id	sid	eid	entity	type
ejpam-4658	1	1	european journal	ORG
ejpam-4658	2	1	16	CARDINAL
ejpam-4658	2	2	2	CARDINAL
ejpam-4658	2	3	2023	CARDINAL
ejpam-4658	2	4	763	CARDINAL
ejpam-4658	2	5	1307-5543	DATE
ejpam-4658	2	6	new york	GPE
ejpam-4658	2	7	1-movable	QUANTITY
ejpam-4658	2	8	armalene h. abragan1,∗	PERSON
ejpam-4658	2	9	helen m. rara2	PERSON
ejpam-4658	3	1	1	CARDINAL
ejpam-4658	3	2	mindanao state university-iligan institute of technology	ORG
ejpam-4658	3	3	9200	CARDINAL
ejpam-4658	3	4	iligan city	GPE
ejpam-4658	3	5	2	CARDINAL
ejpam-4658	3	6	mindanao state university-iligan institute of technology	ORG
ejpam-4658	3	7	9200	CARDINAL
ejpam-4658	3	8	iligan city	GPE
ejpam-4658	3	9	philippines	GPE
ejpam-4658	4	1	1-movable	QUANTITY
ejpam-4658	4	2	∈	ORG
ejpam-4658	4	3	∈	ORG
ejpam-4658	4	4	1-movable	QUANTITY
ejpam-4658	5	1	two	CARDINAL
ejpam-4658	6	1	1-movable	QUANTITY
ejpam-4658	6	2	1-movable	QUANTITY
ejpam-4658	7	1	2020	DATE
ejpam-4658	7	2	05c69	CARDINAL
ejpam-4658	7	3	1-movable	QUANTITY
ejpam-4658	7	4	1-movable	QUANTITY
ejpam-4658	7	5	1	CARDINAL
ejpam-4658	7	6	1960	DATE
ejpam-4658	9	1	1977	DATE
ejpam-4658	9	2	e.j cockayne	PERSON
ejpam-4658	9	3	s.t hedetniemi	PERSON
ejpam-4658	9	4	the notation γ(g	ORG
ejpam-4658	9	5	2	CARDINAL
ejpam-4658	9	6	chartrand et al	ORG
ejpam-4658	10	1	1	CARDINAL
ejpam-4658	10	2	1995	DATE
ejpam-4658	11	1	natarajan	PERSON
ejpam-4658	11	2	2015	CARDINAL
ejpam-4658	12	1	7	CARDINAL
ejpam-4658	13	1	6	CARDINAL
ejpam-4658	14	1	blair et al	PERSON
ejpam-4658	15	1	3	CARDINAL
ejpam-4658	15	2	1-movable	QUANTITY
ejpam-4658	16	1	2011	DATE
ejpam-4658	16	2	1-movable	QUANTITY
ejpam-4658	17	1	armalene.abragan@g.msuiit.edu.ph	PERSON
ejpam-4658	17	2	a. abragan	PERSON
ejpam-4658	17	3	helen.rara@g.msuiit.edu.ph	GPE
ejpam-4658	17	4	h. m. rara	PERSON
ejpam-4658	18	1	763	CARDINAL
ejpam-4658	19	1	2023	CARDINAL
ejpam-4658	20	1	a. h. abragan	PERSON
ejpam-4658	20	2	h. m. rara	PERSON
ejpam-4658	21	1	j. pure	PERSON
ejpam-4658	21	2	16	CARDINAL
ejpam-4658	21	3	2	CARDINAL
ejpam-4658	21	4	2023	CARDINAL
ejpam-4658	21	5	763-772 764	QUANTITY
ejpam-4658	21	6	1-movable	QUANTITY
ejpam-4658	22	1	1-movable	QUANTITY
ejpam-4658	22	2	hinampas	PERSON
ejpam-4658	22	3	4	CARDINAL
ejpam-4658	23	1	1-movable	QUANTITY
ejpam-4658	24	1	1movable	CARDINAL
ejpam-4658	26	1	2	CARDINAL
ejpam-4658	28	1	⊆	CARDINAL
ejpam-4658	28	2	∈	PERSON
ejpam-4658	29	1	2	CARDINAL
ejpam-4658	31	1	⊆	CARDINAL
ejpam-4658	31	2	∈	ORG
ejpam-4658	31	3	w ∈	PERSON
ejpam-4658	32	1	w ∈	ORG
ejpam-4658	32	2	w ∈	ORG
ejpam-4658	33	1	|c∗|	GPE
ejpam-4658	33	2	∈	ORG
ejpam-4658	33	3	2	CARDINAL
ejpam-4658	33	4	|c∗|	GPE
ejpam-4658	33	5	c∗ in g. the hop	ORG
ejpam-4658	33	6	⊆	CARDINAL
ejpam-4658	39	1	⊆	CARDINAL
ejpam-4658	41	1	w	GPE
ejpam-4658	42	1	w	ORG
ejpam-4658	43	1	two	CARDINAL
ejpam-4658	43	2	w	GPE
ejpam-4658	44	1	dim(g	ORG
ejpam-4658	44	2	cardinality dim(g	ORG
ejpam-4658	45	1	two	CARDINAL
ejpam-4658	45	2	∈	ORG
ejpam-4658	45	3	ig[u	ORG
ejpam-4658	46	1	two	CARDINAL
ejpam-4658	46	2	∈	ORG
ejpam-4658	46	3	ig[u	ORG
ejpam-4658	46	4	w	ORG
ejpam-4658	46	5	∈	ORG
ejpam-4658	47	1	a. h. abragan	PERSON
ejpam-4658	47	2	h. m. rara	PERSON
ejpam-4658	48	1	j. pure	PERSON
ejpam-4658	48	2	16	CARDINAL
ejpam-4658	48	3	2	CARDINAL
ejpam-4658	48	4	2023	CARDINAL
ejpam-4658	48	5	763-772 765	QUANTITY
ejpam-4658	48	6	two	CARDINAL
ejpam-4658	48	7	w	GPE
ejpam-4658	50	1	⊆	CARDINAL
ejpam-4658	52	1	1-movable	QUANTITY
ejpam-4658	52	2	∈	ORG
ejpam-4658	52	3	∈	ORG
ejpam-4658	52	4	1-movable	QUANTITY
ejpam-4658	53	1	2	CARDINAL
ejpam-4658	53	2	5	CARDINAL
ejpam-4658	54	1	1	CARDINAL
ejpam-4658	57	1	at least one	CARDINAL
ejpam-4658	60	1	v(g	WORK_OF_ART
ejpam-4658	62	1	1	CARDINAL
ejpam-4658	66	1	2	CARDINAL
ejpam-4658	69	1	hu	PERSON
ejpam-4658	69	2	⊆	CARDINAL
ejpam-4658	70	1	a. h. abragan	PERSON
ejpam-4658	70	2	h. m. rara	PERSON
ejpam-4658	71	1	j. pure	PERSON
ejpam-4658	71	2	16	CARDINAL
ejpam-4658	71	3	2	CARDINAL
ejpam-4658	71	4	2023	CARDINAL
ejpam-4658	71	5	763-772 766	QUANTITY
ejpam-4658	71	6	hu	PERSON
ejpam-4658	71	7	⊆	CARDINAL
ejpam-4658	71	8	γ(h	ORG
ejpam-4658	71	9	1	CARDINAL
ejpam-4658	72	1	1	CARDINAL
ejpam-4658	74	1	3	CARDINAL
ejpam-4658	75	1	1	CARDINAL
ejpam-4658	75	2	γ(h	ORG
ejpam-4658	76	1	g[h	ORG
ejpam-4658	76	2	g[h])\(a×c	NORP
ejpam-4658	76	3	3	CARDINAL
ejpam-4658	76	4	1-movable	QUANTITY
ejpam-4658	77	1	1-movable	QUANTITY
ejpam-4658	78	1	2	CARDINAL
ejpam-4658	79	1	1-movable	QUANTITY
ejpam-4658	80	1	3	CARDINAL
ejpam-4658	81	1	2	CARDINAL
ejpam-4658	84	1	1-movable	QUANTITY
ejpam-4658	85	1	1	CARDINAL
ejpam-4658	86	1	1-movable	QUANTITY
ejpam-4658	86	2	1-movable	QUANTITY
ejpam-4658	87	1	1-movable	QUANTITY
ejpam-4658	88	1	1	CARDINAL
ejpam-4658	88	2	1-movable	QUANTITY
ejpam-4658	90	1	1-movable	QUANTITY
ejpam-4658	91	1	1	CARDINAL
ejpam-4658	93	1	x})∪	GPE
ejpam-4658	93	2	⊆	CARDINAL
ejpam-4658	96	1	1-movable	QUANTITY
ejpam-4658	96	2	2	CARDINAL
ejpam-4658	100	1	n ≥ 1	DATE
ejpam-4658	100	2	⊆	CARDINAL
ejpam-4658	100	3	1-movable	QUANTITY
ejpam-4658	100	4	a. h. abragan	PERSON
ejpam-4658	100	5	h. m. rara	PERSON
ejpam-4658	101	1	j. pure	PERSON
ejpam-4658	101	2	16	CARDINAL
ejpam-4658	101	3	2	CARDINAL
ejpam-4658	101	4	2023	CARDINAL
ejpam-4658	101	5	763	CARDINAL
ejpam-4658	101	6	1-movable	QUANTITY
ejpam-4658	102	1	∈	ORG
ejpam-4658	107	1	1-movable	QUANTITY
ejpam-4658	108	1	∈	ORG
ejpam-4658	110	1	1-movable	QUANTITY
ejpam-4658	111	1	1	CARDINAL
ejpam-4658	113	1	y ∈	PERSON
ejpam-4658	114	1	2	CARDINAL
ejpam-4658	116	1	1-movable	QUANTITY
ejpam-4658	119	1	x})∪	GPE
ejpam-4658	122	1	2	CARDINAL
ejpam-4658	124	1	∈	ORG
ejpam-4658	127	1	1-movable	QUANTITY
ejpam-4658	127	2	g. 4	PERSON
ejpam-4658	128	1	4	CARDINAL
ejpam-4658	129	1	n and γ(g	ORG
ejpam-4658	130	1	1	CARDINAL
ejpam-4658	130	2	1-movable	QUANTITY
ejpam-4658	131	1	1-movable	QUANTITY
ejpam-4658	132	1	⊆	CARDINAL
ejpam-4658	132	2	∈	ORG
ejpam-4658	133	1	1-movable	QUANTITY
ejpam-4658	134	1	4	CARDINAL
ejpam-4658	135	1	a. h. abragan	PERSON
ejpam-4658	135	2	h. m. rara	PERSON
ejpam-4658	136	1	j. pure	PERSON
ejpam-4658	136	2	16	CARDINAL
ejpam-4658	136	3	2	CARDINAL
ejpam-4658	136	4	2023	CARDINAL
ejpam-4658	136	5	763-772 768	QUANTITY
ejpam-4658	137	1	1-movable	QUANTITY
ejpam-4658	139	1	5	CARDINAL
ejpam-4658	142	1	1-movable	QUANTITY
ejpam-4658	143	1	at least one	CARDINAL
ejpam-4658	151	1	⊆	CARDINAL
ejpam-4658	151	2	1-movable	QUANTITY
ejpam-4658	152	1	g+h	ORG
ejpam-4658	153	1	1	CARDINAL
ejpam-4658	153	2	at least one	CARDINAL
ejpam-4658	156	1	v(g	WORK_OF_ART
ejpam-4658	160	1	2	CARDINAL
ejpam-4658	161	1	1-movable	QUANTITY
ejpam-4658	169	1	1	CARDINAL
ejpam-4658	173	1	1	CARDINAL
ejpam-4658	175	1	∈	ORG
ejpam-4658	176	1	∈	ORG
ejpam-4658	177	1	∈	ORG
ejpam-4658	177	2	2	CARDINAL
ejpam-4658	178	1	1	CARDINAL
ejpam-4658	178	2	1-movable	QUANTITY
ejpam-4658	178	3	a. h. abragan	PERSON
ejpam-4658	178	4	h. m. rara	PERSON
ejpam-4658	179	1	j. pure	PERSON
ejpam-4658	179	2	16	CARDINAL
ejpam-4658	179	3	2	CARDINAL
ejpam-4658	179	4	2023	CARDINAL
ejpam-4658	179	5	763-772 769	QUANTITY
ejpam-4658	180	1	1-movable	QUANTITY
ejpam-4658	180	2	g+h	ORG
ejpam-4658	181	1	5	CARDINAL
ejpam-4658	181	2	2	CARDINAL
ejpam-4658	185	1	+ n− ωpnds(h	PERSON
ejpam-4658	186	1	5	CARDINAL
ejpam-4658	186	2	1-movable	QUANTITY
ejpam-4658	186	3	1-movable	QUANTITY
ejpam-4658	187	1	6	CARDINAL
ejpam-4658	188	1	γ(h	ORG
ejpam-4658	189	1	1-movable	QUANTITY
ejpam-4658	190	1	hu	PERSON
ejpam-4658	190	2	⊆	CARDINAL
ejpam-4658	191	1	1-movable	QUANTITY
ejpam-4658	191	2	g ◦h	ORG
ejpam-4658	191	3	2	CARDINAL
ejpam-4658	192	1	hu	PERSON
ejpam-4658	192	2	⊆	CARDINAL
ejpam-4658	194	1	∈	ORG
ejpam-4658	194	2	hu	PERSON
ejpam-4658	195	1	⋃	PERSON
ejpam-4658	195	2	⋃	DATE
ejpam-4658	195	3	2	CARDINAL
ejpam-4658	195	4	hu	PERSON
ejpam-4658	195	5	⊆	CARDINAL
ejpam-4658	196	1	hu	PERSON
ejpam-4658	196	2	⊆	CARDINAL
ejpam-4658	197	1	2	CARDINAL
ejpam-4658	198	1	hu	PERSON
ejpam-4658	199	1	hu	PERSON
ejpam-4658	199	2	∈	ORG
ejpam-4658	199	3	hu)\{p	NORP
ejpam-4658	199	4	⋃	CARDINAL
ejpam-4658	199	5	2	CARDINAL
ejpam-4658	199	6	a. h. abragan	PERSON
ejpam-4658	199	7	h. m. rara	PERSON
ejpam-4658	200	1	j. pure	PERSON
ejpam-4658	200	2	16	CARDINAL
ejpam-4658	200	3	2	CARDINAL
ejpam-4658	200	4	2023	CARDINAL
ejpam-4658	200	5	763-772 770	QUANTITY
ejpam-4658	200	6	1-movable	QUANTITY
ejpam-4658	201	1	1	CARDINAL
ejpam-4658	202	1	6	CARDINAL
ejpam-4658	202	2	hu	PERSON
ejpam-4658	202	3	⊆	CARDINAL
ejpam-4658	204	1	∣∣∣∣ ⋃	ORG
ejpam-4658	204	2	hu	PERSON
ejpam-4658	204	3	⋃	DATE
ejpam-4658	204	4	hu	PERSON
ejpam-4658	204	5	1-movable	QUANTITY
ejpam-4658	204	6	6	CARDINAL
ejpam-4658	205	1	|s∗|	PRODUCT
ejpam-4658	205	2	hu	PERSON
ejpam-4658	207	1	1	CARDINAL
ejpam-4658	207	2	1-movable	QUANTITY
ejpam-4658	207	3	3(4	CARDINAL
ejpam-4658	208	1	12	CARDINAL
ejpam-4658	209	1	6	CARDINAL
ejpam-4658	209	2	1-movable	QUANTITY
ejpam-4658	209	3	1-movable	QUANTITY
ejpam-4658	211	1	1	CARDINAL
ejpam-4658	211	2	γ(h	ORG
ejpam-4658	212	1	1-movable	QUANTITY
ejpam-4658	212	2	g[h	ORG
ejpam-4658	213	1	771	CARDINAL
ejpam-4658	213	2	1-movable	QUANTITY
ejpam-4658	214	1	3	CARDINAL
ejpam-4658	215	1	⊆	CARDINAL
ejpam-4658	216	1	y /∈ c. hence	PERSON
ejpam-4658	217	1	{x	PERSON
ejpam-4658	218	1	⊆	CARDINAL
ejpam-4658	218	2	3	CARDINAL
ejpam-4658	218	3	7	CARDINAL
ejpam-4658	220	1	1	CARDINAL
ejpam-4658	222	1	2	CARDINAL
ejpam-4658	222	2	1	CARDINAL
ejpam-4658	274	1	• •	CARDINAL
ejpam-4658	305	1	1	CARDINAL
ejpam-4658	305	2	1-movable	QUANTITY
ejpam-4658	305	3	1	CARDINAL
ejpam-4658	305	4	g. chartrand	PERSON
ejpam-4658	305	5	l. eroh	PERSON
ejpam-4658	305	6	m. johnson	PERSON
ejpam-4658	307	1	105:99–113, 2000	DATE
ejpam-4658	308	1	2	CARDINAL
ejpam-4658	308	2	f. harary	PERSON
ejpam-4658	308	3	r.a. melter	PERSON
ejpam-4658	309	1	2:191–195	CARDINAL
ejpam-4658	309	2	1976	DATE
ejpam-4658	310	1	3	CARDINAL
ejpam-4658	310	2	blair j.	PERSON
ejpam-4658	310	3	gera r.	PERSON
ejpam-4658	310	4	horton s. movable	PERSON
ejpam-4658	311	1	2011	DATE
ejpam-4658	312	1	4	CARDINAL
ejpam-4658	312	2	g. hinampas jr.	PERSON
ejpam-4658	312	3	sergio r. canoy jr.	PERSON
ejpam-4658	312	4	1-movable	QUANTITY
ejpam-4658	313	1	8(172):8565	GPE
ejpam-4658	313	2	8571	DATE
ejpam-4658	313	3	2014	DATE
ejpam-4658	314	1	5	CARDINAL
ejpam-4658	314	2	gerald bacon monsanto	PERSON
ejpam-4658	314	3	penelyn l.	PERSON
ejpam-4658	314	4	helen m. rara	PERSON
ejpam-4658	316	1	european journal	ORG
ejpam-4658	316	2	jan. 2020	DATE
ejpam-4658	317	1	772	CARDINAL
ejpam-4658	317	2	6	CARDINAL
ejpam-4658	317	3	chidambaram natarajan	PERSON
ejpam-4658	318	1	seria matematica	ORG
ejpam-4658	318	2	23:187–199	CARDINAL
ejpam-4658	318	3	06 2015	DATE
ejpam-4658	319	1	7	CARDINAL
ejpam-4658	319	2	canoy jr sergio	PERSON
ejpam-4658	319	3	mollejon reynaldo villarobe	PERSON
ejpam-4658	319	4	canoy john gabriel e. hop	PERSON
ejpam-4658	320	1	european journal	ORG
ejpam-4658	320	2	12(4):1455–1463, oct. 2019	DATE