1	v1	NOUN
ejpam-6438	497	22	(	(	PUNCT
ejpam-6438	497	23	distinguishes	distinguish	VERB
ejpam-6438	497	24	v1	v1	PROPN
ejpam-6438	497	25	and	and	CCONJ
ejpam-6438	497	26	v3	v3	PROPN
ejpam-6438	497	27	)	)	PUNCT
ejpam-6438	497	28	⇒	⇒	NOUN
ejpam-6438	497	29	s	s	PART
ejpam-6438	497	30	=	=	PUNCT
ejpam-6438	497	31	{	{	PUNCT
ejpam-6438	497	32	v2	v2	PROPN
ejpam-6438	497	33	,	,	PUNCT
ejpam-6438	497	34	v1	v1	NOUN
ejpam-6438	497	35	}	}	PUNCT
ejpam-6438	497	36	•	•	NUM
ejpam-6438	497	37	step	step	NOUN
ejpam-6438	497	38	3	3	NUM
ejpam-6438	497	39	:	:	PUNCT
ejpam-6438	497	40	add	add	VERB
ejpam-6438	497	41	u1	u1	NOUN
ejpam-6438	497	42	(	(	PUNCT
ejpam-6438	497	43	distinguishes	distinguish	VERB
ejpam-6438	497	44	triangle	triangle	NOUN
ejpam-6438	497	45	vertices	vertex	NOUN
ejpam-6438	497	46	)	)	PUNCT
ejpam-6438	497	47	⇒	⇒	NOUN
ejpam-6438	497	48	s	s	PART
ejpam-6438	497	49	=	=	PUNCT
ejpam-6438	497	50	{	{	PUNCT
ejpam-6438	497	51	v2	v2	PROPN
ejpam-6438	497	52	,	,	PUNCT
ejpam-6438	497	53	v1	v1	NOUN
ejpam-6438	497	54	,	,	PUNCT
ejpam-6438	497	55	u1	u1	NOUN
ejpam-6438	497	56	}	}	PUNCT
ejpam-6438	497	57	•	•	NUM
ejpam-6438	497	58	step	step	NOUN
ejpam-6438	497	59	4	4	NUM
ejpam-6438	497	60	:	:	PUNCT
ejpam-6438	497	61	ensure	ensure	VERB
ejpam-6438	497	62	connectivity	connectivity	NOUN
ejpam-6438	497	63	:	:	PUNCT
ejpam-6438	497	64	v2	v2	NOUN
ejpam-6438	497	65	connects	connect	VERB
ejpam-6438	497	66	v1	v1	NOUN
ejpam-6438	497	67	and	and	CCONJ
ejpam-6438	497	68	u1	u1	NOUN
ejpam-6438	497	69	⇒	⇒	NOUN
ejpam-6438	497	70	connected	connect	VERB
ejpam-6438	497	71	•	•	NUM
ejpam-6438	497	72	step	step	NOUN
ejpam-6438	497	73	5	5	NUM
ejpam-6438	497	74	:	:	PUNCT
ejpam-6438	497	75	check	check	VERB
ejpam-6438	497	76	redundancy	redundancy	NOUN
ejpam-6438	497	77	:	:	PUNCT
ejpam-6438	497	78	all	all	DET
ejpam-6438	497	79	vertices	vertex	NOUN
ejpam-6438	497	80	resolved	resolve	VERB
ejpam-6438	497	81	,	,	PUNCT
ejpam-6438	497	82	s	s	VERB
ejpam-6438	497	83	is	be	AUX
ejpam-6438	497	84	minimal	minimal	ADJ
ejpam-6438	497	85	correctness	correctness	NOUN
ejpam-6438	497	86	the	the	DET
ejpam-6438	497	87	algorithm	algorithm	NOUN
ejpam-6438	497	88	ensures	ensure	VERB
ejpam-6438	497	89	that	that	SCONJ
ejpam-6438	497	90	:	:	PUNCT
ejpam-6438	497	91	a.	a.	NOUN
ejpam-6438	497	92	elrokh	elrokh	PROPN
ejpam-6438	497	93	,	,	PUNCT
ejpam-6438	497	94	eman	eman	PROPN
ejpam-6438	497	95	s.	s.	PROPN
ejpam-6438	497	96	almotairi	almotairi	PROPN
ejpam-6438	497	97	,	,	PUNCT
ejpam-6438	497	98	h.	h.	PROPN
ejpam-6438	497	99	mostafa	mostafa	PROPN
ejpam-6438	497	100	/	/	SYM
ejpam-6438	497	101	eur	eur	PROPN
ejpam-6438	497	102	.	.	PUNCT
ejpam-6438	498	1	j.	j.	PROPN
ejpam-6438	498	2	pure	pure	PROPN
ejpam-6438	498	3	appl	appl	PROPN
ejpam-6438	498	4	.	.	PROPN
ejpam-6438	498	5	math	math	PROPN
ejpam-6438	498	6	,	,	PUNCT
ejpam-6438	498	7	18	18	NUM
ejpam-6438	498	8	(	(	PUNCT
ejpam-6438	498	9	3	3	NUM
ejpam-6438	498	10	)	)	PUNCT
ejpam-6438	498	11	(	(	PUNCT
ejpam-6438	498	12	2025	2025	NUM
ejpam-6438	498	13	)	)	PUNCT
ejpam-6438	498	14	,	,	PUNCT
ejpam-6438	498	15	6438	6438	NUM
ejpam-6438	498	16	16	16	NUM
ejpam-6438	498	17	of	of	ADP
ejpam-6438	498	18	18	18	NUM
ejpam-6438	498	19	•	•	NOUN
ejpam-6438	498	20	each	each	DET
ejpam-6438	498	21	vertex	vertex	NOUN
ejpam-6438	498	22	is	be	AUX
ejpam-6438	498	23	uniquely	uniquely	ADV
ejpam-6438	498	24	identified	identify	VERB
ejpam-6438	498	25	by	by	ADP
ejpam-6438	498	26	its	its	PRON
ejpam-6438	498	27	distance	distance	NOUN
ejpam-6438	498	28	vector	vector	NOUN
ejpam-6438	498	29	to	to	ADP
ejpam-6438	498	30	s	s	PRON
ejpam-6438	498	31	•	•	NOUN
ejpam-6438	498	32	the	the	DET
ejpam-6438	498	33	induced	induced	ADJ
ejpam-6438	498	34	subgraph	subgraph	NOUN
ejpam-6438	498	35	g[s	g[s	PROPN
ejpam-6438	498	36	]	]	PUNCT
ejpam-6438	498	37	is	be	AUX
ejpam-6438	498	38	connected	connect	VERB
ejpam-6438	498	39	completeness	completeness	NOUN
ejpam-6438	498	40	the	the	DET
ejpam-6438	498	41	algorithm	algorithm	NOUN
ejpam-6438	498	42	terminates	terminate	VERB
ejpam-6438	498	43	when	when	SCONJ
ejpam-6438	498	44	all	all	DET
ejpam-6438	498	45	vertices	vertex	NOUN
ejpam-6438	498	46	are	be	AUX
ejpam-6438	498	47	resolved	resolve	VERB
ejpam-6438	498	48	and	and	CCONJ
ejpam-6438	498	49	s	s	VERB
ejpam-6438	498	50	is	be	AUX
ejpam-6438	498	51	connected	connect	VERB
ejpam-6438	498	52	.	.	PUNCT
ejpam-6438	499	1	it	it	PRON
ejpam-6438	499	2	guarantees	guarantee	VERB
ejpam-6438	499	3	a	a	DET
ejpam-6438	499	4	valid	valid	ADJ
ejpam-6438	499	5	connected	connect	VERB
ejpam-6438	499	6	resolving	resolving	NOUN
ejpam-6438	499	7	set	set	VERB
ejpam-6438	499	8	.	.	PUNCT
ejpam-6438	500	1	time	time	NOUN
ejpam-6438	500	2	complexity	complexity	PROPN
ejpam-6438	500	3	let	let	VERB
ejpam-6438	500	4	n	n	NOUN
ejpam-6438	500	5	=	=	PUNCT
ejpam-6438	500	6	|v	|v	PROPN
ejpam-6438	500	7	|	|	NOUN
ejpam-6438	500	8	,	,	PUNCT
ejpam-6438	500	9	m	m	VERB
ejpam-6438	500	10	=	=	SYM
ejpam-6438	500	11	|e|	|e|	ADJ
ejpam-6438	500	12	:	:	PUNCT
ejpam-6438	500	13	•	•	NUM
ejpam-6438	500	14	distance	distance	NOUN
ejpam-6438	500	15	computation	computation	NOUN
ejpam-6438	500	16	:	:	PUNCT
ejpam-6438	500	17	o(n2	o(n2	ADV
ejpam-6438	500	18	)	)	PUNCT
ejpam-6438	500	19	using	use	VERB
ejpam-6438	500	20	bfs	bfs	NOUN
ejpam-6438	500	21	for	for	ADP
ejpam-6438	500	22	each	each	DET
ejpam-6438	500	23	vertex	vertex	NOUN
ejpam-6438	500	24	•	•	NOUN
ejpam-6438	500	25	selection	selection	NOUN
ejpam-6438	500	26	loop	loop	NOUN
ejpam-6438	500	27	:	:	PUNCT
ejpam-6438	500	28	o(n2	o(n2	ADJ
ejpam-6438	500	29	)	)	PUNCT
ejpam-6438	500	30	comparisons	comparison	NOUN
ejpam-6438	500	31	•	•	PRON
ejpam-6438	500	32	connectivity	connectivity	NOUN
ejpam-6438	500	33	check	check	NOUN
ejpam-6438	500	34	:	:	PUNCT
ejpam-6438	500	35	o(n+m	o(n+m	ADJ
ejpam-6438	500	36	)	)	PUNCT
ejpam-6438	500	37	•	•	NUM
ejpam-6438	500	38	redundancy	redundancy	NOUN
ejpam-6438	500	39	check	check	NOUN
ejpam-6438	500	40	:	:	PUNCT
ejpam-6438	500	41	o(n2	o(n2	ADV
ejpam-6438	500	42	)	)	PUNCT
ejpam-6438	500	43	total	total	ADJ
ejpam-6438	500	44	time	time	NOUN
ejpam-6438	500	45	complexity	complexity	NOUN
ejpam-6438	500	46	:	:	PUNCT
ejpam-6438	500	47	o(n2	o(n2	ADV
ejpam-6438	500	48	)	)	PUNCT
ejpam-6438	500	49	for	for	ADP
ejpam-6438	500	50	sparse	sparse	ADJ
ejpam-6438	500	51	graphs	graph	NOUN
ejpam-6438	500	52	4	4	NUM
ejpam-6438	500	53	.	.	PUNCT
ejpam-6438	500	54	conclusion	conclusion	NOUN
ejpam-6438	500	55	we	we	PRON
ejpam-6438	500	56	introduced	introduce	VERB
ejpam-6438	500	57	metric	metric	ADJ
ejpam-6438	500	58	and	and	CCONJ
ejpam-6438	500	59	connected	connected	ADJ
ejpam-6438	500	60	metric	metric	ADJ
ejpam-6438	500	61	dimension	dimension	NOUN
ejpam-6438	500	62	of	of	ADP
ejpam-6438	500	63	pn	pn	PROPN
ejpam-6438	500	64	⊙	⊙	PROPN
ejpam-6438	500	65	c3	c3	PROPN
ejpam-6438	500	66	,	,	PUNCT
ejpam-6438	500	67	pn	pn	PROPN
ejpam-6438	500	68	⊙	⊙	PROPN
ejpam-6438	500	69	p3	p3	PROPN
ejpam-6438	500	70	,	,	PUNCT
ejpam-6438	501	1	cn	cn	PROPN
ejpam-6438	501	2	⊙	⊙	PROPN
ejpam-6438	501	3	c3and	c3and	PROPN
ejpam-6438	501	4	cn	cn	PROPN
ejpam-6438	501	5	⊙	⊙	PROPN
ejpam-6438	501	6	p3	p3	PROPN
ejpam-6438	501	7	.	.	PUNCT
ejpam-6438	502	1	graph	graph	VERB
ejpam-6438	502	2	metric	metric	ADJ
ejpam-6438	502	3	dimension	dimension	NOUN
ejpam-6438	502	4	(	(	PUNCT
ejpam-6438	502	5	dim	dim	NOUN
ejpam-6438	502	6	)	)	PUNCT
ejpam-6438	502	7	connected	connect	VERB
ejpam-6438	502	8	metric	metric	ADJ
ejpam-6438	502	9	dimension	dimension	NOUN
ejpam-6438	502	10	(	(	PUNCT
ejpam-6438	502	11	cdim	cdim	PROPN
ejpam-6438	502	12	)	)	PUNCT
ejpam-6438	502	13	pn	pn	PROPN
ejpam-6438	502	14	⊙	⊙	PROPN
ejpam-6438	502	15	p3	p3	PROPN
ejpam-6438	502	16	n	n	PROPN
ejpam-6438	502	17	2n	2n	NUM
ejpam-6438	502	18	pn	pn	PROPN
ejpam-6438	502	19	⊙	⊙	PROPN
ejpam-6438	502	20	c3	c3	PROPN
ejpam-6438	502	21	2n	2n	NUM
ejpam-6438	502	22	3n	3n	NUM
ejpam-6438	502	23	cn	cn	PROPN
ejpam-6438	502	24	⊙	⊙	PROPN
ejpam-6438	502	25	p3	p3	PROPN
ejpam-6438	502	26	n	n	PROPN
ejpam-6438	502	27	2n	2n	NUM
ejpam-6438	503	1	cn	cn	PROPN
ejpam-6438	503	2	⊙	⊙	PROPN
ejpam-6438	503	3	c3	c3	PROPN
ejpam-6438	503	4	2n	2n	NUM
ejpam-6438	503	5	3n	3n	NUM
ejpam-6438	503	6	kim	kim	PROPN
ejpam-6438	503	7	,	,	PUNCT
ejpam-6438	503	8	n	n	PROPN
ejpam-6438	503	9	(	(	PUNCT
ejpam-6438	503	10	m	m	PROPN
ejpam-6438	503	11	odd	odd	ADJ
ejpam-6438	503	12	)	)	PUNCT
ejpam-6438	503	13	2	2	NUM
ejpam-6438	503	14	–	–	PUNCT
ejpam-6438	503	15	table	table	NOUN
ejpam-6438	503	16	1	1	NUM
ejpam-6438	503	17	:	:	PUNCT
ejpam-6438	503	18	summary	summary	NOUN
ejpam-6438	503	19	of	of	ADP
ejpam-6438	503	20	metric	metric	ADJ
ejpam-6438	503	21	and	and	CCONJ
ejpam-6438	503	22	connected	connected	ADJ
ejpam-6438	503	23	metric	metric	ADJ
ejpam-6438	503	24	dimensions	dimension	NOUN
ejpam-6438	503	25	for	for	ADP
ejpam-6438	503	26	various	various	ADJ
ejpam-6438	503	27	graphs	graph	NOUN
ejpam-6438	503	28	in	in	ADP
ejpam-6438	503	29	the	the	DET
ejpam-6438	503	30	future	future	NOUN
ejpam-6438	503	31	,	,	PUNCT
ejpam-6438	503	32	we	we	PRON
ejpam-6438	503	33	will	will	AUX
ejpam-6438	503	34	apply	apply	VERB
ejpam-6438	503	35	all	all	PRON
ejpam-6438	503	36	of	of	ADP
ejpam-6438	503	37	this	this	DET
ejpam-6438	503	38	proofs	proof	NOUN
ejpam-6438	503	39	for	for	ADP
ejpam-6438	503	40	another	another	DET
ejpam-6438	503	41	graphs	graph	NOUN
ejpam-6438	503	42	.	.	PUNCT
ejpam-6438	504	1	the	the	DET
ejpam-6438	504	2	third	third	ADJ
ejpam-6438	504	3	contribution	contribution	NOUN
ejpam-6438	504	4	is	be	AUX
ejpam-6438	504	5	that	that	SCONJ
ejpam-6438	504	6	proposing	propose	VERB
ejpam-6438	504	7	a	a	DET
ejpam-6438	504	8	new	new	ADJ
ejpam-6438	504	9	approximate	approximate	ADJ
ejpam-6438	504	10	algorithm	algorithm	NOUN
ejpam-6438	504	11	which	which	PRON
ejpam-6438	504	12	finds	find	VERB
ejpam-6438	504	13	a	a	DET
ejpam-6438	504	14	minimum	minimum	ADJ
ejpam-6438	504	15	connected	connect	VERB
ejpam-6438	504	16	metric	metric	ADJ
ejpam-6438	504	17	dimension	dimension	NOUN
ejpam-6438	504	18	acknowledgements	acknowledgement	NOUN
ejpam-6438	504	19	the	the	DET
ejpam-6438	504	20	researchers	researcher	NOUN
ejpam-6438	504	21	would	would	AUX
ejpam-6438	504	22	like	like	VERB
ejpam-6438	504	23	to	to	PART
ejpam-6438	504	24	thank	thank	VERB
ejpam-6438	504	25	the	the	DET
ejpam-6438	504	26	deanship	deanship	NOUN
ejpam-6438	504	27	of	of	ADP
ejpam-6438	504	28	graduate	graduate	NOUN
ejpam-6438	504	29	studies	study	NOUN
ejpam-6438	504	30	and	and	CCONJ
ejpam-6438	504	31	scientific	scientific	ADJ
ejpam-6438	504	32	research	research	NOUN
ejpam-6438	504	33	at	at	ADP
ejpam-6438	504	34	qassim	qassim	PROPN
ejpam-6438	504	35	university	university	PROPN
ejpam-6438	504	36	for	for	ADP
ejpam-6438	504	37	financial	financial	ADJ
ejpam-6438	504	38	support	support	NOUN
ejpam-6438	504	39	(	(	PUNCT
ejpam-6438	504	40	qu	qu	NOUN
ejpam-6438	504	41	-	-	NOUN
ejpam-6438	504	42	apc-2025	apc-2025	NOUN
ejpam-6438	504	43	)	)	PUNCT
ejpam-6438	504	44	.	.	PUNCT
ejpam-6438	505	1	a.	a.	PROPN
ejpam-6438	505	2	elrokh	elrokh	PROPN
ejpam-6438	505	3	,	,	PUNCT
ejpam-6438	505	4	eman	eman	PROPN
ejpam-6438	505	5	s.	s.	PROPN
ejpam-6438	505	6	almotairi	almotairi	PROPN
ejpam-6438	505	7	,	,	PUNCT
ejpam-6438	505	8	h.	h.	PROPN
ejpam-6438	505	9	mostafa	mostafa	PROPN
ejpam-6438	505	10	/	/	SYM
ejpam-6438	505	11	eur	eur	PROPN
ejpam-6438	505	12	.	.	PUNCT
ejpam-6438	506	1	j.	j.	PROPN
ejpam-6438	506	2	pure	pure	PROPN
ejpam-6438	506	3	appl	appl	PROPN
ejpam-6438	506	4	.	.	PROPN
ejpam-6438	506	5	math	math	PROPN
ejpam-6438	506	6	,	,	PUNCT
ejpam-6438	506	7	18	18	NUM
ejpam-6438	506	8	(	(	PUNCT
ejpam-6438	506	9	3	3	NUM
ejpam-6438	506	10	)	)	PUNCT
ejpam-6438	506	11	(	(	PUNCT
ejpam-6438	506	12	2025	2025	NUM
ejpam-6438	506	13	)	)	PUNCT
ejpam-6438	506	14	,	,	PUNCT
ejpam-6438	506	15	6438	6438	NUM
ejpam-6438	506	16	17	17	NUM
ejpam-6438	506	17	of	of	ADP
ejpam-6438	506	18	18	18	NUM
ejpam-6438	506	19	data	datum	NOUN
ejpam-6438	506	20	availability	availability	NOUN
ejpam-6438	506	21	statement	statement	NOUN
ejpam-6438	506	22	all	all	DET
ejpam-6438	506	23	data	datum	NOUN
ejpam-6438	506	24	generated	generate	VERB
ejpam-6438	506	25	or	or	CCONJ
ejpam-6438	506	26	analyzed	analyze	VERB
ejpam-6438	506	27	during	during	ADP
ejpam-6438	506	28	this	this	DET
ejpam-6438	506	29	study	study	NOUN
ejpam-6438	506	30	are	be	AUX
ejpam-6438	506	31	included	include	VERB
ejpam-6438	506	32	in	in	ADP
ejpam-6438	506	33	this	this	DET
ejpam-6438	506	34	published	publish	VERB
ejpam-6438	506	35	article	article	NOUN
ejpam-6438	506	36	.	.	PUNCT
ejpam-6438	507	1	references	reference	NOUN
ejpam-6438	507	2	[	[	X
ejpam-6438	507	3	1	1	NUM
ejpam-6438	507	4	]	]	PUNCT
ejpam-6438	507	5	p.	p.	PROPN
ejpam-6438	507	6	j.	j.	PROPN
ejpam-6438	507	7	slater	slater	PROPN
ejpam-6438	507	8	.	.	PUNCT
ejpam-6438	508	1	leaves	leave	NOUN
ejpam-6438	508	2	of	of	ADP
ejpam-6438	508	3	trees	tree	NOUN
ejpam-6438	508	4	.	.	PUNCT
ejpam-6438	509	1	congressus	congressus	PROPN
ejpam-6438	509	2	numerantium	numerantium	PROPN
ejpam-6438	509	3	,	,	PUNCT
ejpam-6438	509	4	14:549–559	14:549–559	NUM
ejpam-6438	509	5	,	,	PUNCT
ejpam-6438	509	6	1975	1975	NUM
ejpam-6438	509	7	.	.	PUNCT
ejpam-6438	510	1	in	in	ADP
ejpam-6438	510	2	proc	proc	NOUN
ejpam-6438	510	3	.	.	PUNCT
ejpam-6438	511	1	6th	6th	ADJ
ejpam-6438	511	2	southeastern	southeastern	ADJ
ejpam-6438	511	3	conf	conf	NOUN
ejpam-6438	511	4	.	.	PUNCT
ejpam-6438	512	1	combinatorics	combinatoric	NOUN
ejpam-6438	512	2	,	,	PUNCT
ejpam-6438	512	3	graph	graph	NOUN
ejpam-6438	512	4	theory	theory	NOUN
ejpam-6438	512	5	,	,	PUNCT
ejpam-6438	512	6	comput	comput	NOUN
ejpam-6438	512	7	.	.	PUNCT
ejpam-6438	512	8	,	,	PUNCT
ejpam-6438	512	9	the	the	DET
ejpam-6438	512	10	netherlands	netherlands	PROPN
ejpam-6438	512	11	.	.	PUNCT
ejpam-6438	513	1	[	[	X
ejpam-6438	513	2	2	2	X
ejpam-6438	513	3	]	]	PUNCT
ejpam-6438	513	4	f.	f.	PROPN
ejpam-6438	513	5	harary	harary	PROPN
ejpam-6438	513	6	and	and	CCONJ
ejpam-6438	513	7	r.	r.	PROPN
ejpam-6438	513	8	a.	a.	NOUN
ejpam-6438	513	9	melter	melter	NOUN
ejpam-6438	513	10	.	.	PUNCT
ejpam-6438	514	1	on	on	ADP
ejpam-6438	514	2	the	the	DET
ejpam-6438	514	3	metric	metric	ADJ
ejpam-6438	514	4	dimension	dimension	NOUN
ejpam-6438	514	5	of	of	ADP
ejpam-6438	514	6	a	a	DET
ejpam-6438	514	7	graph	graph	NOUN
ejpam-6438	514	8	.	.	PUNCT
ejpam-6438	514	9	ars	ars	PROPN
ejpam-6438	514	10	combinatoria	combinatoria	NOUN
ejpam-6438	514	11	,	,	PUNCT
ejpam-6438	514	12	2:191–195	2:191–195	NUM
ejpam-6438	514	13	,	,	PUNCT
ejpam-6438	514	14	1976	1976	NUM
ejpam-6438	514	15	.	.	PUNCT
ejpam-6438	515	1	[	[	X
ejpam-6438	515	2	3	3	X
ejpam-6438	515	3	]	]	X
ejpam-6438	515	4	g.	g.	PROPN
ejpam-6438	515	5	chartrand	chartrand	PROPN
ejpam-6438	515	6	,	,	PUNCT
ejpam-6438	515	7	l.	l.	PROPN
ejpam-6438	515	8	eroh	eroh	PROPN
ejpam-6438	515	9	,	,	PUNCT
ejpam-6438	515	10	m.	m.	NOUN
ejpam-6438	515	11	a.	a.	PROPN
ejpam-6438	515	12	johnson	johnson	PROPN
ejpam-6438	515	13	,	,	PUNCT
ejpam-6438	515	14	and	and	CCONJ
ejpam-6438	515	15	o.	o.	PROPN
ejpam-6438	515	16	r.	r.	PROPN
ejpam-6438	515	17	oellermann	oellermann	PROPN
ejpam-6438	515	18	.	.	PUNCT
ejpam-6438	516	1	resolvability	resolvability	NOUN
ejpam-6438	516	2	in	in	ADP
ejpam-6438	516	3	graphs	graph	NOUN
ejpam-6438	516	4	and	and	CCONJ
ejpam-6438	516	5	the	the	DET
ejpam-6438	516	6	metric	metric	ADJ
ejpam-6438	516	7	dimension	dimension	NOUN
ejpam-6438	516	8	of	of	ADP
ejpam-6438	516	9	a	a	DET
ejpam-6438	516	10	graph	graph	NOUN
ejpam-6438	516	11	.	.	PUNCT
ejpam-6438	517	1	discrete	discrete	ADJ
ejpam-6438	517	2	applied	apply	VERB
ejpam-6438	517	3	mathematics	mathematic	NOUN
ejpam-6438	517	4	,	,	PUNCT
ejpam-6438	517	5	105(1	105(1	PROPN
ejpam-6438	517	6	-	-	SYM
ejpam-6438	517	7	3):99–113	3):99–113	NUM
ejpam-6438	517	8	,	,	PUNCT
ejpam-6438	517	9	2000	2000	NUM
ejpam-6438	517	10	.	.	PUNCT
ejpam-6438	518	1	[	[	X
ejpam-6438	518	2	4	4	X
ejpam-6438	518	3	]	]	X
ejpam-6438	518	4	g.	g.	PROPN
ejpam-6438	518	5	chartrand	chartrand	PROPN
ejpam-6438	518	6	,	,	PUNCT
ejpam-6438	518	7	c.	c.	PROPN
ejpam-6438	518	8	poisson	poisson	PROPN
ejpam-6438	518	9	,	,	PUNCT
ejpam-6438	518	10	and	and	CCONJ
ejpam-6438	518	11	p.	p.	PROPN
ejpam-6438	518	12	zhang	zhang	PROPN
ejpam-6438	518	13	.	.	PUNCT
ejpam-6438	519	1	resolvability	resolvability	NOUN
ejpam-6438	519	2	and	and	CCONJ
ejpam-6438	519	3	the	the	DET
ejpam-6438	519	4	upper	upper	ADJ
ejpam-6438	519	5	dimension	dimension	NOUN
ejpam-6438	519	6	of	of	ADP
ejpam-6438	519	7	graphs	graph	NOUN
ejpam-6438	519	8	.	.	PUNCT
ejpam-6438	520	1	computers	computer	NOUN
ejpam-6438	520	2	and	and	CCONJ
ejpam-6438	520	3	mathematics	mathematic	NOUN
ejpam-6438	520	4	with	with	ADP
ejpam-6438	520	5	applications	application	NOUN
ejpam-6438	520	6	,	,	PUNCT
ejpam-6438	520	7	39(12):19–28	39(12):19–28	NUM
ejpam-6438	520	8	,	,	PUNCT
ejpam-6438	520	9	2000	2000	NUM
ejpam-6438	520	10	.	.	PUNCT
ejpam-6438	521	1	[	[	X
ejpam-6438	521	2	5	5	X
ejpam-6438	521	3	]	]	PUNCT
ejpam-6438	521	4	s.	s.	PROPN
ejpam-6438	521	5	khuller	khuller	PROPN
ejpam-6438	521	6	,	,	PUNCT
ejpam-6438	521	7	b.	b.	PROPN
ejpam-6438	521	8	raghavachari	raghavachari	PROPN
ejpam-6438	521	9	,	,	PUNCT
ejpam-6438	521	10	and	and	CCONJ
ejpam-6438	521	11	a.	a.	NOUN
ejpam-6438	521	12	rosenfeld	rosenfeld	PROPN
ejpam-6438	521	13	.	.	PUNCT
ejpam-6438	522	1	landmarks	landmark	NOUN
ejpam-6438	522	2	in	in	ADP
ejpam-6438	522	3	graphs	graph	NOUN
ejpam-6438	522	4	.	.	PUNCT
ejpam-6438	523	1	discrete	discrete	ADJ
ejpam-6438	523	2	applied	apply	VERB
ejpam-6438	523	3	mathematics	mathematic	NOUN
ejpam-6438	523	4	,	,	PUNCT
ejpam-6438	523	5	70(3):217–229	70(3):217–229	PROPN
ejpam-6438	523	6	,	,	PUNCT
ejpam-6438	523	7	1996	1996	NUM
ejpam-6438	523	8	.	.	PUNCT
ejpam-6438	524	1	[	[	X
ejpam-6438	524	2	6	6	NUM
ejpam-6438	524	3	]	]	PUNCT
ejpam-6438	524	4	m.	m.	NOUN
ejpam-6438	524	5	imran	imran	PROPN
ejpam-6438	524	6	,	,	PUNCT
ejpam-6438	524	7	m.	m.	PROPN
ejpam-6438	524	8	k.	k.	PROPN
ejpam-6438	524	9	siddiqui	siddiqui	PROPN
ejpam-6438	524	10	,	,	PUNCT
ejpam-6438	524	11	and	and	CCONJ
ejpam-6438	524	12	r.	r.	PROPN
ejpam-6438	524	13	naeem	naeem	PROPN
ejpam-6438	524	14	.	.	PUNCT
ejpam-6438	525	1	on	on	ADP
ejpam-6438	525	2	the	the	DET
ejpam-6438	525	3	metric	metric	ADJ
ejpam-6438	525	4	dimension	dimension	NOUN
ejpam-6438	525	5	of	of	ADP
ejpam-6438	525	6	generalized	generalized	ADJ
ejpam-6438	525	7	petersen	petersen	NOUN
ejpam-6438	525	8	multigraphs	multigraph	NOUN
ejpam-6438	525	9	.	.	PUNCT
ejpam-6438	526	1	ieee	ieee	NOUN
ejpam-6438	526	2	access	access	NOUN
ejpam-6438	526	3	,	,	PUNCT
ejpam-6438	526	4	6:74328–74338	6:74328–74338	NUM
ejpam-6438	526	5	,	,	PUNCT
ejpam-6438	526	6	2018	2018	NUM
ejpam-6438	526	7	.	.	PUNCT
ejpam-6438	527	1	[	[	X
ejpam-6438	527	2	7	7	X
ejpam-6438	527	3	]	]	PUNCT
ejpam-6438	527	4	j.-b	j.-b	NOUN
ejpam-6438	527	5	.	.	PUNCT
ejpam-6438	528	1	liu	liu	PROPN
ejpam-6438	528	2	,	,	PUNCT
ejpam-6438	528	3	m.	m.	PROPN
ejpam-6438	528	4	f.	f.	PROPN
ejpam-6438	528	5	nadeem	nadeem	PROPN
ejpam-6438	528	6	,	,	PUNCT
ejpam-6438	528	7	h.	h.	PROPN
ejpam-6438	528	8	m.	m.	PROPN
ejpam-6438	528	9	a.	a.	NOUN
ejpam-6438	528	10	siddiqui	siddiqui	PROPN
ejpam-6438	528	11	,	,	PUNCT
ejpam-6438	528	12	and	and	CCONJ
ejpam-6438	528	13	w.	w.	PROPN
ejpam-6438	528	14	nazir	nazir	PROPN
ejpam-6438	528	15	.	.	PUNCT
ejpam-6438	529	1	computing	compute	VERB
ejpam-6438	529	2	metric	metric	ADJ
ejpam-6438	529	3	dimension	dimension	NOUN
ejpam-6438	529	4	of	of	ADP
ejpam-6438	529	5	certain	certain	ADJ
ejpam-6438	529	6	families	family	NOUN
ejpam-6438	529	7	of	of	ADP
ejpam-6438	529	8	toeplitz	toeplitz	NOUN
ejpam-6438	529	9	graphs	graph	NOUN
ejpam-6438	529	10	.	.	PUNCT
ejpam-6438	530	1	ieee	ieee	NOUN
ejpam-6438	530	2	access	access	NOUN
ejpam-6438	530	3	,	,	PUNCT
ejpam-6438	530	4	7:126734–126741	7:126734–126741	NUM
ejpam-6438	530	5	,	,	PUNCT
ejpam-6438	530	6	2019	2019	NUM
ejpam-6438	530	7	.	.	PUNCT
ejpam-6438	531	1	[	[	X
ejpam-6438	531	2	8	8	NUM
ejpam-6438	531	3	]	]	X
ejpam-6438	531	4	f.	f.	PROPN
ejpam-6438	531	5	s.	s.	PROPN
ejpam-6438	531	6	raj	raj	PROPN
ejpam-6438	531	7	and	and	CCONJ
ejpam-6438	531	8	a.	a.	PROPN
ejpam-6438	531	9	george	george	PROPN
ejpam-6438	531	10	.	.	PUNCT
ejpam-6438	532	1	on	on	ADP
ejpam-6438	532	2	the	the	DET
ejpam-6438	532	3	metric	metric	ADJ
ejpam-6438	532	4	dimension	dimension	NOUN
ejpam-6438	532	5	of	of	ADP
ejpam-6438	532	6	hdn	hdn	PROPN
ejpam-6438	532	7	3	3	NUM
ejpam-6438	532	8	and	and	CCONJ
ejpam-6438	532	9	phdn	phdn	ADJ
ejpam-6438	532	10	3	3	X
ejpam-6438	532	11	.	.	PUNCT
ejpam-6438	533	1	in	in	ADP
ejpam-6438	533	2	proceedings	proceeding	NOUN
ejpam-6438	533	3	of	of	ADP
ejpam-6438	533	4	the	the	DET
ejpam-6438	533	5	ieee	ieee	NOUN
ejpam-6438	533	6	international	international	PROPN
ejpam-6438	533	7	conference	conference	NOUN
ejpam-6438	533	8	on	on	ADP
ejpam-6438	533	9	power	power	NOUN
ejpam-6438	533	10	,	,	PUNCT
ejpam-6438	533	11	control	control	NOUN
ejpam-6438	533	12	,	,	PUNCT
ejpam-6438	533	13	signals	signal	NOUN
ejpam-6438	533	14	and	and	CCONJ
ejpam-6438	533	15	instrumentation	instrumentation	NOUN
ejpam-6438	533	16	engineering	engineering	NOUN
ejpam-6438	533	17	(	(	PUNCT
ejpam-6438	533	18	icpcsi	icpcsi	PROPN
ejpam-6438	533	19	)	)	PUNCT
ejpam-6438	533	20	,	,	PUNCT
ejpam-6438	533	21	pages	page	NOUN
ejpam-6438	533	22	1333–1336	1333–1336	NUM
ejpam-6438	533	23	,	,	PUNCT
ejpam-6438	533	24	september	september	PROPN
ejpam-6438	533	25	2017	2017	NUM
ejpam-6438	533	26	.	.	PUNCT
ejpam-6438	534	1	[	[	X
ejpam-6438	534	2	9	9	X
ejpam-6438	534	3	]	]	PUNCT
ejpam-6438	534	4	j.	j.	PROPN
ejpam-6438	534	5	currie	currie	PROPN
ejpam-6438	534	6	and	and	CCONJ
ejpam-6438	534	7	o.	o.	PROPN
ejpam-6438	534	8	r.	r.	PROPN
ejpam-6438	534	9	oellermann	oellermann	PROPN
ejpam-6438	534	10	.	.	PUNCT
ejpam-6438	535	1	the	the	DET
ejpam-6438	535	2	metric	metric	ADJ
ejpam-6438	535	3	dimension	dimension	NOUN
ejpam-6438	535	4	and	and	CCONJ
ejpam-6438	535	5	metric	metric	ADJ
ejpam-6438	535	6	independence	independence	NOUN
ejpam-6438	535	7	of	of	ADP
ejpam-6438	535	8	a	a	DET
ejpam-6438	535	9	graph	graph	NOUN
ejpam-6438	535	10	.	.	PUNCT
ejpam-6438	535	11	journal	journal	NOUN
ejpam-6438	535	12	of	of	ADP
ejpam-6438	535	13	combinatorial	combinatorial	ADJ
ejpam-6438	535	14	mathematics	mathematic	NOUN
ejpam-6438	535	15	and	and	CCONJ
ejpam-6438	535	16	combinatorial	combinatorial	ADJ
ejpam-6438	535	17	computing	computing	NOUN
ejpam-6438	535	18	,	,	PUNCT
ejpam-6438	535	19	39:157–167	39:157–167	NUM
ejpam-6438	535	20	,	,	PUNCT
ejpam-6438	535	21	2001	2001	NUM
ejpam-6438	535	22	.	.	PUNCT
ejpam-6438	536	1	[	[	X
ejpam-6438	536	2	10	10	NUM
ejpam-6438	536	3	]	]	PUNCT
ejpam-6438	536	4	p.	p.	PROPN
ejpam-6438	536	5	j.	j.	PROPN
ejpam-6438	536	6	slater	slater	PROPN
ejpam-6438	536	7	.	.	PUNCT
ejpam-6438	537	1	leaves	leave	NOUN
ejpam-6438	537	2	of	of	ADP
ejpam-6438	537	3	trees	tree	NOUN
ejpam-6438	537	4	.	.	PUNCT
ejpam-6438	538	1	congressus	congressus	PROPN
ejpam-6438	538	2	numerantium	numerantium	PROPN
ejpam-6438	538	3	,	,	PUNCT
ejpam-6438	538	4	14:549–559	14:549–559	NUM
ejpam-6438	538	5	,	,	PUNCT
ejpam-6438	538	6	1975	1975	NUM
ejpam-6438	538	7	.	.	PUNCT
ejpam-6438	539	1	[	[	X
ejpam-6438	539	2	11	11	NUM
ejpam-6438	539	3	]	]	PUNCT
ejpam-6438	539	4	p.	p.	PROPN
ejpam-6438	539	5	j.	j.	PROPN
ejpam-6438	539	6	slater	slater	PROPN
ejpam-6438	539	7	.	.	PUNCT
ejpam-6438	540	1	dominating	dominating	NOUN
ejpam-6438	540	2	and	and	CCONJ
ejpam-6438	540	3	reference	reference	NOUN
ejpam-6438	540	4	sets	set	NOUN
ejpam-6438	540	5	in	in	ADP
ejpam-6438	540	6	graphs	graph	NOUN
ejpam-6438	540	7	.	.	PUNCT
ejpam-6438	541	1	journal	journal	NOUN
ejpam-6438	541	2	of	of	ADP
ejpam-6438	541	3	mathematical	mathematical	ADJ
ejpam-6438	541	4	and	and	CCONJ
ejpam-6438	541	5	physical	physical	ADJ
ejpam-6438	541	6	sciences	science	NOUN
ejpam-6438	541	7	,	,	PUNCT
ejpam-6438	541	8	22:445–455	22:445–455	PROPN
ejpam-6438	541	9	,	,	PUNCT
ejpam-6438	541	10	1988	1988	NUM
ejpam-6438	541	11	.	.	PUNCT
ejpam-6438	542	1	[	[	X
ejpam-6438	542	2	12	12	NUM
ejpam-6438	542	3	]	]	PUNCT
ejpam-6438	542	4	j.	j.	PROPN
ejpam-6438	542	5	w.	w.	PROPN
ejpam-6438	542	6	essam	essam	PROPN
ejpam-6438	542	7	and	and	CCONJ
ejpam-6438	542	8	m.	m.	PROPN
ejpam-6438	542	9	e.	e.	PROPN
ejpam-6438	542	10	fisher	fisher	PROPN
ejpam-6438	542	11	.	.	PUNCT
ejpam-6438	543	1	some	some	DET
ejpam-6438	543	2	basic	basic	ADJ
ejpam-6438	543	3	definitions	definition	NOUN
ejpam-6438	543	4	in	in	ADP
ejpam-6438	543	5	graph	graph	NOUN
ejpam-6438	543	6	theory	theory	NOUN
ejpam-6438	543	7	.	.	PUNCT
ejpam-6438	544	1	reviews	review	NOUN
ejpam-6438	544	2	of	of	ADP
ejpam-6438	544	3	modern	modern	ADJ
ejpam-6438	544	4	physics	physic	NOUN
ejpam-6438	544	5	,	,	PUNCT
ejpam-6438	544	6	42(2):271	42(2):271	NOUN
ejpam-6438	544	7	,	,	PUNCT
ejpam-6438	544	8	1970	1970	NUM
ejpam-6438	544	9	.	.	PUNCT
ejpam-6438	545	1	[	[	X
ejpam-6438	545	2	13	13	NUM
ejpam-6438	545	3	]	]	X
ejpam-6438	545	4	d.	d.	PROPN
ejpam-6438	545	5	l.	l.	PROPN
ejpam-6438	545	6	boutin	boutin	PROPN
ejpam-6438	545	7	.	.	PUNCT
ejpam-6438	546	1	determining	determine	VERB
ejpam-6438	546	2	sets	set	NOUN
ejpam-6438	546	3	,	,	PUNCT
ejpam-6438	546	4	resolving	resolve	VERB
ejpam-6438	546	5	sets	set	NOUN
ejpam-6438	546	6	,	,	PUNCT
ejpam-6438	546	7	and	and	CCONJ
ejpam-6438	546	8	the	the	DET
ejpam-6438	546	9	exchange	exchange	NOUN
ejpam-6438	546	10	property	property	NOUN
ejpam-6438	546	11	.	.	PUNCT
ejpam-6438	547	1	graphs	graph	NOUN
ejpam-6438	547	2	and	and	CCONJ
ejpam-6438	547	3	combinatorics	combinatoric	NOUN
ejpam-6438	547	4	,	,	PUNCT
ejpam-6438	547	5	25(6):789–806	25(6):789–806	PROPN
ejpam-6438	547	6	,	,	PUNCT
ejpam-6438	547	7	2009	2009	NUM
ejpam-6438	547	8	.	.	PUNCT
ejpam-6438	548	1	[	[	X
ejpam-6438	548	2	14	14	NUM
ejpam-6438	548	3	]	]	X
ejpam-6438	548	4	l.	l.	PROPN
ejpam-6438	548	5	eroh	eroh	PROPN
ejpam-6438	548	6	,	,	PUNCT
ejpam-6438	548	7	c.	c.	PROPN
ejpam-6438	548	8	x.	x.	PROPN
ejpam-6438	548	9	kang	kang	PROPN
ejpam-6438	548	10	,	,	PUNCT
ejpam-6438	548	11	and	and	CCONJ
ejpam-6438	548	12	e.	e.	PROPN
ejpam-6438	548	13	yi	yi	PROPN
ejpam-6438	548	14	.	.	PUNCT
ejpam-6438	549	1	the	the	DET
ejpam-6438	549	2	connected	connect	VERB
ejpam-6438	549	3	metric	metric	ADJ
ejpam-6438	549	4	dimension	dimension	NOUN
ejpam-6438	549	5	at	at	ADP
ejpam-6438	549	6	a	a	DET
ejpam-6438	549	7	vertex	vertex	NOUN
ejpam-6438	549	8	of	of	ADP
ejpam-6438	549	9	a	a	DET
ejpam-6438	549	10	graph	graph	NOUN
ejpam-6438	549	11	.	.	PUNCT
ejpam-6438	550	1	theoretical	theoretical	ADJ
ejpam-6438	550	2	computer	computer	NOUN
ejpam-6438	550	3	science	science	NOUN
ejpam-6438	550	4	,	,	PUNCT
ejpam-6438	550	5	806:53–69	806:53–69	NUM
ejpam-6438	550	6	,	,	PUNCT
ejpam-6438	550	7	2020	2020	NUM
ejpam-6438	550	8	.	.	PUNCT
ejpam-6438	551	1	[	[	X
ejpam-6438	551	2	15	15	NUM
ejpam-6438	551	3	]	]	X
ejpam-6438	551	4	l.	l.	PROPN
ejpam-6438	551	5	susilowati	susilowati	PROPN
ejpam-6438	551	6	,	,	PUNCT
ejpam-6438	551	7	i.	i.	PROPN
ejpam-6438	551	8	sa’adah	sa’adah	PROPN
ejpam-6438	551	9	,	,	PUNCT
ejpam-6438	551	10	r.	r.	PROPN
ejpam-6438	551	11	z.	z.	PROPN
ejpam-6438	551	12	fauziyyah	fauziyyah	PROPN
ejpam-6438	551	13	,	,	PUNCT
ejpam-6438	551	14	and	and	CCONJ
ejpam-6438	551	15	a.	a.	NOUN
ejpam-6438	551	16	erfanian	erfanian	PROPN
ejpam-6438	551	17	.	.	PUNCT
ejpam-6438	552	1	the	the	DET
ejpam-6438	552	2	dominant	dominant	ADJ
ejpam-6438	552	3	metric	metric	ADJ
ejpam-6438	552	4	dimension	dimension	NOUN
ejpam-6438	552	5	of	of	ADP
ejpam-6438	552	6	graphs	graph	NOUN
ejpam-6438	552	7	.	.	PUNCT
ejpam-6438	553	1	heliyon	heliyon	NOUN
ejpam-6438	553	2	,	,	PUNCT
ejpam-6438	553	3	6(3):e03633	6(3):e03633	NUM
ejpam-6438	553	4	,	,	PUNCT
ejpam-6438	553	5	2020	2020	NUM
ejpam-6438	553	6	.	.	PUNCT
ejpam-6438	554	1	[	[	X
ejpam-6438	554	2	16	16	NUM
ejpam-6438	554	3	]	]	PUNCT
ejpam-6438	554	4	a.	a.	NOUN
ejpam-6438	554	5	m.	m.	NOUN
ejpam-6438	554	6	bibi	bibi	PROPN
ejpam-6438	554	7	.	.	PUNCT
ejpam-6438	555	1	split	split	VERB
ejpam-6438	555	2	and	and	CCONJ
ejpam-6438	555	3	non	non	ADJ
ejpam-6438	555	4	split	split	VERB
ejpam-6438	555	5	two	two	NUM
ejpam-6438	555	6	domination	domination	NOUN
ejpam-6438	555	7	number	number	NOUN
ejpam-6438	555	8	of	of	ADP
ejpam-6438	555	9	a	a	DET
ejpam-6438	555	10	graph	graph	NOUN
ejpam-6438	555	11	.	.	PUNCT
ejpam-6438	556	1	international	international	ADJ
ejpam-6438	556	2	journal	journal	NOUN
ejpam-6438	556	3	of	of	ADP
ejpam-6438	556	4	advanced	advanced	ADJ
ejpam-6438	556	5	research	research	NOUN
ejpam-6438	556	6	in	in	ADP
ejpam-6438	556	7	computer	computer	NOUN
ejpam-6438	556	8	science	science	NOUN
ejpam-6438	556	9	,	,	PUNCT
ejpam-6438	556	10	11(4):13–17	11(4):13–17	NUM
ejpam-6438	556	11	,	,	PUNCT
ejpam-6438	556	12	2020	2020	NUM
ejpam-6438	556	13	.	.	PUNCT
ejpam-6438	557	1	[	[	X
ejpam-6438	557	2	17	17	NUM
ejpam-6438	557	3	]	]	PUNCT
ejpam-6438	557	4	j.	j.	PROPN
ejpam-6438	557	5	mohamad	mohamad	PROPN
ejpam-6438	557	6	and	and	CCONJ
ejpam-6438	557	7	h.	h.	PROPN
ejpam-6438	557	8	rara	rara	PROPN
ejpam-6438	557	9	.	.	PUNCT
ejpam-6438	558	1	strong	strong	ADJ
ejpam-6438	558	2	resolving	resolve	VERB
ejpam-6438	558	3	hop	hop	NOUN
ejpam-6438	558	4	domination	domination	NOUN
ejpam-6438	558	5	in	in	ADP
ejpam-6438	558	6	graphs	graph	NOUN
ejpam-6438	558	7	.	.	PUNCT
ejpam-6438	559	1	european	european	ADJ
ejpam-6438	559	2	journal	journal	PROPN
ejpam-6438	559	3	of	of	ADP
ejpam-6438	559	4	pure	pure	ADJ
ejpam-6438	559	5	and	and	CCONJ
ejpam-6438	559	6	applied	applied	ADJ
ejpam-6438	559	7	mathematics	mathematic	NOUN
ejpam-6438	559	8	,	,	PUNCT
ejpam-6438	559	9	16(1):131–143	16(1):131–143	PROPN
ejpam-6438	559	10	,	,	PUNCT
ejpam-6438	559	11	2023	2023	NUM
ejpam-6438	559	12	.	.	PUNCT
ejpam-6438	560	1	[	[	X
ejpam-6438	560	2	18	18	NUM
ejpam-6438	560	3	]	]	X
ejpam-6438	560	4	s.	s.	PROPN
ejpam-6438	560	5	nada	nada	PROPN
ejpam-6438	560	6	,	,	PUNCT
ejpam-6438	560	7	a.	a.	NOUN
ejpam-6438	560	8	elrokh	elrokh	NOUN
ejpam-6438	560	9	,	,	PUNCT
ejpam-6438	560	10	and	and	CCONJ
ejpam-6438	560	11	atef	atef	PROPN
ejpam-6438	560	12	abd	abd	PROPN
ejpam-6438	560	13	el	el	PROPN
ejpam-6438	560	14	-	-	PROPN
ejpam-6438	560	15	hay	hay	PROPN
ejpam-6438	560	16	.	.	PUNCT
ejpam-6438	561	1	on	on	ADP
ejpam-6438	561	2	signed	sign	VERB
ejpam-6438	561	3	product	product	NOUN
ejpam-6438	561	4	cordial	cordial	ADJ
ejpam-6438	561	5	of	of	ADP
ejpam-6438	561	6	cone	cone	NOUN
ejpam-6438	561	7	graph	graph	NOUN
ejpam-6438	561	8	a.	a.	NOUN
ejpam-6438	561	9	elrokh	elrokh	NOUN
ejpam-6438	561	10	,	,	PUNCT
ejpam-6438	561	11	eman	eman	PROPN
ejpam-6438	561	12	s.	s.	PROPN
ejpam-6438	561	13	almotairi	almotairi	PROPN
ejpam-6438	561	14	,	,	PUNCT
ejpam-6438	561	15	h.	h.	PROPN
ejpam-6438	561	16	mostafa	mostafa	PROPN
ejpam-6438	561	17	/	/	SYM
ejpam-6438	561	18	eur	eur	PROPN
ejpam-6438	561	19	.	.	PUNCT
ejpam-6438	562	1	j.	j.	PROPN
ejpam-6438	562	2	pure	pure	PROPN
ejpam-6438	562	3	appl	appl	PROPN
ejpam-6438	562	4	.	.	PROPN
ejpam-6438	562	5	math	math	PROPN
ejpam-6438	562	6	,	,	PUNCT
ejpam-6438	562	7	18	18	NUM
ejpam-6438	562	8	(	(	PUNCT
ejpam-6438	562	9	3	3	NUM
ejpam-6438	562	10	)	)	PUNCT
ejpam-6438	562	11	(	(	PUNCT
ejpam-6438	562	12	2025	2025	NUM
ejpam-6438	562	13	)	)	PUNCT
ejpam-6438	562	14	,	,	PUNCT
ejpam-6438	562	15	6438	6438	NUM
ejpam-6438	562	16	18	18	NUM
ejpam-6438	562	17	of	of	ADP
ejpam-6438	562	18	18	18	NUM
ejpam-6438	562	19	and	and	CCONJ
ejpam-6438	562	20	its	its	PRON
ejpam-6438	562	21	second	second	ADJ
ejpam-6438	562	22	power	power	NOUN
ejpam-6438	562	23	.	.	PUNCT
ejpam-6438	563	1	turkish	turkish	ADJ
ejpam-6438	563	2	journal	journal	NOUN
ejpam-6438	563	3	of	of	ADP
ejpam-6438	563	4	computer	computer	NOUN
ejpam-6438	563	5	and	and	CCONJ
ejpam-6438	563	6	mathematics	mathematics	PROPN
ejpam-6438	563	7	education	education	NOUN
ejpam-6438	563	8	(	(	PUNCT
ejpam-6438	563	9	turcomat	turcomat	NOUN
ejpam-6438	563	10	)	)	PUNCT
ejpam-6438	563	11	,	,	PUNCT
ejpam-6438	563	12	13(3):597–606	13(3):597–606	NUM
ejpam-6438	563	13	,	,	PUNCT
ejpam-6438	563	14	2022	2022	NUM
ejpam-6438	563	15	.	.	PUNCT
ejpam-6438	564	1	[	[	X
ejpam-6438	564	2	19	19	NUM
ejpam-6438	564	3	]	]	X
ejpam-6438	564	4	o.	o.	PROPN
ejpam-6438	564	5	favaron	favaron	PROPN
ejpam-6438	564	6	,	,	PUNCT
ejpam-6438	564	7	h.	h.	PROPN
ejpam-6438	564	8	karami	karami	PROPN
ejpam-6438	564	9	,	,	PUNCT
ejpam-6438	564	10	r.	r.	PROPN
ejpam-6438	564	11	khoeilar	khoeilar	PROPN
ejpam-6438	564	12	,	,	PUNCT
ejpam-6438	564	13	and	and	CCONJ
ejpam-6438	564	14	s.	s.	PROPN
ejpam-6438	564	15	m.	m.	PROPN
ejpam-6438	564	16	sheikholeslami	sheikholeslami	PROPN
ejpam-6438	564	17	.	.	PUNCT
ejpam-6438	565	1	on	on	ADP
ejpam-6438	565	2	the	the	DET
ejpam-6438	565	3	roman	roman	ADJ
ejpam-6438	565	4	domination	domination	NOUN
ejpam-6438	565	5	number	number	NOUN
ejpam-6438	565	6	of	of	ADP
ejpam-6438	565	7	a	a	DET
ejpam-6438	565	8	graph	graph	NOUN
ejpam-6438	565	9	.	.	PUNCT
ejpam-6438	565	10	discrete	discrete	ADJ
ejpam-6438	565	11	mathematics	mathematic	NOUN
ejpam-6438	565	12	,	,	PUNCT
ejpam-6438	565	13	309(10):3447–3451	309(10):3447–3451	NUM
ejpam-6438	565	14	,	,	PUNCT
ejpam-6438	565	15	2009	2009	NUM
ejpam-6438	565	16	.	.	PUNCT
ejpam-6438	566	1	[	[	X
ejpam-6438	566	2	20	20	NUM
ejpam-6438	566	3	]	]	PUNCT
ejpam-6438	566	4	a.	a.	NOUN
ejpam-6438	566	5	elrokh	elrokh	NOUN
ejpam-6438	566	6	,	,	PUNCT
ejpam-6438	566	7	y.	y.	PROPN
ejpam-6438	566	8	elmshtaye	elmshtaye	VERB
ejpam-6438	566	9	,	,	PUNCT
ejpam-6438	566	10	and	and	CCONJ
ejpam-6438	566	11	atef	atef	PROPN
ejpam-6438	566	12	abd	abd	PROPN
ejpam-6438	566	13	el	el	PROPN
ejpam-6438	566	14	-	-	PROPN
ejpam-6438	566	15	hay	hay	PROPN
ejpam-6438	566	16	.	.	PUNCT
ejpam-6438	567	1	the	the	DET
ejpam-6438	567	2	cordiality	cordiality	NOUN
ejpam-6438	567	3	of	of	ADP
ejpam-6438	567	4	cone	cone	NOUN
ejpam-6438	567	5	and	and	CCONJ
ejpam-6438	567	6	lemniscate	lemniscate	PROPN
ejpam-6438	567	7	graphs	graph	NOUN
ejpam-6438	567	8	.	.	PUNCT
ejpam-6438	568	1	applied	apply	VERB
ejpam-6438	568	2	mathematics	mathematics	PROPN
ejpam-6438	568	3	&	&	CCONJ
ejpam-6438	568	4	information	information	NOUN
ejpam-6438	568	5	sciences	sciences	PROPN
ejpam-6438	568	6	,	,	PUNCT
ejpam-6438	568	7	16:1027–1034	16:1027–1034	NUM
ejpam-6438	568	8	,	,	PUNCT
ejpam-6438	568	9	2022	2022	NUM
ejpam-6438	568	10	.	.	PUNCT
ejpam-6438	569	1	[	[	X
ejpam-6438	569	2	21	21	NUM
ejpam-6438	569	3	]	]	PUNCT
ejpam-6438	569	4	a.	a.	NOUN
ejpam-6438	569	5	abd	abd	PROPN
ejpam-6438	569	6	el	el	PROPN
ejpam-6438	569	7	-	-	PROPN
ejpam-6438	569	8	hay	hay	PROPN
ejpam-6438	569	9	and	and	CCONJ
ejpam-6438	569	10	a.	a.	NOUN
ejpam-6438	569	11	rabie	rabie	PROPN
ejpam-6438	569	12	.	.	PUNCT
ejpam-6438	570	1	signed	sign	VERB
ejpam-6438	570	2	product	product	NOUN
ejpam-6438	570	3	cordial	cordial	ADJ
ejpam-6438	570	4	labeling	labeling	NOUN
ejpam-6438	570	5	of	of	ADP
ejpam-6438	570	6	corona	corona	NOUN
ejpam-6438	570	7	product	product	NOUN
ejpam-6438	570	8	between	between	ADP
ejpam-6438	570	9	paths	path	NOUN
ejpam-6438	570	10	and	and	CCONJ
ejpam-6438	570	11	second	second	ADJ
ejpam-6438	570	12	power	power	NOUN
ejpam-6438	570	13	of	of	ADP
ejpam-6438	570	14	fan	fan	NOUN
ejpam-6438	570	15	graphs	graph	NOUN
ejpam-6438	570	16	.	.	PUNCT
ejpam-6438	571	1	italian	italian	ADJ
ejpam-6438	571	2	journal	journal	NOUN
ejpam-6438	571	3	of	of	ADP
ejpam-6438	571	4	pure	pure	ADJ
ejpam-6438	571	5	and	and	CCONJ
ejpam-6438	571	6	applied	applied	ADJ
ejpam-6438	571	7	mathematics	mathematic	NOUN
ejpam-6438	571	8	,	,	PUNCT
ejpam-6438	571	9	48:287–294	48:287–294	NUM
ejpam-6438	571	10	,	,	PUNCT
ejpam-6438	571	11	2022	2022	NUM
ejpam-6438	571	12	.	.	PUNCT
ejpam-6438	572	1	[	[	X
ejpam-6438	572	2	22	22	NUM
ejpam-6438	572	3	]	]	PUNCT
ejpam-6438	572	4	ashraf	ashraf	NOUN
ejpam-6438	572	5	elrokh	elrokh	VERB
ejpam-6438	572	6	,	,	PUNCT
ejpam-6438	572	7	mohammed	mohammed	PROPN
ejpam-6438	572	8	m.	m.	PROPN
ejpam-6438	572	9	ali	ali	PROPN
ejpam-6438	572	10	al	al	PROPN
ejpam-6438	572	11	-	-	PUNCT
ejpam-6438	572	12	shamiri	shamiri	PROPN
ejpam-6438	572	13	,	,	PUNCT
ejpam-6438	572	14	and	and	CCONJ
ejpam-6438	572	15	atef	atef	PROPN
ejpam-6438	572	16	abd	abd	PROPN
ejpam-6438	572	17	el	el	PROPN
ejpam-6438	572	18	-	-	PROPN
ejpam-6438	572	19	hay	hay	PROPN
ejpam-6438	572	20	.	.	PUNCT
ejpam-6438	573	1	a	a	DET
ejpam-6438	573	2	novel	novel	ADJ
ejpam-6438	573	3	problem	problem	NOUN
ejpam-6438	573	4	for	for	ADP
ejpam-6438	573	5	solving	solve	VERB
ejpam-6438	573	6	permuted	permute	VERB
ejpam-6438	573	7	cordial	cordial	ADJ
ejpam-6438	573	8	labeling	labeling	NOUN
ejpam-6438	573	9	of	of	ADP
ejpam-6438	573	10	graphs	graph	NOUN
ejpam-6438	573	11	.	.	PUNCT
ejpam-6438	574	1	symmetry	symmetry	NOUN
ejpam-6438	574	2	,	,	PUNCT
ejpam-6438	574	3	15(4):825	15(4):825	PROPN
ejpam-6438	574	4	,	,	PUNCT
ejpam-6438	574	5	2023	2023	NUM
ejpam-6438	574	6	.	.	PUNCT
ejpam-6438	575	1	[	[	X
ejpam-6438	575	2	23	23	NUM
ejpam-6438	575	3	]	]	X
ejpam-6438	575	4	atef	atef	PROPN
ejpam-6438	575	5	abd	abd	PROPN
ejpam-6438	575	6	el	el	PROPN
ejpam-6438	575	7	-	-	PROPN
ejpam-6438	575	8	hay	hay	PROPN
ejpam-6438	575	9	and	and	CCONJ
ejpam-6438	575	10	a.	a.	NOUN
ejpam-6438	575	11	elrokh	elrokh	PROPN
ejpam-6438	575	12	.	.	PUNCT
ejpam-6438	576	1	total	total	ADJ
ejpam-6438	576	2	cordial	cordial	ADJ
ejpam-6438	576	3	labeling	labeling	NOUN
ejpam-6438	576	4	of	of	ADP
ejpam-6438	576	5	corona	corona	NOUN
ejpam-6438	576	6	product	product	NOUN
ejpam-6438	576	7	of	of	ADP
ejpam-6438	576	8	paths	path	NOUN
ejpam-6438	576	9	and	and	CCONJ
ejpam-6438	576	10	second	second	ADJ
ejpam-6438	576	11	power	power	NOUN
ejpam-6438	576	12	of	of	ADP
ejpam-6438	576	13	fan	fan	NOUN
ejpam-6438	576	14	graph	graph	NOUN
ejpam-6438	576	15	.	.	PUNCT
ejpam-6438	577	1	turkish	turkish	ADJ
ejpam-6438	577	2	journal	journal	NOUN
ejpam-6438	577	3	of	of	ADP
ejpam-6438	577	4	computer	computer	NOUN
ejpam-6438	577	5	and	and	CCONJ
ejpam-6438	577	6	mathematics	mathematics	PROPN
ejpam-6438	577	7	education	education	NOUN
ejpam-6438	577	8	(	(	PUNCT
ejpam-6438	577	9	turcomat	turcomat	NOUN
ejpam-6438	577	10	)	)	PUNCT
ejpam-6438	577	11	,	,	PUNCT
ejpam-6438	577	12	13(3):681–690	13(3):681–690	PROPN
ejpam-6438	577	13	,	,	PUNCT
ejpam-6438	577	14	2022	2022	NUM
ejpam-6438	577	15	.	.	PUNCT
ejpam-6438	578	1	[	[	X
ejpam-6438	578	2	24	24	NUM
ejpam-6438	578	3	]	]	PUNCT
ejpam-6438	578	4	ashraf	ashraf	NOUN
ejpam-6438	578	5	elrokh	elrokh	VERB
ejpam-6438	578	6	,	,	PUNCT
ejpam-6438	578	7	mohammed	mohammed	PROPN
ejpam-6438	578	8	m.	m.	PROPN
ejpam-6438	578	9	ali	ali	PROPN
ejpam-6438	578	10	al	al	PROPN
ejpam-6438	578	11	-	-	PUNCT
ejpam-6438	578	12	shamiri	shamiri	PROPN
ejpam-6438	578	13	,	,	PUNCT
ejpam-6438	578	14	and	and	CCONJ
ejpam-6438	578	15	atef	atef	PROPN
ejpam-6438	578	16	abd	abd	PROPN
ejpam-6438	578	17	el	el	PROPN
ejpam-6438	578	18	-	-	PROPN
ejpam-6438	578	19	hay	hay	PROPN
ejpam-6438	578	20	.	.	PUNCT
ejpam-6438	579	1	a	a	DET
ejpam-6438	579	2	novel	novel	ADJ
ejpam-6438	579	3	radio	radio	NOUN
ejpam-6438	579	4	geometric	geometric	ADJ
ejpam-6438	579	5	mean	mean	NOUN
ejpam-6438	579	6	algorithm	algorithm	NOUN
ejpam-6438	579	7	for	for	ADP
ejpam-6438	579	8	a	a	DET
ejpam-6438	579	9	graph	graph	NOUN
ejpam-6438	579	10	.	.	PUNCT
ejpam-6438	579	11	symmetry	symmetry	NOUN
ejpam-6438	579	12	,	,	PUNCT
ejpam-6438	579	13	15(3):570	15(3):570	NOUN
ejpam-6438	579	14	,	,	PUNCT
ejpam-6438	579	15	2023	2023	NUM
ejpam-6438	579	16	.	.	PUNCT
ejpam-6438	580	1	[	[	X
ejpam-6438	580	2	25	25	NUM
ejpam-6438	580	3	]	]	PUNCT
ejpam-6438	580	4	a.	a.	NOUN
ejpam-6438	580	5	abd	abd	PROPN
ejpam-6438	580	6	el	el	PROPN
ejpam-6438	580	7	-	-	PROPN
ejpam-6438	580	8	hay	hay	PROPN
ejpam-6438	580	9	,	,	PUNCT
ejpam-6438	580	10	y.	y.	PROPN
ejpam-6438	580	11	elmshtaye	elmshtaye	VERB
ejpam-6438	580	12	,	,	PUNCT
ejpam-6438	580	13	and	and	CCONJ
ejpam-6438	580	14	a.	a.	NOUN
ejpam-6438	580	15	elrokh	elrokh	NOUN
ejpam-6438	580	16	.	.	PUNCT
ejpam-6438	581	1	solving	solve	VERB
ejpam-6438	581	2	signed	sign	VERB
ejpam-6438	581	3	product	product	NOUN
ejpam-6438	581	4	cordial	cordial	ADJ
ejpam-6438	581	5	labeling	labeling	NOUN
ejpam-6438	581	6	of	of	ADP
ejpam-6438	581	7	corona	corona	NOUN
ejpam-6438	581	8	products	product	NOUN
ejpam-6438	581	9	of	of	ADP
ejpam-6438	581	10	paths	path	NOUN
ejpam-6438	581	11	and	and	CCONJ
ejpam-6438	581	12	the	the	DET
ejpam-6438	581	13	third	third	ADJ
ejpam-6438	581	14	power	power	NOUN
ejpam-6438	581	15	of	of	ADP
ejpam-6438	581	16	lemniscate	lemniscate	PROPN
ejpam-6438	581	17	graphs	graph	NOUN
ejpam-6438	581	18	.	.	PUNCT
ejpam-6438	582	1	turkish	turkish	ADJ
ejpam-6438	582	2	journal	journal	NOUN
ejpam-6438	582	3	of	of	ADP
ejpam-6438	582	4	computer	computer	NOUN
ejpam-6438	582	5	and	and	CCONJ
ejpam-6438	582	6	mathematics	mathematics	PROPN
ejpam-6438	582	7	education	education	NOUN
ejpam-6438	582	8	(	(	PUNCT
ejpam-6438	582	9	turcomat	turcomat	NOUN
ejpam-6438	582	10	)	)	PUNCT
ejpam-6438	582	11	,	,	PUNCT
ejpam-6438	582	12	14(2):806–823	14(2):806–823	NUM
ejpam-6438	582	13	,	,	PUNCT
ejpam-6438	582	14	2023	2023	NUM
ejpam-6438	582	15	.	.	PUNCT
ejpam-6438	583	1	[	[	X
ejpam-6438	583	2	26	26	NUM
ejpam-6438	583	3	]	]	PUNCT
ejpam-6438	583	4	k.	k.	PROPN
ejpam-6438	583	5	a.	a.	PROPN
ejpam-6438	583	6	alsatami	alsatami	PROPN
ejpam-6438	583	7	,	,	PUNCT
ejpam-6438	583	8	y.	y.	PROPN
ejpam-6438	583	9	algrawani	algrawani	PROPN
ejpam-6438	583	10	,	,	PUNCT
ejpam-6438	583	11	and	and	CCONJ
ejpam-6438	583	12	a.	a.	PROPN
ejpam-6438	583	13	abd	abd	PROPN
ejpam-6438	583	14	el	el	PROPN
ejpam-6438	583	15	-	-	PROPN
ejpam-6438	583	16	hay	hay	PROPN
ejpam-6438	583	17	.	.	PUNCT
ejpam-6438	584	1	a	a	DET
ejpam-6438	584	2	novel	novel	ADJ
ejpam-6438	584	3	problem	problem	NOUN
ejpam-6438	584	4	and	and	CCONJ
ejpam-6438	584	5	algorithm	algorithm	NOUN
ejpam-6438	584	6	for	for	ADP
ejpam-6438	584	7	solving	solve	VERB
ejpam-6438	584	8	permuted	permute	VERB
ejpam-6438	584	9	cordial	cordial	ADJ
ejpam-6438	584	10	labeling	labeling	NOUN
ejpam-6438	584	11	of	of	ADP
ejpam-6438	584	12	corona	corona	NOUN
ejpam-6438	584	13	product	product	NOUN
ejpam-6438	584	14	between	between	ADP
ejpam-6438	584	15	two	two	NUM
ejpam-6438	584	16	graphs	graph	NOUN
ejpam-6438	584	17	.	.	PUNCT
ejpam-6438	585	1	mathematical	mathematical	ADJ
ejpam-6438	585	2	models	model	NOUN
ejpam-6438	585	3	in	in	ADP
ejpam-6438	585	4	engineering	engineering	NOUN
ejpam-6438	585	5	,	,	PUNCT
ejpam-6438	585	6	11(1):1–11	11(1):1–11	NUM
ejpam-6438	585	7	,	,	PUNCT
ejpam-6438	585	8	2025	2025	NUM
ejpam-6438	585	9	.	.	PUNCT
ejpam-6438	586	1	[	[	X
ejpam-6438	586	2	27	27	NUM
ejpam-6438	586	3	]	]	X
ejpam-6438	586	4	atef	atef	PROPN
ejpam-6438	586	5	abd	abd	PROPN
ejpam-6438	586	6	el	el	PROPN
ejpam-6438	586	7	-	-	PROPN
ejpam-6438	586	8	hay	hay	PROPN
ejpam-6438	586	9	,	,	PUNCT
ejpam-6438	586	10	khalid	khalid	PROPN
ejpam-6438	586	11	a.	a.	PROPN
ejpam-6438	586	12	alsatami	alsatami	PROPN
ejpam-6438	586	13	,	,	PUNCT
ejpam-6438	586	14	ashraf	ashraf	PROPN
ejpam-6438	586	15	elrokh	elrokh	VERB
ejpam-6438	586	16	,	,	PUNCT
ejpam-6438	586	17	and	and	CCONJ
ejpam-6438	586	18	aya	aya	PROPN
ejpam-6438	586	19	rabie	rabie	PROPN
ejpam-6438	586	20	.	.	PUNCT
ejpam-6438	587	1	cordial	cordial	ADJ
ejpam-6438	587	2	labeling	labeling	NOUN
ejpam-6438	587	3	of	of	ADP
ejpam-6438	587	4	corona	corona	NOUN
ejpam-6438	587	5	product	product	NOUN
ejpam-6438	587	6	of	of	ADP
ejpam-6438	587	7	paths	path	NOUN
ejpam-6438	587	8	and	and	CCONJ
ejpam-6438	587	9	fourth	fourth	ADJ
ejpam-6438	587	10	order	order	NOUN
ejpam-6438	587	11	of	of	ADP
ejpam-6438	587	12	lemniscate	lemniscate	PROPN
ejpam-6438	587	13	graphs	graph	NOUN
ejpam-6438	587	14	.	.	PUNCT
ejpam-6438	588	1	european	european	ADJ
ejpam-6438	588	2	journal	journal	PROPN
ejpam-6438	588	3	of	of	ADP
ejpam-6438	588	4	pure	pure	ADJ
ejpam-6438	588	5	and	and	CCONJ
ejpam-6438	588	6	applied	applied	ADJ
ejpam-6438	588	7	mathematics	mathematic	NOUN
ejpam-6438	588	8	,	,	PUNCT
ejpam-6438	588	9	18(1):5470	18(1):5470	NUM
ejpam-6438	588	10	,	,	PUNCT
ejpam-6438	588	11	2025	2025	NUM
ejpam-6438	588	12	.	.	PUNCT
ejpam-6438	589	1	[	[	X
ejpam-6438	589	2	28	28	NUM
ejpam-6438	589	3	]	]	X
ejpam-6438	589	4	atef	atef	PROPN
ejpam-6438	589	5	abd	abd	PROPN
ejpam-6438	589	6	el	el	PROPN
ejpam-6438	589	7	-	-	PROPN
ejpam-6438	589	8	hay	hay	PROPN
ejpam-6438	589	9	,	,	PUNCT
ejpam-6438	589	10	khalid	khalid	PROPN
ejpam-6438	589	11	a.	a.	PROPN
ejpam-6438	589	12	alsatami	alsatami	PROPN
ejpam-6438	589	13	,	,	PUNCT
ejpam-6438	589	14	and	and	CCONJ
ejpam-6438	589	15	ashraf	ashraf	PROPN
ejpam-6438	589	16	elrokh	elrokh	VERB
ejpam-6438	589	17	.	.	PUNCT
ejpam-6438	590	1	a	a	DET
ejpam-6438	590	2	novel	novel	ADJ
ejpam-6438	590	3	problem	problem	NOUN
ejpam-6438	590	4	and	and	CCONJ
ejpam-6438	590	5	algorithm	algorithm	NOUN
ejpam-6438	590	6	for	for	ADP
ejpam-6438	590	7	solving	solve	VERB
ejpam-6438	590	8	cordial	cordial	ADJ
ejpam-6438	590	9	labeling	labeling	NOUN
ejpam-6438	590	10	of	of	ADP
ejpam-6438	590	11	some	some	DET
ejpam-6438	590	12	fifth	fifth	ADJ
ejpam-6438	590	13	power	power	NOUN
ejpam-6438	590	14	of	of	ADP
ejpam-6438	590	15	graphs	graph	NOUN
ejpam-6438	590	16	.	.	PUNCT
ejpam-6438	591	1	european	european	ADJ
ejpam-6438	591	2	journal	journal	PROPN
ejpam-6438	591	3	of	of	ADP
ejpam-6438	591	4	pure	pure	ADJ
ejpam-6438	591	5	and	and	CCONJ
ejpam-6438	591	6	applied	applied	ADJ
ejpam-6438	591	7	mathematics	mathematic	NOUN
ejpam-6438	591	8	,	,	PUNCT
ejpam-6438	591	9	18(1):5812	18(1):5812	NUM
ejpam-6438	591	10	,	,	PUNCT
ejpam-6438	591	11	2025	2025	NUM
ejpam-6438	591	12	.	.	PUNCT
ejpam-6438	592	1	[	[	X
ejpam-6438	592	2	29	29	NUM
ejpam-6438	592	3	]	]	X
ejpam-6438	592	4	y.	y.	PROPN
ejpam-6438	592	5	elmshtaye	elmshtaye	PROPN
ejpam-6438	592	6	,	,	PUNCT
ejpam-6438	592	7	a.	a.	NOUN
ejpam-6438	592	8	elrokh	elrokh	NOUN
ejpam-6438	592	9	,	,	PUNCT
ejpam-6438	592	10	and	and	CCONJ
ejpam-6438	592	11	a.	a.	PROPN
ejpam-6438	592	12	abd	abd	PROPN
ejpam-6438	592	13	el	el	PROPN
ejpam-6438	592	14	-	-	PROPN
ejpam-6438	592	15	hay	hay	PROPN
ejpam-6438	592	16	.	.	PUNCT
ejpam-6438	593	1	total	total	PROPN
ejpam-6438	593	2	cordial	cordial	ADJ
ejpam-6438	593	3	for	for	ADP
ejpam-6438	593	4	the	the	DET
ejpam-6438	593	5	corona	corona	NOUN
ejpam-6438	593	6	product	product	NOUN
ejpam-6438	593	7	of	of	ADP
ejpam-6438	593	8	paths	path	NOUN
ejpam-6438	593	9	and	and	CCONJ
ejpam-6438	593	10	the	the	DET
ejpam-6438	593	11	third	third	ADJ
ejpam-6438	593	12	power	power	NOUN
ejpam-6438	593	13	of	of	ADP
ejpam-6438	593	14	double	double	ADJ
ejpam-6438	593	15	fans	fan	NOUN
ejpam-6438	593	16	-	-	PUNCT
ejpam-6438	593	17	generalized	generalize	VERB
ejpam-6438	593	18	fans	fan	NOUN
ejpam-6438	593	19	.	.	PUNCT
ejpam-6438	594	1	advances	advance	NOUN
ejpam-6438	594	2	and	and	CCONJ
ejpam-6438	594	3	applications	application	NOUN
ejpam-6438	594	4	in	in	ADP
ejpam-6438	594	5	discrete	discrete	ADJ
ejpam-6438	594	6	mathematics	mathematic	NOUN
ejpam-6438	594	7	,	,	PUNCT
ejpam-6438	594	8	42(4):303–334	42(4):303–334	PROPN
ejpam-6438	594	9	,	,	PUNCT
ejpam-6438	594	10	2025	2025	NUM
ejpam-6438	594	11	.	.	PUNCT