id	sid	tid	token	lemma	pos
ejpam-5555	1	1	european	european	PROPN
ejpam-5555	1	2	journal	journal	PROPN
ejpam-5555	1	3	of	of	ADP
ejpam-5555	1	4	pure	pure	ADJ
ejpam-5555	1	5	and	and	CCONJ
ejpam-5555	1	6	applied	applied	ADJ
ejpam-5555	1	7	mathematics	mathematic	NOUN
ejpam-5555	1	8	2025	2025	NUM
ejpam-5555	1	9	,	,	PUNCT
ejpam-5555	1	10	vol	vol	NOUN
ejpam-5555	1	11	.	.	PROPN
ejpam-5555	1	12	18	18	NUM
ejpam-5555	1	13	,	,	PUNCT
ejpam-5555	1	14	issue	issue	NOUN
ejpam-5555	1	15	1	1	NUM
ejpam-5555	1	16	,	,	PUNCT
ejpam-5555	1	17	article	article	NOUN
ejpam-5555	1	18	number	number	NOUN
ejpam-5555	1	19	5555	5555	NUM
ejpam-5555	1	20	issn	issn	VERB
ejpam-5555	1	21	1307	1307	NUM
ejpam-5555	1	22	-	-	SYM
ejpam-5555	1	23	5543	5543	NUM
ejpam-5555	1	24	–	–	PUNCT
ejpam-5555	1	25	ejpam.com	ejpam.com	X
ejpam-5555	1	26	published	publish	VERB
ejpam-5555	1	27	by	by	ADP
ejpam-5555	1	28	new	new	PROPN
ejpam-5555	1	29	york	york	PROPN
ejpam-5555	1	30	business	business	PROPN
ejpam-5555	1	31	global	global	PROPN
ejpam-5555	1	32	edge	edge	PROPN
ejpam-5555	1	33	geodetic	geodetic	ADJ
ejpam-5555	1	34	dominating	dominating	NOUN
ejpam-5555	1	35	sets	set	NOUN
ejpam-5555	1	36	of	of	ADP
ejpam-5555	1	37	some	some	DET
ejpam-5555	1	38	graphs	graph	NOUN
ejpam-5555	1	39	clint	clint	NOUN
ejpam-5555	1	40	joy	joy	PROPN
ejpam-5555	1	41	m.	m.	PROPN
ejpam-5555	1	42	quije1,2	quije1,2	PROPN
ejpam-5555	1	43	,	,	PUNCT
ejpam-5555	1	44	rochelleo	rochelleo	PROPN
ejpam-5555	1	45	e.	e.	PROPN
ejpam-5555	1	46	mariano3	mariano3	PROPN
ejpam-5555	1	47	,	,	PUNCT
ejpam-5555	1	48	eman	eman	PROPN
ejpam-5555	1	49	c.	c.	PROPN
ejpam-5555	1	50	ahmad3,∗	ahmad3,∗	PROPN
ejpam-5555	1	51	1	1	NUM
ejpam-5555	1	52	mathematics	mathematics	NOUN
ejpam-5555	1	53	department	department	NOUN
ejpam-5555	1	54	,	,	PUNCT
ejpam-5555	1	55	college	college	NOUN
ejpam-5555	1	56	of	of	ADP
ejpam-5555	1	57	science	science	NOUN
ejpam-5555	1	58	and	and	CCONJ
ejpam-5555	1	59	information	information	NOUN
ejpam-5555	1	60	technology	technology	NOUN
ejpam-5555	1	61	,	,	PUNCT
ejpam-5555	1	62	ateneo	ateneo	PROPN
ejpam-5555	1	63	de	de	PROPN
ejpam-5555	1	64	zamboanga	zamboanga	PROPN
ejpam-5555	1	65	university	university	PROPN
ejpam-5555	1	66	,	,	PUNCT
ejpam-5555	1	67	zamboanga	zamboanga	PROPN
ejpam-5555	1	68	city	city	PROPN
ejpam-5555	1	69	,	,	PUNCT
ejpam-5555	1	70	philippines	philippines	PROPN
ejpam-5555	1	71	2	2	NUM
ejpam-5555	1	72	institute	institute	NOUN
ejpam-5555	1	73	of	of	ADP
ejpam-5555	1	74	arts	art	NOUN
ejpam-5555	1	75	and	and	CCONJ
ejpam-5555	1	76	sciences	science	NOUN
ejpam-5555	1	77	,	,	PUNCT
ejpam-5555	1	78	tangub	tangub	NOUN
ejpam-5555	1	79	city	city	PROPN
ejpam-5555	1	80	global	global	PROPN
ejpam-5555	1	81	college	college	PROPN
ejpam-5555	1	82	,	,	PUNCT
ejpam-5555	1	83	tangub	tangub	NOUN
ejpam-5555	1	84	city	city	NOUN
ejpam-5555	1	85	,	,	PUNCT
ejpam-5555	1	86	philippines	philippines	PROPN
ejpam-5555	1	87	3	3	NUM
ejpam-5555	1	88	department	department	NOUN
ejpam-5555	1	89	of	of	ADP
ejpam-5555	1	90	mathematics	mathematic	NOUN
ejpam-5555	1	91	and	and	CCONJ
ejpam-5555	1	92	statistics	statistic	NOUN
ejpam-5555	1	93	,	,	PUNCT
ejpam-5555	1	94	college	college	NOUN
ejpam-5555	1	95	of	of	ADP
ejpam-5555	1	96	science	science	NOUN
ejpam-5555	1	97	and	and	CCONJ
ejpam-5555	1	98	mathematics	mathematic	NOUN
ejpam-5555	1	99	,	,	PUNCT
ejpam-5555	1	100	western	western	ADJ
ejpam-5555	1	101	mindanao	mindanao	PROPN
ejpam-5555	1	102	state	state	PROPN
ejpam-5555	1	103	university	university	PROPN
ejpam-5555	1	104	,	,	PUNCT
ejpam-5555	1	105	zamboanga	zamboanga	PROPN
ejpam-5555	1	106	city	city	PROPN
ejpam-5555	1	107	,	,	PUNCT
ejpam-5555	1	108	philippines	philippine	NOUN
ejpam-5555	1	109	abstract	abstract	ADJ
ejpam-5555	1	110	.	.	PUNCT
ejpam-5555	2	1	let	let	VERB
ejpam-5555	2	2	g	g	PRON
ejpam-5555	2	3	be	be	AUX
ejpam-5555	2	4	a	a	DET
ejpam-5555	2	5	simple	simple	ADJ
ejpam-5555	2	6	graph	graph	NOUN
ejpam-5555	2	7	.	.	PUNCT
ejpam-5555	3	1	a	a	DET
ejpam-5555	3	2	subset	subset	NOUN
ejpam-5555	3	3	d	d	NOUN
ejpam-5555	3	4	of	of	ADP
ejpam-5555	3	5	vertices	vertex	NOUN
ejpam-5555	3	6	in	in	ADP
ejpam-5555	3	7	g	g	PROPN
ejpam-5555	3	8	is	be	AUX
ejpam-5555	3	9	a	a	DET
ejpam-5555	3	10	dominating	dominating	NOUN
ejpam-5555	3	11	set	set	NOUN
ejpam-5555	3	12	of	of	ADP
ejpam-5555	3	13	g	g	PROPN
ejpam-5555	3	14	if	if	SCONJ
ejpam-5555	3	15	every	every	DET
ejpam-5555	3	16	vertex	vertex	NOUN
ejpam-5555	3	17	not	not	PART
ejpam-5555	3	18	in	in	ADP
ejpam-5555	3	19	d	d	PROPN
ejpam-5555	3	20	has	have	AUX
ejpam-5555	3	21	at	at	ADV
ejpam-5555	3	22	least	least	ADV
ejpam-5555	3	23	one	one	NUM
ejpam-5555	3	24	neighbor	neighbor	NOUN
ejpam-5555	3	25	in	in	ADP
ejpam-5555	3	26	d.	d.	PROPN
ejpam-5555	3	27	the	the	DET
ejpam-5555	3	28	domination	domination	NOUN
ejpam-5555	3	29	number	number	PROPN
ejpam-5555	3	30	γ(g	γ(g	PROPN
ejpam-5555	3	31	)	)	PUNCT
ejpam-5555	3	32	of	of	ADP
ejpam-5555	3	33	g	g	PROPN
ejpam-5555	3	34	is	be	AUX
ejpam-5555	3	35	the	the	DET
ejpam-5555	3	36	minimum	minimum	ADJ
ejpam-5555	3	37	cardinality	cardinality	NOUN
ejpam-5555	3	38	of	of	ADP
ejpam-5555	3	39	a	a	DET
ejpam-5555	3	40	dominating	dominating	NOUN
ejpam-5555	3	41	set	set	NOUN
ejpam-5555	3	42	of	of	ADP
ejpam-5555	3	43	g.	g.	PROPN
ejpam-5555	3	44	an	an	DET
ejpam-5555	3	45	edge	edge	NOUN
ejpam-5555	3	46	geodetic	geodetic	ADJ
ejpam-5555	3	47	set	set	NOUN
ejpam-5555	3	48	of	of	ADP
ejpam-5555	3	49	g	g	PROPN
ejpam-5555	3	50	is	be	AUX
ejpam-5555	3	51	a	a	DET
ejpam-5555	3	52	set	set	NOUN
ejpam-5555	3	53	s	s	NOUN
ejpam-5555	3	54	⊆	⊆	NUM
ejpam-5555	3	55	v	v	NOUN
ejpam-5555	3	56	(	(	PUNCT
ejpam-5555	3	57	g	g	NOUN
ejpam-5555	3	58	)	)	PUNCT
ejpam-5555	3	59	such	such	ADJ
ejpam-5555	3	60	that	that	SCONJ
ejpam-5555	3	61	every	every	DET
ejpam-5555	3	62	edge	edge	NOUN
ejpam-5555	3	63	of	of	ADP
ejpam-5555	3	64	g	g	NOUN
ejpam-5555	3	65	is	be	AUX
ejpam-5555	3	66	contained	contain	VERB
ejpam-5555	3	67	in	in	ADP
ejpam-5555	3	68	a	a	DET
ejpam-5555	3	69	geodetic	geodetic	NOUN
ejpam-5555	3	70	joining	join	VERB
ejpam-5555	3	71	some	some	DET
ejpam-5555	3	72	pair	pair	NOUN
ejpam-5555	3	73	of	of	ADP
ejpam-5555	3	74	vertices	vertex	NOUN
ejpam-5555	3	75	in	in	ADP
ejpam-5555	3	76	s.	s.	PROPN
ejpam-5555	3	77	the	the	DET
ejpam-5555	3	78	edge	edge	NOUN
ejpam-5555	3	79	geodetic	geodetic	ADJ
ejpam-5555	3	80	number	number	NOUN
ejpam-5555	3	81	ge(g	ge(g	PROPN
ejpam-5555	3	82	)	)	PUNCT
ejpam-5555	3	83	of	of	ADP
ejpam-5555	3	84	g	g	PROPN
ejpam-5555	3	85	is	be	AUX
ejpam-5555	3	86	the	the	DET
ejpam-5555	3	87	minimum	minimum	ADJ
ejpam-5555	3	88	cardinality	cardinality	NOUN
ejpam-5555	3	89	of	of	ADP
ejpam-5555	3	90	edge	edge	NOUN
ejpam-5555	3	91	geodetic	geodetic	ADJ
ejpam-5555	3	92	set	set	NOUN
ejpam-5555	3	93	.	.	PUNCT
ejpam-5555	4	1	a	a	DET
ejpam-5555	4	2	set	set	NOUN
ejpam-5555	4	3	of	of	ADP
ejpam-5555	4	4	vertices	vertex	NOUN
ejpam-5555	4	5	s	s	PART
ejpam-5555	4	6	in	in	ADP
ejpam-5555	4	7	g	g	PROPN
ejpam-5555	4	8	is	be	AUX
ejpam-5555	4	9	an	an	DET
ejpam-5555	4	10	edge	edge	NOUN
ejpam-5555	4	11	geodetic	geodetic	ADJ
ejpam-5555	4	12	dominating	dominating	NOUN
ejpam-5555	4	13	set	set	NOUN
ejpam-5555	4	14	of	of	ADP
ejpam-5555	4	15	g	g	PROPN
ejpam-5555	4	16	if	if	SCONJ
ejpam-5555	4	17	s	s	VERB
ejpam-5555	4	18	is	be	AUX
ejpam-5555	4	19	both	both	PRON
ejpam-5555	4	20	an	an	DET
ejpam-5555	4	21	edge	edge	NOUN
ejpam-5555	4	22	geodetic	geodetic	ADJ
ejpam-5555	4	23	set	set	NOUN
ejpam-5555	4	24	and	and	CCONJ
ejpam-5555	4	25	a	a	DET
ejpam-5555	4	26	dominating	dominating	NOUN
ejpam-5555	4	27	set	set	NOUN
ejpam-5555	4	28	.	.	PUNCT
ejpam-5555	5	1	the	the	DET
ejpam-5555	5	2	minimum	minimum	ADJ
ejpam-5555	5	3	cardinality	cardinality	NOUN
ejpam-5555	5	4	of	of	ADP
ejpam-5555	5	5	an	an	DET
ejpam-5555	5	6	edge	edge	NOUN
ejpam-5555	5	7	geodetic	geodetic	ADJ
ejpam-5555	5	8	dominating	dominating	NOUN
ejpam-5555	5	9	set	set	NOUN
ejpam-5555	5	10	of	of	ADP
ejpam-5555	5	11	g	g	PROPN
ejpam-5555	5	12	is	be	AUX
ejpam-5555	5	13	its	its	PRON
ejpam-5555	5	14	edge	edge	NOUN
ejpam-5555	5	15	geodetic	geodetic	ADJ
ejpam-5555	5	16	domination	domination	NOUN
ejpam-5555	5	17	number	number	NOUN
ejpam-5555	5	18	and	and	CCONJ
ejpam-5555	5	19	is	be	AUX
ejpam-5555	5	20	denoted	denote	VERB
ejpam-5555	5	21	by	by	ADP
ejpam-5555	5	22	γge(g	γge(g	PROPN
ejpam-5555	5	23	)	)	PUNCT
ejpam-5555	5	24	.	.	PUNCT
ejpam-5555	6	1	in	in	ADP
ejpam-5555	6	2	this	this	DET
ejpam-5555	6	3	study	study	NOUN
ejpam-5555	6	4	,	,	PUNCT
ejpam-5555	6	5	we	we	PRON
ejpam-5555	6	6	determined	determine	VERB
ejpam-5555	6	7	the	the	DET
ejpam-5555	6	8	edge	edge	NOUN
ejpam-5555	6	9	geodetic	geodetic	ADJ
ejpam-5555	6	10	domination	domination	NOUN
ejpam-5555	6	11	number	number	NOUN
ejpam-5555	6	12	of	of	ADP
ejpam-5555	6	13	graphs	graph	NOUN
ejpam-5555	6	14	obtained	obtain	VERB
ejpam-5555	6	15	through	through	ADP
ejpam-5555	6	16	the	the	DET
ejpam-5555	6	17	deletion	deletion	NOUN
ejpam-5555	6	18	of	of	ADP
ejpam-5555	6	19	independent	independent	ADJ
ejpam-5555	6	20	edges	edge	NOUN
ejpam-5555	6	21	of	of	ADP
ejpam-5555	6	22	complete	complete	ADJ
ejpam-5555	6	23	graphs	graph	NOUN
ejpam-5555	6	24	and	and	CCONJ
ejpam-5555	6	25	graphs	graph	NOUN
ejpam-5555	6	26	resulting	result	VERB
ejpam-5555	6	27	from	from	ADP
ejpam-5555	6	28	the	the	DET
ejpam-5555	6	29	kr	kr	PROPN
ejpam-5555	6	30	-	-	PUNCT
ejpam-5555	6	31	gluing	gluing	NOUN
ejpam-5555	6	32	of	of	ADP
ejpam-5555	6	33	complete	complete	ADJ
ejpam-5555	6	34	graphs	graph	NOUN
ejpam-5555	6	35	.	.	PUNCT
ejpam-5555	7	1	it	it	PRON
ejpam-5555	7	2	is	be	AUX
ejpam-5555	7	3	also	also	ADV
ejpam-5555	7	4	shown	show	VERB
ejpam-5555	7	5	that	that	SCONJ
ejpam-5555	7	6	for	for	ADP
ejpam-5555	7	7	any	any	DET
ejpam-5555	7	8	positive	positive	ADJ
ejpam-5555	7	9	integers	integer	NOUN
ejpam-5555	7	10	2	2	NUM
ejpam-5555	7	11	≤	≤	NOUN
ejpam-5555	7	12	a	a	DET
ejpam-5555	7	13	≤	≤	NUM
ejpam-5555	7	14	b	b	NOUN
ejpam-5555	7	15	,	,	PUNCT
ejpam-5555	7	16	there	there	PRON
ejpam-5555	7	17	exists	exist	VERB
ejpam-5555	7	18	a	a	DET
ejpam-5555	7	19	connected	connected	ADJ
ejpam-5555	7	20	graph	graph	NOUN
ejpam-5555	7	21	g	g	ADP
ejpam-5555	7	22	such	such	ADJ
ejpam-5555	7	23	that	that	PRON
ejpam-5555	7	24	ge(g	ge(g	PUNCT
ejpam-5555	7	25	)	)	PUNCT
ejpam-5555	8	1	=	=	PUNCT
ejpam-5555	8	2	a	a	PROPN
ejpam-5555	8	3	and	and	CCONJ
ejpam-5555	8	4	γge(g	γge(g	PROPN
ejpam-5555	8	5	)	)	PUNCT
ejpam-5555	8	6	=	=	SYM
ejpam-5555	8	7	b.	b.	PROPN
ejpam-5555	8	8	2020	2020	NUM
ejpam-5555	8	9	mathematics	mathematics	PROPN
ejpam-5555	8	10	subject	subject	NOUN
ejpam-5555	8	11	classifications	classification	NOUN
ejpam-5555	8	12	:	:	PUNCT
ejpam-5555	8	13	05c69	05c69	NUM
ejpam-5555	8	14	,	,	PUNCT
ejpam-5555	8	15	05c76	05c76	DET
ejpam-5555	8	16	key	key	ADJ
ejpam-5555	8	17	words	word	NOUN
ejpam-5555	8	18	and	and	CCONJ
ejpam-5555	8	19	phrases	phrase	NOUN
ejpam-5555	8	20	:	:	PUNCT
ejpam-5555	8	21	dominating	dominate	VERB
ejpam-5555	8	22	set	set	NOUN
ejpam-5555	8	23	,	,	PUNCT
ejpam-5555	8	24	domination	domination	NOUN
ejpam-5555	8	25	number	number	NOUN
ejpam-5555	8	26	,	,	PUNCT
ejpam-5555	8	27	edge	edge	NOUN
ejpam-5555	8	28	geodetic	geodetic	ADJ
ejpam-5555	8	29	,	,	PUNCT
ejpam-5555	8	30	complete	complete	ADJ
ejpam-5555	8	31	graphs	graph	NOUN
ejpam-5555	8	32	,	,	PUNCT
ejpam-5555	8	33	deletion	deletion	NOUN
ejpam-5555	8	34	of	of	ADP
ejpam-5555	8	35	independent	independent	ADJ
ejpam-5555	8	36	edges	edge	NOUN
ejpam-5555	8	37	,	,	PUNCT
ejpam-5555	8	38	kr	kr	PROPN
ejpam-5555	8	39	-	-	PUNCT
ejpam-5555	8	40	gluing	gluing	NOUN
ejpam-5555	8	41	,	,	PUNCT
ejpam-5555	8	42	realization	realization	NOUN
ejpam-5555	8	43	result	result	NOUN
ejpam-5555	8	44	or	or	CCONJ
ejpam-5555	8	45	result	result	NOUN
ejpam-5555	8	46	of	of	ADP
ejpam-5555	8	47	comprehension	comprehension	NOUN
ejpam-5555	8	48	1	1	NUM
ejpam-5555	8	49	.	.	PUNCT
ejpam-5555	9	1	introduction	introduction	NOUN
ejpam-5555	9	2	several	several	ADJ
ejpam-5555	9	3	studies	study	NOUN
ejpam-5555	9	4	have	have	AUX
ejpam-5555	9	5	been	be	AUX
ejpam-5555	9	6	conducted	conduct	VERB
ejpam-5555	9	7	regarding	regard	VERB
ejpam-5555	9	8	geodetic	geodetic	ADJ
ejpam-5555	9	9	sets	set	NOUN
ejpam-5555	9	10	,	,	PUNCT
ejpam-5555	9	11	geodetic	geodetic	ADJ
ejpam-5555	9	12	bounds	bound	NOUN
ejpam-5555	9	13	and	and	CCONJ
ejpam-5555	9	14	edge	edge	VERB
ejpam-5555	9	15	geodetic	geodetic	ADJ
ejpam-5555	9	16	sets	set	NOUN
ejpam-5555	9	17	in	in	ADP
ejpam-5555	9	18	graphs	graph	NOUN
ejpam-5555	9	19	.	.	PUNCT
ejpam-5555	10	1	asdain	asdain	PROPN
ejpam-5555	10	2	et	et	PROPN
ejpam-5555	10	3	al	al	PROPN
ejpam-5555	10	4	.	.	PUNCT
ejpam-5555	11	1	[	[	X
ejpam-5555	11	2	1	1	NUM
ejpam-5555	11	3	]	]	PUNCT
ejpam-5555	11	4	,	,	PUNCT
ejpam-5555	11	5	chartrand	chartrand	PROPN
ejpam-5555	11	6	et	et	PROPN
ejpam-5555	11	7	al	al	PROPN
ejpam-5555	11	8	.	.	PUNCT
ejpam-5555	12	1	[	[	X
ejpam-5555	12	2	3	3	NUM
ejpam-5555	12	3	]	]	PUNCT
ejpam-5555	12	4	,	,	PUNCT
ejpam-5555	12	5	mariano	mariano	PROPN
ejpam-5555	12	6	and	and	CCONJ
ejpam-5555	12	7	canoy	canoy	ADJ
ejpam-5555	12	8	[	[	X
ejpam-5555	12	9	8	8	NUM
ejpam-5555	12	10	]	]	PUNCT
ejpam-5555	12	11	,	,	PUNCT
ejpam-5555	12	12	and	and	CCONJ
ejpam-5555	12	13	santhakumaran	santhakumaran	PROPN
ejpam-5555	12	14	and	and	CCONJ
ejpam-5555	12	15	john	john	PROPN
ejpam-5555	13	1	[	[	X
ejpam-5555	13	2	12	12	NUM
ejpam-5555	13	3	]	]	PUNCT
ejpam-5555	13	4	,	,	PUNCT
ejpam-5555	13	5	are	be	AUX
ejpam-5555	13	6	some	some	DET
ejpam-5555	13	7	researchers	researcher	NOUN
ejpam-5555	13	8	who	who	PRON
ejpam-5555	13	9	have	have	AUX
ejpam-5555	13	10	done	do	VERB
ejpam-5555	13	11	many	many	ADJ
ejpam-5555	13	12	results	result	NOUN
ejpam-5555	13	13	in	in	ADP
ejpam-5555	13	14	this	this	DET
ejpam-5555	13	15	area	area	NOUN
ejpam-5555	13	16	.	.	PUNCT
ejpam-5555	14	1	the	the	DET
ejpam-5555	14	2	results	result	NOUN
ejpam-5555	14	3	include	include	VERB
ejpam-5555	14	4	determining	determine	VERB
ejpam-5555	14	5	the	the	DET
ejpam-5555	14	6	geodetic	geodetic	ADJ
ejpam-5555	14	7	and	and	CCONJ
ejpam-5555	14	8	edge	edge	VERB
ejpam-5555	14	9	geodetic	geodetic	ADJ
ejpam-5555	14	10	number	number	NOUN
ejpam-5555	14	11	of	of	ADP
ejpam-5555	14	12	graphs	graph	NOUN
ejpam-5555	14	13	employing	employ	VERB
ejpam-5555	14	14	the	the	DET
ejpam-5555	14	15	unary	unary	ADJ
ejpam-5555	14	16	and	and	CCONJ
ejpam-5555	14	17	binary	binary	ADJ
ejpam-5555	14	18	operations	operation	NOUN
ejpam-5555	14	19	in	in	ADP
ejpam-5555	14	20	graphs	graph	NOUN
ejpam-5555	14	21	such	such	ADJ
ejpam-5555	14	22	as	as	ADP
ejpam-5555	14	23	,	,	PUNCT
ejpam-5555	14	24	the	the	DET
ejpam-5555	14	25	deletion	deletion	NOUN
ejpam-5555	14	26	of	of	ADP
ejpam-5555	14	27	independent	independent	ADJ
ejpam-5555	14	28	edges	edge	NOUN
ejpam-5555	14	29	of	of	ADP
ejpam-5555	14	30	complete	complete	ADJ
ejpam-5555	14	31	graphs	graph	NOUN
ejpam-5555	14	32	,	,	PUNCT
ejpam-5555	14	33	kr	kr	PROPN
ejpam-5555	14	34	-	-	PUNCT
ejpam-5555	14	35	gluing	gluing	NOUN
ejpam-5555	14	36	,	,	PUNCT
ejpam-5555	14	37	join	join	NOUN
ejpam-5555	14	38	,	,	PUNCT
ejpam-5555	14	39	corona	corona	NOUN
ejpam-5555	14	40	,	,	PUNCT
ejpam-5555	14	41	composition	composition	NOUN
ejpam-5555	14	42	,	,	PUNCT
ejpam-5555	14	43	and	and	CCONJ
ejpam-5555	14	44	cartesian	cartesian	ADJ
ejpam-5555	14	45	products	product	NOUN
ejpam-5555	14	46	of	of	ADP
ejpam-5555	14	47	graphs	graph	NOUN
ejpam-5555	14	48	,	,	PUNCT
ejpam-5555	14	49	among	among	ADP
ejpam-5555	14	50	others	other	NOUN
ejpam-5555	14	51	.	.	PUNCT
ejpam-5555	15	1	∗corresponding	∗corresponde	VERB
ejpam-5555	15	2	author	author	NOUN
ejpam-5555	15	3	.	.	PUNCT
ejpam-5555	16	1	doi	doi	NOUN
ejpam-5555	16	2	:	:	PUNCT
ejpam-5555	16	3	https://doi.org/10.29020/nybg.ejpam.v18i1.5555	https://doi.org/10.29020/nybg.ejpam.v18i1.5555	NUM
ejpam-5555	16	4	email	email	NOUN
ejpam-5555	16	5	addresses	address	NOUN
ejpam-5555	16	6	:	:	PUNCT
ejpam-5555	16	7	cjquije@gadtc.edu.ph	cjquije@gadtc.edu.ph	PROPN
ejpam-5555	16	8	(	(	PUNCT
ejpam-5555	16	9	c.j	c.j	NOUN
ejpam-5555	16	10	.	.	NOUN
ejpam-5555	16	11	quije	quije	PROPN
ejpam-5555	16	12	)	)	PUNCT
ejpam-5555	16	13	,	,	PUNCT
ejpam-5555	16	14	mariano.rochelleo@wmsu.edu.ph	mariano.rochelleo@wmsu.edu.ph	PROPN
ejpam-5555	16	15	(	(	PUNCT
ejpam-5555	16	16	r.	r.	PROPN
ejpam-5555	16	17	mariano	mariano	PROPN
ejpam-5555	16	18	)	)	PUNCT
ejpam-5555	16	19	,	,	PUNCT
ejpam-5555	16	20	ahmad.eman@wmsu.edu.ph	ahmad.eman@wmsu.edu.ph	PROPN
ejpam-5555	16	21	(	(	PUNCT
ejpam-5555	16	22	e.	e.	PROPN
ejpam-5555	16	23	ahmad	ahmad	PROPN
ejpam-5555	16	24	)	)	PUNCT
ejpam-5555	16	25	https://www.ejpam.com	https://www.ejpam.com	X
ejpam-5555	17	1	1	1	NUM
ejpam-5555	17	2	copyright	copyright	NOUN
ejpam-5555	17	3	:	:	PUNCT
ejpam-5555	17	4	©	©	PROPN
ejpam-5555	17	5	2025	2025	NUM
ejpam-5555	17	6	the	the	DET
ejpam-5555	17	7	author(s	author(s	NOUN
ejpam-5555	17	8	)	)	PUNCT
ejpam-5555	17	9	.	.	PUNCT
ejpam-5555	18	1	(	(	PUNCT
ejpam-5555	18	2	cc	cc	NOUN
ejpam-5555	18	3	by	by	ADP
ejpam-5555	18	4	-	-	PUNCT
ejpam-5555	18	5	nc	nc	PROPN
ejpam-5555	18	6	4.0	4.0	NUM
ejpam-5555	18	7	)	)	PUNCT
ejpam-5555	18	8	c.j	c.j	PROPN
ejpam-5555	18	9	.	.	PROPN
ejpam-5555	18	10	quije	quije	PROPN
ejpam-5555	18	11	,	,	PUNCT
ejpam-5555	18	12	r.	r.	PROPN
ejpam-5555	18	13	mariano	mariano	PROPN
ejpam-5555	18	14	,	,	PUNCT
ejpam-5555	18	15	e.	e.	PROPN
ejpam-5555	18	16	ahmad	ahmad	PROPN
ejpam-5555	18	17	/	/	SYM
ejpam-5555	18	18	eur	eur	PROPN
ejpam-5555	18	19	.	.	PUNCT
ejpam-5555	19	1	j.	j.	PROPN
ejpam-5555	19	2	pure	pure	PROPN
ejpam-5555	19	3	appl	appl	PROPN
ejpam-5555	19	4	.	.	PROPN
ejpam-5555	19	5	math	math	PROPN
ejpam-5555	19	6	,	,	PUNCT
ejpam-5555	19	7	18	18	NUM
ejpam-5555	19	8	(	(	PUNCT
ejpam-5555	19	9	1	1	NUM
ejpam-5555	19	10	)	)	PUNCT
ejpam-5555	19	11	(	(	PUNCT
ejpam-5555	19	12	2025	2025	NUM
ejpam-5555	19	13	)	)	PUNCT
ejpam-5555	19	14	,	,	PUNCT
ejpam-5555	19	15	5555	5555	NUM
ejpam-5555	19	16	2	2	NUM
ejpam-5555	19	17	of	of	ADP
ejpam-5555	19	18	8	8	NUM
ejpam-5555	19	19	besides	besides	SCONJ
ejpam-5555	19	20	geodetic	geodetic	ADJ
ejpam-5555	19	21	set	set	NOUN
ejpam-5555	19	22	and	and	CCONJ
ejpam-5555	19	23	edge	edge	VERB
ejpam-5555	19	24	geodetic	geodetic	ADJ
ejpam-5555	19	25	sets	set	NOUN
ejpam-5555	19	26	in	in	ADP
ejpam-5555	19	27	graphs	graph	NOUN
ejpam-5555	19	28	,	,	PUNCT
ejpam-5555	19	29	there	there	PRON
ejpam-5555	19	30	are	be	VERB
ejpam-5555	19	31	also	also	ADV
ejpam-5555	19	32	a	a	DET
ejpam-5555	19	33	lot	lot	NOUN
ejpam-5555	19	34	of	of	ADP
ejpam-5555	19	35	studies	study	NOUN
ejpam-5555	19	36	done	do	VERB
ejpam-5555	19	37	due	due	ADP
ejpam-5555	19	38	to	to	ADP
ejpam-5555	19	39	dominating	dominating	NOUN
ejpam-5555	19	40	sets	set	NOUN
ejpam-5555	19	41	in	in	ADP
ejpam-5555	19	42	graphs	graph	NOUN
ejpam-5555	19	43	.	.	PUNCT
ejpam-5555	20	1	in	in	ADP
ejpam-5555	20	2	[	[	X
ejpam-5555	20	3	13	13	NUM
ejpam-5555	20	4	]	]	PUNCT
ejpam-5555	20	5	,	,	PUNCT
ejpam-5555	20	6	it	it	PRON
ejpam-5555	20	7	was	be	AUX
ejpam-5555	20	8	defined	define	VERB
ejpam-5555	20	9	that	that	SCONJ
ejpam-5555	20	10	a	a	DET
ejpam-5555	20	11	subset	subset	NOUN
ejpam-5555	20	12	d	d	NOUN
ejpam-5555	20	13	of	of	ADP
ejpam-5555	20	14	vertices	vertex	NOUN
ejpam-5555	20	15	in	in	ADP
ejpam-5555	20	16	g	g	PROPN
ejpam-5555	20	17	is	be	AUX
ejpam-5555	20	18	called	call	VERB
ejpam-5555	20	19	dominating	dominating	NOUN
ejpam-5555	20	20	set	set	VERB
ejpam-5555	20	21	if	if	SCONJ
ejpam-5555	20	22	every	every	DET
ejpam-5555	20	23	vertex	vertex	NOUN
ejpam-5555	20	24	not	not	PART
ejpam-5555	20	25	in	in	ADP
ejpam-5555	20	26	d	d	PROPN
ejpam-5555	20	27	has	have	AUX
ejpam-5555	20	28	at	at	ADV
ejpam-5555	20	29	least	least	ADV
ejpam-5555	20	30	one	one	NUM
ejpam-5555	20	31	neighbor	neighbor	NOUN
ejpam-5555	20	32	in	in	ADP
ejpam-5555	20	33	d.	d.	PROPN
ejpam-5555	20	34	the	the	DET
ejpam-5555	20	35	domination	domination	NOUN
ejpam-5555	20	36	number	number	PROPN
ejpam-5555	20	37	γ(g	γ(g	PROPN
ejpam-5555	20	38	)	)	PUNCT
ejpam-5555	20	39	of	of	ADP
ejpam-5555	20	40	g	g	PROPN
ejpam-5555	20	41	is	be	AUX
ejpam-5555	20	42	the	the	DET
ejpam-5555	20	43	minimum	minimum	ADJ
ejpam-5555	20	44	cardinality	cardinality	NOUN
ejpam-5555	20	45	of	of	ADP
ejpam-5555	20	46	a	a	DET
ejpam-5555	20	47	dominating	dominating	NOUN
ejpam-5555	20	48	set	set	NOUN
ejpam-5555	20	49	of	of	ADP
ejpam-5555	20	50	g.	g.	PROPN
ejpam-5555	20	51	the	the	DET
ejpam-5555	20	52	notion	notion	NOUN
ejpam-5555	20	53	of	of	ADP
ejpam-5555	20	54	domination	domination	NOUN
ejpam-5555	20	55	for	for	ADP
ejpam-5555	20	56	some	some	DET
ejpam-5555	20	57	classes	class	NOUN
ejpam-5555	20	58	of	of	ADP
ejpam-5555	20	59	graphs	graph	NOUN
ejpam-5555	20	60	were	be	AUX
ejpam-5555	20	61	studied	study	VERB
ejpam-5555	20	62	by	by	ADP
ejpam-5555	20	63	castaneda	castaneda	PROPN
ejpam-5555	20	64	et	et	PROPN
ejpam-5555	20	65	.	.	PUNCT
ejpam-5555	21	1	al	al	PROPN
ejpam-5555	21	2	in	in	ADP
ejpam-5555	21	3	[	[	X
ejpam-5555	21	4	2	2	NUM
ejpam-5555	21	5	]	]	PUNCT
ejpam-5555	21	6	.	.	PUNCT
ejpam-5555	22	1	they	they	PRON
ejpam-5555	22	2	considered	consider	VERB
ejpam-5555	22	3	variations	variation	NOUN
ejpam-5555	22	4	of	of	ADP
ejpam-5555	22	5	the	the	DET
ejpam-5555	22	6	concept	concept	NOUN
ejpam-5555	22	7	of	of	ADP
ejpam-5555	22	8	domination	domination	NOUN
ejpam-5555	22	9	in	in	ADP
ejpam-5555	22	10	a	a	DET
ejpam-5555	22	11	graph	graph	NOUN
ejpam-5555	22	12	.	.	PUNCT
ejpam-5555	23	1	with	with	ADP
ejpam-5555	23	2	the	the	DET
ejpam-5555	23	3	extensive	extensive	ADJ
ejpam-5555	23	4	results	result	NOUN
ejpam-5555	23	5	on	on	ADP
ejpam-5555	23	6	the	the	DET
ejpam-5555	23	7	above	above	ADV
ejpam-5555	23	8	-	-	PUNCT
ejpam-5555	23	9	mentioned	mention	VERB
ejpam-5555	23	10	graph	graph	NOUN
ejpam-5555	23	11	invariants	invariant	NOUN
ejpam-5555	23	12	,	,	PUNCT
ejpam-5555	23	13	a	a	DET
ejpam-5555	23	14	number	number	NOUN
ejpam-5555	23	15	of	of	ADP
ejpam-5555	23	16	researchers	researcher	NOUN
ejpam-5555	23	17	have	have	AUX
ejpam-5555	23	18	ventured	venture	VERB
ejpam-5555	23	19	into	into	ADP
ejpam-5555	23	20	making	make	VERB
ejpam-5555	23	21	an	an	DET
ejpam-5555	23	22	offshoot	offshoot	NOUN
ejpam-5555	23	23	of	of	ADP
ejpam-5555	23	24	the	the	DET
ejpam-5555	23	25	study	study	NOUN
ejpam-5555	23	26	.	.	PUNCT
ejpam-5555	24	1	as	as	ADP
ejpam-5555	24	2	a	a	DET
ejpam-5555	24	3	consequence	consequence	NOUN
ejpam-5555	24	4	,	,	PUNCT
ejpam-5555	24	5	the	the	DET
ejpam-5555	24	6	concept	concept	NOUN
ejpam-5555	24	7	of	of	ADP
ejpam-5555	24	8	geodetic	geodetic	ADJ
ejpam-5555	24	9	domination	domination	NOUN
ejpam-5555	24	10	in	in	ADP
ejpam-5555	24	11	graphs	graph	NOUN
ejpam-5555	24	12	has	have	AUX
ejpam-5555	24	13	been	be	AUX
ejpam-5555	24	14	coined	coin	VERB
ejpam-5555	24	15	.	.	PUNCT
ejpam-5555	25	1	apparently	apparently	ADV
ejpam-5555	25	2	,	,	PUNCT
ejpam-5555	25	3	this	this	PRON
ejpam-5555	25	4	has	have	AUX
ejpam-5555	25	5	been	be	AUX
ejpam-5555	25	6	extended	extend	VERB
ejpam-5555	25	7	to	to	ADP
ejpam-5555	25	8	the	the	DET
ejpam-5555	25	9	thought	thought	NOUN
ejpam-5555	25	10	of	of	ADP
ejpam-5555	25	11	the	the	DET
ejpam-5555	25	12	edge	edge	NOUN
ejpam-5555	25	13	geodetic	geodetic	ADJ
ejpam-5555	25	14	domination	domination	NOUN
ejpam-5555	25	15	in	in	ADP
ejpam-5555	25	16	graphs	graph	NOUN
ejpam-5555	25	17	.	.	PUNCT
ejpam-5555	26	1	due	due	ADP
ejpam-5555	26	2	to	to	ADP
ejpam-5555	26	3	the	the	DET
ejpam-5555	26	4	former	former	ADJ
ejpam-5555	26	5	,	,	PUNCT
ejpam-5555	26	6	there	there	PRON
ejpam-5555	26	7	have	have	AUX
ejpam-5555	26	8	been	be	AUX
ejpam-5555	26	9	quite	quite	DET
ejpam-5555	26	10	a	a	DET
ejpam-5555	26	11	number	number	NOUN
ejpam-5555	26	12	of	of	ADP
ejpam-5555	26	13	results	result	NOUN
ejpam-5555	26	14	that	that	PRON
ejpam-5555	26	15	were	be	AUX
ejpam-5555	26	16	generated	generate	VERB
ejpam-5555	26	17	from	from	ADP
ejpam-5555	26	18	the	the	DET
ejpam-5555	26	19	geodetic	geodetic	ADJ
ejpam-5555	26	20	domination	domination	NOUN
ejpam-5555	26	21	in	in	ADP
ejpam-5555	26	22	graphs	graph	NOUN
ejpam-5555	26	23	.	.	PUNCT
ejpam-5555	27	1	escuadra	escuadra	PROPN
ejpam-5555	27	2	et	et	PROPN
ejpam-5555	27	3	al	al	PROPN
ejpam-5555	27	4	.	.	PUNCT
ejpam-5555	28	1	[	[	X
ejpam-5555	28	2	4	4	NUM
ejpam-5555	28	3	]	]	PUNCT
ejpam-5555	28	4	,	,	PUNCT
ejpam-5555	28	5	vijayan	vijayan	PROPN
ejpam-5555	28	6	et	et	PROPN
ejpam-5555	28	7	al	al	PROPN
ejpam-5555	28	8	.	.	PUNCT
ejpam-5555	29	1	[	[	X
ejpam-5555	29	2	15	15	NUM
ejpam-5555	29	3	]	]	PUNCT
ejpam-5555	29	4	are	be	AUX
ejpam-5555	29	5	among	among	ADP
ejpam-5555	29	6	those	those	DET
ejpam-5555	29	7	researchers	researcher	NOUN
ejpam-5555	29	8	who	who	PRON
ejpam-5555	29	9	have	have	AUX
ejpam-5555	29	10	contributed	contribute	VERB
ejpam-5555	29	11	significant	significant	ADJ
ejpam-5555	29	12	results	result	NOUN
ejpam-5555	29	13	in	in	ADP
ejpam-5555	29	14	this	this	DET
ejpam-5555	29	15	endeavor	endeavor	NOUN
ejpam-5555	29	16	.	.	PUNCT
ejpam-5555	30	1	only	only	ADV
ejpam-5555	30	2	very	very	ADV
ejpam-5555	30	3	few	few	ADJ
ejpam-5555	30	4	,	,	PUNCT
ejpam-5555	30	5	however	however	ADV
ejpam-5555	30	6	,	,	PUNCT
ejpam-5555	30	7	have	have	AUX
ejpam-5555	30	8	undergone	undergo	VERB
ejpam-5555	30	9	studies	study	NOUN
ejpam-5555	30	10	on	on	ADP
ejpam-5555	30	11	the	the	DET
ejpam-5555	30	12	edge	edge	NOUN
ejpam-5555	30	13	geodetic	geodetic	ADJ
ejpam-5555	30	14	domination	domination	NOUN
ejpam-5555	30	15	in	in	ADP
ejpam-5555	30	16	graphs	graph	NOUN
ejpam-5555	30	17	.	.	PUNCT
ejpam-5555	31	1	stalin	stalin	PROPN
ejpam-5555	31	2	et	et	PROPN
ejpam-5555	31	3	al	al	PROPN
ejpam-5555	31	4	.	.	PUNCT
ejpam-5555	32	1	[	[	X
ejpam-5555	32	2	13	13	NUM
ejpam-5555	32	3	]	]	PUNCT
ejpam-5555	32	4	and	and	CCONJ
ejpam-5555	32	5	samodivkin	samodivkin	NOUN
ejpam-5555	33	1	[	[	X
ejpam-5555	33	2	9	9	NUM
ejpam-5555	33	3	]	]	PUNCT
ejpam-5555	33	4	,	,	PUNCT
ejpam-5555	33	5	made	make	VERB
ejpam-5555	33	6	some	some	DET
ejpam-5555	33	7	results	result	NOUN
ejpam-5555	33	8	on	on	ADP
ejpam-5555	33	9	the	the	DET
ejpam-5555	33	10	edge	edge	NOUN
ejpam-5555	33	11	geodetic	geodetic	ADJ
ejpam-5555	33	12	domination	domination	NOUN
ejpam-5555	33	13	in	in	ADP
ejpam-5555	33	14	graphs	graph	NOUN
ejpam-5555	33	15	.	.	PUNCT
ejpam-5555	34	1	there	there	PRON
ejpam-5555	34	2	were	be	VERB
ejpam-5555	34	3	results	result	NOUN
ejpam-5555	34	4	with	with	ADP
ejpam-5555	34	5	some	some	DET
ejpam-5555	34	6	realizations	realization	NOUN
ejpam-5555	34	7	done	do	VERB
ejpam-5555	34	8	for	for	ADP
ejpam-5555	34	9	the	the	DET
ejpam-5555	34	10	edge	edge	NOUN
ejpam-5555	34	11	geodetic	geodetic	ADJ
ejpam-5555	34	12	dominating	dominating	NOUN
ejpam-5555	34	13	number	number	NOUN
ejpam-5555	34	14	of	of	ADP
ejpam-5555	34	15	graphs	graph	NOUN
ejpam-5555	34	16	.	.	PUNCT
ejpam-5555	35	1	a	a	DET
ejpam-5555	35	2	number	number	NOUN
ejpam-5555	35	3	of	of	ADP
ejpam-5555	35	4	these	these	DET
ejpam-5555	35	5	results	result	NOUN
ejpam-5555	35	6	were	be	AUX
ejpam-5555	35	7	preliminaries	preliminary	NOUN
ejpam-5555	35	8	that	that	PRON
ejpam-5555	35	9	include	include	VERB
ejpam-5555	35	10	edge	edge	NOUN
ejpam-5555	35	11	geodetic	geodetic	ADJ
ejpam-5555	35	12	dominating	dominating	NOUN
ejpam-5555	35	13	number	number	NOUN
ejpam-5555	35	14	of	of	ADP
ejpam-5555	35	15	(	(	PUNCT
ejpam-5555	35	16	special	special	ADJ
ejpam-5555	35	17	)	)	PUNCT
ejpam-5555	35	18	graph	graph	NOUN
ejpam-5555	35	19	in	in	ADP
ejpam-5555	35	20	unary	unary	ADJ
ejpam-5555	35	21	operation	operation	NOUN
ejpam-5555	35	22	.	.	PUNCT
ejpam-5555	36	1	note	note	NOUN
ejpam-5555	36	2	,	,	PUNCT
ejpam-5555	36	3	however	however	ADV
ejpam-5555	36	4	,	,	PUNCT
ejpam-5555	36	5	that	that	SCONJ
ejpam-5555	36	6	the	the	DET
ejpam-5555	36	7	edge	edge	NOUN
ejpam-5555	36	8	geodetic	geodetic	ADJ
ejpam-5555	36	9	dominating	dominating	NOUN
ejpam-5555	36	10	number	number	NOUN
ejpam-5555	36	11	in	in	ADP
ejpam-5555	36	12	the	the	DET
ejpam-5555	36	13	binary	binary	ADJ
ejpam-5555	36	14	operation	operation	NOUN
ejpam-5555	36	15	of	of	ADP
ejpam-5555	36	16	graphs	graph	NOUN
ejpam-5555	36	17	is	be	AUX
ejpam-5555	36	18	not	not	PART
ejpam-5555	36	19	that	that	ADV
ejpam-5555	36	20	extensive	extensive	ADJ
ejpam-5555	36	21	yet	yet	ADV
ejpam-5555	36	22	.	.	PUNCT
ejpam-5555	37	1	though	though	SCONJ
ejpam-5555	37	2	there	there	PRON
ejpam-5555	37	3	were	be	VERB
ejpam-5555	37	4	attempts	attempt	NOUN
ejpam-5555	37	5	to	to	PART
ejpam-5555	37	6	explore	explore	VERB
ejpam-5555	37	7	on	on	ADP
ejpam-5555	37	8	this	this	DET
ejpam-5555	37	9	area	area	NOUN
ejpam-5555	37	10	but	but	CCONJ
ejpam-5555	37	11	the	the	DET
ejpam-5555	37	12	amount	amount	NOUN
ejpam-5555	37	13	of	of	ADP
ejpam-5555	37	14	results	result	NOUN
ejpam-5555	37	15	done	do	VERB
ejpam-5555	37	16	is	be	AUX
ejpam-5555	37	17	still	still	ADV
ejpam-5555	37	18	meager	meager	ADJ
ejpam-5555	37	19	.	.	PUNCT
ejpam-5555	38	1	to	to	PART
ejpam-5555	38	2	cite	cite	VERB
ejpam-5555	38	3	a	a	DET
ejpam-5555	38	4	few	few	ADJ
ejpam-5555	38	5	,	,	PUNCT
ejpam-5555	38	6	stalin	stalin	PROPN
ejpam-5555	38	7	et	et	PROPN
ejpam-5555	38	8	al	al	PROPN
ejpam-5555	38	9	.	.	PUNCT
ejpam-5555	39	1	[	[	X
ejpam-5555	39	2	13	13	NUM
ejpam-5555	39	3	]	]	PUNCT
ejpam-5555	39	4	in	in	ADP
ejpam-5555	39	5	their	their	PRON
ejpam-5555	39	6	article	article	NOUN
ejpam-5555	39	7	,	,	PUNCT
ejpam-5555	39	8	”	"	PUNCT
ejpam-5555	39	9	edge	edge	NOUN
ejpam-5555	39	10	geodetic	geodetic	ADJ
ejpam-5555	39	11	dominations	domination	NOUN
ejpam-5555	39	12	in	in	ADP
ejpam-5555	39	13	graphs	graph	NOUN
ejpam-5555	39	14	”	"	PUNCT
ejpam-5555	39	15	,	,	PUNCT
ejpam-5555	39	16	determined	determine	VERB
ejpam-5555	39	17	the	the	DET
ejpam-5555	39	18	edge	edge	NOUN
ejpam-5555	39	19	geodetic	geodetic	ADJ
ejpam-5555	39	20	number	number	NOUN
ejpam-5555	39	21	of	of	ADP
ejpam-5555	39	22	certain	certain	ADJ
ejpam-5555	39	23	classes	class	NOUN
ejpam-5555	39	24	of	of	ADP
ejpam-5555	39	25	graphs	graph	NOUN
ejpam-5555	39	26	.	.	PUNCT
ejpam-5555	40	1	necessary	necessary	ADJ
ejpam-5555	40	2	conditions	condition	NOUN
ejpam-5555	40	3	for	for	ADP
ejpam-5555	40	4	connected	connected	ADJ
ejpam-5555	40	5	graphs	graph	NOUN
ejpam-5555	40	6	of	of	ADP
ejpam-5555	40	7	order	order	NOUN
ejpam-5555	40	8	p	p	NOUN
ejpam-5555	40	9	with	with	ADP
ejpam-5555	40	10	edge	edge	NOUN
ejpam-5555	40	11	geodetic	geodetic	ADJ
ejpam-5555	40	12	domination	domination	NOUN
ejpam-5555	40	13	number	number	NOUN
ejpam-5555	40	14	p	p	NOUN
ejpam-5555	40	15	or	or	CCONJ
ejpam-5555	40	16	p-1	p-1	NOUN
ejpam-5555	40	17	are	be	AUX
ejpam-5555	40	18	given	give	VERB
ejpam-5555	40	19	.	.	PUNCT
ejpam-5555	41	1	they	they	PRON
ejpam-5555	41	2	also	also	ADV
ejpam-5555	41	3	had	have	AUX
ejpam-5555	41	4	shown	show	VERB
ejpam-5555	41	5	that	that	SCONJ
ejpam-5555	41	6	for	for	ADP
ejpam-5555	41	7	every	every	DET
ejpam-5555	41	8	two	two	NUM
ejpam-5555	41	9	integers	integer	NOUN
ejpam-5555	41	10	a	a	DET
ejpam-5555	41	11	,	,	PUNCT
ejpam-5555	41	12	b	b	NOUN
ejpam-5555	41	13	≥	≥	NUM
ejpam-5555	41	14	2	2	NUM
ejpam-5555	41	15	with	with	ADP
ejpam-5555	41	16	2	2	NUM
ejpam-5555	41	17	≤	≤	NOUN
ejpam-5555	41	18	a	a	DET
ejpam-5555	41	19	<	<	X
ejpam-5555	41	20	b	b	NOUN
ejpam-5555	41	21	and	and	CCONJ
ejpam-5555	41	22	b−	b−	PROPN
ejpam-5555	41	23	a−	a−	PROPN
ejpam-5555	41	24	1	1	NUM
ejpam-5555	41	25	>	>	SYM
ejpam-5555	41	26	0	0	NUM
ejpam-5555	41	27	,	,	PUNCT
ejpam-5555	41	28	there	there	PRON
ejpam-5555	41	29	is	be	VERB
ejpam-5555	41	30	a	a	DET
ejpam-5555	41	31	connected	connected	ADJ
ejpam-5555	41	32	graph	graph	NOUN
ejpam-5555	41	33	g	g	ADP
ejpam-5555	41	34	such	such	ADJ
ejpam-5555	41	35	that	that	PRON
ejpam-5555	41	36	γg(g	γg(g	NOUN
ejpam-5555	41	37	)	)	PUNCT
ejpam-5555	41	38	=	=	SYM
ejpam-5555	41	39	a	a	PRON
ejpam-5555	41	40	and	and	CCONJ
ejpam-5555	41	41	γg1(g	γg1(g	NUM
ejpam-5555	41	42	)	)	PUNCT
ejpam-5555	42	1	=	=	SYM
ejpam-5555	42	2	b	b	NOUN
ejpam-5555	42	3	,	,	PUNCT
ejpam-5555	42	4	where	where	SCONJ
ejpam-5555	42	5	γg(g	γg(g	PUNCT
ejpam-5555	42	6	)	)	PUNCT
ejpam-5555	42	7	is	be	AUX
ejpam-5555	42	8	the	the	DET
ejpam-5555	42	9	geodetic	geodetic	ADJ
ejpam-5555	42	10	domination	domination	NOUN
ejpam-5555	42	11	number	number	NOUN
ejpam-5555	42	12	of	of	ADP
ejpam-5555	42	13	a	a	DET
ejpam-5555	42	14	graph	graph	NOUN
ejpam-5555	42	15	.	.	PUNCT
ejpam-5555	43	1	since	since	SCONJ
ejpam-5555	43	2	limited	limited	ADJ
ejpam-5555	43	3	results	result	NOUN
ejpam-5555	43	4	are	be	AUX
ejpam-5555	43	5	done	do	VERB
ejpam-5555	43	6	on	on	ADP
ejpam-5555	43	7	the	the	DET
ejpam-5555	43	8	edge	edge	NOUN
ejpam-5555	43	9	geodetic	geodetic	ADJ
ejpam-5555	43	10	dominating	dominating	NOUN
ejpam-5555	43	11	number	number	NOUN
ejpam-5555	43	12	of	of	ADP
ejpam-5555	43	13	some	some	DET
ejpam-5555	43	14	graphs	graph	NOUN
ejpam-5555	43	15	,	,	PUNCT
ejpam-5555	43	16	it	it	PRON
ejpam-5555	43	17	is	be	AUX
ejpam-5555	43	18	in	in	ADP
ejpam-5555	43	19	this	this	DET
ejpam-5555	43	20	regard	regard	NOUN
ejpam-5555	43	21	that	that	SCONJ
ejpam-5555	43	22	a	a	DET
ejpam-5555	43	23	revisit	revisit	NOUN
ejpam-5555	43	24	to	to	ADP
ejpam-5555	43	25	the	the	DET
ejpam-5555	43	26	foregoing	forego	VERB
ejpam-5555	43	27	topic	topic	NOUN
ejpam-5555	43	28	was	be	AUX
ejpam-5555	43	29	undertaken	undertake	VERB
ejpam-5555	43	30	and	and	CCONJ
ejpam-5555	43	31	some	some	DET
ejpam-5555	43	32	results	result	NOUN
ejpam-5555	43	33	were	be	AUX
ejpam-5555	43	34	generated	generate	VERB
ejpam-5555	43	35	.	.	PUNCT
ejpam-5555	44	1	in	in	ADP
ejpam-5555	44	2	doing	do	VERB
ejpam-5555	44	3	this	this	DET
ejpam-5555	44	4	study	study	NOUN
ejpam-5555	44	5	,	,	PUNCT
ejpam-5555	44	6	the	the	DET
ejpam-5555	44	7	following	follow	VERB
ejpam-5555	44	8	terminologies	terminology	NOUN
ejpam-5555	44	9	from	from	ADP
ejpam-5555	44	10	[	[	X
ejpam-5555	44	11	1–15	1–15	NUM
ejpam-5555	44	12	]	]	PUNCT
ejpam-5555	44	13	are	be	AUX
ejpam-5555	44	14	necessary	necessary	ADJ
ejpam-5555	44	15	.	.	PUNCT
ejpam-5555	45	1	a	a	DET
ejpam-5555	45	2	simple	simple	ADJ
ejpam-5555	45	3	graph	graph	NOUN
ejpam-5555	45	4	g(v	g(v	PROPN
ejpam-5555	45	5	,	,	PUNCT
ejpam-5555	45	6	e	e	NOUN
ejpam-5555	45	7	)	)	PUNCT
ejpam-5555	45	8	is	be	AUX
ejpam-5555	45	9	an	an	DET
ejpam-5555	45	10	undirected	undirected	ADJ
ejpam-5555	45	11	graph	graph	NOUN
ejpam-5555	45	12	without	without	ADP
ejpam-5555	45	13	loops	loop	NOUN
ejpam-5555	45	14	or	or	CCONJ
ejpam-5555	45	15	multiple	multiple	ADJ
ejpam-5555	45	16	edges	edge	NOUN
ejpam-5555	45	17	.	.	PUNCT
ejpam-5555	46	1	v	v	X
ejpam-5555	46	2	(	(	PUNCT
ejpam-5555	46	3	g	g	NOUN
ejpam-5555	46	4	)	)	PUNCT
ejpam-5555	46	5	and	and	CCONJ
ejpam-5555	46	6	e(g	e(g	PROPN
ejpam-5555	46	7	)	)	PUNCT
ejpam-5555	46	8	denote	denote	VERB
ejpam-5555	46	9	the	the	DET
ejpam-5555	46	10	vertex	vertex	NOUN
ejpam-5555	46	11	and	and	CCONJ
ejpam-5555	46	12	the	the	DET
ejpam-5555	46	13	edge	edge	NOUN
ejpam-5555	46	14	sets	set	NOUN
ejpam-5555	46	15	of	of	ADP
ejpam-5555	46	16	a	a	DET
ejpam-5555	46	17	graph	graph	NOUN
ejpam-5555	46	18	g	g	NOUN
ejpam-5555	46	19	,	,	PUNCT
ejpam-5555	46	20	respectively	respectively	ADV
ejpam-5555	46	21	.	.	PUNCT
ejpam-5555	47	1	let	let	VERB
ejpam-5555	47	2	s	s	PRON
ejpam-5555	47	3	⊆	⊆	NUM
ejpam-5555	47	4	v	v	NOUN
ejpam-5555	47	5	(	(	PUNCT
ejpam-5555	47	6	g	g	NOUN
ejpam-5555	47	7	)	)	PUNCT
ejpam-5555	47	8	.	.	PUNCT
ejpam-5555	48	1	the	the	DET
ejpam-5555	48	2	induced	induced	ADJ
ejpam-5555	48	3	subgraph	subgraph	NOUN
ejpam-5555	48	4	⟨s⟩	⟨s⟩	PROPN
ejpam-5555	48	5	of	of	ADP
ejpam-5555	48	6	g	g	PROPN
ejpam-5555	48	7	is	be	AUX
ejpam-5555	48	8	the	the	DET
ejpam-5555	48	9	graph	graph	NOUN
ejpam-5555	48	10	⟨s⟩	⟨s⟩	PROPN
ejpam-5555	48	11	with	with	ADP
ejpam-5555	48	12	vertex	vertex	NOUN
ejpam-5555	48	13	set	set	NOUN
ejpam-5555	48	14	s	s	PART
ejpam-5555	48	15	and	and	CCONJ
ejpam-5555	48	16	edge	edge	NOUN
ejpam-5555	48	17	set	set	NOUN
ejpam-5555	48	18	{	{	PUNCT
ejpam-5555	48	19	xy	xy	PROPN
ejpam-5555	48	20	∈	∈	PROPN
ejpam-5555	48	21	e(g)|x	e(g)|x	PROPN
ejpam-5555	48	22	,	,	PUNCT
ejpam-5555	48	23	y	y	PROPN
ejpam-5555	48	24	∈	∈	PROPN
ejpam-5555	48	25	s	s	PART
ejpam-5555	48	26	}	}	PUNCT
ejpam-5555	48	27	.	.	PUNCT
ejpam-5555	49	1	the	the	DET
ejpam-5555	49	2	maximum	maximum	ADJ
ejpam-5555	49	3	degree	degree	NOUN
ejpam-5555	49	4	of	of	ADP
ejpam-5555	49	5	g	g	NOUN
ejpam-5555	49	6	,	,	PUNCT
ejpam-5555	49	7	denoted	denote	VERB
ejpam-5555	49	8	by	by	ADP
ejpam-5555	49	9	∆(g	∆(g	PROPN
ejpam-5555	49	10	)	)	PUNCT
ejpam-5555	49	11	is	be	AUX
ejpam-5555	49	12	given	give	VERB
ejpam-5555	49	13	by	by	ADP
ejpam-5555	49	14	∆(g	∆(g	NOUN
ejpam-5555	49	15	)	)	PUNCT
ejpam-5555	49	16	=	=	PUNCT
ejpam-5555	49	17	max{degg(v	max{degg(v	NOUN
ejpam-5555	49	18	)	)	PUNCT
ejpam-5555	49	19	:	:	PUNCT
ejpam-5555	49	20	v	v	X
ejpam-5555	49	21	∈	∈	PROPN
ejpam-5555	49	22	v	v	NOUN
ejpam-5555	49	23	(	(	PUNCT
ejpam-5555	49	24	g	g	NOUN
ejpam-5555	49	25	)	)	PUNCT
ejpam-5555	49	26	}	}	PUNCT
ejpam-5555	49	27	.	.	PUNCT
ejpam-5555	50	1	the	the	DET
ejpam-5555	50	2	open	open	ADJ
ejpam-5555	50	3	neighborhood	neighborhood	NOUN
ejpam-5555	50	4	of	of	ADP
ejpam-5555	50	5	the	the	DET
ejpam-5555	50	6	vertex	vertex	NOUN
ejpam-5555	50	7	v	v	NOUN
ejpam-5555	50	8	in	in	ADP
ejpam-5555	50	9	a	a	DET
ejpam-5555	50	10	graph	graph	NOUN
ejpam-5555	50	11	g	g	NOUN
ejpam-5555	50	12	is	be	AUX
ejpam-5555	50	13	the	the	DET
ejpam-5555	50	14	set	set	NOUN
ejpam-5555	50	15	n(v	n(v	PROPN
ejpam-5555	50	16	)	)	PUNCT
ejpam-5555	50	17	=	=	PRON
ejpam-5555	51	1	{	{	PUNCT
ejpam-5555	51	2	u	u	NOUN
ejpam-5555	51	3	∈	∈	PROPN
ejpam-5555	51	4	v	v	NOUN
ejpam-5555	51	5	(	(	PUNCT
ejpam-5555	51	6	g	g	NOUN
ejpam-5555	51	7	)	)	PUNCT
ejpam-5555	51	8	:	:	PUNCT
ejpam-5555	51	9	uv	uv	PROPN
ejpam-5555	51	10	∈	∈	PROPN
ejpam-5555	51	11	e(g	e(g	PROPN
ejpam-5555	51	12	)	)	PUNCT
ejpam-5555	51	13	}	}	PUNCT
ejpam-5555	51	14	.	.	PUNCT
ejpam-5555	52	1	the	the	DET
ejpam-5555	52	2	closed	closed	ADJ
ejpam-5555	52	3	neighborhood	neighborhood	NOUN
ejpam-5555	52	4	of	of	ADP
ejpam-5555	52	5	v	v	NOUN
ejpam-5555	52	6	is	be	AUX
ejpam-5555	52	7	n	n	PRON
ejpam-5555	52	8	[	[	X
ejpam-5555	52	9	v	v	X
ejpam-5555	52	10	]	]	X
ejpam-5555	52	11	=	=	PUNCT
ejpam-5555	52	12	n(v	n(v	PROPN
ejpam-5555	52	13	)	)	PUNCT
ejpam-5555	52	14	∪	∪	NOUN
ejpam-5555	52	15	{	{	PUNCT
ejpam-5555	52	16	v	v	NOUN
ejpam-5555	52	17	}	}	PUNCT
ejpam-5555	52	18	.	.	PUNCT
ejpam-5555	53	1	a	a	DET
ejpam-5555	53	2	subset	subset	NOUN
ejpam-5555	53	3	d	d	NOUN
ejpam-5555	53	4	of	of	ADP
ejpam-5555	53	5	vertices	vertex	NOUN
ejpam-5555	53	6	in	in	ADP
ejpam-5555	53	7	g	g	PROPN
ejpam-5555	53	8	is	be	AUX
ejpam-5555	53	9	called	call	VERB
ejpam-5555	53	10	dominating	dominating	NOUN
ejpam-5555	53	11	set	set	VERB
ejpam-5555	53	12	if	if	SCONJ
ejpam-5555	53	13	every	every	DET
ejpam-5555	53	14	vertex	vertex	NOUN
ejpam-5555	53	15	not	not	PART
ejpam-5555	53	16	in	in	ADP
ejpam-5555	53	17	d	d	PROPN
ejpam-5555	53	18	has	have	AUX
ejpam-5555	53	19	at	at	ADV
ejpam-5555	53	20	least	least	ADV
ejpam-5555	53	21	one	one	NUM
ejpam-5555	53	22	neighbor	neighbor	NOUN
ejpam-5555	53	23	in	in	ADP
ejpam-5555	53	24	d.	d.	PROPN
ejpam-5555	53	25	the	the	DET
ejpam-5555	53	26	domination	domination	NOUN
ejpam-5555	53	27	number	number	PROPN
ejpam-5555	53	28	γ(g	γ(g	PROPN
ejpam-5555	53	29	)	)	PUNCT
ejpam-5555	53	30	of	of	ADP
ejpam-5555	53	31	g	g	PROPN
ejpam-5555	53	32	is	be	AUX
ejpam-5555	53	33	the	the	DET
ejpam-5555	53	34	minimum	minimum	ADJ
ejpam-5555	53	35	cardinality	cardinality	NOUN
ejpam-5555	53	36	of	of	ADP
ejpam-5555	53	37	a	a	DET
ejpam-5555	53	38	dominating	dominating	NOUN
ejpam-5555	53	39	set	set	NOUN
ejpam-5555	53	40	of	of	ADP
ejpam-5555	53	41	g.	g.	PROPN
ejpam-5555	53	42	a	a	DET
ejpam-5555	53	43	geodetic	geodetic	ADJ
ejpam-5555	53	44	set	set	NOUN
ejpam-5555	53	45	of	of	ADP
ejpam-5555	53	46	g	g	PROPN
ejpam-5555	53	47	is	be	AUX
ejpam-5555	53	48	a	a	DET
ejpam-5555	53	49	set	set	NOUN
ejpam-5555	53	50	s	s	NOUN
ejpam-5555	53	51	⊆	⊆	NUM
ejpam-5555	53	52	v	v	NOUN
ejpam-5555	53	53	(	(	PUNCT
ejpam-5555	53	54	g	g	NOUN
ejpam-5555	53	55	)	)	PUNCT
ejpam-5555	53	56	such	such	ADJ
ejpam-5555	53	57	that	that	SCONJ
ejpam-5555	53	58	every	every	DET
ejpam-5555	53	59	vertex	vertex	NOUN
ejpam-5555	53	60	of	of	ADP
ejpam-5555	53	61	g	g	PROPN
ejpam-5555	53	62	is	be	AUX
ejpam-5555	53	63	contained	contain	VERB
ejpam-5555	53	64	in	in	ADP
ejpam-5555	53	65	a	a	DET
ejpam-5555	53	66	geodesic	geodesic	NOUN
ejpam-5555	53	67	joining	join	VERB
ejpam-5555	53	68	some	some	DET
ejpam-5555	53	69	pair	pair	NOUN
ejpam-5555	53	70	of	of	ADP
ejpam-5555	53	71	vertices	vertex	NOUN
ejpam-5555	53	72	in	in	ADP
ejpam-5555	53	73	s.	s.	PROPN
ejpam-5555	53	74	the	the	DET
ejpam-5555	53	75	geodetic	geodetic	ADJ
ejpam-5555	53	76	number	number	NOUN
ejpam-5555	53	77	g(g	g(g	NOUN
ejpam-5555	53	78	)	)	PUNCT
ejpam-5555	53	79	of	of	ADP
ejpam-5555	53	80	g	g	PROPN
ejpam-5555	53	81	is	be	AUX
ejpam-5555	53	82	the	the	DET
ejpam-5555	53	83	minimum	minimum	ADJ
ejpam-5555	53	84	order	order	NOUN
ejpam-5555	53	85	of	of	ADP
ejpam-5555	53	86	its	its	PRON
ejpam-5555	53	87	geodetic	geodetic	ADJ
ejpam-5555	53	88	sets	set	NOUN
ejpam-5555	53	89	and	and	CCONJ
ejpam-5555	53	90	any	any	DET
ejpam-5555	53	91	geodetic	geodetic	ADJ
ejpam-5555	53	92	set	set	NOUN
ejpam-5555	53	93	of	of	ADP
ejpam-5555	53	94	order	order	NOUN
ejpam-5555	53	95	g(g	g(g	NOUN
ejpam-5555	53	96	)	)	PUNCT
ejpam-5555	53	97	is	be	AUX
ejpam-5555	53	98	a	a	DET
ejpam-5555	53	99	geodetic	geodetic	ADJ
ejpam-5555	53	100	basis	basis	NOUN
ejpam-5555	53	101	.	.	PUNCT
ejpam-5555	54	1	an	an	DET
ejpam-5555	54	2	edge	edge	NOUN
ejpam-5555	54	3	geodetic	geodetic	ADJ
ejpam-5555	54	4	set	set	NOUN
ejpam-5555	54	5	of	of	ADP
ejpam-5555	54	6	g	g	PROPN
ejpam-5555	54	7	is	be	AUX
ejpam-5555	54	8	a	a	DET
ejpam-5555	54	9	set	set	NOUN
ejpam-5555	54	10	s	s	NOUN
ejpam-5555	54	11	⊆	⊆	NUM
ejpam-5555	54	12	v	v	NOUN
ejpam-5555	54	13	(	(	PUNCT
ejpam-5555	54	14	g	g	NOUN
ejpam-5555	54	15	)	)	PUNCT
ejpam-5555	54	16	such	such	ADJ
ejpam-5555	54	17	that	that	SCONJ
ejpam-5555	54	18	every	every	DET
ejpam-5555	54	19	edge	edge	NOUN
ejpam-5555	54	20	of	of	ADP
ejpam-5555	54	21	g	g	NOUN
ejpam-5555	54	22	is	be	AUX
ejpam-5555	54	23	contained	contain	VERB
ejpam-5555	54	24	in	in	ADP
ejpam-5555	54	25	a	a	DET
ejpam-5555	54	26	geodesic	geodesic	NOUN
ejpam-5555	54	27	joining	join	VERB
ejpam-5555	54	28	some	some	DET
ejpam-5555	54	29	pair	pair	NOUN
ejpam-5555	54	30	of	of	ADP
ejpam-5555	54	31	vertices	vertex	NOUN
ejpam-5555	54	32	in	in	ADP
ejpam-5555	54	33	s.	s.	PROPN
ejpam-5555	54	34	the	the	DET
ejpam-5555	54	35	edge	edge	NOUN
ejpam-5555	54	36	geodetic	geodetic	ADJ
ejpam-5555	54	37	number	number	NOUN
ejpam-5555	54	38	ge(g	ge(g	PROPN
ejpam-5555	54	39	)	)	PUNCT
ejpam-5555	54	40	of	of	ADP
ejpam-5555	54	41	g	g	PROPN
ejpam-5555	54	42	is	be	AUX
ejpam-5555	54	43	the	the	DET
ejpam-5555	54	44	c.j	c.j	PROPN
ejpam-5555	54	45	.	.	PROPN
ejpam-5555	54	46	quije	quije	PROPN
ejpam-5555	54	47	,	,	PUNCT
ejpam-5555	54	48	r.	r.	PROPN
ejpam-5555	54	49	mariano	mariano	PROPN
ejpam-5555	54	50	,	,	PUNCT
ejpam-5555	54	51	e.	e.	PROPN
ejpam-5555	54	52	ahmad	ahmad	PROPN
ejpam-5555	54	53	/	/	SYM
ejpam-5555	54	54	eur	eur	PROPN
ejpam-5555	54	55	.	.	PUNCT
ejpam-5555	55	1	j.	j.	PROPN
ejpam-5555	55	2	pure	pure	PROPN
ejpam-5555	55	3	appl	appl	PROPN
ejpam-5555	55	4	.	.	PROPN
ejpam-5555	55	5	math	math	PROPN
ejpam-5555	55	6	,	,	PUNCT
ejpam-5555	55	7	18	18	NUM
ejpam-5555	55	8	(	(	PUNCT
ejpam-5555	55	9	1	1	NUM
ejpam-5555	55	10	)	)	PUNCT
ejpam-5555	55	11	(	(	PUNCT
ejpam-5555	55	12	2025	2025	NUM
ejpam-5555	55	13	)	)	PUNCT
ejpam-5555	55	14	,	,	PUNCT
ejpam-5555	55	15	5555	5555	NUM
ejpam-5555	55	16	3	3	NUM
ejpam-5555	55	17	of	of	ADP
ejpam-5555	55	18	8	8	NUM
ejpam-5555	55	19	minimum	minimum	ADJ
ejpam-5555	55	20	order	order	NOUN
ejpam-5555	55	21	of	of	ADP
ejpam-5555	55	22	its	its	PRON
ejpam-5555	55	23	edge	edge	NOUN
ejpam-5555	55	24	geodetic	geodetic	ADJ
ejpam-5555	55	25	sets	set	NOUN
ejpam-5555	55	26	and	and	CCONJ
ejpam-5555	55	27	any	any	DET
ejpam-5555	55	28	edge	edge	NOUN
ejpam-5555	55	29	geodetic	geodetic	ADJ
ejpam-5555	55	30	set	set	NOUN
ejpam-5555	55	31	of	of	ADP
ejpam-5555	55	32	order	order	NOUN
ejpam-5555	55	33	ge(g	ge(g	PUNCT
ejpam-5555	55	34	)	)	PUNCT
ejpam-5555	55	35	is	be	AUX
ejpam-5555	55	36	an	an	DET
ejpam-5555	55	37	edge	edge	NOUN
ejpam-5555	55	38	geodetic	geodetic	ADJ
ejpam-5555	55	39	basis	basis	NOUN
ejpam-5555	55	40	of	of	ADP
ejpam-5555	55	41	g	g	PROPN
ejpam-5555	55	42	or	or	CCONJ
ejpam-5555	55	43	a	a	DET
ejpam-5555	55	44	ge	ge	NOUN
ejpam-5555	55	45	-	-	PUNCT
ejpam-5555	55	46	set	set	NOUN
ejpam-5555	55	47	of	of	ADP
ejpam-5555	55	48	g.	g.	PROPN
ejpam-5555	55	49	a	a	DET
ejpam-5555	55	50	set	set	NOUN
ejpam-5555	55	51	of	of	ADP
ejpam-5555	55	52	vertices	vertex	NOUN
ejpam-5555	55	53	s	s	PART
ejpam-5555	55	54	in	in	ADP
ejpam-5555	55	55	g	g	PROPN
ejpam-5555	55	56	is	be	AUX
ejpam-5555	55	57	called	call	VERB
ejpam-5555	55	58	a	a	DET
ejpam-5555	55	59	geodetic	geodetic	ADJ
ejpam-5555	55	60	dominating	dominating	NOUN
ejpam-5555	55	61	set	set	NOUN
ejpam-5555	55	62	of	of	ADP
ejpam-5555	55	63	g	g	PROPN
ejpam-5555	55	64	if	if	SCONJ
ejpam-5555	55	65	s	s	VERB
ejpam-5555	55	66	is	be	AUX
ejpam-5555	55	67	both	both	PRON
ejpam-5555	55	68	geodetic	geodetic	ADJ
ejpam-5555	55	69	set	set	NOUN
ejpam-5555	55	70	and	and	CCONJ
ejpam-5555	55	71	a	a	DET
ejpam-5555	55	72	dominating	dominating	NOUN
ejpam-5555	55	73	set	set	NOUN
ejpam-5555	55	74	.	.	PUNCT
ejpam-5555	56	1	the	the	DET
ejpam-5555	56	2	minimum	minimum	ADJ
ejpam-5555	56	3	cardinality	cardinality	NOUN
ejpam-5555	56	4	of	of	ADP
ejpam-5555	56	5	a	a	DET
ejpam-5555	56	6	geodetic	geodetic	ADJ
ejpam-5555	56	7	dominating	dominating	NOUN
ejpam-5555	56	8	set	set	NOUN
ejpam-5555	56	9	of	of	ADP
ejpam-5555	56	10	g	g	PROPN
ejpam-5555	56	11	is	be	AUX
ejpam-5555	56	12	its	its	PRON
ejpam-5555	56	13	geodetic	geodetic	ADJ
ejpam-5555	56	14	domination	domination	NOUN
ejpam-5555	56	15	number	number	NOUN
ejpam-5555	56	16	and	and	CCONJ
ejpam-5555	56	17	is	be	AUX
ejpam-5555	56	18	denoted	denote	VERB
ejpam-5555	56	19	by	by	ADP
ejpam-5555	56	20	γg(g	γg(g	NOUN
ejpam-5555	56	21	)	)	PUNCT
ejpam-5555	56	22	.	.	PUNCT
ejpam-5555	57	1	an	an	DET
ejpam-5555	57	2	geodetic	geodetic	ADJ
ejpam-5555	57	3	dominating	dominating	NOUN
ejpam-5555	57	4	set	set	NOUN
ejpam-5555	57	5	of	of	ADP
ejpam-5555	57	6	size	size	NOUN
ejpam-5555	57	7	γg(g	γg(g	PRON
ejpam-5555	57	8	)	)	PUNCT
ejpam-5555	57	9	is	be	AUX
ejpam-5555	57	10	said	say	VERB
ejpam-5555	57	11	to	to	PART
ejpam-5555	57	12	be	be	AUX
ejpam-5555	57	13	a	a	DET
ejpam-5555	57	14	γg	γg	ADV
ejpam-5555	57	15	-	-	PUNCT
ejpam-5555	57	16	set	set	NOUN
ejpam-5555	57	17	.	.	PUNCT
ejpam-5555	58	1	let	let	VERB
ejpam-5555	58	2	g	g	PRON
ejpam-5555	58	3	be	be	AUX
ejpam-5555	58	4	a	a	DET
ejpam-5555	58	5	connected	connected	ADJ
ejpam-5555	58	6	graph	graph	NOUN
ejpam-5555	58	7	.	.	PUNCT
ejpam-5555	59	1	a	a	DET
ejpam-5555	59	2	set	set	NOUN
ejpam-5555	59	3	of	of	ADP
ejpam-5555	59	4	vertices	vertex	NOUN
ejpam-5555	59	5	s	s	PART
ejpam-5555	59	6	in	in	ADP
ejpam-5555	59	7	g	g	PROPN
ejpam-5555	59	8	is	be	AUX
ejpam-5555	59	9	called	call	VERB
ejpam-5555	59	10	an	an	DET
ejpam-5555	59	11	edge	edge	NOUN
ejpam-5555	59	12	geodetic	geodetic	ADJ
ejpam-5555	59	13	dominating	dominating	NOUN
ejpam-5555	59	14	set	set	NOUN
ejpam-5555	59	15	of	of	ADP
ejpam-5555	59	16	g	g	PROPN
ejpam-5555	59	17	if	if	SCONJ
ejpam-5555	59	18	s	s	VERB
ejpam-5555	59	19	is	be	AUX
ejpam-5555	59	20	both	both	PRON
ejpam-5555	59	21	edge	edge	ADJ
ejpam-5555	59	22	geodetic	geodetic	ADJ
ejpam-5555	59	23	set	set	NOUN
ejpam-5555	59	24	and	and	CCONJ
ejpam-5555	59	25	a	a	DET
ejpam-5555	59	26	dominating	dominating	NOUN
ejpam-5555	59	27	set	set	NOUN
ejpam-5555	59	28	.	.	PUNCT
ejpam-5555	60	1	the	the	DET
ejpam-5555	60	2	minimum	minimum	ADJ
ejpam-5555	60	3	cardinality	cardinality	NOUN
ejpam-5555	60	4	of	of	ADP
ejpam-5555	60	5	an	an	DET
ejpam-5555	60	6	edge	edge	NOUN
ejpam-5555	60	7	geodetic	geodetic	ADJ
ejpam-5555	60	8	dominating	dominating	NOUN
ejpam-5555	60	9	set	set	NOUN
ejpam-5555	60	10	of	of	ADP
ejpam-5555	60	11	g	g	PROPN
ejpam-5555	60	12	is	be	AUX
ejpam-5555	60	13	its	its	PRON
ejpam-5555	60	14	edge	edge	NOUN
ejpam-5555	60	15	geodetic	geodetic	ADJ
ejpam-5555	60	16	domination	domination	NOUN
ejpam-5555	60	17	number	number	NOUN
ejpam-5555	60	18	and	and	CCONJ
ejpam-5555	60	19	is	be	AUX
ejpam-5555	60	20	denoted	denote	VERB
ejpam-5555	60	21	by	by	ADP
ejpam-5555	60	22	γge(g	γge(g	PROPN
ejpam-5555	60	23	)	)	PUNCT
ejpam-5555	60	24	.	.	PUNCT
ejpam-5555	61	1	an	an	DET
ejpam-5555	61	2	edge	edge	NOUN
ejpam-5555	61	3	geodetic	geodetic	ADJ
ejpam-5555	61	4	dominating	dominating	NOUN
ejpam-5555	61	5	set	set	NOUN
ejpam-5555	61	6	of	of	ADP
ejpam-5555	61	7	size	size	NOUN
ejpam-5555	61	8	γge(g	γge(g	PROPN
ejpam-5555	61	9	)	)	PUNCT
ejpam-5555	61	10	is	be	AUX
ejpam-5555	61	11	said	say	VERB
ejpam-5555	61	12	to	to	PART
ejpam-5555	61	13	be	be	AUX
ejpam-5555	61	14	a	a	DET
ejpam-5555	61	15	γge	γge	NOUN
ejpam-5555	61	16	-	-	PUNCT
ejpam-5555	61	17	set	set	NOUN
ejpam-5555	61	18	.	.	PUNCT
ejpam-5555	62	1	a	a	DET
ejpam-5555	62	2	vertex	vertex	NOUN
ejpam-5555	62	3	v	v	NOUN
ejpam-5555	62	4	is	be	AUX
ejpam-5555	62	5	an	an	DET
ejpam-5555	62	6	extreme	extreme	ADJ
ejpam-5555	62	7	vertex	vertex	NOUN
ejpam-5555	62	8	of	of	ADP
ejpam-5555	62	9	a	a	DET
ejpam-5555	62	10	graph	graph	NOUN
ejpam-5555	62	11	g	g	NOUN
ejpam-5555	62	12	if	if	SCONJ
ejpam-5555	62	13	the	the	DET
ejpam-5555	62	14	subgraph	subgraph	NOUN
ejpam-5555	62	15	induced	induce	VERB
ejpam-5555	62	16	by	by	ADP
ejpam-5555	62	17	its	its	PRON
ejpam-5555	62	18	neighbors	neighbor	NOUN
ejpam-5555	62	19	is	be	AUX
ejpam-5555	62	20	complete	complete	ADJ
ejpam-5555	62	21	.	.	PUNCT
ejpam-5555	63	1	the	the	DET
ejpam-5555	63	2	set	set	NOUN
ejpam-5555	63	3	of	of	ADP
ejpam-5555	63	4	all	all	DET
ejpam-5555	63	5	extreme	extreme	ADJ
ejpam-5555	63	6	vertices	vertex	NOUN
ejpam-5555	63	7	of	of	ADP
ejpam-5555	63	8	g	g	PROPN
ejpam-5555	63	9	is	be	AUX
ejpam-5555	63	10	denoted	denote	VERB
ejpam-5555	63	11	by	by	ADP
ejpam-5555	63	12	ext(g	ext(g	PROPN
ejpam-5555	63	13	)	)	PUNCT
ejpam-5555	63	14	.	.	PUNCT
ejpam-5555	64	1	a	a	DET
ejpam-5555	64	2	vertex	vertex	NOUN
ejpam-5555	64	3	v	v	NOUN
ejpam-5555	64	4	in	in	ADP
ejpam-5555	64	5	a	a	DET
ejpam-5555	64	6	connected	connected	ADJ
ejpam-5555	64	7	graph	graph	NOUN
ejpam-5555	64	8	g	g	NOUN
ejpam-5555	64	9	is	be	AUX
ejpam-5555	64	10	said	say	VERB
ejpam-5555	64	11	to	to	PART
ejpam-5555	64	12	be	be	AUX
ejpam-5555	64	13	a	a	DET
ejpam-5555	64	14	semi	semi	ADJ
ejpam-5555	64	15	-	-	ADJ
ejpam-5555	64	16	extreme	extreme	ADJ
ejpam-5555	64	17	vertex	vertex	NOUN
ejpam-5555	64	18	if	if	SCONJ
ejpam-5555	64	19	it	it	PRON
ejpam-5555	64	20	has	have	VERB
ejpam-5555	64	21	a	a	DET
ejpam-5555	64	22	neighbor	neighbor	NOUN
ejpam-5555	64	23	,	,	PUNCT
ejpam-5555	64	24	say	say	VERB
ejpam-5555	64	25	u	u	NOUN
ejpam-5555	64	26	,	,	PUNCT
ejpam-5555	64	27	with	with	ADP
ejpam-5555	64	28	n	n	PRON
ejpam-5555	64	29	[	[	X
ejpam-5555	64	30	v	v	X
ejpam-5555	64	31	]	]	X
ejpam-5555	64	32	⊆	⊆	NUM
ejpam-5555	64	33	n	n	NOUN
ejpam-5555	64	34	[	[	X
ejpam-5555	64	35	u	u	X
ejpam-5555	64	36	]	]	X
ejpam-5555	64	37	.	.	PUNCT
ejpam-5555	65	1	the	the	DET
ejpam-5555	65	2	set	set	NOUN
ejpam-5555	65	3	of	of	ADP
ejpam-5555	65	4	all	all	DET
ejpam-5555	65	5	semi	semi	ADJ
ejpam-5555	65	6	-	-	ADJ
ejpam-5555	65	7	extreme	extreme	ADJ
ejpam-5555	65	8	vertices	vertex	NOUN
ejpam-5555	65	9	of	of	ADP
ejpam-5555	65	10	g	g	PROPN
ejpam-5555	65	11	is	be	AUX
ejpam-5555	65	12	denoted	denote	VERB
ejpam-5555	65	13	by	by	ADP
ejpam-5555	65	14	se(g	se(g	NUM
ejpam-5555	65	15	)	)	PUNCT
ejpam-5555	65	16	.	.	PUNCT
ejpam-5555	66	1	a	a	DET
ejpam-5555	66	2	cutvertex	cutvertex	NOUN
ejpam-5555	66	3	of	of	ADP
ejpam-5555	66	4	a	a	DET
ejpam-5555	66	5	connected	connected	ADJ
ejpam-5555	66	6	graph	graph	NOUN
ejpam-5555	66	7	g	g	PROPN
ejpam-5555	66	8	is	be	AUX
ejpam-5555	66	9	the	the	DET
ejpam-5555	66	10	vertex	vertex	NOUN
ejpam-5555	66	11	whose	whose	DET
ejpam-5555	66	12	deletion	deletion	NOUN
ejpam-5555	66	13	increases	increase	VERB
ejpam-5555	66	14	the	the	DET
ejpam-5555	66	15	number	number	NOUN
ejpam-5555	66	16	of	of	ADP
ejpam-5555	66	17	components	component	NOUN
ejpam-5555	66	18	of	of	ADP
ejpam-5555	66	19	the	the	DET
ejpam-5555	66	20	subgraph	subgraph	NOUN
ejpam-5555	66	21	of	of	ADP
ejpam-5555	66	22	g	g	PROPN
ejpam-5555	66	23	,	,	PUNCT
ejpam-5555	66	24	that	that	ADV
ejpam-5555	66	25	is	is	ADV
ejpam-5555	66	26	,	,	PUNCT
ejpam-5555	66	27	u	u	NOUN
ejpam-5555	66	28	is	be	AUX
ejpam-5555	66	29	a	a	DET
ejpam-5555	66	30	cutvertex	cutvertex	NOUN
ejpam-5555	66	31	if	if	SCONJ
ejpam-5555	67	1	and	and	CCONJ
ejpam-5555	67	2	only	only	ADV
ejpam-5555	67	3	if	if	SCONJ
ejpam-5555	67	4	⟨g−	⟨g−	PROPN
ejpam-5555	67	5	u⟩	u⟩	VERB
ejpam-5555	67	6	is	be	AUX
ejpam-5555	67	7	disconnected	disconnect	VERB
ejpam-5555	67	8	.	.	PUNCT
ejpam-5555	68	1	the	the	DET
ejpam-5555	68	2	deletion	deletion	NOUN
ejpam-5555	68	3	or	or	CCONJ
ejpam-5555	68	4	removal	removal	NOUN
ejpam-5555	68	5	of	of	ADP
ejpam-5555	68	6	a	a	DET
ejpam-5555	68	7	proper	proper	ADJ
ejpam-5555	68	8	subset	subset	NOUN
ejpam-5555	68	9	s	s	NOUN
ejpam-5555	68	10	of	of	ADP
ejpam-5555	68	11	vertices	vertex	NOUN
ejpam-5555	68	12	of	of	ADP
ejpam-5555	68	13	g	g	PROPN
ejpam-5555	68	14	results	result	NOUN
ejpam-5555	68	15	in	in	ADP
ejpam-5555	68	16	that	that	DET
ejpam-5555	68	17	subgraph	subgraph	NOUN
ejpam-5555	68	18	g	g	PROPN
ejpam-5555	68	19	\	\	PROPN
ejpam-5555	68	20	s	s	PROPN
ejpam-5555	68	21	of	of	ADP
ejpam-5555	68	22	g	g	NOUN
ejpam-5555	68	23	consisting	consist	VERB
ejpam-5555	68	24	of	of	ADP
ejpam-5555	68	25	all	all	DET
ejpam-5555	68	26	vertices	vertex	NOUN
ejpam-5555	68	27	of	of	ADP
ejpam-5555	68	28	g	g	NOUN
ejpam-5555	68	29	not	not	PART
ejpam-5555	68	30	in	in	ADP
ejpam-5555	68	31	s	s	PRON
ejpam-5555	68	32	and	and	CCONJ
ejpam-5555	68	33	all	all	DET
ejpam-5555	68	34	edges	edge	NOUN
ejpam-5555	68	35	not	not	PART
ejpam-5555	68	36	incident	incident	NOUN
ejpam-5555	68	37	with	with	ADP
ejpam-5555	68	38	a	a	DET
ejpam-5555	68	39	vertex	vertex	NOUN
ejpam-5555	68	40	in	in	ADP
ejpam-5555	68	41	s.	s.	PROPN
ejpam-5555	68	42	the	the	DET
ejpam-5555	68	43	deletion	deletion	NOUN
ejpam-5555	68	44	of	of	ADP
ejpam-5555	68	45	a	a	DET
ejpam-5555	68	46	vertex	vertex	NOUN
ejpam-5555	68	47	u	u	NOUN
ejpam-5555	68	48	of	of	ADP
ejpam-5555	68	49	g	g	PROPN
ejpam-5555	68	50	results	result	NOUN
ejpam-5555	68	51	in	in	ADP
ejpam-5555	68	52	that	that	DET
ejpam-5555	68	53	subgraph	subgraph	NOUN
ejpam-5555	68	54	g	g	PROPN
ejpam-5555	68	55	\	\	NOUN
ejpam-5555	68	56	u	u	NOUN
ejpam-5555	68	57	of	of	ADP
ejpam-5555	68	58	g	g	NOUN
ejpam-5555	68	59	consisting	consist	VERB
ejpam-5555	68	60	of	of	ADP
ejpam-5555	68	61	all	all	DET
ejpam-5555	68	62	vertices	vertex	NOUN
ejpam-5555	68	63	of	of	ADP
ejpam-5555	68	64	g	g	NOUN
ejpam-5555	68	65	except	except	SCONJ
ejpam-5555	68	66	u	u	NOUN
ejpam-5555	68	67	and	and	CCONJ
ejpam-5555	68	68	all	all	DET
ejpam-5555	68	69	edges	edge	NOUN
ejpam-5555	68	70	not	not	PART
ejpam-5555	68	71	incident	incident	NOUN
ejpam-5555	68	72	with	with	ADP
ejpam-5555	68	73	a	a	DET
ejpam-5555	68	74	vertex	vertex	NOUN
ejpam-5555	68	75	u.	u.	NOUN
ejpam-5555	68	76	on	on	ADP
ejpam-5555	68	77	the	the	DET
ejpam-5555	68	78	other	other	ADJ
ejpam-5555	68	79	hand	hand	NOUN
ejpam-5555	68	80	,	,	PUNCT
ejpam-5555	68	81	the	the	DET
ejpam-5555	68	82	deletion	deletion	NOUN
ejpam-5555	68	83	of	of	ADP
ejpam-5555	68	84	a	a	DET
ejpam-5555	68	85	subset	subset	NOUN
ejpam-5555	68	86	x	x	PUNCT
ejpam-5555	68	87	of	of	ADP
ejpam-5555	68	88	edges	edge	NOUN
ejpam-5555	68	89	yields	yield	VERB
ejpam-5555	68	90	the	the	DET
ejpam-5555	68	91	spanning	span	VERB
ejpam-5555	68	92	subgraph	subgraph	NOUN
ejpam-5555	68	93	g	g	PROPN
ejpam-5555	68	94	\x	\x	NOUN
ejpam-5555	68	95	containing	contain	VERB
ejpam-5555	68	96	all	all	DET
ejpam-5555	68	97	edges	edge	NOUN
ejpam-5555	68	98	of	of	ADP
ejpam-5555	68	99	g	g	NOUN
ejpam-5555	68	100	not	not	PART
ejpam-5555	68	101	in	in	ADP
ejpam-5555	68	102	x.	x.	NOUN
ejpam-5555	68	103	let	let	VERB
ejpam-5555	68	104	g1	g1	PROPN
ejpam-5555	68	105	,	,	PUNCT
ejpam-5555	68	106	g2	g2	PROPN
ejpam-5555	68	107	,	,	PUNCT
ejpam-5555	68	108	.	.	PUNCT
ejpam-5555	68	109	.	.	PUNCT
ejpam-5555	69	1	.	.	PUNCT
ejpam-5555	70	1	,	,	PUNCT
ejpam-5555	70	2	gt	gt	PROPN
ejpam-5555	70	3	be	be	AUX
ejpam-5555	70	4	disjoint	disjoint	NOUN
ejpam-5555	70	5	graphs	graph	NOUN
ejpam-5555	70	6	each	each	PRON
ejpam-5555	70	7	containing	contain	VERB
ejpam-5555	70	8	a	a	DET
ejpam-5555	70	9	complete	complete	ADJ
ejpam-5555	70	10	subgraph	subgraph	NOUN
ejpam-5555	70	11	kr	kr	PROPN
ejpam-5555	70	12	(	(	PUNCT
ejpam-5555	70	13	r	r	NOUN
ejpam-5555	70	14	≥	≥	NOUN
ejpam-5555	70	15	1	1	NUM
ejpam-5555	70	16	)	)	PUNCT
ejpam-5555	70	17	.	.	PUNCT
ejpam-5555	71	1	let	let	VERB
ejpam-5555	71	2	g	g	NOUN
ejpam-5555	71	3	be	be	AUX
ejpam-5555	71	4	the	the	DET
ejpam-5555	71	5	graph	graph	NOUN
ejpam-5555	71	6	obtained	obtain	VERB
ejpam-5555	71	7	from	from	ADP
ejpam-5555	71	8	the	the	DET
ejpam-5555	71	9	union	union	NOUN
ejpam-5555	71	10	of	of	ADP
ejpam-5555	71	11	t	t	PROPN
ejpam-5555	71	12	graphs	graph	NOUN
ejpam-5555	71	13	gi	gi	VERB
ejpam-5555	71	14	by	by	ADP
ejpam-5555	71	15	identifying	identify	VERB
ejpam-5555	71	16	the	the	DET
ejpam-5555	71	17	kr	kr	PROPN
ejpam-5555	71	18	’s	’s	PART
ejpam-5555	71	19	(	(	PUNCT
ejpam-5555	71	20	one	one	NUM
ejpam-5555	71	21	from	from	ADP
ejpam-5555	71	22	each	each	DET
ejpam-5555	71	23	gi	gi	NOUN
ejpam-5555	71	24	)	)	PUNCT
ejpam-5555	71	25	in	in	ADP
ejpam-5555	71	26	an	an	DET
ejpam-5555	71	27	arbitrary	arbitrary	ADJ
ejpam-5555	71	28	way	way	NOUN
ejpam-5555	71	29	.	.	PUNCT
ejpam-5555	72	1	we	we	PRON
ejpam-5555	72	2	call	call	VERB
ejpam-5555	72	3	g	g	PROPN
ejpam-5555	72	4	a	a	DET
ejpam-5555	72	5	kr	kr	NOUN
ejpam-5555	72	6	-	-	PUNCT
ejpam-5555	72	7	gluing	gluing	NOUN
ejpam-5555	72	8	of	of	ADP
ejpam-5555	72	9	g1	g1	NOUN
ejpam-5555	72	10	,	,	PUNCT
ejpam-5555	72	11	g2	g2	PROPN
ejpam-5555	72	12	,	,	PUNCT
ejpam-5555	72	13	.	.	PUNCT
ejpam-5555	72	14	.	.	PUNCT
ejpam-5555	73	1	.	.	PUNCT
ejpam-5555	74	1	,	,	PUNCT
ejpam-5555	74	2	gt	gt	PROPN
ejpam-5555	74	3	.	.	PUNCT
ejpam-5555	75	1	in	in	ADP
ejpam-5555	75	2	particular	particular	ADJ
ejpam-5555	75	3	,	,	PUNCT
ejpam-5555	75	4	when	when	SCONJ
ejpam-5555	75	5	r	r	NOUN
ejpam-5555	75	6	=	=	SYM
ejpam-5555	75	7	1	1	NUM
ejpam-5555	75	8	(	(	PUNCT
ejpam-5555	75	9	respectively	respectively	ADV
ejpam-5555	75	10	r	r	NOUN
ejpam-5555	75	11	=	=	SYM
ejpam-5555	75	12	2	2	X
ejpam-5555	75	13	)	)	PUNCT
ejpam-5555	75	14	we	we	PRON
ejpam-5555	75	15	say	say	VERB
ejpam-5555	75	16	g	g	PROPN
ejpam-5555	75	17	is	be	AUX
ejpam-5555	75	18	a	a	DET
ejpam-5555	75	19	vertex	vertex	NOUN
ejpam-5555	75	20	-	-	PUNCT
ejpam-5555	75	21	gluing	gluing	NOUN
ejpam-5555	75	22	(	(	PUNCT
ejpam-5555	75	23	respectively	respectively	ADV
ejpam-5555	75	24	an	an	DET
ejpam-5555	75	25	edge	edge	NOUN
ejpam-5555	75	26	-	-	PUNCT
ejpam-5555	75	27	gluing	gluing	NOUN
ejpam-5555	75	28	)	)	PUNCT
ejpam-5555	75	29	of	of	ADP
ejpam-5555	75	30	g1	g1	PROPN
ejpam-5555	75	31	,	,	PUNCT
ejpam-5555	75	32	g2	g2	PROPN
ejpam-5555	75	33	,	,	PUNCT
ejpam-5555	75	34	.	.	PUNCT
ejpam-5555	75	35	.	.	PUNCT
ejpam-5555	76	1	.	.	PUNCT
ejpam-5555	77	1	,	,	PUNCT
ejpam-5555	77	2	gt	gt	PROPN
ejpam-5555	77	3	.	.	PROPN
ejpam-5555	77	4	2	2	NUM
ejpam-5555	77	5	.	.	PUNCT
ejpam-5555	77	6	preliminaries	preliminary	NOUN
ejpam-5555	77	7	the	the	DET
ejpam-5555	77	8	following	follow	VERB
ejpam-5555	77	9	are	be	AUX
ejpam-5555	77	10	the	the	DET
ejpam-5555	77	11	known	know	VERB
ejpam-5555	77	12	results	result	NOUN
ejpam-5555	77	13	related	relate	VERB
ejpam-5555	77	14	to	to	ADP
ejpam-5555	77	15	this	this	DET
ejpam-5555	77	16	study	study	NOUN
ejpam-5555	77	17	.	.	PUNCT
ejpam-5555	78	1	remark	remark	NOUN
ejpam-5555	78	2	1	1	NUM
ejpam-5555	78	3	.	.	PUNCT
ejpam-5555	79	1	[	[	X
ejpam-5555	79	2	8	8	NUM
ejpam-5555	79	3	]	]	PUNCT
ejpam-5555	79	4	let	let	VERB
ejpam-5555	79	5	g	g	PRON
ejpam-5555	79	6	be	be	AUX
ejpam-5555	79	7	a	a	DET
ejpam-5555	79	8	nontrivial	nontrivial	ADJ
ejpam-5555	79	9	connected	connect	VERB
ejpam-5555	79	10	graph	graph	NOUN
ejpam-5555	79	11	.	.	PUNCT
ejpam-5555	80	1	then	then	ADV
ejpam-5555	80	2	v	v	X
ejpam-5555	80	3	(	(	PUNCT
ejpam-5555	80	4	g	g	NOUN
ejpam-5555	80	5	)	)	PUNCT
ejpam-5555	80	6	is	be	AUX
ejpam-5555	80	7	an	an	DET
ejpam-5555	80	8	edge	edge	NOUN
ejpam-5555	80	9	geodetic	geodetic	ADJ
ejpam-5555	80	10	dominating	dominating	NOUN
ejpam-5555	80	11	set	set	NOUN
ejpam-5555	80	12	of	of	ADP
ejpam-5555	80	13	g.	g.	PROPN
ejpam-5555	80	14	theorem	theorem	VERB
ejpam-5555	80	15	1	1	NUM
ejpam-5555	80	16	.	.	PUNCT
ejpam-5555	81	1	[	[	X
ejpam-5555	81	2	13	13	NUM
ejpam-5555	81	3	]	]	X
ejpam-5555	81	4	if	if	SCONJ
ejpam-5555	81	5	g	g	PROPN
ejpam-5555	81	6	has	have	VERB
ejpam-5555	81	7	at	at	ADV
ejpam-5555	81	8	least	least	ADV
ejpam-5555	81	9	two	two	NUM
ejpam-5555	81	10	vertices	vertex	NOUN
ejpam-5555	81	11	of	of	ADP
ejpam-5555	81	12	degree	degree	NOUN
ejpam-5555	81	13	n−	n−	NOUN
ejpam-5555	81	14	1	1	NUM
ejpam-5555	81	15	,	,	PUNCT
ejpam-5555	81	16	then	then	ADV
ejpam-5555	81	17	γge(g	γge(g	PROPN
ejpam-5555	81	18	)	)	PUNCT
ejpam-5555	81	19	=	=	SYM
ejpam-5555	82	1	n	n	PRON
ejpam-5555	82	2	theorem	theorem	NOUN
ejpam-5555	82	3	2	2	NUM
ejpam-5555	82	4	.	.	PUNCT
ejpam-5555	83	1	[	[	X
ejpam-5555	83	2	13	13	NUM
ejpam-5555	83	3	]	]	PUNCT
ejpam-5555	83	4	for	for	ADP
ejpam-5555	83	5	the	the	DET
ejpam-5555	83	6	complete	complete	ADJ
ejpam-5555	83	7	graph	graph	NOUN
ejpam-5555	83	8	kn	kn	PROPN
ejpam-5555	83	9	with	with	ADP
ejpam-5555	83	10	n	n	PRON
ejpam-5555	83	11	≥	≥	NUM
ejpam-5555	83	12	2	2	NUM
ejpam-5555	83	13	,	,	PUNCT
ejpam-5555	83	14	γge(kn	γge(kn	NUM
ejpam-5555	83	15	)	)	PUNCT
ejpam-5555	83	16	=	=	SYM
ejpam-5555	83	17	n.	n.	NOUN
ejpam-5555	83	18	theorem	theorem	VERB
ejpam-5555	83	19	3	3	NUM
ejpam-5555	83	20	.	.	PUNCT
ejpam-5555	84	1	[	[	X
ejpam-5555	84	2	12	12	NUM
ejpam-5555	84	3	]	]	PUNCT
ejpam-5555	84	4	each	each	DET
ejpam-5555	84	5	extreme	extreme	ADJ
ejpam-5555	84	6	vertex	vertex	NOUN
ejpam-5555	84	7	of	of	ADP
ejpam-5555	84	8	g	g	PROPN
ejpam-5555	84	9	belongs	belong	VERB
ejpam-5555	84	10	to	to	ADP
ejpam-5555	84	11	every	every	DET
ejpam-5555	84	12	edge	edge	NOUN
ejpam-5555	84	13	geodetic	geodetic	ADJ
ejpam-5555	84	14	cover	cover	NOUN
ejpam-5555	84	15	of	of	ADP
ejpam-5555	84	16	g.	g.	PROPN
ejpam-5555	84	17	in	in	ADP
ejpam-5555	84	18	particular	particular	ADJ
ejpam-5555	84	19	,	,	PUNCT
ejpam-5555	84	20	each	each	PRON
ejpam-5555	84	21	end	end	VERB
ejpam-5555	84	22	vertex	vertex	NOUN
ejpam-5555	84	23	of	of	ADP
ejpam-5555	84	24	g	g	PROPN
ejpam-5555	84	25	belongs	belong	VERB
ejpam-5555	84	26	to	to	ADP
ejpam-5555	84	27	every	every	DET
ejpam-5555	84	28	edge	edge	NOUN
ejpam-5555	84	29	geodetic	geodetic	ADJ
ejpam-5555	84	30	cover	cover	NOUN
ejpam-5555	84	31	of	of	ADP
ejpam-5555	84	32	g	g	NOUN
ejpam-5555	84	33	theorem	theorem	ADJ
ejpam-5555	84	34	4	4	NUM
ejpam-5555	84	35	.	.	PUNCT
ejpam-5555	85	1	[	[	X
ejpam-5555	85	2	13	13	NUM
ejpam-5555	85	3	]	]	X
ejpam-5555	85	4	if	if	SCONJ
ejpam-5555	85	5	g	g	PROPN
ejpam-5555	85	6	has	have	VERB
ejpam-5555	85	7	exactly	exactly	ADV
ejpam-5555	85	8	one	one	NUM
ejpam-5555	85	9	vertex	vertex	NOUN
ejpam-5555	85	10	of	of	ADP
ejpam-5555	85	11	degree	degree	NOUN
ejpam-5555	85	12	n−	n−	NOUN
ejpam-5555	85	13	1	1	NUM
ejpam-5555	85	14	,	,	PUNCT
ejpam-5555	85	15	then	then	ADV
ejpam-5555	85	16	γge(g	γge(g	PROPN
ejpam-5555	85	17	)	)	PUNCT
ejpam-5555	86	1	=	=	PUNCT
ejpam-5555	86	2	n−	n−	NOUN
ejpam-5555	86	3	1	1	NUM
ejpam-5555	86	4	.	.	PUNCT
ejpam-5555	87	1	c.j	c.j	X
ejpam-5555	87	2	.	.	PROPN
ejpam-5555	87	3	quije	quije	PROPN
ejpam-5555	87	4	,	,	PUNCT
ejpam-5555	87	5	r.	r.	PROPN
ejpam-5555	87	6	mariano	mariano	PROPN
ejpam-5555	87	7	,	,	PUNCT
ejpam-5555	87	8	e.	e.	PROPN
ejpam-5555	87	9	ahmad	ahmad	PROPN
ejpam-5555	87	10	/	/	SYM
ejpam-5555	87	11	eur	eur	PROPN
ejpam-5555	87	12	.	.	PUNCT
ejpam-5555	88	1	j.	j.	PROPN
ejpam-5555	88	2	pure	pure	PROPN
ejpam-5555	88	3	appl	appl	PROPN
ejpam-5555	88	4	.	.	PROPN
ejpam-5555	88	5	math	math	PROPN
ejpam-5555	88	6	,	,	PUNCT
ejpam-5555	88	7	18	18	NUM
ejpam-5555	88	8	(	(	PUNCT
ejpam-5555	88	9	1	1	NUM
ejpam-5555	88	10	)	)	PUNCT
ejpam-5555	88	11	(	(	PUNCT
ejpam-5555	88	12	2025	2025	NUM
ejpam-5555	88	13	)	)	PUNCT
ejpam-5555	88	14	,	,	PUNCT
ejpam-5555	88	15	5555	5555	NUM
ejpam-5555	88	16	4	4	NUM
ejpam-5555	88	17	of	of	ADP
ejpam-5555	88	18	8	8	NUM
ejpam-5555	88	19	3	3	NUM
ejpam-5555	88	20	.	.	PUNCT
ejpam-5555	88	21	main	main	ADJ
ejpam-5555	88	22	results	result	NOUN
ejpam-5555	88	23	3.1	3.1	NUM
ejpam-5555	88	24	.	.	PUNCT
ejpam-5555	89	1	deletion	deletion	NOUN
ejpam-5555	89	2	of	of	ADP
ejpam-5555	89	3	independent	independent	ADJ
ejpam-5555	89	4	edges	edge	NOUN
ejpam-5555	89	5	of	of	ADP
ejpam-5555	89	6	complete	complete	ADJ
ejpam-5555	89	7	graphs	graph	NOUN
ejpam-5555	89	8	theorem	theorem	VERB
ejpam-5555	89	9	5	5	NUM
ejpam-5555	89	10	.	.	PUNCT
ejpam-5555	90	1	let	let	VERB
ejpam-5555	90	2	g	g	PRON
ejpam-5555	90	3	be	be	AUX
ejpam-5555	90	4	a	a	DET
ejpam-5555	90	5	complete	complete	ADJ
ejpam-5555	90	6	graph	graph	NOUN
ejpam-5555	90	7	of	of	ADP
ejpam-5555	90	8	order	order	NOUN
ejpam-5555	90	9	n	n	PRON
ejpam-5555	90	10	≥	≥	NOUN
ejpam-5555	90	11	4	4	NUM
ejpam-5555	90	12	.	.	PUNCT
ejpam-5555	91	1	let	let	VERB
ejpam-5555	91	2	s	s	PRON
ejpam-5555	91	3	⊆	⊆	NUM
ejpam-5555	91	4	v	v	NOUN
ejpam-5555	91	5	(	(	PUNCT
ejpam-5555	91	6	h	h	NOUN
ejpam-5555	91	7	)	)	PUNCT
ejpam-5555	91	8	,	,	PUNCT
ejpam-5555	91	9	where	where	SCONJ
ejpam-5555	91	10	h	h	NOUN
ejpam-5555	91	11	is	be	AUX
ejpam-5555	91	12	a	a	DET
ejpam-5555	91	13	connected	connected	ADJ
ejpam-5555	91	14	subgraph	subgraph	NOUN
ejpam-5555	91	15	of	of	ADP
ejpam-5555	91	16	g	g	PROPN
ejpam-5555	91	17	obtained	obtain	VERB
ejpam-5555	91	18	by	by	ADP
ejpam-5555	91	19	deleting	delete	VERB
ejpam-5555	91	20	m	m	PRON
ejpam-5555	91	21	≤	≤	NOUN
ejpam-5555	91	22	⌊n2	⌊n2	PUNCT
ejpam-5555	91	23	⌋	⌋	NOUN
ejpam-5555	91	24	independent	independent	ADJ
ejpam-5555	91	25	edges	edge	NOUN
ejpam-5555	91	26	in	in	ADP
ejpam-5555	91	27	g.	g.	PROPN
ejpam-5555	91	28	i.	i.	PROPN
ejpam-5555	91	29	if	if	SCONJ
ejpam-5555	91	30	m	m	VERB
ejpam-5555	91	31	<	<	X
ejpam-5555	91	32	⌊n2	⌊n2	X
ejpam-5555	91	33	⌋	⌋	PROPN
ejpam-5555	91	34	,	,	PUNCT
ejpam-5555	91	35	then	then	ADV
ejpam-5555	91	36	s	s	VERB
ejpam-5555	91	37	is	be	AUX
ejpam-5555	91	38	an	an	DET
ejpam-5555	91	39	edge	edge	NOUN
ejpam-5555	91	40	geodetic	geodetic	ADJ
ejpam-5555	91	41	dominating	dominating	NOUN
ejpam-5555	91	42	set	set	NOUN
ejpam-5555	91	43	of	of	ADP
ejpam-5555	91	44	h	h	NOUN
ejpam-5555	91	45	if	if	SCONJ
ejpam-5555	92	1	and	and	CCONJ
ejpam-5555	92	2	only	only	ADV
ejpam-5555	92	3	if	if	SCONJ
ejpam-5555	92	4	s	s	VERB
ejpam-5555	92	5	=	=	SYM
ejpam-5555	92	6	v	v	PROPN
ejpam-5555	92	7	(	(	PUNCT
ejpam-5555	92	8	h	h	NOUN
ejpam-5555	92	9	)	)	PUNCT
ejpam-5555	92	10	.	.	PUNCT
ejpam-5555	93	1	ii	ii	PROPN
ejpam-5555	93	2	.	.	PUNCT
ejpam-5555	94	1	if	if	SCONJ
ejpam-5555	94	2	m	m	ADV
ejpam-5555	94	3	=	=	SYM
ejpam-5555	94	4	⌊n2	⌊n2	X
ejpam-5555	94	5	⌋	⌋	NOUN
ejpam-5555	94	6	and	and	CCONJ
ejpam-5555	94	7	n	n	PRON
ejpam-5555	94	8	is	be	AUX
ejpam-5555	94	9	odd	odd	ADJ
ejpam-5555	94	10	,	,	PUNCT
ejpam-5555	94	11	then	then	ADV
ejpam-5555	94	12	s	s	VERB
ejpam-5555	94	13	is	be	AUX
ejpam-5555	94	14	an	an	DET
ejpam-5555	94	15	edge	edge	NOUN
ejpam-5555	94	16	geodetic	geodetic	ADJ
ejpam-5555	94	17	dominating	dominating	NOUN
ejpam-5555	94	18	set	set	NOUN
ejpam-5555	94	19	of	of	ADP
ejpam-5555	94	20	h	h	NOUN
ejpam-5555	94	21	if	if	SCONJ
ejpam-5555	95	1	and	and	CCONJ
ejpam-5555	95	2	only	only	ADV
ejpam-5555	95	3	if	if	SCONJ
ejpam-5555	95	4	s	s	VERB
ejpam-5555	95	5	=	=	SYM
ejpam-5555	95	6	v	v	PROPN
ejpam-5555	95	7	(	(	PUNCT
ejpam-5555	95	8	h	h	NOUN
ejpam-5555	95	9	)	)	PUNCT
ejpam-5555	95	10	\	\	NOUN
ejpam-5555	95	11	{	{	PUNCT
ejpam-5555	95	12	v	v	NOUN
ejpam-5555	95	13	}	}	PUNCT
ejpam-5555	95	14	or	or	CCONJ
ejpam-5555	95	15	s	s	X
ejpam-5555	95	16	=	=	SYM
ejpam-5555	95	17	v	v	PROPN
ejpam-5555	95	18	(	(	PUNCT
ejpam-5555	95	19	h	h	NOUN
ejpam-5555	95	20	)	)	PUNCT
ejpam-5555	95	21	,	,	PUNCT
ejpam-5555	95	22	v	v	NOUN
ejpam-5555	95	23	is	be	AUX
ejpam-5555	95	24	the	the	DET
ejpam-5555	95	25	vertex	vertex	NOUN
ejpam-5555	95	26	of	of	ADP
ejpam-5555	95	27	degree	degree	NOUN
ejpam-5555	95	28	n−	n−	NOUN
ejpam-5555	95	29	1	1	NUM
ejpam-5555	95	30	in	in	ADP
ejpam-5555	95	31	h.	h.	PROPN
ejpam-5555	95	32	iii	iii	PROPN
ejpam-5555	95	33	.	.	PUNCT
ejpam-5555	96	1	if	if	SCONJ
ejpam-5555	96	2	m	m	PROPN
ejpam-5555	96	3	=	=	SYM
ejpam-5555	96	4	⌊n2	⌊n2	X
ejpam-5555	96	5	⌋	⌋	NOUN
ejpam-5555	96	6	and	and	CCONJ
ejpam-5555	96	7	n	n	NUM
ejpam-5555	96	8	is	be	AUX
ejpam-5555	96	9	even	even	ADV
ejpam-5555	96	10	,	,	PUNCT
ejpam-5555	96	11	then	then	ADV
ejpam-5555	96	12	s	s	VERB
ejpam-5555	96	13	is	be	AUX
ejpam-5555	96	14	an	an	DET
ejpam-5555	96	15	edge	edge	NOUN
ejpam-5555	96	16	geodetic	geodetic	ADJ
ejpam-5555	96	17	dominating	dominating	NOUN
ejpam-5555	96	18	set	set	NOUN
ejpam-5555	96	19	of	of	ADP
ejpam-5555	96	20	h	h	NOUN
ejpam-5555	96	21	if	if	SCONJ
ejpam-5555	97	1	and	and	CCONJ
ejpam-5555	97	2	only	only	ADV
ejpam-5555	97	3	if	if	SCONJ
ejpam-5555	97	4	s	s	VERB
ejpam-5555	97	5	=	=	SYM
ejpam-5555	97	6	v	v	PROPN
ejpam-5555	97	7	(	(	PUNCT
ejpam-5555	97	8	h	h	NOUN
ejpam-5555	97	9	)	)	PUNCT
ejpam-5555	97	10	\	\	NOUN
ejpam-5555	97	11	{	{	PUNCT
ejpam-5555	97	12	u	u	NOUN
ejpam-5555	97	13	,	,	PUNCT
ejpam-5555	97	14	v	v	NOUN
ejpam-5555	97	15	}	}	PUNCT
ejpam-5555	97	16	or	or	CCONJ
ejpam-5555	97	17	s	s	X
ejpam-5555	97	18	=	=	SYM
ejpam-5555	97	19	v	v	PROPN
ejpam-5555	97	20	(	(	PUNCT
ejpam-5555	97	21	h	h	NOUN
ejpam-5555	97	22	)	)	PUNCT
ejpam-5555	97	23	\	\	NOUN
ejpam-5555	97	24	{	{	PUNCT
ejpam-5555	97	25	v	v	NOUN
ejpam-5555	97	26	}	}	PUNCT
ejpam-5555	97	27	or	or	CCONJ
ejpam-5555	97	28	s	s	X
ejpam-5555	97	29	=	=	SYM
ejpam-5555	97	30	v	v	PROPN
ejpam-5555	97	31	(	(	PUNCT
ejpam-5555	97	32	h	h	NOUN
ejpam-5555	97	33	)	)	PUNCT
ejpam-5555	97	34	\	\	NOUN
ejpam-5555	97	35	{	{	PUNCT
ejpam-5555	97	36	u	u	NOUN
ejpam-5555	97	37	}	}	PUNCT
ejpam-5555	97	38	or	or	CCONJ
ejpam-5555	97	39	s	s	NOUN
ejpam-5555	97	40	=	=	SYM
ejpam-5555	97	41	v	v	PROPN
ejpam-5555	97	42	(	(	PUNCT
ejpam-5555	97	43	h	h	NOUN
ejpam-5555	97	44	)	)	PUNCT
ejpam-5555	97	45	,	,	PUNCT
ejpam-5555	97	46	where	where	SCONJ
ejpam-5555	97	47	vertices	vertice	VERB
ejpam-5555	97	48	u	u	NOUN
ejpam-5555	97	49	and	and	CCONJ
ejpam-5555	97	50	v	v	NOUN
ejpam-5555	97	51	are	be	AUX
ejpam-5555	97	52	not	not	PART
ejpam-5555	97	53	adjacent	adjacent	ADJ
ejpam-5555	97	54	in	in	ADP
ejpam-5555	97	55	h.	h.	PROPN
ejpam-5555	97	56	proof	proof	NOUN
ejpam-5555	97	57	.	.	PUNCT
ejpam-5555	98	1	let	let	VERB
ejpam-5555	98	2	g	g	PRON
ejpam-5555	98	3	be	be	AUX
ejpam-5555	98	4	a	a	DET
ejpam-5555	98	5	complete	complete	ADJ
ejpam-5555	98	6	graph	graph	NOUN
ejpam-5555	98	7	of	of	ADP
ejpam-5555	98	8	order	order	NOUN
ejpam-5555	98	9	n	n	PRON
ejpam-5555	98	10	≥	≥	NOUN
ejpam-5555	98	11	4	4	NUM
ejpam-5555	98	12	.	.	PUNCT
ejpam-5555	98	13	suppose	suppose	VERB
ejpam-5555	98	14	h	h	NOUN
ejpam-5555	98	15	is	be	AUX
ejpam-5555	98	16	a	a	DET
ejpam-5555	98	17	connected	connected	ADJ
ejpam-5555	98	18	subgraph	subgraph	NOUN
ejpam-5555	98	19	of	of	ADP
ejpam-5555	98	20	g	g	PROPN
ejpam-5555	98	21	obtained	obtain	VERB
ejpam-5555	98	22	by	by	ADP
ejpam-5555	98	23	deleting	delete	VERB
ejpam-5555	98	24	m	m	ADP
ejpam-5555	98	25	independent	independent	ADJ
ejpam-5555	98	26	edges	edge	NOUN
ejpam-5555	98	27	in	in	ADP
ejpam-5555	98	28	g.	g.	PROPN
ejpam-5555	98	29	if	if	SCONJ
ejpam-5555	98	30	1	1	NUM
ejpam-5555	98	31	≤	≤	NUM
ejpam-5555	98	32	m	m	VERB
ejpam-5555	98	33	<	<	X
ejpam-5555	98	34	⌊n2	⌊n2	PROPN
ejpam-5555	98	35	⌋	⌋	ADJ
ejpam-5555	98	36	,	,	PUNCT
ejpam-5555	98	37	then	then	ADV
ejpam-5555	98	38	the	the	DET
ejpam-5555	98	39	subgraph	subgraph	NOUN
ejpam-5555	98	40	h	h	PROPN
ejpam-5555	98	41	contains	contain	VERB
ejpam-5555	98	42	two	two	NUM
ejpam-5555	98	43	or	or	CCONJ
ejpam-5555	98	44	more	more	ADJ
ejpam-5555	98	45	vertices	vertex	NOUN
ejpam-5555	98	46	v	v	NOUN
ejpam-5555	98	47	with	with	ADP
ejpam-5555	98	48	∆	∆	PROPN
ejpam-5555	98	49	(	(	PUNCT
ejpam-5555	98	50	⟨n(v)⟩	⟨n(v)⟩	X
ejpam-5555	98	51	)	)	PUNCT
ejpam-5555	98	52	=	=	PUNCT
ejpam-5555	99	1	|n(v)|	|n(v)|	NUM
ejpam-5555	99	2	−	−	PROPN
ejpam-5555	99	3	1	1	NUM
ejpam-5555	99	4	for	for	ADP
ejpam-5555	99	5	all	all	DET
ejpam-5555	99	6	v	v	ADP
ejpam-5555	99	7	∈	∈	NOUN
ejpam-5555	99	8	v	v	NOUN
ejpam-5555	99	9	(	(	PUNCT
ejpam-5555	99	10	h	h	NOUN
ejpam-5555	99	11	)	)	PUNCT
ejpam-5555	99	12	.	.	PUNCT
ejpam-5555	100	1	by	by	ADP
ejpam-5555	100	2	theorem	theorem	NOUN
ejpam-5555	100	3	1	1	NUM
ejpam-5555	100	4	and	and	CCONJ
ejpam-5555	100	5	remark	remark	NOUN
ejpam-5555	100	6	1	1	NUM
ejpam-5555	100	7	,	,	PUNCT
ejpam-5555	100	8	s	s	VERB
ejpam-5555	100	9	is	be	AUX
ejpam-5555	100	10	an	an	DET
ejpam-5555	100	11	edge	edge	NOUN
ejpam-5555	100	12	geodetic	geodetic	ADJ
ejpam-5555	100	13	dominating	dominating	NOUN
ejpam-5555	100	14	set	set	NOUN
ejpam-5555	100	15	of	of	ADP
ejpam-5555	100	16	h	h	NOUN
ejpam-5555	100	17	if	if	SCONJ
ejpam-5555	101	1	and	and	CCONJ
ejpam-5555	101	2	only	only	ADV
ejpam-5555	101	3	if	if	SCONJ
ejpam-5555	101	4	s	s	VERB
ejpam-5555	101	5	=	=	SYM
ejpam-5555	101	6	v	v	PROPN
ejpam-5555	101	7	(	(	PUNCT
ejpam-5555	101	8	h	h	NOUN
ejpam-5555	101	9	)	)	PUNCT
ejpam-5555	101	10	.	.	PUNCT
ejpam-5555	102	1	this	this	PRON
ejpam-5555	102	2	proves	prove	VERB
ejpam-5555	102	3	(	(	PUNCT
ejpam-5555	102	4	i	i	NOUN
ejpam-5555	102	5	)	)	PUNCT
ejpam-5555	102	6	.	.	PUNCT
ejpam-5555	103	1	if	if	SCONJ
ejpam-5555	103	2	m	m	ADV
ejpam-5555	103	3	=	=	SYM
ejpam-5555	103	4	⌊n2	⌊n2	X
ejpam-5555	103	5	⌋	⌋	NOUN
ejpam-5555	103	6	and	and	CCONJ
ejpam-5555	103	7	n	n	PRON
ejpam-5555	103	8	is	be	AUX
ejpam-5555	103	9	odd	odd	ADJ
ejpam-5555	103	10	,	,	PUNCT
ejpam-5555	103	11	then	then	ADV
ejpam-5555	103	12	m	m	VERB
ejpam-5555	103	13	=	=	SYM
ejpam-5555	103	14	⌊n2	⌊n2	PUNCT
ejpam-5555	103	15	⌋	⌋	NUM
ejpam-5555	104	1	=	=	SYM
ejpam-5555	104	2	n−1	n−1	PROPN
ejpam-5555	104	3	2	2	NUM
ejpam-5555	104	4	.	.	PUNCT
ejpam-5555	105	1	hence	hence	ADV
ejpam-5555	105	2	,	,	PUNCT
ejpam-5555	105	3	the	the	DET
ejpam-5555	105	4	subgraph	subgraph	NOUN
ejpam-5555	105	5	h	h	PROPN
ejpam-5555	105	6	contains	contain	VERB
ejpam-5555	105	7	a	a	DET
ejpam-5555	105	8	unique	unique	ADJ
ejpam-5555	105	9	vertex	vertex	NOUN
ejpam-5555	105	10	v	v	ADP
ejpam-5555	105	11	∈	∈	NOUN
ejpam-5555	105	12	v	v	NOUN
ejpam-5555	105	13	(	(	PUNCT
ejpam-5555	105	14	h	h	NOUN
ejpam-5555	105	15	)	)	PUNCT
ejpam-5555	105	16	such	such	ADJ
ejpam-5555	105	17	that	that	PRON
ejpam-5555	105	18	degg(v	degg(v	PROPN
ejpam-5555	105	19	)	)	PUNCT
ejpam-5555	105	20	=	=	PUNCT
ejpam-5555	105	21	n−	n−	NOUN
ejpam-5555	105	22	1	1	NUM
ejpam-5555	105	23	.	.	PUNCT
ejpam-5555	106	1	thus	thus	ADV
ejpam-5555	106	2	,	,	PUNCT
ejpam-5555	106	3	by	by	ADP
ejpam-5555	106	4	remark	remark	NOUN
ejpam-5555	106	5	1	1	NUM
ejpam-5555	106	6	,	,	PUNCT
ejpam-5555	106	7	theorem	theorem	VERB
ejpam-5555	106	8	1	1	NUM
ejpam-5555	106	9	and	and	CCONJ
ejpam-5555	106	10	theorem	theorem	VERB
ejpam-5555	106	11	3	3	NUM
ejpam-5555	106	12	,	,	PUNCT
ejpam-5555	106	13	s	s	VERB
ejpam-5555	106	14	is	be	AUX
ejpam-5555	106	15	an	an	DET
ejpam-5555	106	16	edge	edge	NOUN
ejpam-5555	106	17	geodetic	geodetic	ADJ
ejpam-5555	106	18	set	set	NOUN
ejpam-5555	106	19	of	of	ADP
ejpam-5555	106	20	h	h	NOUN
ejpam-5555	106	21	and	and	CCONJ
ejpam-5555	106	22	consequently	consequently	ADV
ejpam-5555	106	23	,	,	PUNCT
ejpam-5555	106	24	an	an	DET
ejpam-5555	106	25	edge	edge	NOUN
ejpam-5555	106	26	geodetic	geodetic	ADJ
ejpam-5555	106	27	dominating	dominating	NOUN
ejpam-5555	106	28	set	set	NOUN
ejpam-5555	106	29	of	of	ADP
ejpam-5555	106	30	h	h	NOUN
ejpam-5555	106	31	if	if	SCONJ
ejpam-5555	107	1	and	and	CCONJ
ejpam-5555	107	2	only	only	ADV
ejpam-5555	107	3	if	if	SCONJ
ejpam-5555	107	4	s	s	VERB
ejpam-5555	107	5	=	=	SYM
ejpam-5555	107	6	v	v	PROPN
ejpam-5555	107	7	(	(	PUNCT
ejpam-5555	107	8	h	h	NOUN
ejpam-5555	107	9	)	)	PUNCT
ejpam-5555	107	10	\	\	NOUN
ejpam-5555	107	11	{	{	PUNCT
ejpam-5555	107	12	v	v	NOUN
ejpam-5555	107	13	}	}	PUNCT
ejpam-5555	107	14	or	or	CCONJ
ejpam-5555	107	15	s	s	X
ejpam-5555	107	16	=	=	SYM
ejpam-5555	107	17	v	v	PROPN
ejpam-5555	107	18	(	(	PUNCT
ejpam-5555	107	19	h	h	NOUN
ejpam-5555	107	20	)	)	PUNCT
ejpam-5555	107	21	,	,	PUNCT
ejpam-5555	107	22	where	where	SCONJ
ejpam-5555	107	23	v	v	NOUN
ejpam-5555	107	24	is	be	AUX
ejpam-5555	107	25	the	the	DET
ejpam-5555	107	26	vertex	vertex	NOUN
ejpam-5555	107	27	of	of	ADP
ejpam-5555	107	28	degree	degree	NOUN
ejpam-5555	107	29	n−	n−	NOUN
ejpam-5555	107	30	1	1	NUM
ejpam-5555	107	31	in	in	ADP
ejpam-5555	107	32	h.	h.	PROPN
ejpam-5555	107	33	this	this	PRON
ejpam-5555	107	34	proves	prove	VERB
ejpam-5555	107	35	(	(	PUNCT
ejpam-5555	107	36	ii	ii	NOUN
ejpam-5555	107	37	)	)	PUNCT
ejpam-5555	107	38	.	.	PUNCT
ejpam-5555	108	1	suppose	suppose	VERB
ejpam-5555	108	2	m	m	VERB
ejpam-5555	108	3	=	=	SYM
ejpam-5555	108	4	⌊n2	⌊n2	X
ejpam-5555	108	5	⌋	⌋	NOUN
ejpam-5555	108	6	and	and	CCONJ
ejpam-5555	108	7	n	n	NUM
ejpam-5555	108	8	is	be	AUX
ejpam-5555	108	9	even	even	ADV
ejpam-5555	108	10	.	.	PUNCT
ejpam-5555	109	1	consider	consider	VERB
ejpam-5555	109	2	a	a	DET
ejpam-5555	109	3	pair	pair	NOUN
ejpam-5555	109	4	(	(	PUNCT
ejpam-5555	109	5	u	u	NOUN
ejpam-5555	109	6	,	,	PUNCT
ejpam-5555	109	7	v	v	NOUN
ejpam-5555	109	8	)	)	PUNCT
ejpam-5555	109	9	of	of	ADP
ejpam-5555	109	10	vertices	vertex	NOUN
ejpam-5555	109	11	in	in	ADP
ejpam-5555	109	12	h	h	NOUN
ejpam-5555	109	13	such	such	ADJ
ejpam-5555	109	14	that	that	SCONJ
ejpam-5555	109	15	u	u	PROPN
ejpam-5555	109	16	is	be	AUX
ejpam-5555	109	17	not	not	PART
ejpam-5555	109	18	adjacent	adjacent	ADJ
ejpam-5555	109	19	to	to	ADP
ejpam-5555	109	20	v	v	NOUN
ejpam-5555	109	21	in	in	ADP
ejpam-5555	109	22	h.	h.	PROPN
ejpam-5555	109	23	then	then	ADV
ejpam-5555	109	24	we	we	PRON
ejpam-5555	109	25	claim	claim	VERB
ejpam-5555	109	26	that	that	SCONJ
ejpam-5555	109	27	s	s	VERB
ejpam-5555	109	28	=	=	SYM
ejpam-5555	109	29	v	v	PROPN
ejpam-5555	109	30	(	(	PUNCT
ejpam-5555	109	31	h)\{u	h)\{u	PROPN
ejpam-5555	109	32	,	,	PUNCT
ejpam-5555	109	33	v	v	NOUN
ejpam-5555	109	34	}	}	PUNCT
ejpam-5555	109	35	is	be	AUX
ejpam-5555	109	36	a	a	DET
ejpam-5555	109	37	minimum	minimum	ADJ
ejpam-5555	109	38	edge	edge	NOUN
ejpam-5555	109	39	geodetic	geodetic	ADJ
ejpam-5555	109	40	dominating	dominating	NOUN
ejpam-5555	109	41	set	set	NOUN
ejpam-5555	109	42	.	.	PUNCT
ejpam-5555	110	1	to	to	PART
ejpam-5555	110	2	prove	prove	VERB
ejpam-5555	110	3	this	this	DET
ejpam-5555	110	4	claim	claim	NOUN
ejpam-5555	110	5	,	,	PUNCT
ejpam-5555	110	6	let	let	VERB
ejpam-5555	110	7	x	x	PRON
ejpam-5555	110	8	,	,	PUNCT
ejpam-5555	110	9	y	y	PROPN
ejpam-5555	110	10	∈	∈	PROPN
ejpam-5555	110	11	v	v	ADP
ejpam-5555	110	12	(	(	PUNCT
ejpam-5555	110	13	h	h	NOUN
ejpam-5555	110	14	)	)	PUNCT
ejpam-5555	110	15	such	such	ADJ
ejpam-5555	110	16	that	that	SCONJ
ejpam-5555	110	17	xy	xy	PROPN
ejpam-5555	110	18	∈	∈	PROPN
ejpam-5555	110	19	e(h	e(h	PROPN
ejpam-5555	110	20	)	)	PUNCT
ejpam-5555	110	21	and	and	CCONJ
ejpam-5555	110	22	consider	consider	VERB
ejpam-5555	110	23	the	the	DET
ejpam-5555	110	24	following	follow	VERB
ejpam-5555	110	25	cases	case	NOUN
ejpam-5555	110	26	:	:	PUNCT
ejpam-5555	110	27	case	case	NOUN
ejpam-5555	110	28	1	1	X
ejpam-5555	110	29	.	.	PUNCT
ejpam-5555	110	30	suppose	suppose	VERB
ejpam-5555	110	31	x	x	PRON
ejpam-5555	110	32	,	,	PUNCT
ejpam-5555	110	33	y	y	PROPN
ejpam-5555	110	34	∈	∈	PROPN
ejpam-5555	110	35	s.	s.	PROPN
ejpam-5555	110	36	then	then	ADV
ejpam-5555	110	37	xy	xy	PROPN
ejpam-5555	110	38	is	be	AUX
ejpam-5555	110	39	contained	contain	VERB
ejpam-5555	110	40	in	in	ADP
ejpam-5555	110	41	the	the	DET
ejpam-5555	110	42	x−	x−	PROPN
ejpam-5555	110	43	y	y	PROPN
ejpam-5555	110	44	geodesic	geodesic	NOUN
ejpam-5555	110	45	.	.	PUNCT
ejpam-5555	111	1	case	case	NOUN
ejpam-5555	111	2	2	2	X
ejpam-5555	111	3	.	.	PUNCT
ejpam-5555	111	4	suppose	suppose	VERB
ejpam-5555	111	5	x	x	SYM
ejpam-5555	111	6	=	=	PUNCT
ejpam-5555	111	7	u	u	NOUN
ejpam-5555	111	8	or	or	CCONJ
ejpam-5555	111	9	x	x	X
ejpam-5555	111	10	=	=	SYM
ejpam-5555	111	11	v	v	PROPN
ejpam-5555	111	12	and	and	CCONJ
ejpam-5555	111	13	y	y	PROPN
ejpam-5555	111	14	∈	∈	PROPN
ejpam-5555	111	15	s.	s.	PROPN
ejpam-5555	111	16	without	without	ADP
ejpam-5555	111	17	loss	loss	NOUN
ejpam-5555	111	18	of	of	ADP
ejpam-5555	111	19	generality	generality	NOUN
ejpam-5555	111	20	,	,	PUNCT
ejpam-5555	111	21	assume	assume	VERB
ejpam-5555	111	22	x	x	X
ejpam-5555	111	23	=	=	SYM
ejpam-5555	111	24	u.	u.	AUX
ejpam-5555	111	25	pick	pick	VERB
ejpam-5555	111	26	z	z	PROPN
ejpam-5555	111	27	∈	∈	PROPN
ejpam-5555	111	28	v	v	ADP
ejpam-5555	111	29	(	(	PUNCT
ejpam-5555	111	30	h	h	NOUN
ejpam-5555	111	31	)	)	PUNCT
ejpam-5555	111	32	\	\	NOUN
ejpam-5555	111	33	{	{	PUNCT
ejpam-5555	111	34	y	y	NOUN
ejpam-5555	111	35	}	}	PUNCT
ejpam-5555	111	36	such	such	ADJ
ejpam-5555	111	37	that	that	SCONJ
ejpam-5555	111	38	zy	zy	PROPN
ejpam-5555	111	39	/∈	/∈	PUNCT
ejpam-5555	112	1	e(h	e(h	PROPN
ejpam-5555	112	2	)	)	PUNCT
ejpam-5555	112	3	.	.	PUNCT
ejpam-5555	113	1	then	then	ADV
ejpam-5555	113	2	uz	uz	PROPN
ejpam-5555	113	3	∈	∈	PROPN
ejpam-5555	113	4	e(h	e(h	PROPN
ejpam-5555	113	5	)	)	PUNCT
ejpam-5555	113	6	.	.	PUNCT
ejpam-5555	114	1	therefore	therefore	ADV
ejpam-5555	114	2	,	,	PUNCT
ejpam-5555	114	3	[	[	X
ejpam-5555	114	4	z	z	X
ejpam-5555	114	5	,	,	PUNCT
ejpam-5555	114	6	u	u	NOUN
ejpam-5555	114	7	,	,	PUNCT
ejpam-5555	114	8	y	y	PROPN
ejpam-5555	114	9	]	]	X
ejpam-5555	114	10	is	be	AUX
ejpam-5555	114	11	a	a	DET
ejpam-5555	114	12	z	z	NOUN
ejpam-5555	114	13	−	−	NOUN
ejpam-5555	114	14	y	y	PROPN
ejpam-5555	114	15	geodesic	geodesic	NOUN
ejpam-5555	114	16	containing	contain	VERB
ejpam-5555	114	17	uy	uy	PROPN
ejpam-5555	114	18	∈	∈	PROPN
ejpam-5555	114	19	e(h	e(h	PROPN
ejpam-5555	114	20	)	)	PUNCT
ejpam-5555	114	21	.	.	PUNCT
ejpam-5555	115	1	hence	hence	ADV
ejpam-5555	115	2	,	,	PUNCT
ejpam-5555	115	3	s	s	NOUN
ejpam-5555	115	4	=	=	SYM
ejpam-5555	115	5	v	v	PROPN
ejpam-5555	115	6	(	(	PUNCT
ejpam-5555	115	7	h	h	NOUN
ejpam-5555	115	8	)	)	PUNCT
ejpam-5555	115	9	\	\	NOUN
ejpam-5555	115	10	{	{	PUNCT
ejpam-5555	115	11	u	u	NOUN
ejpam-5555	115	12	,	,	PUNCT
ejpam-5555	115	13	v	v	NOUN
ejpam-5555	115	14	}	}	PUNCT
ejpam-5555	115	15	,	,	PUNCT
ejpam-5555	115	16	where	where	SCONJ
ejpam-5555	115	17	uv	uv	NOUN
ejpam-5555	115	18	/∈	/∈	PUNCT
ejpam-5555	115	19	e(h	e(h	PROPN
ejpam-5555	115	20	)	)	PUNCT
ejpam-5555	115	21	,	,	PUNCT
ejpam-5555	115	22	is	be	AUX
ejpam-5555	115	23	an	an	DET
ejpam-5555	115	24	edge	edge	NOUN
ejpam-5555	115	25	geodetic	geodetic	ADJ
ejpam-5555	115	26	set	set	NOUN
ejpam-5555	115	27	.	.	PUNCT
ejpam-5555	116	1	in	in	ADP
ejpam-5555	116	2	addition	addition	NOUN
ejpam-5555	116	3	,	,	PUNCT
ejpam-5555	116	4	y	y	PROPN
ejpam-5555	116	5	∈	∈	PROPN
ejpam-5555	116	6	s	s	VERB
ejpam-5555	116	7	is	be	AUX
ejpam-5555	116	8	adjacent	adjacent	ADJ
ejpam-5555	116	9	to	to	ADP
ejpam-5555	116	10	u	u	NOUN
ejpam-5555	116	11	and	and	CCONJ
ejpam-5555	116	12	v	v	NOUN
ejpam-5555	116	13	,	,	PUNCT
ejpam-5555	116	14	hence	hence	ADV
ejpam-5555	116	15	,	,	PUNCT
ejpam-5555	116	16	s	s	PART
ejpam-5555	116	17	is	be	AUX
ejpam-5555	116	18	an	an	DET
ejpam-5555	116	19	edge	edge	NOUN
ejpam-5555	116	20	geodetic	geodetic	ADJ
ejpam-5555	116	21	dominating	dominating	NOUN
ejpam-5555	116	22	set	set	NOUN
ejpam-5555	116	23	.	.	PUNCT
ejpam-5555	117	1	next	next	ADV
ejpam-5555	117	2	,	,	PUNCT
ejpam-5555	117	3	let	let	VERB
ejpam-5555	118	1	d	d	PROPN
ejpam-5555	118	2	⊆	⊆	NUM
ejpam-5555	118	3	v	v	ADP
ejpam-5555	118	4	(	(	PUNCT
ejpam-5555	118	5	h	h	NOUN
ejpam-5555	118	6	)	)	PUNCT
ejpam-5555	118	7	and	and	CCONJ
ejpam-5555	118	8	let	let	VERB
ejpam-5555	118	9	t	t	NOUN
ejpam-5555	118	10	=	=	SYM
ejpam-5555	118	11	v	v	PROPN
ejpam-5555	118	12	(	(	PUNCT
ejpam-5555	118	13	h	h	NOUN
ejpam-5555	118	14	)	)	PUNCT
ejpam-5555	118	15	\	\	PUNCT
ejpam-5555	119	1	d	d	X
ejpam-5555	119	2	,	,	PUNCT
ejpam-5555	119	3	where	where	SCONJ
ejpam-5555	119	4	|d|	|d|	PROPN
ejpam-5555	119	5	≥	≥	PUNCT
ejpam-5555	119	6	3	3	NUM
ejpam-5555	119	7	or	or	CCONJ
ejpam-5555	119	8	⟨d⟩	⟨d⟩	PROPN
ejpam-5555	119	9	contains	contain	VERB
ejpam-5555	119	10	k2	k2	NOUN
ejpam-5555	119	11	.	.	PUNCT
ejpam-5555	120	1	by	by	ADP
ejpam-5555	120	2	definition	definition	NOUN
ejpam-5555	120	3	of	of	ADP
ejpam-5555	120	4	independent	independent	ADJ
ejpam-5555	120	5	edges	edge	NOUN
ejpam-5555	120	6	,	,	PUNCT
ejpam-5555	120	7	there	there	PRON
ejpam-5555	120	8	exists	exist	VERB
ejpam-5555	120	9	u	u	NOUN
ejpam-5555	120	10	,	,	PUNCT
ejpam-5555	120	11	v	v	NOUN
ejpam-5555	120	12	∈	∈	PROPN
ejpam-5555	120	13	d	d	NOUN
ejpam-5555	120	14	such	such	ADJ
ejpam-5555	120	15	that	that	DET
ejpam-5555	120	16	uv	uv	PROPN
ejpam-5555	120	17	∈	∈	PROPN
ejpam-5555	120	18	e(h	e(h	PROPN
ejpam-5555	120	19	)	)	PUNCT
ejpam-5555	120	20	.	.	PUNCT
ejpam-5555	121	1	then	then	ADV
ejpam-5555	121	2	there	there	PRON
ejpam-5555	121	3	exist	exist	VERB
ejpam-5555	121	4	a	a	DET
ejpam-5555	121	5	unique	unique	ADJ
ejpam-5555	121	6	a	a	PRON
ejpam-5555	121	7	and	and	CCONJ
ejpam-5555	121	8	a	a	DET
ejpam-5555	121	9	unique	unique	ADJ
ejpam-5555	121	10	b	b	NOUN
ejpam-5555	121	11	in	in	ADP
ejpam-5555	121	12	s	s	PRON
ejpam-5555	121	13	such	such	ADJ
ejpam-5555	121	14	that	that	PRON
ejpam-5555	121	15	au	au	PROPN
ejpam-5555	121	16	,	,	PUNCT
ejpam-5555	121	17	vb	vb	NOUN
ejpam-5555	121	18	/∈	/∈	PUNCT
ejpam-5555	121	19	e(h	e(h	PROPN
ejpam-5555	121	20	)	)	PUNCT
ejpam-5555	121	21	.	.	PUNCT
ejpam-5555	122	1	since	since	SCONJ
ejpam-5555	122	2	ux	ux	PROPN
ejpam-5555	122	3	∈	∈	PROPN
ejpam-5555	122	4	e(h	e(h	PROPN
ejpam-5555	122	5	)	)	PUNCT
ejpam-5555	122	6	for	for	ADP
ejpam-5555	122	7	all	all	DET
ejpam-5555	122	8	x	x	SYM
ejpam-5555	122	9	∈	∈	PROPN
ejpam-5555	122	10	v	v	NOUN
ejpam-5555	122	11	(	(	PUNCT
ejpam-5555	122	12	h	h	NOUN
ejpam-5555	122	13	)	)	PUNCT
ejpam-5555	122	14	\	\	NOUN
ejpam-5555	122	15	{	{	PUNCT
ejpam-5555	122	16	a	a	NOUN
ejpam-5555	122	17	}	}	PUNCT
ejpam-5555	122	18	and	and	CCONJ
ejpam-5555	122	19	vz	vz	PROPN
ejpam-5555	122	20	∈	∈	PROPN
ejpam-5555	122	21	e(h	e(h	PROPN
ejpam-5555	122	22	)	)	PUNCT
ejpam-5555	122	23	for	for	ADP
ejpam-5555	122	24	all	all	DET
ejpam-5555	122	25	z	z	NOUN
ejpam-5555	122	26	∈	∈	PROPN
ejpam-5555	122	27	v	v	ADP
ejpam-5555	122	28	(	(	PUNCT
ejpam-5555	122	29	h	h	NOUN
ejpam-5555	122	30	)	)	PUNCT
ejpam-5555	122	31	\	\	NOUN
ejpam-5555	122	32	{	{	PUNCT
ejpam-5555	122	33	b	b	NOUN
ejpam-5555	122	34	}	}	PUNCT
ejpam-5555	122	35	,	,	PUNCT
ejpam-5555	122	36	it	it	PRON
ejpam-5555	122	37	follows	follow	VERB
ejpam-5555	122	38	that	that	SCONJ
ejpam-5555	122	39	[	[	X
ejpam-5555	122	40	u	u	NOUN
ejpam-5555	122	41	,	,	PUNCT
ejpam-5555	122	42	v	v	ADP
ejpam-5555	122	43	]	]	PUNCT
ejpam-5555	122	44	,	,	PUNCT
ejpam-5555	122	45	[	[	X
ejpam-5555	122	46	a	a	X
ejpam-5555	122	47	,	,	PUNCT
ejpam-5555	122	48	v	v	NOUN
ejpam-5555	122	49	,	,	PUNCT
ejpam-5555	122	50	u	u	NOUN
ejpam-5555	122	51	]	]	X
ejpam-5555	122	52	and	and	CCONJ
ejpam-5555	122	53	[	[	X
ejpam-5555	122	54	b	b	X
ejpam-5555	122	55	,	,	PUNCT
ejpam-5555	122	56	u	u	NOUN
ejpam-5555	122	57	,	,	PUNCT
ejpam-5555	122	58	v	v	NOUN
ejpam-5555	122	59	]	]	X
ejpam-5555	122	60	are	be	AUX
ejpam-5555	122	61	the	the	DET
ejpam-5555	122	62	only	only	ADJ
ejpam-5555	122	63	geodesics	geodesic	NOUN
ejpam-5555	122	64	containing	contain	VERB
ejpam-5555	122	65	uv	uv	NOUN
ejpam-5555	122	66	.	.	PUNCT
ejpam-5555	123	1	thus	thus	ADV
ejpam-5555	123	2	,	,	PUNCT
ejpam-5555	123	3	t	t	PROPN
ejpam-5555	123	4	is	be	AUX
ejpam-5555	123	5	not	not	PART
ejpam-5555	123	6	an	an	DET
ejpam-5555	123	7	edge	edge	NOUN
ejpam-5555	123	8	geodetic	geodetic	ADJ
ejpam-5555	123	9	set	set	NOUN
ejpam-5555	123	10	of	of	ADP
ejpam-5555	123	11	h.	h.	PROPN
ejpam-5555	123	12	therefore	therefore	ADV
ejpam-5555	123	13	,	,	PUNCT
ejpam-5555	123	14	s	s	VERB
ejpam-5555	123	15	is	be	AUX
ejpam-5555	123	16	an	an	DET
ejpam-5555	123	17	edge	edge	NOUN
ejpam-5555	123	18	geodetic	geodetic	ADJ
ejpam-5555	123	19	dominating	dominating	NOUN
ejpam-5555	123	20	set	set	NOUN
ejpam-5555	123	21	of	of	ADP
ejpam-5555	123	22	h	h	NOUN
ejpam-5555	123	23	if	if	SCONJ
ejpam-5555	124	1	and	and	CCONJ
ejpam-5555	124	2	only	only	ADV
ejpam-5555	124	3	if	if	SCONJ
ejpam-5555	124	4	s	s	VERB
ejpam-5555	124	5	=	=	SYM
ejpam-5555	124	6	v	v	PROPN
ejpam-5555	124	7	(	(	PUNCT
ejpam-5555	124	8	h	h	NOUN
ejpam-5555	124	9	)	)	PUNCT
ejpam-5555	124	10	\	\	NOUN
ejpam-5555	124	11	{	{	PUNCT
ejpam-5555	124	12	u	u	NOUN
ejpam-5555	124	13	,	,	PUNCT
ejpam-5555	124	14	v	v	NOUN
ejpam-5555	124	15	}	}	PUNCT
ejpam-5555	124	16	or	or	CCONJ
ejpam-5555	124	17	s	s	X
ejpam-5555	124	18	=	=	SYM
ejpam-5555	124	19	v	v	PROPN
ejpam-5555	124	20	(	(	PUNCT
ejpam-5555	124	21	h	h	NOUN
ejpam-5555	124	22	)	)	PUNCT
ejpam-5555	124	23	\	\	NOUN
ejpam-5555	124	24	{	{	PUNCT
ejpam-5555	124	25	v	v	NOUN
ejpam-5555	124	26	}	}	PUNCT
ejpam-5555	124	27	or	or	CCONJ
ejpam-5555	124	28	s	s	X
ejpam-5555	124	29	=	=	SYM
ejpam-5555	124	30	v	v	PROPN
ejpam-5555	124	31	(	(	PUNCT
ejpam-5555	124	32	h	h	NOUN
ejpam-5555	124	33	)	)	PUNCT
ejpam-5555	124	34	,	,	PUNCT
ejpam-5555	124	35	where	where	SCONJ
ejpam-5555	124	36	vertices	vertice	VERB
ejpam-5555	124	37	u	u	NOUN
ejpam-5555	124	38	and	and	CCONJ
ejpam-5555	124	39	v	v	NOUN
ejpam-5555	124	40	are	be	AUX
ejpam-5555	124	41	not	not	PART
ejpam-5555	124	42	adjacent	adjacent	ADJ
ejpam-5555	124	43	in	in	ADP
ejpam-5555	124	44	h.	h.	PROPN
ejpam-5555	124	45	this	this	PRON
ejpam-5555	124	46	proves	prove	VERB
ejpam-5555	124	47	(	(	PUNCT
ejpam-5555	124	48	iii	iii	NOUN
ejpam-5555	124	49	)	)	PUNCT
ejpam-5555	124	50	.	.	PUNCT
ejpam-5555	125	1	c.j	c.j	PROPN
ejpam-5555	125	2	.	.	PROPN
ejpam-5555	125	3	quije	quije	PROPN
ejpam-5555	125	4	,	,	PUNCT
ejpam-5555	125	5	r.	r.	PROPN
ejpam-5555	125	6	mariano	mariano	PROPN
ejpam-5555	125	7	,	,	PUNCT
ejpam-5555	125	8	e.	e.	PROPN
ejpam-5555	125	9	ahmad	ahmad	PROPN
ejpam-5555	125	10	/	/	SYM
ejpam-5555	125	11	eur	eur	PROPN
ejpam-5555	125	12	.	.	PUNCT
ejpam-5555	126	1	j.	j.	PROPN
ejpam-5555	126	2	pure	pure	PROPN
ejpam-5555	126	3	appl	appl	PROPN
ejpam-5555	126	4	.	.	PROPN
ejpam-5555	126	5	math	math	PROPN
ejpam-5555	126	6	,	,	PUNCT
ejpam-5555	126	7	18	18	NUM
ejpam-5555	126	8	(	(	PUNCT
ejpam-5555	126	9	1	1	NUM
ejpam-5555	126	10	)	)	PUNCT
ejpam-5555	126	11	(	(	PUNCT
ejpam-5555	126	12	2025	2025	NUM
ejpam-5555	126	13	)	)	PUNCT
ejpam-5555	126	14	,	,	PUNCT
ejpam-5555	126	15	5555	5555	NUM
ejpam-5555	126	16	5	5	NUM
ejpam-5555	126	17	of	of	ADP
ejpam-5555	126	18	8	8	NUM
ejpam-5555	126	19	corollary	corollary	ADJ
ejpam-5555	126	20	1	1	NUM
ejpam-5555	126	21	.	.	PUNCT
ejpam-5555	127	1	let	let	VERB
ejpam-5555	127	2	g	g	PRON
ejpam-5555	127	3	be	be	AUX
ejpam-5555	127	4	a	a	DET
ejpam-5555	127	5	complete	complete	ADJ
ejpam-5555	127	6	graph	graph	NOUN
ejpam-5555	127	7	of	of	ADP
ejpam-5555	127	8	order	order	NOUN
ejpam-5555	127	9	n.	n.	NOUN
ejpam-5555	127	10	if	if	SCONJ
ejpam-5555	127	11	h	h	NOUN
ejpam-5555	127	12	is	be	AUX
ejpam-5555	127	13	a	a	DET
ejpam-5555	127	14	connected	connected	ADJ
ejpam-5555	127	15	subgraph	subgraph	NOUN
ejpam-5555	127	16	of	of	ADP
ejpam-5555	127	17	g	g	PROPN
ejpam-5555	127	18	obtained	obtain	VERB
ejpam-5555	127	19	by	by	ADP
ejpam-5555	127	20	deleting	delete	VERB
ejpam-5555	127	21	m	m	ADP
ejpam-5555	127	22	independent	independent	ADJ
ejpam-5555	127	23	edges	edge	NOUN
ejpam-5555	127	24	in	in	ADP
ejpam-5555	127	25	g	g	NOUN
ejpam-5555	127	26	,	,	PUNCT
ejpam-5555	127	27	then	then	ADV
ejpam-5555	127	28	γge(h	γge(h	PROPN
ejpam-5555	127	29	)	)	PUNCT
ejpam-5555	128	1	=	=	PUNCT
ejpam-5555	129	1			PRON
ejpam-5555	129	2	n	n	ADV
ejpam-5555	129	3	if	if	SCONJ
ejpam-5555	129	4	m	m	ADV
ejpam-5555	129	5	<	<	X
ejpam-5555	129	6	⌊n2	⌊n2	PUNCT
ejpam-5555	129	7	⌋	⌋	NUM
ejpam-5555	129	8	n−	n−	NOUN
ejpam-5555	129	9	1	1	NUM
ejpam-5555	129	10	if	if	SCONJ
ejpam-5555	129	11	m	m	VERB
ejpam-5555	129	12	=	=	SYM
ejpam-5555	129	13	⌊n2	⌊n2	X
ejpam-5555	129	14	⌋	⌋	NOUN
ejpam-5555	129	15	and	and	CCONJ
ejpam-5555	129	16	n	n	PRON
ejpam-5555	129	17	is	be	AUX
ejpam-5555	129	18	odd	odd	ADJ
ejpam-5555	129	19	n−	n−	NOUN
ejpam-5555	129	20	2	2	NUM
ejpam-5555	129	21	if	if	SCONJ
ejpam-5555	129	22	m	m	VERB
ejpam-5555	129	23	=	=	SYM
ejpam-5555	129	24	⌊n2	⌊n2	X
ejpam-5555	129	25	⌋	⌋	NOUN
ejpam-5555	129	26	and	and	CCONJ
ejpam-5555	129	27	n	n	NOUN
ejpam-5555	129	28	is	be	AUX
ejpam-5555	129	29	even	even	ADV
ejpam-5555	129	30	3.2	3.2	NUM
ejpam-5555	129	31	.	.	PUNCT
ejpam-5555	130	1	kr	kr	PROPN
ejpam-5555	130	2	-	-	PUNCT
ejpam-5555	130	3	gluing	gluing	NOUN
ejpam-5555	130	4	of	of	ADP
ejpam-5555	130	5	complete	complete	ADJ
ejpam-5555	130	6	graphs	graph	NOUN
ejpam-5555	130	7	theorem	theorem	VERB
ejpam-5555	130	8	6	6	NUM
ejpam-5555	130	9	.	.	PUNCT
ejpam-5555	131	1	let	let	VERB
ejpam-5555	131	2	p	p	PRON
ejpam-5555	131	3	,	,	PUNCT
ejpam-5555	131	4	q	q	INTJ
ejpam-5555	131	5	,	,	PUNCT
ejpam-5555	131	6	r	r	NOUN
ejpam-5555	131	7	be	be	VERB
ejpam-5555	131	8	positive	positive	ADJ
ejpam-5555	131	9	integers	integer	NOUN
ejpam-5555	131	10	such	such	ADJ
ejpam-5555	131	11	that	that	SCONJ
ejpam-5555	131	12	1	1	NUM
ejpam-5555	131	13	≤	≤	NUM
ejpam-5555	131	14	r	r	NOUN
ejpam-5555	131	15	≤	≤	NOUN
ejpam-5555	131	16	p	p	PROPN
ejpam-5555	131	17	≤	≤	PROPN
ejpam-5555	131	18	q.	q.	PROPN
ejpam-5555	131	19	let	let	VERB
ejpam-5555	131	20	g	g	NOUN
ejpam-5555	131	21	be	be	AUX
ejpam-5555	131	22	the	the	DET
ejpam-5555	131	23	kr	kr	PROPN
ejpam-5555	131	24	-	-	PUNCT
ejpam-5555	131	25	gluing	gluing	NOUN
ejpam-5555	131	26	of	of	ADP
ejpam-5555	131	27	kp	kp	PROPN
ejpam-5555	131	28	and	and	CCONJ
ejpam-5555	131	29	kq	kq	PROPN
ejpam-5555	131	30	and	and	CCONJ
ejpam-5555	131	31	s	s	VERB
ejpam-5555	131	32	⊆	⊆	NUM
ejpam-5555	131	33	v	v	NOUN
ejpam-5555	131	34	(	(	PUNCT
ejpam-5555	131	35	g	g	NOUN
ejpam-5555	131	36	)	)	PUNCT
ejpam-5555	131	37	.	.	PUNCT
ejpam-5555	132	1	i	i	PRON
ejpam-5555	132	2	if	if	SCONJ
ejpam-5555	132	3	1	1	NUM
ejpam-5555	132	4	=	=	SYM
ejpam-5555	132	5	r	r	NOUN
ejpam-5555	132	6	<	<	X
ejpam-5555	132	7	p	p	X
ejpam-5555	132	8	≤	≤	PROPN
ejpam-5555	132	9	q	q	NOUN
ejpam-5555	132	10	,	,	PUNCT
ejpam-5555	132	11	then	then	ADV
ejpam-5555	132	12	s	s	VERB
ejpam-5555	132	13	=	=	SYM
ejpam-5555	132	14	v	v	PROPN
ejpam-5555	132	15	(	(	PUNCT
ejpam-5555	132	16	g)\v	g)\v	PROPN
ejpam-5555	132	17	(	(	PUNCT
ejpam-5555	132	18	kr	kr	PROPN
ejpam-5555	132	19	)	)	PUNCT
ejpam-5555	132	20	is	be	AUX
ejpam-5555	132	21	the	the	DET
ejpam-5555	132	22	edge	edge	NOUN
ejpam-5555	132	23	geodetic	geodetic	ADJ
ejpam-5555	132	24	dominating	dominating	NOUN
ejpam-5555	132	25	basis	basis	NOUN
ejpam-5555	132	26	of	of	ADP
ejpam-5555	132	27	g.	g.	PROPN
ejpam-5555	132	28	ii	ii	PROPN
ejpam-5555	132	29	if	if	SCONJ
ejpam-5555	132	30	1	1	NUM
ejpam-5555	132	31	<	<	X
ejpam-5555	132	32	r	r	NOUN
ejpam-5555	132	33	<	<	X
ejpam-5555	132	34	p	p	X
ejpam-5555	132	35	≤	≤	PROPN
ejpam-5555	132	36	q	q	NOUN
ejpam-5555	132	37	,	,	PUNCT
ejpam-5555	132	38	then	then	ADV
ejpam-5555	132	39	v	v	X
ejpam-5555	132	40	(	(	PUNCT
ejpam-5555	132	41	g	g	NOUN
ejpam-5555	132	42	)	)	PUNCT
ejpam-5555	132	43	is	be	AUX
ejpam-5555	132	44	the	the	DET
ejpam-5555	132	45	edge	edge	NOUN
ejpam-5555	132	46	geodetic	geodetic	ADJ
ejpam-5555	132	47	dominating	dominating	NOUN
ejpam-5555	132	48	basis	basis	NOUN
ejpam-5555	132	49	of	of	ADP
ejpam-5555	132	50	g.	g.	PROPN
ejpam-5555	132	51	iii	iii	PROPN
ejpam-5555	133	1	if	if	SCONJ
ejpam-5555	133	2	1	1	NUM
ejpam-5555	133	3	<	<	X
ejpam-5555	133	4	r	r	NOUN
ejpam-5555	133	5	=	=	PUNCT
ejpam-5555	133	6	p	p	NOUN
ejpam-5555	133	7	≤	≤	NUM
ejpam-5555	133	8	q	q	NOUN
ejpam-5555	133	9	,	,	PUNCT
ejpam-5555	133	10	then	then	ADV
ejpam-5555	133	11	v	v	X
ejpam-5555	133	12	(	(	PUNCT
ejpam-5555	133	13	g	g	NOUN
ejpam-5555	133	14	)	)	PUNCT
ejpam-5555	133	15	is	be	AUX
ejpam-5555	133	16	the	the	DET
ejpam-5555	133	17	edge	edge	NOUN
ejpam-5555	133	18	geodetic	geodetic	ADJ
ejpam-5555	133	19	dominating	dominating	NOUN
ejpam-5555	133	20	basis	basis	NOUN
ejpam-5555	133	21	of	of	ADP
ejpam-5555	133	22	g.	g.	PROPN
ejpam-5555	133	23	proof	proof	NOUN
ejpam-5555	133	24	.	.	PUNCT
ejpam-5555	134	1	i	i	PRON
ejpam-5555	134	2	since	since	SCONJ
ejpam-5555	134	3	v	v	PROPN
ejpam-5555	134	4	(	(	PUNCT
ejpam-5555	134	5	kr	kr	PROPN
ejpam-5555	134	6	)	)	PUNCT
ejpam-5555	134	7	=	=	PRON
ejpam-5555	134	8	{	{	PUNCT
ejpam-5555	134	9	v	v	NOUN
ejpam-5555	134	10	}	}	PUNCT
ejpam-5555	134	11	,	,	PUNCT
ejpam-5555	134	12	then	then	ADV
ejpam-5555	134	13	all	all	DET
ejpam-5555	134	14	the	the	DET
ejpam-5555	134	15	elements	element	NOUN
ejpam-5555	134	16	of	of	ADP
ejpam-5555	134	17	kp	kp	PROPN
ejpam-5555	134	18	\	\	PROPN
ejpam-5555	134	19	{	{	PUNCT
ejpam-5555	134	20	v	v	NOUN
ejpam-5555	134	21	}	}	PUNCT
ejpam-5555	134	22	and	and	CCONJ
ejpam-5555	134	23	kq	kq	PROPN
ejpam-5555	134	24	\	\	PROPN
ejpam-5555	134	25	{	{	PUNCT
ejpam-5555	134	26	v	v	NOUN
ejpam-5555	134	27	}	}	PUNCT
ejpam-5555	134	28	are	be	AUX
ejpam-5555	134	29	neighbors	neighbor	NOUN
ejpam-5555	134	30	of	of	ADP
ejpam-5555	134	31	v	v	NOUN
ejpam-5555	134	32	in	in	ADP
ejpam-5555	134	33	g.	g.	PROPN
ejpam-5555	135	1	this	this	PRON
ejpam-5555	135	2	implies	imply	VERB
ejpam-5555	135	3	that	that	SCONJ
ejpam-5555	135	4	v	v	NOUN
ejpam-5555	135	5	is	be	AUX
ejpam-5555	135	6	the	the	DET
ejpam-5555	135	7	only	only	ADJ
ejpam-5555	135	8	vertex	vertex	NOUN
ejpam-5555	135	9	in	in	ADP
ejpam-5555	135	10	g	g	NOUN
ejpam-5555	135	11	with	with	ADP
ejpam-5555	135	12	degg(v	degg(v	PROPN
ejpam-5555	135	13	)	)	PUNCT
ejpam-5555	135	14	=	=	SYM
ejpam-5555	135	15	|v	|v	PROPN
ejpam-5555	135	16	(	(	PUNCT
ejpam-5555	135	17	g)|	g)|	INTJ
ejpam-5555	135	18	−	−	NOUN
ejpam-5555	135	19	1	1	NUM
ejpam-5555	135	20	.	.	PUNCT
ejpam-5555	136	1	thus	thus	ADV
ejpam-5555	136	2	,	,	PUNCT
ejpam-5555	136	3	by	by	ADP
ejpam-5555	136	4	theorem	theorem	NOUN
ejpam-5555	136	5	4	4	NUM
ejpam-5555	136	6	,	,	PUNCT
ejpam-5555	136	7	γge(g	γge(g	PROPN
ejpam-5555	136	8	)	)	PUNCT
ejpam-5555	136	9	=	=	SYM
ejpam-5555	136	10	|v	|v	PROPN
ejpam-5555	136	11	(	(	PUNCT
ejpam-5555	136	12	g)|	g)|	INTJ
ejpam-5555	136	13	−	−	NOUN
ejpam-5555	136	14	1	1	NUM
ejpam-5555	136	15	with	with	ADP
ejpam-5555	136	16	v	v	NOUN
ejpam-5555	136	17	(	(	PUNCT
ejpam-5555	136	18	g	g	NOUN
ejpam-5555	136	19	)	)	PUNCT
ejpam-5555	136	20	\	\	NOUN
ejpam-5555	137	1	{	{	PUNCT
ejpam-5555	137	2	v	v	NOUN
ejpam-5555	137	3	(	(	PUNCT
ejpam-5555	137	4	kr	kr	PROPN
ejpam-5555	137	5	)	)	PUNCT
ejpam-5555	137	6	}	}	PUNCT
ejpam-5555	137	7	is	be	AUX
ejpam-5555	137	8	the	the	DET
ejpam-5555	137	9	unique	unique	ADJ
ejpam-5555	137	10	edge	edge	NOUN
ejpam-5555	137	11	geodetic	geodetic	ADJ
ejpam-5555	137	12	dominating	dominating	NOUN
ejpam-5555	137	13	basis	basis	NOUN
ejpam-5555	137	14	of	of	ADP
ejpam-5555	137	15	g.	g.	PROPN
ejpam-5555	137	16	ii	ii	PROPN
ejpam-5555	138	1	if	if	SCONJ
ejpam-5555	138	2	1	1	NUM
ejpam-5555	138	3	<	<	X
ejpam-5555	138	4	r	r	NOUN
ejpam-5555	138	5	<	<	X
ejpam-5555	138	6	p	p	X
ejpam-5555	138	7	≤	≤	PROPN
ejpam-5555	138	8	q	q	NOUN
ejpam-5555	138	9	,	,	PUNCT
ejpam-5555	138	10	then	then	ADV
ejpam-5555	138	11	every	every	DET
ejpam-5555	138	12	vertex	vertex	NOUN
ejpam-5555	138	13	v	v	ADP
ejpam-5555	138	14	∈	∈	PROPN
ejpam-5555	138	15	v	v	NOUN
ejpam-5555	138	16	(	(	PUNCT
ejpam-5555	138	17	kr	kr	PROPN
ejpam-5555	138	18	)	)	PUNCT
ejpam-5555	138	19	has	have	VERB
ejpam-5555	138	20	degree	degree	NOUN
ejpam-5555	138	21	|v	|v	NOUN
ejpam-5555	138	22	(	(	PUNCT
ejpam-5555	138	23	g)|	g)|	INTJ
ejpam-5555	138	24	−	−	NOUN
ejpam-5555	138	25	1	1	NUM
ejpam-5555	138	26	.	.	PUNCT
ejpam-5555	139	1	since	since	SCONJ
ejpam-5555	139	2	|v	|v	PROPN
ejpam-5555	139	3	(	(	PUNCT
ejpam-5555	139	4	kr)|	kr)|	PROPN
ejpam-5555	139	5	=	=	SYM
ejpam-5555	139	6	r	r	NOUN
ejpam-5555	139	7	>	>	X
ejpam-5555	139	8	1	1	NUM
ejpam-5555	139	9	,	,	PUNCT
ejpam-5555	139	10	then	then	ADV
ejpam-5555	139	11	g	g	PROPN
ejpam-5555	139	12	contains	contain	VERB
ejpam-5555	139	13	more	more	ADJ
ejpam-5555	139	14	than	than	ADP
ejpam-5555	139	15	one	one	NUM
ejpam-5555	139	16	vertex	vertex	NOUN
ejpam-5555	139	17	of	of	ADP
ejpam-5555	139	18	degree	degree	NOUN
ejpam-5555	139	19	|v	|v	PROPN
ejpam-5555	139	20	(	(	PUNCT
ejpam-5555	139	21	g)|−1	g)|−1	PROPN
ejpam-5555	139	22	.	.	PUNCT
ejpam-5555	140	1	hence	hence	ADV
ejpam-5555	140	2	,	,	PUNCT
ejpam-5555	140	3	by	by	ADP
ejpam-5555	140	4	theorem	theorem	NOUN
ejpam-5555	140	5	1	1	NUM
ejpam-5555	140	6	,	,	PUNCT
ejpam-5555	140	7	γge(g	γge(g	PROPN
ejpam-5555	140	8	)	)	PUNCT
ejpam-5555	140	9	=	=	SYM
ejpam-5555	140	10	|v	|v	PROPN
ejpam-5555	140	11	(	(	PUNCT
ejpam-5555	140	12	g)|	g)|	NOUN
ejpam-5555	140	13	and	and	CCONJ
ejpam-5555	140	14	v	v	NOUN
ejpam-5555	140	15	(	(	PUNCT
ejpam-5555	140	16	g	g	NOUN
ejpam-5555	140	17	)	)	PUNCT
ejpam-5555	140	18	is	be	AUX
ejpam-5555	140	19	the	the	DET
ejpam-5555	140	20	edge	edge	NOUN
ejpam-5555	140	21	geodetic	geodetic	ADJ
ejpam-5555	140	22	dominating	dominating	NOUN
ejpam-5555	140	23	basis	basis	NOUN
ejpam-5555	140	24	of	of	ADP
ejpam-5555	140	25	g.	g.	PROPN
ejpam-5555	140	26	iii	iii	PROPN
ejpam-5555	141	1	if	if	SCONJ
ejpam-5555	141	2	1	1	NUM
ejpam-5555	141	3	<	<	X
ejpam-5555	141	4	r	r	NOUN
ejpam-5555	141	5	=	=	PUNCT
ejpam-5555	141	6	p	p	NOUN
ejpam-5555	141	7	≤	≤	NUM
ejpam-5555	141	8	q	q	NOUN
ejpam-5555	141	9	,	,	PUNCT
ejpam-5555	141	10	then	then	ADV
ejpam-5555	141	11	g	g	PROPN
ejpam-5555	141	12	=	=	SYM
ejpam-5555	141	13	kq	kq	PROPN
ejpam-5555	141	14	.	.	PUNCT
ejpam-5555	142	1	since	since	SCONJ
ejpam-5555	142	2	kq	kq	PROPN
ejpam-5555	142	3	is	be	AUX
ejpam-5555	142	4	a	a	DET
ejpam-5555	142	5	complete	complete	ADJ
ejpam-5555	142	6	graph	graph	NOUN
ejpam-5555	142	7	,	,	PUNCT
ejpam-5555	142	8	by	by	ADP
ejpam-5555	142	9	theorem	theorem	NOUN
ejpam-5555	142	10	2	2	NUM
ejpam-5555	142	11	,	,	PUNCT
ejpam-5555	142	12	γge(g	γge(g	PROPN
ejpam-5555	142	13	)	)	PUNCT
ejpam-5555	142	14	=	=	SYM
ejpam-5555	142	15	|v	|v	PROPN
ejpam-5555	142	16	(	(	PUNCT
ejpam-5555	142	17	g)|	g)|	VERB
ejpam-5555	142	18	with	with	ADP
ejpam-5555	142	19	v	v	NOUN
ejpam-5555	142	20	(	(	PUNCT
ejpam-5555	142	21	g	g	NOUN
ejpam-5555	142	22	)	)	PUNCT
ejpam-5555	142	23	as	as	ADP
ejpam-5555	142	24	the	the	DET
ejpam-5555	142	25	edge	edge	NOUN
ejpam-5555	142	26	geodetic	geodetic	ADJ
ejpam-5555	142	27	dominating	dominating	NOUN
ejpam-5555	142	28	basis	basis	NOUN
ejpam-5555	142	29	of	of	ADP
ejpam-5555	142	30	g.	g.	PROPN
ejpam-5555	142	31	corollary	corollary	NOUN
ejpam-5555	142	32	2	2	PROPN
ejpam-5555	142	33	.	.	PUNCT
ejpam-5555	143	1	let	let	VERB
ejpam-5555	143	2	p	p	PRON
ejpam-5555	143	3	,	,	PUNCT
ejpam-5555	143	4	q	q	INTJ
ejpam-5555	143	5	,	,	PUNCT
ejpam-5555	143	6	r	r	NOUN
ejpam-5555	143	7	be	be	VERB
ejpam-5555	143	8	positive	positive	ADJ
ejpam-5555	143	9	integers	integer	NOUN
ejpam-5555	143	10	such	such	ADJ
ejpam-5555	143	11	that	that	SCONJ
ejpam-5555	143	12	1	1	NUM
ejpam-5555	143	13	≤	≤	NUM
ejpam-5555	143	14	r	r	NOUN
ejpam-5555	143	15	≤	≤	NOUN
ejpam-5555	143	16	p	p	PROPN
ejpam-5555	143	17	≤	≤	PROPN
ejpam-5555	143	18	q.	q.	PROPN
ejpam-5555	143	19	let	let	VERB
ejpam-5555	143	20	g	g	NOUN
ejpam-5555	143	21	be	be	AUX
ejpam-5555	143	22	the	the	DET
ejpam-5555	143	23	kr	kr	PROPN
ejpam-5555	143	24	-	-	PUNCT
ejpam-5555	143	25	gluing	gluing	NOUN
ejpam-5555	143	26	of	of	ADP
ejpam-5555	143	27	kp	kp	PROPN
ejpam-5555	143	28	and	and	CCONJ
ejpam-5555	143	29	kq	kq	PROPN
ejpam-5555	143	30	and	and	CCONJ
ejpam-5555	143	31	s	s	VERB
ejpam-5555	143	32	⊆	⊆	NUM
ejpam-5555	143	33	v	v	NOUN
ejpam-5555	143	34	(	(	PUNCT
ejpam-5555	143	35	g	g	NOUN
ejpam-5555	143	36	)	)	PUNCT
ejpam-5555	143	37	,	,	PUNCT
ejpam-5555	143	38	then	then	ADV
ejpam-5555	143	39	γge(g	γge(g	PROPN
ejpam-5555	143	40	)	)	PUNCT
ejpam-5555	143	41	=	=	PUNCT
ejpam-5555	144	1			PRON
ejpam-5555	144	2	|v	|v	VERB
ejpam-5555	144	3	(	(	PUNCT
ejpam-5555	144	4	g)|	g)|	INTJ
ejpam-5555	144	5	−	−	PROPN
ejpam-5555	144	6	1	1	NUM
ejpam-5555	144	7	if	if	SCONJ
ejpam-5555	144	8	1	1	NUM
ejpam-5555	144	9	=	=	SYM
ejpam-5555	144	10	r	r	NOUN
ejpam-5555	144	11	<	<	X
ejpam-5555	144	12	p	p	X
ejpam-5555	144	13	≤	≤	PROPN
ejpam-5555	144	14	q	q	NOUN
ejpam-5555	144	15	|v	|v	NOUN
ejpam-5555	144	16	(	(	PUNCT
ejpam-5555	144	17	g)|	g)|	VERB
ejpam-5555	144	18	if	if	SCONJ
ejpam-5555	144	19	1	1	NUM
ejpam-5555	144	20	<	<	X
ejpam-5555	144	21	r	r	NOUN
ejpam-5555	144	22	<	<	X
ejpam-5555	144	23	p	p	X
ejpam-5555	144	24	≤	≤	PROPN
ejpam-5555	144	25	q	q	NOUN
ejpam-5555	144	26	|v	|v	NOUN
ejpam-5555	144	27	(	(	PUNCT
ejpam-5555	144	28	g)|	g)|	VERB
ejpam-5555	144	29	if	if	SCONJ
ejpam-5555	144	30	1	1	NUM
ejpam-5555	144	31	<	<	X
ejpam-5555	144	32	r	r	NOUN
ejpam-5555	144	33	=	=	PUNCT
ejpam-5555	144	34	p	p	NOUN
ejpam-5555	144	35	≤	≤	PROPN
ejpam-5555	144	36	q	q	PROPN
ejpam-5555	144	37	3.3	3.3	NUM
ejpam-5555	144	38	.	.	PUNCT
ejpam-5555	145	1	result	result	NOUN
ejpam-5555	145	2	of	of	ADP
ejpam-5555	145	3	comprehension	comprehension	NOUN
ejpam-5555	145	4	theorem	theorem	VERB
ejpam-5555	145	5	7	7	NUM
ejpam-5555	145	6	.	.	X
ejpam-5555	145	7	for	for	ADP
ejpam-5555	145	8	any	any	DET
ejpam-5555	145	9	positive	positive	ADJ
ejpam-5555	145	10	integers	integer	NOUN
ejpam-5555	145	11	2	2	NUM
ejpam-5555	145	12	≤	≤	NOUN
ejpam-5555	145	13	a	a	DET
ejpam-5555	145	14	≤	≤	NUM
ejpam-5555	145	15	b	b	NOUN
ejpam-5555	145	16	,	,	PUNCT
ejpam-5555	145	17	there	there	PRON
ejpam-5555	145	18	exists	exist	VERB
ejpam-5555	145	19	a	a	DET
ejpam-5555	145	20	connected	connected	ADJ
ejpam-5555	145	21	graph	graph	NOUN
ejpam-5555	145	22	g	g	ADP
ejpam-5555	145	23	such	such	ADJ
ejpam-5555	145	24	that	that	PRON
ejpam-5555	145	25	ge(g	ge(g	PUNCT
ejpam-5555	145	26	)	)	PUNCT
ejpam-5555	146	1	=	=	PUNCT
ejpam-5555	146	2	a	a	PROPN
ejpam-5555	146	3	and	and	CCONJ
ejpam-5555	146	4	γge(g	γge(g	PROPN
ejpam-5555	146	5	)	)	PUNCT
ejpam-5555	147	1	=	=	SYM
ejpam-5555	147	2	b.	b.	PROPN
ejpam-5555	147	3	c.j	c.j	PROPN
ejpam-5555	147	4	.	.	PROPN
ejpam-5555	147	5	quije	quije	PROPN
ejpam-5555	147	6	,	,	PUNCT
ejpam-5555	147	7	r.	r.	PROPN
ejpam-5555	147	8	mariano	mariano	PROPN
ejpam-5555	147	9	,	,	PUNCT
ejpam-5555	147	10	e.	e.	PROPN
ejpam-5555	147	11	ahmad	ahmad	PROPN
ejpam-5555	147	12	/	/	SYM
ejpam-5555	147	13	eur	eur	PROPN
ejpam-5555	147	14	.	.	PUNCT
ejpam-5555	148	1	j.	j.	PROPN
ejpam-5555	148	2	pure	pure	PROPN
ejpam-5555	148	3	appl	appl	PROPN
ejpam-5555	148	4	.	.	PROPN
ejpam-5555	148	5	math	math	PROPN
ejpam-5555	148	6	,	,	PUNCT
ejpam-5555	148	7	18	18	NUM
ejpam-5555	148	8	(	(	PUNCT
ejpam-5555	148	9	1	1	NUM
ejpam-5555	148	10	)	)	PUNCT
ejpam-5555	148	11	(	(	PUNCT
ejpam-5555	148	12	2025	2025	NUM
ejpam-5555	148	13	)	)	PUNCT
ejpam-5555	148	14	,	,	PUNCT
ejpam-5555	148	15	5555	5555	NUM
ejpam-5555	148	16	6	6	NUM
ejpam-5555	148	17	of	of	ADP
ejpam-5555	148	18	8	8	NUM
ejpam-5555	148	19	proof	proof	NOUN
ejpam-5555	148	20	.	.	PUNCT
ejpam-5555	149	1	if	if	SCONJ
ejpam-5555	149	2	a	a	DET
ejpam-5555	149	3	=	=	SYM
ejpam-5555	149	4	b	b	NOUN
ejpam-5555	149	5	,	,	PUNCT
ejpam-5555	149	6	consider	consider	VERB
ejpam-5555	149	7	the	the	DET
ejpam-5555	149	8	complete	complete	ADJ
ejpam-5555	149	9	graph	graph	NOUN
ejpam-5555	149	10	g	g	PROPN
ejpam-5555	149	11	=	=	SYM
ejpam-5555	149	12	ka	ka	PROPN
ejpam-5555	149	13	.	.	PUNCT
ejpam-5555	149	14	then	then	ADV
ejpam-5555	149	15	by	by	ADP
ejpam-5555	149	16	theorem	theorem	NOUN
ejpam-5555	149	17	2	2	NUM
ejpam-5555	149	18	,	,	PUNCT
ejpam-5555	149	19	γge(g	γge(g	PROPN
ejpam-5555	149	20	)	)	PUNCT
ejpam-5555	150	1	=	=	PUNCT
ejpam-5555	150	2	a.	a.	NOUN
ejpam-5555	151	1	if	if	SCONJ
ejpam-5555	151	2	2	2	NUM
ejpam-5555	151	3	=	=	SYM
ejpam-5555	151	4	a	a	DET
ejpam-5555	151	5	<	<	X
ejpam-5555	151	6	b	b	NOUN
ejpam-5555	151	7	with	with	ADP
ejpam-5555	151	8	ge(g	ge(g	PROPN
ejpam-5555	151	9	)	)	PUNCT
ejpam-5555	151	10	=	=	SYM
ejpam-5555	151	11	2	2	NUM
ejpam-5555	151	12	and	and	CCONJ
ejpam-5555	151	13	γge(g	γge(g	NOUN
ejpam-5555	151	14	)	)	PUNCT
ejpam-5555	152	1	=	=	SYM
ejpam-5555	152	2	3	3	X
ejpam-5555	152	3	,	,	PUNCT
ejpam-5555	152	4	consider	consider	VERB
ejpam-5555	152	5	the	the	DET
ejpam-5555	152	6	path	path	NOUN
ejpam-5555	152	7	p	p	NOUN
ejpam-5555	152	8	:	:	PUNCT
ejpam-5555	152	9	u1	u1	NOUN
ejpam-5555	152	10	,	,	PUNCT
ejpam-5555	152	11	u2	u2	NOUN
ejpam-5555	152	12	,	,	PUNCT
ejpam-5555	152	13	.	.	PUNCT
ejpam-5555	152	14	.	.	PUNCT
ejpam-5555	153	1	.	.	PUNCT
ejpam-5555	154	1	,	,	PUNCT
ejpam-5555	154	2	u7	u7	PROPN
ejpam-5555	154	3	.	.	PUNCT
ejpam-5555	155	1	for	for	ADP
ejpam-5555	155	2	b	b	PROPN
ejpam-5555	155	3	≥	≥	NUM
ejpam-5555	155	4	4	4	NUM
ejpam-5555	155	5	,	,	PUNCT
ejpam-5555	155	6	letg	letg	PROPN
ejpam-5555	155	7	be	be	VERB
ejpam-5555	155	8	the	the	DET
ejpam-5555	155	9	graph	graph	NOUN
ejpam-5555	155	10	obtained	obtain	VERB
ejpam-5555	155	11	from	from	ADP
ejpam-5555	155	12	the	the	DET
ejpam-5555	155	13	path	path	NOUN
ejpam-5555	155	14	on	on	ADP
ejpam-5555	155	15	seven	seven	NUM
ejpam-5555	155	16	vertices	vertex	NOUN
ejpam-5555	155	17	p	p	NOUN
ejpam-5555	155	18	:	:	PUNCT
ejpam-5555	155	19	u1	u1	NOUN
ejpam-5555	155	20	,	,	PUNCT
ejpam-5555	155	21	u2	u2	NOUN
ejpam-5555	155	22	,	,	PUNCT
ejpam-5555	155	23	.	.	PUNCT
ejpam-5555	155	24	.	.	PUNCT
ejpam-5555	156	1	.	.	PUNCT
ejpam-5555	157	1	,	,	PUNCT
ejpam-5555	157	2	u7	u7	PROPN
ejpam-5555	157	3	by	by	ADP
ejpam-5555	157	4	adding	add	VERB
ejpam-5555	157	5	(	(	PUNCT
ejpam-5555	157	6	b−	b−	PROPN
ejpam-5555	157	7	3	3	NUM
ejpam-5555	157	8	)	)	PUNCT
ejpam-5555	157	9	sets	set	NOUN
ejpam-5555	157	10	of	of	ADP
ejpam-5555	157	11	three	three	NUM
ejpam-5555	157	12	new	new	ADJ
ejpam-5555	157	13	vertices	vertex	NOUN
ejpam-5555	157	14	vij	vij	PROPN
ejpam-5555	157	15	,	,	PUNCT
ejpam-5555	157	16	namely	namely	ADV
ejpam-5555	157	17	,	,	PUNCT
ejpam-5555	157	18	{	{	PUNCT
ejpam-5555	157	19	v11	v11	NOUN
ejpam-5555	157	20	,	,	PUNCT
ejpam-5555	157	21	v21	v21	NOUN
ejpam-5555	157	22	,	,	PUNCT
ejpam-5555	157	23	v31	v31	PROPN
ejpam-5555	157	24	}	}	PUNCT
ejpam-5555	157	25	,	,	PUNCT
ejpam-5555	157	26	{	{	PUNCT
ejpam-5555	157	27	v12	v12	VERB
ejpam-5555	157	28	,	,	PUNCT
ejpam-5555	157	29	v22	v22	NOUN
ejpam-5555	157	30	,	,	PUNCT
ejpam-5555	157	31	v32	v32	X
ejpam-5555	157	32	}	}	PUNCT
ejpam-5555	157	33	,	,	PUNCT
ejpam-5555	157	34	.	.	PUNCT
ejpam-5555	157	35	.	.	PUNCT
ejpam-5555	158	1	.	.	PUNCT
ejpam-5555	159	1	,	,	PUNCT
ejpam-5555	159	2	{	{	PUNCT
ejpam-5555	159	3	v1(b−3	v1(b−3	NOUN
ejpam-5555	159	4	)	)	PUNCT
ejpam-5555	159	5	,	,	PUNCT
ejpam-5555	159	6	v2(b−3	v2(b−3	NUM
ejpam-5555	159	7	)	)	PUNCT
ejpam-5555	159	8	,	,	PUNCT
ejpam-5555	159	9	v3(b−3	v3(b−3	NOUN
ejpam-5555	159	10	)	)	PUNCT
ejpam-5555	159	11	}	}	PUNCT
ejpam-5555	159	12	for	for	ADP
ejpam-5555	159	13	i	i	PROPN
ejpam-5555	159	14	=	=	NOUN
ejpam-5555	159	15	1	1	NUM
ejpam-5555	159	16	,	,	PUNCT
ejpam-5555	159	17	2	2	NUM
ejpam-5555	159	18	,	,	PUNCT
ejpam-5555	159	19	3	3	NUM
ejpam-5555	159	20	and	and	CCONJ
ejpam-5555	159	21	1	1	NUM
ejpam-5555	159	22	≤	≤	NUM
ejpam-5555	160	1	j	j	PROPN
ejpam-5555	160	2	≤	≤	PROPN
ejpam-5555	160	3	b	b	NOUN
ejpam-5555	160	4	−	−	PROPN
ejpam-5555	160	5	3	3	NUM
ejpam-5555	160	6	,	,	PUNCT
ejpam-5555	160	7	with	with	ADP
ejpam-5555	160	8	the	the	DET
ejpam-5555	160	9	paths	path	NOUN
ejpam-5555	160	10	p1	p1	NOUN
ejpam-5555	160	11	:	:	PUNCT
ejpam-5555	160	12	u2	u2	NOUN
ejpam-5555	160	13	,	,	PUNCT
ejpam-5555	160	14	v11	v11	NOUN
ejpam-5555	160	15	,	,	PUNCT
ejpam-5555	160	16	v21	v21	NOUN
ejpam-5555	160	17	,	,	PUNCT
ejpam-5555	160	18	v31	v31	NOUN
ejpam-5555	160	19	,	,	PUNCT
ejpam-5555	160	20	u6	u6	NOUN
ejpam-5555	160	21	,	,	PUNCT
ejpam-5555	160	22	p2	p2	PROPN
ejpam-5555	160	23	:	:	PUNCT
ejpam-5555	160	24	u2	u2	NOUN
ejpam-5555	160	25	,	,	PUNCT
ejpam-5555	160	26	v12	v12	VERB
ejpam-5555	160	27	,	,	PUNCT
ejpam-5555	160	28	v22	v22	NOUN
ejpam-5555	160	29	,	,	PUNCT
ejpam-5555	160	30	v32	v32	PROPN
ejpam-5555	160	31	,	,	PUNCT
ejpam-5555	160	32	u6	u6	NOUN
ejpam-5555	160	33	,	,	PUNCT
ejpam-5555	160	34	.	.	PUNCT
ejpam-5555	160	35	.	.	PUNCT
ejpam-5555	160	36	.	.	PUNCT
ejpam-5555	161	1	,	,	PUNCT
ejpam-5555	161	2	p(b−3	p(b−3	NOUN
ejpam-5555	161	3	)	)	PUNCT
ejpam-5555	161	4	:	:	PUNCT
ejpam-5555	162	1	u2	u2	NOUN
ejpam-5555	162	2	,	,	PUNCT
ejpam-5555	162	3	v1(b−3	v1(b−3	NOUN
ejpam-5555	162	4	)	)	PUNCT
ejpam-5555	162	5	,	,	PUNCT
ejpam-5555	162	6	v2(b−3	v2(b−3	NUM
ejpam-5555	162	7	)	)	PUNCT
ejpam-5555	162	8	,	,	PUNCT
ejpam-5555	162	9	v3(b−3	v3(b−3	NOUN
ejpam-5555	162	10	)	)	PUNCT
ejpam-5555	162	11	,	,	PUNCT
ejpam-5555	162	12	u6	u6	VERB
ejpam-5555	162	13	such	such	ADJ
ejpam-5555	162	14	that	that	DET
ejpam-5555	162	15	vik	vik	NOUN
ejpam-5555	162	16	is	be	AUX
ejpam-5555	162	17	not	not	PART
ejpam-5555	162	18	adjacent	adjacent	ADJ
ejpam-5555	162	19	to	to	ADP
ejpam-5555	162	20	vij	vij	PROPN
ejpam-5555	162	21	,	,	PUNCT
ejpam-5555	162	22	where	where	SCONJ
ejpam-5555	162	23	j	j	PROPN
ejpam-5555	162	24	̸=	̸=	PROPN
ejpam-5555	162	25	k	k	PROPN
ejpam-5555	162	26	and	and	CCONJ
ejpam-5555	162	27	j	j	PROPN
ejpam-5555	162	28	,	,	PUNCT
ejpam-5555	162	29	k	k	PROPN
ejpam-5555	162	30	=	=	SYM
ejpam-5555	162	31	1	1	NUM
ejpam-5555	162	32	,	,	PUNCT
ejpam-5555	162	33	2	2	NUM
ejpam-5555	162	34	,	,	PUNCT
ejpam-5555	162	35	3	3	NUM
ejpam-5555	162	36	,	,	PUNCT
ejpam-5555	162	37	.	.	PUNCT
ejpam-5555	162	38	.	.	PUNCT
ejpam-5555	162	39	.	.	PUNCT
ejpam-5555	163	1	,	,	PUNCT
ejpam-5555	163	2	b−	b−	PROPN
ejpam-5555	163	3	3	3	NUM
ejpam-5555	163	4	.	.	PUNCT
ejpam-5555	164	1	the	the	DET
ejpam-5555	164	2	graph	graph	NOUN
ejpam-5555	164	3	is	be	AUX
ejpam-5555	164	4	shown	show	VERB
ejpam-5555	164	5	in	in	ADP
ejpam-5555	164	6	figure	figure	NOUN
ejpam-5555	164	7	1	1	NUM
ejpam-5555	164	8	.	.	PUNCT
ejpam-5555	164	9	figure	figure	NOUN
ejpam-5555	164	10	1	1	NUM
ejpam-5555	164	11	:	:	PUNCT
ejpam-5555	164	12	a	a	DET
ejpam-5555	164	13	graph	graph	NOUN
ejpam-5555	164	14	g	g	NOUN
ejpam-5555	164	15	from	from	ADP
ejpam-5555	164	16	the	the	DET
ejpam-5555	164	17	figure	figure	NOUN
ejpam-5555	164	18	,	,	PUNCT
ejpam-5555	164	19	{	{	PUNCT
ejpam-5555	164	20	u1	u1	NOUN
ejpam-5555	164	21	,	,	PUNCT
ejpam-5555	164	22	u7	u7	PROPN
ejpam-5555	164	23	}	}	PUNCT
ejpam-5555	164	24	is	be	AUX
ejpam-5555	164	25	the	the	DET
ejpam-5555	164	26	edge	edge	ADJ
ejpam-5555	164	27	geodetic	geodetic	ADJ
ejpam-5555	164	28	basis	basis	NOUN
ejpam-5555	164	29	of	of	ADP
ejpam-5555	164	30	g	g	NOUN
ejpam-5555	164	31	,	,	PUNCT
ejpam-5555	165	1	so	so	SCONJ
ejpam-5555	165	2	that	that	SCONJ
ejpam-5555	165	3	ge(g	ge(g	PUNCT
ejpam-5555	165	4	)	)	PUNCT
ejpam-5555	165	5	=	=	SYM
ejpam-5555	165	6	2	2	X
ejpam-5555	165	7	.	.	PUNCT
ejpam-5555	165	8	moreover	moreover	ADV
ejpam-5555	165	9	,	,	PUNCT
ejpam-5555	165	10	since	since	SCONJ
ejpam-5555	165	11	{	{	PUNCT
ejpam-5555	165	12	u1	u1	PROPN
ejpam-5555	165	13	,	,	PUNCT
ejpam-5555	165	14	u7	u7	PROPN
ejpam-5555	165	15	}	}	PUNCT
ejpam-5555	165	16	is	be	AUX
ejpam-5555	165	17	an	an	DET
ejpam-5555	165	18	edge	edge	NOUN
ejpam-5555	165	19	geodetic	geodetic	ADJ
ejpam-5555	165	20	basis	basis	NOUN
ejpam-5555	165	21	,	,	PUNCT
ejpam-5555	165	22	we	we	PRON
ejpam-5555	165	23	need	need	VERB
ejpam-5555	165	24	to	to	PART
ejpam-5555	165	25	include	include	VERB
ejpam-5555	165	26	this	this	PRON
ejpam-5555	165	27	to	to	ADP
ejpam-5555	165	28	any	any	DET
ejpam-5555	165	29	edge	edge	NOUN
ejpam-5555	165	30	geodetic	geodetic	ADJ
ejpam-5555	165	31	dominating	dominating	NOUN
ejpam-5555	165	32	basis	basis	NOUN
ejpam-5555	165	33	of	of	ADP
ejpam-5555	165	34	g.	g.	PROPN
ejpam-5555	165	35	in	in	ADP
ejpam-5555	165	36	addition	addition	NOUN
ejpam-5555	165	37	,	,	PUNCT
ejpam-5555	165	38	u2	u2	NOUN
ejpam-5555	165	39	and	and	CCONJ
ejpam-5555	165	40	u6	u6	NOUN
ejpam-5555	165	41	are	be	AUX
ejpam-5555	165	42	dominated	dominate	VERB
ejpam-5555	165	43	by	by	ADP
ejpam-5555	165	44	u1	u1	NOUN
ejpam-5555	165	45	and	and	CCONJ
ejpam-5555	165	46	u7	u7	PROPN
ejpam-5555	165	47	,	,	PUNCT
ejpam-5555	165	48	respectively	respectively	ADV
ejpam-5555	165	49	.	.	PUNCT
ejpam-5555	166	1	thus	thus	ADV
ejpam-5555	166	2	,	,	PUNCT
ejpam-5555	166	3	we	we	PRON
ejpam-5555	166	4	are	be	AUX
ejpam-5555	166	5	left	leave	VERB
ejpam-5555	166	6	with	with	ADP
ejpam-5555	166	7	u3	u3	PROPN
ejpam-5555	166	8	,	,	PUNCT
ejpam-5555	166	9	u4	u4	PROPN
ejpam-5555	166	10	,	,	PUNCT
ejpam-5555	166	11	u5	u5	PROPN
ejpam-5555	166	12	and	and	CCONJ
ejpam-5555	166	13	vij	vij	NOUN
ejpam-5555	166	14	for	for	ADP
ejpam-5555	166	15	i	i	PRON
ejpam-5555	166	16	=	=	NOUN
ejpam-5555	166	17	1	1	NUM
ejpam-5555	166	18	,	,	PUNCT
ejpam-5555	166	19	2	2	NUM
ejpam-5555	166	20	,	,	PUNCT
ejpam-5555	166	21	3	3	NUM
ejpam-5555	166	22	and	and	CCONJ
ejpam-5555	166	23	1	1	NUM
ejpam-5555	166	24	≤	≤	NUM
ejpam-5555	166	25	j	j	PROPN
ejpam-5555	166	26	≤	≤	PROPN
ejpam-5555	166	27	b	b	PROPN
ejpam-5555	166	28	−	−	PROPN
ejpam-5555	166	29	3	3	NUM
ejpam-5555	166	30	which	which	PRON
ejpam-5555	166	31	are	be	AUX
ejpam-5555	166	32	nondominated	nondominate	VERB
ejpam-5555	166	33	vertices	vertex	NOUN
ejpam-5555	166	34	.	.	PUNCT
ejpam-5555	167	1	to	to	PART
ejpam-5555	167	2	get	get	VERB
ejpam-5555	167	3	the	the	DET
ejpam-5555	167	4	minimum	minimum	ADJ
ejpam-5555	167	5	cardinality	cardinality	NOUN
ejpam-5555	167	6	of	of	ADP
ejpam-5555	167	7	an	an	DET
ejpam-5555	167	8	edge	edge	NOUN
ejpam-5555	167	9	geodetic	geodetic	ADJ
ejpam-5555	167	10	dominating	dominating	NOUN
ejpam-5555	167	11	set	set	NOUN
ejpam-5555	167	12	,	,	PUNCT
ejpam-5555	167	13	we	we	PRON
ejpam-5555	167	14	have	have	VERB
ejpam-5555	167	15	to	to	PART
ejpam-5555	167	16	choose	choose	VERB
ejpam-5555	167	17	those	those	DET
ejpam-5555	167	18	vertices	vertex	NOUN
ejpam-5555	167	19	at	at	ADP
ejpam-5555	167	20	the	the	DET
ejpam-5555	167	21	center	center	NOUN
ejpam-5555	167	22	,	,	PUNCT
ejpam-5555	167	23	hence	hence	ADV
ejpam-5555	167	24	,	,	PUNCT
ejpam-5555	167	25	we	we	PRON
ejpam-5555	167	26	pick	pick	VERB
ejpam-5555	167	27	u4	u4	PROPN
ejpam-5555	167	28	and	and	CCONJ
ejpam-5555	167	29	v2j(1	v2j(1	DET
ejpam-5555	167	30	≤	≤	NUM
ejpam-5555	167	31	j	j	PROPN
ejpam-5555	167	32	≤	≤	NUM
ejpam-5555	167	33	b−	b−	PROPN
ejpam-5555	167	34	3	3	NUM
ejpam-5555	167	35	)	)	PUNCT
ejpam-5555	167	36	.	.	PUNCT
ejpam-5555	168	1	therefore	therefore	ADV
ejpam-5555	168	2	,	,	PUNCT
ejpam-5555	168	3	γge(g	γge(g	PROPN
ejpam-5555	168	4	)	)	PUNCT
ejpam-5555	168	5	=	=	PUNCT
ejpam-5555	168	6	ge(g	ge(g	PUNCT
ejpam-5555	168	7	)	)	PUNCT
ejpam-5555	169	1	+	+	CCONJ
ejpam-5555	169	2	(	(	PUNCT
ejpam-5555	169	3	b−	b−	NOUN
ejpam-5555	169	4	3	3	NUM
ejpam-5555	169	5	)	)	PUNCT
ejpam-5555	169	6	+	+	CCONJ
ejpam-5555	169	7	1	1	NUM
ejpam-5555	169	8	=	=	SYM
ejpam-5555	169	9	2	2	NUM
ejpam-5555	169	10	+	+	NUM
ejpam-5555	169	11	b−	b−	NOUN
ejpam-5555	169	12	3	3	NUM
ejpam-5555	169	13	+	+	SYM
ejpam-5555	169	14	1	1	NUM
ejpam-5555	169	15	=	=	SYM
ejpam-5555	169	16	b.	b.	NOUN
ejpam-5555	170	1	if	if	SCONJ
ejpam-5555	170	2	2	2	NUM
ejpam-5555	170	3	<	<	X
ejpam-5555	170	4	a	a	DET
ejpam-5555	170	5	<	<	X
ejpam-5555	170	6	b	b	NOUN
ejpam-5555	170	7	,	,	PUNCT
ejpam-5555	170	8	for	for	ADP
ejpam-5555	170	9	b	b	NOUN
ejpam-5555	170	10	=	=	SYM
ejpam-5555	170	11	a+1	a+1	PROPN
ejpam-5555	170	12	,	,	PUNCT
ejpam-5555	170	13	consider	consider	VERB
ejpam-5555	170	14	the	the	DET
ejpam-5555	170	15	graph	graph	NOUN
ejpam-5555	170	16	obtained	obtain	VERB
ejpam-5555	170	17	from	from	ADP
ejpam-5555	170	18	the	the	DET
ejpam-5555	170	19	path	path	NOUN
ejpam-5555	170	20	on	on	ADP
ejpam-5555	170	21	eight	eight	NUM
ejpam-5555	170	22	vertices	vertex	NOUN
ejpam-5555	170	23	p	p	NOUN
ejpam-5555	170	24	:	:	PUNCT
ejpam-5555	170	25	u1	u1	NOUN
ejpam-5555	170	26	,	,	PUNCT
ejpam-5555	170	27	u2	u2	NOUN
ejpam-5555	170	28	,	,	PUNCT
ejpam-5555	170	29	u3	u3	NOUN
ejpam-5555	170	30	,	,	PUNCT
ejpam-5555	170	31	.	.	PUNCT
ejpam-5555	170	32	.	.	PUNCT
ejpam-5555	171	1	.	.	PUNCT
ejpam-5555	172	1	,	,	PUNCT
ejpam-5555	172	2	u8	u8	PROPN
ejpam-5555	172	3	by	by	ADP
ejpam-5555	172	4	adding	add	VERB
ejpam-5555	172	5	a−	a−	PROPN
ejpam-5555	172	6	2	2	NUM
ejpam-5555	172	7	vertices	vertex	NOUN
ejpam-5555	172	8	,	,	PUNCT
ejpam-5555	172	9	w1	w1	NOUN
ejpam-5555	172	10	,	,	PUNCT
ejpam-5555	172	11	w2	w2	NOUN
ejpam-5555	172	12	,	,	PUNCT
ejpam-5555	172	13	.	.	PUNCT
ejpam-5555	172	14	.	.	PUNCT
ejpam-5555	172	15	.	.	PUNCT
ejpam-5555	173	1	wa−2	wa−2	PROPN
ejpam-5555	173	2	and	and	CCONJ
ejpam-5555	173	3	joining	join	VERB
ejpam-5555	173	4	each	each	DET
ejpam-5555	173	5	wi(1	wi(1	PROPN
ejpam-5555	173	6	≤	≤	PUNCT
ejpam-5555	174	1	i	i	PROPN
ejpam-5555	174	2	≤	≤	PROPN
ejpam-5555	174	3	a−2	a−2	PROPN
ejpam-5555	174	4	)	)	PUNCT
ejpam-5555	174	5	with	with	ADP
ejpam-5555	174	6	u3	u3	PROPN
ejpam-5555	174	7	.	.	PUNCT
ejpam-5555	175	1	however	however	ADV
ejpam-5555	175	2	,	,	PUNCT
ejpam-5555	175	3	for	for	ADP
ejpam-5555	175	4	b	b	PROPN
ejpam-5555	175	5	>	>	X
ejpam-5555	175	6	a+1	a+1	PROPN
ejpam-5555	175	7	,	,	PUNCT
ejpam-5555	175	8	let	let	VERB
ejpam-5555	175	9	g	g	PRON
ejpam-5555	175	10	be	be	AUX
ejpam-5555	175	11	the	the	DET
ejpam-5555	175	12	graph	graph	NOUN
ejpam-5555	175	13	obtained	obtain	VERB
ejpam-5555	175	14	from	from	ADP
ejpam-5555	175	15	the	the	DET
ejpam-5555	175	16	path	path	NOUN
ejpam-5555	175	17	on	on	ADP
ejpam-5555	175	18	eight	eight	NUM
ejpam-5555	175	19	vertices	vertex	NOUN
ejpam-5555	175	20	p	p	NOUN
ejpam-5555	175	21	:	:	PUNCT
ejpam-5555	175	22	u1	u1	NOUN
ejpam-5555	175	23	,	,	PUNCT
ejpam-5555	175	24	u2	u2	NOUN
ejpam-5555	175	25	,	,	PUNCT
ejpam-5555	175	26	u3	u3	NOUN
ejpam-5555	175	27	,	,	PUNCT
ejpam-5555	175	28	.	.	PUNCT
ejpam-5555	175	29	.	.	PUNCT
ejpam-5555	176	1	.	.	PUNCT
ejpam-5555	177	1	,	,	PUNCT
ejpam-5555	177	2	u8	u8	PROPN
ejpam-5555	177	3	by	by	ADP
ejpam-5555	177	4	adding	add	VERB
ejpam-5555	177	5	a−2	a−2	PROPN
ejpam-5555	177	6	vertices	vertex	NOUN
ejpam-5555	177	7	,	,	PUNCT
ejpam-5555	177	8	w1	w1	NOUN
ejpam-5555	177	9	,	,	PUNCT
ejpam-5555	177	10	w2	w2	NOUN
ejpam-5555	177	11	,	,	PUNCT
ejpam-5555	177	12	.	.	PUNCT
ejpam-5555	177	13	.	.	PUNCT
ejpam-5555	177	14	.	.	PUNCT
ejpam-5555	178	1	wa−2	wa−2	PROPN
ejpam-5555	178	2	and	and	CCONJ
ejpam-5555	178	3	(	(	PUNCT
ejpam-5555	178	4	b−a−1	b−a−1	NOUN
ejpam-5555	178	5	)	)	PUNCT
ejpam-5555	178	6	sets	set	NOUN
ejpam-5555	178	7	of	of	ADP
ejpam-5555	178	8	three	three	NUM
ejpam-5555	178	9	new	new	ADJ
ejpam-5555	178	10	vertices	vertex	NOUN
ejpam-5555	178	11	,	,	PUNCT
ejpam-5555	178	12	namely	namely	ADV
ejpam-5555	178	13	,	,	PUNCT
ejpam-5555	178	14	{	{	PUNCT
ejpam-5555	178	15	v11	v11	NOUN
ejpam-5555	178	16	,	,	PUNCT
ejpam-5555	178	17	v21	v21	NOUN
ejpam-5555	178	18	,	,	PUNCT
ejpam-5555	178	19	v31	v31	PROPN
ejpam-5555	178	20	}	}	PUNCT
ejpam-5555	178	21	,	,	PUNCT
ejpam-5555	178	22	{	{	PUNCT
ejpam-5555	178	23	v12	v12	VERB
ejpam-5555	178	24	,	,	PUNCT
ejpam-5555	178	25	v22	v22	NOUN
ejpam-5555	178	26	,	,	PUNCT
ejpam-5555	178	27	v32	v32	X
ejpam-5555	178	28	}	}	PUNCT
ejpam-5555	178	29	,	,	PUNCT
ejpam-5555	178	30	.	.	PUNCT
ejpam-5555	178	31	.	.	PUNCT
ejpam-5555	179	1	.	.	PUNCT
ejpam-5555	180	1	,	,	PUNCT
ejpam-5555	180	2	{	{	PUNCT
ejpam-5555	180	3	v1(b−a−1	v1(b−a−1	X
ejpam-5555	180	4	)	)	PUNCT
ejpam-5555	180	5	,	,	PUNCT
ejpam-5555	180	6	v2(b−a−1	v2(b−a−1	PROPN
ejpam-5555	180	7	)	)	PUNCT
ejpam-5555	180	8	,	,	PUNCT
ejpam-5555	180	9	v3(b−a−1	v3(b−a−1	NUM
ejpam-5555	180	10	)	)	PUNCT
ejpam-5555	180	11	}	}	PUNCT
ejpam-5555	181	1	for	for	ADP
ejpam-5555	181	2	i	i	PROPN
ejpam-5555	181	3	=	=	NOUN
ejpam-5555	181	4	1	1	NUM
ejpam-5555	181	5	,	,	PUNCT
ejpam-5555	181	6	2	2	NUM
ejpam-5555	181	7	,	,	PUNCT
ejpam-5555	181	8	3	3	NUM
ejpam-5555	181	9	,	,	PUNCT
ejpam-5555	181	10	with	with	ADP
ejpam-5555	181	11	the	the	DET
ejpam-5555	181	12	paths	path	NOUN
ejpam-5555	181	13	p1	p1	NOUN
ejpam-5555	181	14	:	:	PUNCT
ejpam-5555	181	15	u3	u3	NOUN
ejpam-5555	181	16	,	,	PUNCT
ejpam-5555	181	17	v11	v11	NOUN
ejpam-5555	181	18	,	,	PUNCT
ejpam-5555	181	19	v21	v21	NOUN
ejpam-5555	181	20	,	,	PUNCT
ejpam-5555	181	21	v31	v31	PROPN
ejpam-5555	181	22	,	,	PUNCT
ejpam-5555	181	23	u7	u7	PROPN
ejpam-5555	181	24	,	,	PUNCT
ejpam-5555	181	25	p2	p2	PROPN
ejpam-5555	181	26	:	:	PUNCT
ejpam-5555	181	27	u3	u3	NOUN
ejpam-5555	181	28	,	,	PUNCT
ejpam-5555	181	29	v12	v12	VERB
ejpam-5555	181	30	,	,	PUNCT
ejpam-5555	181	31	v22	v22	NOUN
ejpam-5555	181	32	,	,	PUNCT
ejpam-5555	181	33	v32	v32	PROPN
ejpam-5555	181	34	,	,	PUNCT
ejpam-5555	181	35	u7	u7	PROPN
ejpam-5555	181	36	,	,	PUNCT
ejpam-5555	181	37	.	.	PUNCT
ejpam-5555	181	38	.	.	PUNCT
ejpam-5555	181	39	.	.	PUNCT
ejpam-5555	182	1	,	,	PUNCT
ejpam-5555	182	2	pb−a−1	pb−a−1	PROPN
ejpam-5555	182	3	:	:	PUNCT
ejpam-5555	182	4	u3	u3	PROPN
ejpam-5555	182	5	,	,	PUNCT
ejpam-5555	182	6	v1(b−a−1	v1(b−a−1	NOUN
ejpam-5555	182	7	)	)	PUNCT
ejpam-5555	182	8	,	,	PUNCT
ejpam-5555	182	9	v2(b−a−1	v2(b−a−1	PROPN
ejpam-5555	182	10	)	)	PUNCT
ejpam-5555	182	11	,	,	PUNCT
ejpam-5555	182	12	v3(b−a−1	v3(b−a−1	NUM
ejpam-5555	182	13	)	)	PUNCT
ejpam-5555	182	14	,	,	PUNCT
ejpam-5555	182	15	u7	u7	PROPN
ejpam-5555	182	16	such	such	ADJ
ejpam-5555	182	17	that	that	SCONJ
ejpam-5555	182	18	vik	vik	NOUN
ejpam-5555	182	19	is	be	AUX
ejpam-5555	182	20	not	not	PART
ejpam-5555	182	21	adjacent	adjacent	ADJ
ejpam-5555	182	22	to	to	ADP
ejpam-5555	182	23	vij	vij	PROPN
ejpam-5555	182	24	,	,	PUNCT
ejpam-5555	182	25	j	j	PROPN
ejpam-5555	182	26	̸=	̸=	PROPN
ejpam-5555	182	27	k	k	PROPN
ejpam-5555	182	28	and	and	CCONJ
ejpam-5555	182	29	j	j	PROPN
ejpam-5555	182	30	,	,	PUNCT
ejpam-5555	182	31	k	k	PROPN
ejpam-5555	182	32	=	=	SYM
ejpam-5555	182	33	1	1	NUM
ejpam-5555	182	34	,	,	PUNCT
ejpam-5555	182	35	2	2	NUM
ejpam-5555	182	36	,	,	PUNCT
ejpam-5555	182	37	3	3	NUM
ejpam-5555	182	38	,	,	PUNCT
ejpam-5555	182	39	.	.	PUNCT
ejpam-5555	182	40	.	.	PUNCT
ejpam-5555	183	1	.	.	PUNCT
ejpam-5555	184	1	,	,	PUNCT
ejpam-5555	184	2	b−	b−	PROPN
ejpam-5555	184	3	a−	a−	PROPN
ejpam-5555	184	4	1	1	NUM
ejpam-5555	184	5	and	and	CCONJ
ejpam-5555	184	6	joining	join	VERB
ejpam-5555	184	7	each	each	DET
ejpam-5555	184	8	wi(1	wi(1	PROPN
ejpam-5555	184	9	≤	≤	PUNCT
ejpam-5555	184	10	i	i	PRON
ejpam-5555	184	11	≤	≤	ADJ
ejpam-5555	184	12	a−	a−	PROPN
ejpam-5555	184	13	2	2	NUM
ejpam-5555	184	14	)	)	PUNCT
ejpam-5555	184	15	with	with	ADP
ejpam-5555	184	16	u3	u3	PROPN
ejpam-5555	184	17	.	.	PUNCT
ejpam-5555	185	1	the	the	DET
ejpam-5555	185	2	graph	graph	NOUN
ejpam-5555	185	3	g	g	NOUN
ejpam-5555	185	4	is	be	AUX
ejpam-5555	185	5	shown	show	VERB
ejpam-5555	185	6	in	in	ADP
ejpam-5555	185	7	figure	figure	NOUN
ejpam-5555	185	8	2	2	NUM
ejpam-5555	185	9	.	.	PUNCT
ejpam-5555	186	1	let	let	VERB
ejpam-5555	186	2	s	s	PRON
ejpam-5555	186	3	=	=	NOUN
ejpam-5555	186	4	{	{	PUNCT
ejpam-5555	186	5	u1	u1	PROPN
ejpam-5555	186	6	,	,	PUNCT
ejpam-5555	186	7	u8	u8	PROPN
ejpam-5555	186	8	,	,	PUNCT
ejpam-5555	186	9	w1	w1	NOUN
ejpam-5555	186	10	,	,	PUNCT
ejpam-5555	186	11	w2	w2	NOUN
ejpam-5555	186	12	,	,	PUNCT
ejpam-5555	186	13	.	.	PUNCT
ejpam-5555	186	14	.	.	PUNCT
ejpam-5555	187	1	.	.	PUNCT
ejpam-5555	188	1	,	,	PUNCT
ejpam-5555	188	2	wa−2	wa−2	PROPN
ejpam-5555	188	3	}	}	PUNCT
ejpam-5555	188	4	.	.	PUNCT
ejpam-5555	189	1	it	it	PRON
ejpam-5555	189	2	is	be	AUX
ejpam-5555	189	3	clear	clear	ADJ
ejpam-5555	189	4	that	that	SCONJ
ejpam-5555	189	5	this	this	PRON
ejpam-5555	189	6	is	be	AUX
ejpam-5555	189	7	an	an	DET
ejpam-5555	189	8	edge	edge	NOUN
ejpam-5555	189	9	geodetic	geodetic	ADJ
ejpam-5555	189	10	basis	basis	NOUN
ejpam-5555	189	11	of	of	ADP
ejpam-5555	189	12	g	g	NOUN
ejpam-5555	189	13	,	,	PUNCT
ejpam-5555	190	1	so	so	SCONJ
ejpam-5555	190	2	that	that	SCONJ
ejpam-5555	190	3	ge(g	ge(g	PUNCT
ejpam-5555	190	4	)	)	PUNCT
ejpam-5555	190	5	=	=	PUNCT
ejpam-5555	190	6	a	a	DET
ejpam-5555	190	7	−	−	PROPN
ejpam-5555	190	8	2	2	NUM
ejpam-5555	190	9	+	+	CCONJ
ejpam-5555	190	10	2	2	NUM
ejpam-5555	190	11	=	=	NOUN
ejpam-5555	190	12	a.	a.	NOUN
ejpam-5555	190	13	moreover	moreover	ADV
ejpam-5555	190	14	,	,	PUNCT
ejpam-5555	190	15	u2	u2	PROPN
ejpam-5555	190	16	,	,	PUNCT
ejpam-5555	190	17	u7	u7	PROPN
ejpam-5555	190	18	,	,	PUNCT
ejpam-5555	190	19	and	and	CCONJ
ejpam-5555	190	20	u3	u3	NOUN
ejpam-5555	190	21	are	be	AUX
ejpam-5555	190	22	dominated	dominate	VERB
ejpam-5555	190	23	by	by	ADP
ejpam-5555	190	24	u1	u1	PROPN
ejpam-5555	190	25	,	,	PUNCT
ejpam-5555	190	26	u8	u8	PROPN
ejpam-5555	190	27	and	and	CCONJ
ejpam-5555	190	28	wi	wi	PROPN
ejpam-5555	190	29	,	,	PUNCT
ejpam-5555	190	30	respectively	respectively	ADV
ejpam-5555	190	31	.	.	PUNCT
ejpam-5555	191	1	hence	hence	ADV
ejpam-5555	191	2	,	,	PUNCT
ejpam-5555	191	3	we	we	PRON
ejpam-5555	191	4	are	be	AUX
ejpam-5555	191	5	left	leave	VERB
ejpam-5555	191	6	with	with	ADP
ejpam-5555	191	7	u4	u4	PROPN
ejpam-5555	191	8	,	,	PUNCT
ejpam-5555	191	9	u5	u5	PROPN
ejpam-5555	191	10	,	,	PUNCT
ejpam-5555	191	11	u6	u6	PROPN
ejpam-5555	191	12	,	,	PUNCT
ejpam-5555	191	13	vij	vij	NOUN
ejpam-5555	191	14	for	for	ADP
ejpam-5555	191	15	i	i	PROPN
ejpam-5555	191	16	=	=	NOUN
ejpam-5555	191	17	1	1	NUM
ejpam-5555	191	18	,	,	PUNCT
ejpam-5555	191	19	2	2	NUM
ejpam-5555	191	20	,	,	PUNCT
ejpam-5555	191	21	3	3	NUM
ejpam-5555	191	22	and	and	CCONJ
ejpam-5555	191	23	1	1	NUM
ejpam-5555	191	24	≤	≤	NUM
ejpam-5555	191	25	j	j	PROPN
ejpam-5555	191	26	≤	≤	PROPN
ejpam-5555	191	27	b	b	NOUN
ejpam-5555	191	28	−	−	PROPN
ejpam-5555	191	29	a	a	DET
ejpam-5555	191	30	−	−	PROPN
ejpam-5555	191	31	1	1	NUM
ejpam-5555	191	32	which	which	PRON
ejpam-5555	191	33	are	be	AUX
ejpam-5555	191	34	nondominated	nondominate	VERB
ejpam-5555	191	35	vertices	vertex	NOUN
ejpam-5555	191	36	.	.	PUNCT
ejpam-5555	192	1	to	to	PART
ejpam-5555	192	2	get	get	VERB
ejpam-5555	192	3	the	the	DET
ejpam-5555	192	4	minimum	minimum	ADJ
ejpam-5555	192	5	cardinality	cardinality	NOUN
ejpam-5555	192	6	of	of	ADP
ejpam-5555	192	7	edge	edge	NOUN
ejpam-5555	192	8	geodetic	geodetic	ADJ
ejpam-5555	192	9	dominating	dominating	NOUN
ejpam-5555	192	10	set	set	NOUN
ejpam-5555	192	11	,	,	PUNCT
ejpam-5555	192	12	we	we	PRON
ejpam-5555	192	13	need	need	VERB
ejpam-5555	192	14	to	to	PART
ejpam-5555	192	15	choose	choose	VERB
ejpam-5555	192	16	u5	u5	PROPN
ejpam-5555	192	17	,	,	PUNCT
ejpam-5555	192	18	and	and	CCONJ
ejpam-5555	192	19	v2j	v2j	VERB
ejpam-5555	192	20	for	for	ADP
ejpam-5555	192	21	(	(	PUNCT
ejpam-5555	192	22	1	1	NUM
ejpam-5555	192	23	≤	≤	NUM
ejpam-5555	192	24	j	j	PROPN
ejpam-5555	192	25	≤	≤	NOUN
ejpam-5555	192	26	b−	b−	PROPN
ejpam-5555	192	27	a−	a−	PROPN
ejpam-5555	192	28	1	1	NUM
ejpam-5555	192	29	)	)	PUNCT
ejpam-5555	192	30	.	.	PUNCT
ejpam-5555	193	1	therefore	therefore	ADV
ejpam-5555	193	2	,	,	PUNCT
ejpam-5555	193	3	γge(g	γge(g	PROPN
ejpam-5555	193	4	)	)	PUNCT
ejpam-5555	193	5	=	=	PUNCT
ejpam-5555	193	6	ge(g	ge(g	PUNCT
ejpam-5555	193	7	)	)	PUNCT
ejpam-5555	194	1	+	+	CCONJ
ejpam-5555	194	2	(	(	PUNCT
ejpam-5555	194	3	b−	b−	PROPN
ejpam-5555	194	4	a−	a−	PROPN
ejpam-5555	194	5	1	1	NUM
ejpam-5555	194	6	)	)	PUNCT
ejpam-5555	194	7	+	+	CCONJ
ejpam-5555	194	8	1	1	NUM
ejpam-5555	194	9	=	=	SYM
ejpam-5555	194	10	a+	a+	PUNCT
ejpam-5555	194	11	b−	b−	NOUN
ejpam-5555	194	12	a−	a−	PROPN
ejpam-5555	194	13	1	1	NUM
ejpam-5555	194	14	+	+	CCONJ
ejpam-5555	194	15	1	1	NUM
ejpam-5555	194	16	=	=	SYM
ejpam-5555	194	17	b.	b.	PROPN
ejpam-5555	194	18	c.j	c.j	PROPN
ejpam-5555	194	19	.	.	PROPN
ejpam-5555	194	20	quije	quije	PROPN
ejpam-5555	194	21	,	,	PUNCT
ejpam-5555	194	22	r.	r.	PROPN
ejpam-5555	194	23	mariano	mariano	PROPN
ejpam-5555	194	24	,	,	PUNCT
ejpam-5555	194	25	e.	e.	PROPN
ejpam-5555	194	26	ahmad	ahmad	PROPN
ejpam-5555	194	27	/	/	SYM
ejpam-5555	194	28	eur	eur	PROPN
ejpam-5555	194	29	.	.	PUNCT
ejpam-5555	195	1	j.	j.	PROPN
ejpam-5555	195	2	pure	pure	PROPN
ejpam-5555	195	3	appl	appl	PROPN
ejpam-5555	195	4	.	.	PROPN
ejpam-5555	195	5	math	math	PROPN
ejpam-5555	195	6	,	,	PUNCT
ejpam-5555	195	7	18	18	NUM
ejpam-5555	195	8	(	(	PUNCT
ejpam-5555	195	9	1	1	NUM
ejpam-5555	195	10	)	)	PUNCT
ejpam-5555	195	11	(	(	PUNCT
ejpam-5555	195	12	2025	2025	NUM
ejpam-5555	195	13	)	)	PUNCT
ejpam-5555	195	14	,	,	PUNCT
ejpam-5555	195	15	5555	5555	NUM
ejpam-5555	195	16	7	7	NUM
ejpam-5555	195	17	of	of	ADP
ejpam-5555	195	18	8	8	NUM
ejpam-5555	195	19	figure	figure	NOUN
ejpam-5555	195	20	2	2	NUM
ejpam-5555	195	21	:	:	PUNCT
ejpam-5555	195	22	a	a	DET
ejpam-5555	195	23	graph	graph	NOUN
ejpam-5555	195	24	g	g	PROPN
ejpam-5555	195	25	4	4	NUM
ejpam-5555	195	26	.	.	PUNCT
ejpam-5555	195	27	conclusion	conclusion	NOUN
ejpam-5555	195	28	and	and	CCONJ
ejpam-5555	195	29	recommendation	recommendation	NOUN
ejpam-5555	195	30	this	this	DET
ejpam-5555	195	31	study	study	NOUN
ejpam-5555	195	32	introduced	introduce	VERB
ejpam-5555	195	33	and	and	CCONJ
ejpam-5555	195	34	investigated	investigate	VERB
ejpam-5555	195	35	the	the	DET
ejpam-5555	195	36	concept	concept	NOUN
ejpam-5555	195	37	of	of	ADP
ejpam-5555	195	38	edge	edge	NOUN
ejpam-5555	195	39	geodetic	geodetic	ADJ
ejpam-5555	195	40	dominating	dominating	NOUN
ejpam-5555	195	41	set	set	NOUN
ejpam-5555	195	42	s	s	PROPN
ejpam-5555	195	43	of	of	ADP
ejpam-5555	195	44	the	the	DET
ejpam-5555	195	45	graph	graph	NOUN
ejpam-5555	195	46	g.	g.	PROPN
ejpam-5555	196	1	the	the	DET
ejpam-5555	196	2	authors	author	NOUN
ejpam-5555	196	3	primary	primary	ADJ
ejpam-5555	196	4	focus	focus	NOUN
ejpam-5555	196	5	has	have	AUX
ejpam-5555	196	6	been	be	AUX
ejpam-5555	196	7	on	on	ADP
ejpam-5555	196	8	the	the	DET
ejpam-5555	196	9	following	follow	VERB
ejpam-5555	196	10	areas	area	NOUN
ejpam-5555	196	11	:	:	PUNCT
ejpam-5555	196	12	deletion	deletion	NOUN
ejpam-5555	196	13	of	of	ADP
ejpam-5555	196	14	independent	independent	ADJ
ejpam-5555	196	15	edges	edge	NOUN
ejpam-5555	196	16	of	of	ADP
ejpam-5555	196	17	complete	complete	ADJ
ejpam-5555	196	18	graph	graph	NOUN
ejpam-5555	196	19	,	,	PUNCT
ejpam-5555	196	20	the	the	DET
ejpam-5555	196	21	kr	kr	NOUN
ejpam-5555	196	22	-	-	PUNCT
ejpam-5555	196	23	gluing	gluing	NOUN
ejpam-5555	196	24	of	of	ADP
ejpam-5555	196	25	complete	complete	ADJ
ejpam-5555	196	26	graphs	graph	NOUN
ejpam-5555	196	27	,	,	PUNCT
ejpam-5555	196	28	and	and	CCONJ
ejpam-5555	196	29	result	result	NOUN
ejpam-5555	196	30	of	of	ADP
ejpam-5555	196	31	comprehension	comprehension	NOUN
ejpam-5555	196	32	.	.	PUNCT
ejpam-5555	197	1	researchers	researcher	NOUN
ejpam-5555	197	2	who	who	PRON
ejpam-5555	197	3	are	be	AUX
ejpam-5555	197	4	interested	interested	ADJ
ejpam-5555	197	5	in	in	ADP
ejpam-5555	197	6	this	this	DET
ejpam-5555	197	7	concept	concept	NOUN
ejpam-5555	197	8	can	can	AUX
ejpam-5555	197	9	further	far	ADV
ejpam-5555	197	10	generate	generate	VERB
ejpam-5555	197	11	results	result	NOUN
ejpam-5555	197	12	in	in	ADP
ejpam-5555	197	13	the	the	DET
ejpam-5555	197	14	various	various	ADJ
ejpam-5555	197	15	graph	graph	NOUN
ejpam-5555	197	16	operations	operation	NOUN
ejpam-5555	197	17	that	that	PRON
ejpam-5555	197	18	include	include	VERB
ejpam-5555	197	19	cartesian	cartesian	ADJ
ejpam-5555	197	20	product	product	NOUN
ejpam-5555	197	21	and	and	CCONJ
ejpam-5555	197	22	composition	composition	NOUN
ejpam-5555	197	23	of	of	ADP
ejpam-5555	197	24	graphs	graph	NOUN
ejpam-5555	197	25	,	,	PUNCT
ejpam-5555	197	26	among	among	ADP
ejpam-5555	197	27	many	many	ADJ
ejpam-5555	197	28	others	other	NOUN
ejpam-5555	197	29	.	.	PUNCT
ejpam-5555	198	1	furthermore	furthermore	ADV
ejpam-5555	198	2	,	,	PUNCT
ejpam-5555	198	3	they	they	PRON
ejpam-5555	198	4	may	may	AUX
ejpam-5555	198	5	explore	explore	VERB
ejpam-5555	198	6	and	and	CCONJ
ejpam-5555	198	7	analyze	analyze	VERB
ejpam-5555	198	8	the	the	DET
ejpam-5555	198	9	bounds	bound	NOUN
ejpam-5555	198	10	in	in	ADP
ejpam-5555	198	11	relation	relation	NOUN
ejpam-5555	198	12	to	to	ADP
ejpam-5555	198	13	other	other	ADJ
ejpam-5555	198	14	well	well	ADV
ejpam-5555	198	15	-	-	PUNCT
ejpam-5555	198	16	established	establish	VERB
ejpam-5555	198	17	parameters	parameter	NOUN
ejpam-5555	198	18	in	in	ADP
ejpam-5555	198	19	graph	graph	NOUN
ejpam-5555	198	20	theory	theory	NOUN
ejpam-5555	198	21	.	.	PUNCT
ejpam-5555	199	1	acknowledgements	acknowledgement	NOUN
ejpam-5555	199	2	the	the	DET
ejpam-5555	199	3	authors	author	NOUN
ejpam-5555	199	4	extend	extend	VERB
ejpam-5555	199	5	their	their	PRON
ejpam-5555	199	6	sincere	sincere	ADJ
ejpam-5555	199	7	gratitude	gratitude	NOUN
ejpam-5555	199	8	to	to	ADP
ejpam-5555	199	9	the	the	DET
ejpam-5555	199	10	panel	panel	NOUN
ejpam-5555	199	11	of	of	ADP
ejpam-5555	199	12	reviewers	reviewer	NOUN
ejpam-5555	199	13	for	for	ADP
ejpam-5555	199	14	their	their	PRON
ejpam-5555	199	15	insightful	insightful	ADJ
ejpam-5555	199	16	comments	comment	NOUN
ejpam-5555	199	17	and	and	CCONJ
ejpam-5555	199	18	recommendations	recommendation	NOUN
ejpam-5555	199	19	,	,	PUNCT
ejpam-5555	199	20	which	which	PRON
ejpam-5555	199	21	significantly	significantly	ADV
ejpam-5555	199	22	enhanced	enhance	VERB
ejpam-5555	199	23	the	the	DET
ejpam-5555	199	24	quality	quality	NOUN
ejpam-5555	199	25	of	of	ADP
ejpam-5555	199	26	this	this	DET
ejpam-5555	199	27	paper	paper	NOUN
ejpam-5555	199	28	.	.	PUNCT
ejpam-5555	200	1	additionally	additionally	ADV
ejpam-5555	200	2	,	,	PUNCT
ejpam-5555	200	3	the	the	DET
ejpam-5555	200	4	authors	author	NOUN
ejpam-5555	200	5	express	express	VERB
ejpam-5555	200	6	their	their	PRON
ejpam-5555	200	7	appreciation	appreciation	NOUN
ejpam-5555	200	8	to	to	ADP
ejpam-5555	200	9	ateneo	ateneo	X
ejpam-5555	200	10	de	de	PROPN
ejpam-5555	200	11	zamboanga	zamboanga	PROPN
ejpam-5555	200	12	university	university	PROPN
ejpam-5555	200	13	,	,	PUNCT
ejpam-5555	200	14	tangub	tangub	NOUN
ejpam-5555	200	15	city	city	PROPN
ejpam-5555	200	16	global	global	PROPN
ejpam-5555	200	17	college	college	PROPN
ejpam-5555	200	18	,	,	PUNCT
ejpam-5555	200	19	and	and	CCONJ
ejpam-5555	200	20	western	western	ADJ
ejpam-5555	200	21	mindanao	mindanao	PROPN
ejpam-5555	200	22	state	state	PROPN
ejpam-5555	200	23	university	university	PROPN
ejpam-5555	200	24	for	for	ADP
ejpam-5555	200	25	supporting	support	VERB
ejpam-5555	200	26	this	this	DET
ejpam-5555	200	27	research	research	NOUN
ejpam-5555	200	28	.	.	PUNCT
ejpam-5555	201	1	references	reference	NOUN
ejpam-5555	201	2	[	[	X
ejpam-5555	201	3	1	1	NUM
ejpam-5555	201	4	]	]	PUNCT
ejpam-5555	201	5	a.	a.	NOUN
ejpam-5555	201	6	asdain	asdain	PROPN
ejpam-5555	201	7	,	,	PUNCT
ejpam-5555	201	8	j.	j.	PROPN
ejpam-5555	201	9	i.	i.	PROPN
ejpam-5555	201	10	salim	salim	PROPN
ejpam-5555	201	11	,	,	PUNCT
ejpam-5555	201	12	and	and	CCONJ
ejpam-5555	201	13	r.	r.	PROPN
ejpam-5555	201	14	g.	g.	PROPN
ejpam-5555	201	15	artes	artes	PROPN
ejpam-5555	201	16	jr	jr	PROPN
ejpam-5555	201	17	.	.	PROPN
ejpam-5555	201	18	geodetic	geodetic	ADJ
ejpam-5555	201	19	bounds	bound	NOUN
ejpam-5555	201	20	in	in	ADP
ejpam-5555	201	21	graphs	graph	NOUN
ejpam-5555	201	22	.	.	PUNCT
ejpam-5555	202	1	international	international	ADJ
ejpam-5555	202	2	journal	journal	NOUN
ejpam-5555	202	3	of	of	ADP
ejpam-5555	202	4	mathematics	mathematic	NOUN
ejpam-5555	202	5	and	and	CCONJ
ejpam-5555	202	6	computer	computer	NOUN
ejpam-5555	202	7	science	science	NOUN
ejpam-5555	202	8	,	,	PUNCT
ejpam-5555	202	9	18(4):767–771	18(4):767–771	NUM
ejpam-5555	202	10	,	,	PUNCT
ejpam-5555	202	11	2023	2023	NUM
ejpam-5555	202	12	.	.	PUNCT
ejpam-5555	203	1	[	[	X
ejpam-5555	203	2	2	2	NUM
ejpam-5555	203	3	]	]	PUNCT
ejpam-5555	203	4	a.	a.	NOUN
ejpam-5555	203	5	t.	t.	PROPN
ejpam-5555	203	6	castaneda	castaneda	PROPN
ejpam-5555	203	7	,	,	PUNCT
ejpam-5555	203	8	m.	m.	PROPN
ejpam-5555	203	9	a.	a.	PROPN
ejpam-5555	203	10	medina	medina	PROPN
ejpam-5555	203	11	,	,	PUNCT
ejpam-5555	203	12	and	and	CCONJ
ejpam-5555	203	13	l.	l.	PROPN
ejpam-5555	203	14	ruivivar	ruivivar	PROPN
ejpam-5555	203	15	.	.	PUNCT
ejpam-5555	204	1	notions	notion	NOUN
ejpam-5555	204	2	of	of	ADP
ejpam-5555	204	3	domination	domination	NOUN
ejpam-5555	204	4	for	for	ADP
ejpam-5555	204	5	some	some	DET
ejpam-5555	204	6	classes	class	NOUN
ejpam-5555	204	7	of	of	ADP
ejpam-5555	204	8	graphs	graph	NOUN
ejpam-5555	204	9	.	.	PUNCT
ejpam-5555	205	1	dlsu	dlsu	PROPN
ejpam-5555	205	2	research	research	PROPN
ejpam-5555	205	3	congress	congress	PROPN
ejpam-5555	205	4	,	,	PUNCT
ejpam-5555	205	5	2016	2016	NUM
ejpam-5555	205	6	.	.	PUNCT
ejpam-5555	206	1	[	[	X
ejpam-5555	206	2	3	3	X
ejpam-5555	206	3	]	]	X
ejpam-5555	206	4	g.	g.	PROPN
ejpam-5555	206	5	chartrand	chartrand	PROPN
ejpam-5555	206	6	,	,	PUNCT
ejpam-5555	206	7	f.	f.	PROPN
ejpam-5555	206	8	harary	harary	PROPN
ejpam-5555	206	9	,	,	PUNCT
ejpam-5555	206	10	and	and	CCONJ
ejpam-5555	206	11	p.	p.	PROPN
ejpam-5555	206	12	zhang	zhang	PROPN
ejpam-5555	206	13	.	.	PUNCT
ejpam-5555	207	1	geodetic	geodetic	ADJ
ejpam-5555	207	2	sets	set	NOUN
ejpam-5555	207	3	in	in	ADP
ejpam-5555	207	4	graphs	graph	NOUN
ejpam-5555	207	5	.	.	PUNCT
ejpam-5555	208	1	discussioness	discussioness	NOUN
ejpam-5555	208	2	mathematicae	mathematicae	PROPN
ejpam-5555	208	3	graph	graph	NOUN
ejpam-5555	208	4	theory	theory	NOUN
ejpam-5555	208	5	,	,	PUNCT
ejpam-5555	208	6	20(1):129–138	20(1):129–138	PROPN
ejpam-5555	208	7	,	,	PUNCT
ejpam-5555	208	8	2000	2000	NUM
ejpam-5555	208	9	.	.	PUNCT
ejpam-5555	209	1	c.j	c.j	X
ejpam-5555	209	2	.	.	PROPN
ejpam-5555	209	3	quije	quije	PROPN
ejpam-5555	209	4	,	,	PUNCT
ejpam-5555	209	5	r.	r.	PROPN
ejpam-5555	209	6	mariano	mariano	PROPN
ejpam-5555	209	7	,	,	PUNCT
ejpam-5555	209	8	e.	e.	PROPN
ejpam-5555	209	9	ahmad	ahmad	PROPN
ejpam-5555	209	10	/	/	SYM
ejpam-5555	209	11	eur	eur	PROPN
ejpam-5555	209	12	.	.	PUNCT
ejpam-5555	210	1	j.	j.	PROPN
ejpam-5555	210	2	pure	pure	PROPN
ejpam-5555	210	3	appl	appl	PROPN
ejpam-5555	210	4	.	.	PROPN
ejpam-5555	210	5	math	math	PROPN
ejpam-5555	210	6	,	,	PUNCT
ejpam-5555	210	7	18	18	NUM
ejpam-5555	210	8	(	(	PUNCT
ejpam-5555	210	9	1	1	NUM
ejpam-5555	210	10	)	)	PUNCT
ejpam-5555	210	11	(	(	PUNCT
ejpam-5555	210	12	2025	2025	NUM
ejpam-5555	210	13	)	)	PUNCT
ejpam-5555	210	14	,	,	PUNCT
ejpam-5555	210	15	5555	5555	NUM
ejpam-5555	210	16	8	8	NUM
ejpam-5555	210	17	of	of	ADP
ejpam-5555	210	18	8	8	NUM
ejpam-5555	210	19	[	[	SYM
ejpam-5555	210	20	4	4	NUM
ejpam-5555	210	21	]	]	X
ejpam-5555	210	22	h.	h.	PROPN
ejpam-5555	210	23	escuadro	escuadro	PROPN
ejpam-5555	210	24	,	,	PUNCT
ejpam-5555	210	25	r.	r.	PROPN
ejpam-5555	210	26	gera	gera	PROPN
ejpam-5555	210	27	,	,	PUNCT
ejpam-5555	210	28	a.	a.	NOUN
ejpam-5555	210	29	hansberg	hansberg	PROPN
ejpam-5555	210	30	,	,	PUNCT
ejpam-5555	210	31	n.	n.	PROPN
ejpam-5555	210	32	jafari	jafari	PROPN
ejpam-5555	210	33	rad	rad	PROPN
ejpam-5555	210	34	,	,	PUNCT
ejpam-5555	210	35	and	and	CCONJ
ejpam-5555	210	36	l.	l.	PROPN
ejpam-5555	210	37	volkmann	volkmann	PROPN
ejpam-5555	210	38	.	.	PUNCT
ejpam-5555	211	1	geodetic	geodetic	ADJ
ejpam-5555	211	2	domination	domination	NOUN
ejpam-5555	211	3	in	in	ADP
ejpam-5555	211	4	graphs	graph	NOUN
ejpam-5555	211	5	.	.	PUNCT
ejpam-5555	212	1	journal	journal	NOUN
ejpam-5555	212	2	of	of	ADP
ejpam-5555	212	3	combinatorial	combinatorial	ADJ
ejpam-5555	212	4	mathematics	mathematic	NOUN
ejpam-5555	212	5	and	and	CCONJ
ejpam-5555	212	6	combinatorial	combinatorial	ADJ
ejpam-5555	212	7	computing	computing	NOUN
ejpam-5555	212	8	,	,	PUNCT
ejpam-5555	212	9	77:89–101	77:89–101	NUM
ejpam-5555	212	10	,	,	PUNCT
ejpam-5555	212	11	2011	2011	NUM
ejpam-5555	212	12	.	.	PUNCT
ejpam-5555	213	1	[	[	X
ejpam-5555	213	2	5	5	NUM
ejpam-5555	213	3	]	]	PUNCT
ejpam-5555	213	4	a.	a.	NOUN
ejpam-5555	213	5	gamorez	gamorez	NOUN
ejpam-5555	213	6	and	and	CCONJ
ejpam-5555	213	7	s.	s.	PROPN
ejpam-5555	213	8	canoy	canoy	PROPN
ejpam-5555	213	9	jr	jr	PROPN
ejpam-5555	213	10	.	.	PROPN
ejpam-5555	213	11	monophonic	monophonic	ADJ
ejpam-5555	213	12	eccentric	eccentric	ADJ
ejpam-5555	213	13	domination	domination	NOUN
ejpam-5555	213	14	numbers	number	NOUN
ejpam-5555	213	15	of	of	ADP
ejpam-5555	213	16	graphs	graph	NOUN
ejpam-5555	213	17	.	.	PUNCT
ejpam-5555	214	1	european	european	ADJ
ejpam-5555	214	2	journal	journal	PROPN
ejpam-5555	214	3	of	of	ADP
ejpam-5555	214	4	pure	pure	ADJ
ejpam-5555	214	5	and	and	CCONJ
ejpam-5555	214	6	applied	applied	ADJ
ejpam-5555	214	7	mathematics	mathematic	NOUN
ejpam-5555	214	8	,	,	PUNCT
ejpam-5555	214	9	15(2):635–645	15(2):635–645	PROPN
ejpam-5555	214	10	,	,	PUNCT
ejpam-5555	214	11	2022	2022	NUM
ejpam-5555	214	12	.	.	PUNCT
ejpam-5555	215	1	[	[	X
ejpam-5555	215	2	6	6	NUM
ejpam-5555	215	3	]	]	PUNCT
ejpam-5555	215	4	a.	a.	NOUN
ejpam-5555	215	5	hansberg	hansberg	PROPN
ejpam-5555	215	6	and	and	CCONJ
ejpam-5555	215	7	l.	l.	PROPN
ejpam-5555	215	8	volkmann	volkmann	PROPN
ejpam-5555	215	9	.	.	PUNCT
ejpam-5555	216	1	on	on	ADP
ejpam-5555	216	2	the	the	DET
ejpam-5555	216	3	geodetic	geodetic	ADJ
ejpam-5555	216	4	and	and	CCONJ
ejpam-5555	216	5	geodetic	geodetic	ADJ
ejpam-5555	216	6	domination	domination	NOUN
ejpam-5555	216	7	number	number	NOUN
ejpam-5555	216	8	of	of	ADP
ejpam-5555	216	9	a	a	DET
ejpam-5555	216	10	graph	graph	NOUN
ejpam-5555	216	11	.	.	PUNCT
ejpam-5555	216	12	discrete	discrete	ADJ
ejpam-5555	216	13	mathematics	mathematic	NOUN
ejpam-5555	216	14	,	,	PUNCT
ejpam-5555	216	15	310(15–16):2140–2146	310(15–16):2140–2146	NUM
ejpam-5555	216	16	,	,	PUNCT
ejpam-5555	216	17	2010	2010	NUM
ejpam-5555	216	18	.	.	PUNCT
ejpam-5555	217	1	[	[	X
ejpam-5555	217	2	7	7	X
ejpam-5555	217	3	]	]	PUNCT
ejpam-5555	217	4	j.	j.	PROPN
ejpam-5555	217	5	harris	harris	PROPN
ejpam-5555	217	6	,	,	PUNCT
ejpam-5555	217	7	j.	j.	PROPN
ejpam-5555	217	8	hirst	hirst	PROPN
ejpam-5555	217	9	,	,	PUNCT
ejpam-5555	217	10	and	and	CCONJ
ejpam-5555	217	11	m.	m.	NOUN
ejpam-5555	217	12	mossinghoff	mossinghoff	PROPN
ejpam-5555	217	13	.	.	PUNCT
ejpam-5555	217	14	combinatorics	combinatoric	NOUN
ejpam-5555	217	15	and	and	CCONJ
ejpam-5555	217	16	graph	graph	NOUN
ejpam-5555	217	17	theory	theory	NOUN
ejpam-5555	217	18	.	.	PUNCT
ejpam-5555	218	1	springer	springer	NOUN
ejpam-5555	218	2	science	science	NOUN
ejpam-5555	218	3	+	+	CCONJ
ejpam-5555	218	4	business	business	NOUN
ejpam-5555	218	5	media	medium	NOUN
ejpam-5555	218	6	,	,	PUNCT
ejpam-5555	218	7	lawrence	lawrence	PROPN
ejpam-5555	218	8	university	university	PROPN
ejpam-5555	218	9	,	,	PUNCT
ejpam-5555	218	10	2008	2008	NUM
ejpam-5555	218	11	.	.	PUNCT
ejpam-5555	219	1	[	[	X
ejpam-5555	219	2	8	8	NUM
ejpam-5555	219	3	]	]	PUNCT
ejpam-5555	219	4	r.	r.	PROPN
ejpam-5555	219	5	mariano	mariano	PROPN
ejpam-5555	219	6	and	and	CCONJ
ejpam-5555	219	7	s.	s.	PROPN
ejpam-5555	219	8	canoy	canoy	PROPN
ejpam-5555	219	9	jr	jr	PROPN
ejpam-5555	219	10	.	.	PROPN
ejpam-5555	219	11	edge	edge	PROPN
ejpam-5555	219	12	geodetic	geodetic	ADJ
ejpam-5555	219	13	cover	cover	NOUN
ejpam-5555	219	14	in	in	ADP
ejpam-5555	219	15	graphs	graph	NOUN
ejpam-5555	219	16	.	.	PUNCT
ejpam-5555	220	1	international	international	ADJ
ejpam-5555	220	2	mathematical	mathematical	PROPN
ejpam-5555	220	3	forum	forum	PROPN
ejpam-5555	220	4	,	,	PUNCT
ejpam-5555	220	5	4:2301–2310	4:2301–2310	NUM
ejpam-5555	220	6	,	,	PUNCT
ejpam-5555	220	7	2009	2009	NUM
ejpam-5555	220	8	.	.	PUNCT
ejpam-5555	221	1	[	[	X
ejpam-5555	221	2	9	9	NUM
ejpam-5555	221	3	]	]	X
ejpam-5555	221	4	v.	v.	CCONJ
ejpam-5555	221	5	samodivkin	samodivkin	NOUN
ejpam-5555	221	6	.	.	PUNCT
ejpam-5555	222	1	on	on	ADP
ejpam-5555	222	2	the	the	DET
ejpam-5555	222	3	edge	edge	NOUN
ejpam-5555	222	4	geodetic	geodetic	ADJ
ejpam-5555	222	5	and	and	CCONJ
ejpam-5555	222	6	edge	edge	VERB
ejpam-5555	222	7	geodetic	geodetic	ADJ
ejpam-5555	222	8	domination	domination	NOUN
ejpam-5555	222	9	number	number	NOUN
ejpam-5555	222	10	of	of	ADP
ejpam-5555	222	11	a	a	DET
ejpam-5555	222	12	graph	graph	NOUN
ejpam-5555	222	13	.	.	PUNCT
ejpam-5555	222	14	communications	communication	NOUN
ejpam-5555	222	15	in	in	ADP
ejpam-5555	222	16	combinatorics	combinatoric	NOUN
ejpam-5555	222	17	and	and	CCONJ
ejpam-5555	222	18	optimization	optimization	NOUN
ejpam-5555	222	19	,	,	PUNCT
ejpam-5555	222	20	5:41–54	5:41–54	NUM
ejpam-5555	222	21	,	,	PUNCT
ejpam-5555	222	22	2020	2020	NUM
ejpam-5555	222	23	.	.	PUNCT
ejpam-5555	223	1	[	[	X
ejpam-5555	223	2	10	10	NUM
ejpam-5555	223	3	]	]	X
ejpam-5555	223	4	e.	e.	PROPN
ejpam-5555	223	5	sandueta	sandueta	PROPN
ejpam-5555	223	6	and	and	CCONJ
ejpam-5555	223	7	s.	s.	PROPN
ejpam-5555	223	8	canoy	canoy	PROPN
ejpam-5555	223	9	jr	jr	PROPN
ejpam-5555	223	10	.	.	PROPN
ejpam-5555	223	11	weakly	weakly	ADJ
ejpam-5555	223	12	connected	connected	ADJ
ejpam-5555	223	13	domination	domination	NOUN
ejpam-5555	223	14	in	in	ADP
ejpam-5555	223	15	graphs	graph	NOUN
ejpam-5555	223	16	resulting	result	VERB
ejpam-5555	223	17	from	from	ADP
ejpam-5555	223	18	some	some	DET
ejpam-5555	223	19	graph	graph	NOUN
ejpam-5555	223	20	operations	operation	NOUN
ejpam-5555	223	21	.	.	PUNCT
ejpam-5555	224	1	international	international	ADJ
ejpam-5555	224	2	mathematical	mathematical	PROPN
ejpam-5555	224	3	forum	forum	PROPN
ejpam-5555	224	4	,	,	PUNCT
ejpam-5555	224	5	6:1031–1035	6:1031–1035	NUM
ejpam-5555	224	6	,	,	PUNCT
ejpam-5555	224	7	2011	2011	NUM
ejpam-5555	224	8	.	.	PUNCT
ejpam-5555	225	1	[	[	X
ejpam-5555	225	2	11	11	NUM
ejpam-5555	225	3	]	]	PUNCT
ejpam-5555	225	4	a.	a.	NOUN
ejpam-5555	225	5	p.	p.	NOUN
ejpam-5555	225	6	santhakumaran	santhakumaran	NOUN
ejpam-5555	225	7	.	.	PUNCT
ejpam-5555	226	1	comment	comment	NOUN
ejpam-5555	226	2	on	on	ADP
ejpam-5555	226	3	edge	edge	NOUN
ejpam-5555	226	4	geodetic	geodetic	ADJ
ejpam-5555	226	5	cover	cover	NOUN
ejpam-5555	226	6	in	in	ADP
ejpam-5555	226	7	graphs	graph	NOUN
ejpam-5555	226	8	.	.	PUNCT
ejpam-5555	227	1	proyecciones	proyecciones	PROPN
ejpam-5555	227	2	journal	journal	PROPN
ejpam-5555	227	3	of	of	ADP
ejpam-5555	227	4	mathematics	mathematic	NOUN
ejpam-5555	227	5	,	,	PUNCT
ejpam-5555	227	6	34:343–350	34:343–350	PROPN
ejpam-5555	227	7	,	,	PUNCT
ejpam-5555	227	8	2015	2015	NUM
ejpam-5555	227	9	.	.	PUNCT
ejpam-5555	228	1	[	[	X
ejpam-5555	228	2	12	12	NUM
ejpam-5555	228	3	]	]	PUNCT
ejpam-5555	228	4	a.	a.	NOUN
ejpam-5555	228	5	p.	p.	NOUN
ejpam-5555	228	6	santhakumaran	santhakumaran	PROPN
ejpam-5555	228	7	and	and	CCONJ
ejpam-5555	228	8	j.	j.	PROPN
ejpam-5555	228	9	john	john	PROPN
ejpam-5555	228	10	.	.	PROPN
ejpam-5555	229	1	edge	edge	PROPN
ejpam-5555	229	2	geodetic	geodetic	ADJ
ejpam-5555	229	3	number	number	NOUN
ejpam-5555	229	4	of	of	ADP
ejpam-5555	229	5	a	a	DET
ejpam-5555	229	6	graph	graph	NOUN
ejpam-5555	229	7	.	.	PUNCT
ejpam-5555	230	1	journal	journal	NOUN
ejpam-5555	230	2	of	of	ADP
ejpam-5555	230	3	discrete	discrete	ADJ
ejpam-5555	230	4	mathematical	mathematical	ADJ
ejpam-5555	230	5	sciences	science	NOUN
ejpam-5555	230	6	and	and	CCONJ
ejpam-5555	230	7	cryptography	cryptography	NOUN
ejpam-5555	230	8	,	,	PUNCT
ejpam-5555	230	9	10:415–432	10:415–432	NUM
ejpam-5555	230	10	,	,	PUNCT
ejpam-5555	230	11	2007	2007	NUM
ejpam-5555	230	12	.	.	PUNCT
ejpam-5555	231	1	[	[	X
ejpam-5555	231	2	13	13	NUM
ejpam-5555	231	3	]	]	X
ejpam-5555	231	4	d.	d.	PROPN
ejpam-5555	231	5	stalin	stalin	PROPN
ejpam-5555	231	6	and	and	CCONJ
ejpam-5555	231	7	j.	j.	PROPN
ejpam-5555	231	8	john	john	PROPN
ejpam-5555	231	9	.	.	PROPN
ejpam-5555	231	10	edge	edge	PROPN
ejpam-5555	231	11	geodetic	geodetic	ADJ
ejpam-5555	231	12	dominations	domination	NOUN
ejpam-5555	231	13	in	in	ADP
ejpam-5555	231	14	graphs	graph	NOUN
ejpam-5555	231	15	.	.	PUNCT
ejpam-5555	232	1	international	international	ADJ
ejpam-5555	232	2	journal	journal	NOUN
ejpam-5555	232	3	of	of	ADP
ejpam-5555	232	4	pure	pure	ADJ
ejpam-5555	232	5	and	and	CCONJ
ejpam-5555	232	6	applied	applied	ADJ
ejpam-5555	232	7	mathematics	mathematic	NOUN
ejpam-5555	232	8	,	,	PUNCT
ejpam-5555	232	9	116:31–40	116:31–40	NUM
ejpam-5555	232	10	,	,	PUNCT
ejpam-5555	232	11	2017	2017	NUM
ejpam-5555	232	12	.	.	PUNCT
ejpam-5555	233	1	[	[	X
ejpam-5555	233	2	14	14	NUM
ejpam-5555	233	3	]	]	PUNCT
ejpam-5555	233	4	p.	p.	NOUN
ejpam-5555	233	5	a.	a.	NOUN
ejpam-5555	233	6	p.	p.	PROPN
ejpam-5555	233	7	sudhahar	sudhahar	PROPN
ejpam-5555	233	8	,	,	PUNCT
ejpam-5555	233	9	a.	a.	NOUN
ejpam-5555	233	10	ajitha	ajitha	PROPN
ejpam-5555	233	11	,	,	PUNCT
ejpam-5555	233	12	and	and	CCONJ
ejpam-5555	233	13	a.	a.	PROPN
ejpam-5555	233	14	subramanian	subramanian	PROPN
ejpam-5555	233	15	.	.	PUNCT
ejpam-5555	234	1	edge	edge	PROPN
ejpam-5555	234	2	geodetic	geodetic	ADJ
ejpam-5555	234	3	domination	domination	NOUN
ejpam-5555	234	4	number	number	NOUN
ejpam-5555	234	5	of	of	ADP
ejpam-5555	234	6	a	a	DET
ejpam-5555	234	7	graph	graph	NOUN
ejpam-5555	234	8	.	.	PUNCT
ejpam-5555	235	1	international	international	ADJ
ejpam-5555	235	2	journal	journal	NOUN
ejpam-5555	235	3	of	of	ADP
ejpam-5555	235	4	mathematics	mathematic	NOUN
ejpam-5555	235	5	and	and	CCONJ
ejpam-5555	235	6	its	its	PRON
ejpam-5555	235	7	applications	application	NOUN
ejpam-5555	235	8	,	,	PUNCT
ejpam-5555	235	9	4:45–50	4:45–50	NOUN
ejpam-5555	235	10	,	,	PUNCT
ejpam-5555	235	11	2016	2016	NUM
ejpam-5555	235	12	.	.	PUNCT
ejpam-5555	236	1	[	[	X
ejpam-5555	236	2	15	15	NUM
ejpam-5555	236	3	]	]	X
ejpam-5555	236	4	a.	a.	NOUN
ejpam-5555	236	5	vijayan	vijayan	PROPN
ejpam-5555	236	6	and	and	CCONJ
ejpam-5555	236	7	n.	n.	PROPN
ejpam-5555	236	8	jaspin	jaspin	NOUN
ejpam-5555	236	9	beaula	beaula	ADV
ejpam-5555	236	10	.	.	PUNCT
ejpam-5555	237	1	geodetic	geodetic	ADJ
ejpam-5555	237	2	dominating	dominating	NOUN
ejpam-5555	237	3	sets	set	NOUN
ejpam-5555	237	4	and	and	CCONJ
ejpam-5555	237	5	geodetic	geodetic	ADJ
ejpam-5555	237	6	dominating	dominating	NOUN
ejpam-5555	237	7	polynomials	polynomial	NOUN
ejpam-5555	237	8	of	of	ADP
ejpam-5555	237	9	cycles	cycle	NOUN
ejpam-5555	237	10	.	.	PUNCT
ejpam-5555	238	1	international	international	ADJ
ejpam-5555	238	2	journal	journal	PROPN
ejpam-5555	238	3	of	of	ADP
ejpam-5555	238	4	engineering	engineering	NOUN
ejpam-5555	238	5	science	science	NOUN
ejpam-5555	238	6	and	and	CCONJ
ejpam-5555	238	7	computing	computing	NOUN
ejpam-5555	238	8	,	,	PUNCT
ejpam-5555	238	9	6:3774–3779	6:3774–3779	NUM
ejpam-5555	238	10	,	,	PUNCT
ejpam-5555	238	11	2016	2016	NUM
ejpam-5555	238	12	.	.	PUNCT