id	sid	eid	entity	type
ejpam-4440	1	1	european journal	ORG
ejpam-4440	2	1	15	CARDINAL
ejpam-4440	2	2	3	CARDINAL
ejpam-4440	2	3	2022	CARDINAL
ejpam-4440	2	4	1201	CARDINAL
ejpam-4440	2	5	1307-5543	DATE
ejpam-4440	3	1	new york	GPE
ejpam-4440	3	2	helyn c.	PERSON
ejpam-4440	3	3	helen m. rara1	PERSON
ejpam-4440	4	1	1	CARDINAL
ejpam-4440	4	2	mindanao state university-iligan institute of technology	ORG
ejpam-4440	4	3	9200	CARDINAL
ejpam-4440	4	4	iligan city	GPE
ejpam-4440	4	5	philippines	GPE
ejpam-4440	6	1	1-movable	QUANTITY
ejpam-4440	6	2	∈	ORG
ejpam-4440	6	3	∈	ORG
ejpam-4440	6	4	1-movable	QUANTITY
ejpam-4440	6	5	γ1 msr(g	DATE
ejpam-4440	6	6	1-movable	QUANTITY
ejpam-4440	7	1	1-movable	QUANTITY
ejpam-4440	7	2	two	CARDINAL
ejpam-4440	8	1	1-movable	QUANTITY
ejpam-4440	8	2	1-movable	QUANTITY
ejpam-4440	9	1	2020	DATE
ejpam-4440	9	2	05c69	CARDINAL
ejpam-4440	9	3	1	CARDINAL
ejpam-4440	9	4	c. berge	PERSON
ejpam-4440	9	5	1958	DATE
ejpam-4440	9	6	4	CARDINAL
ejpam-4440	12	1	al	PERSON
ejpam-4440	13	1	6	CARDINAL
ejpam-4440	14	1	peters-fransen	PERSON
ejpam-4440	15	1	11	CARDINAL
ejpam-4440	16	1	slater	PERSON
ejpam-4440	17	1	14	CARDINAL
ejpam-4440	18	1	1	CARDINAL
ejpam-4440	18	2	10	CARDINAL
ejpam-4440	21	1	https://doi.org/10.29020/nybg.ejpam.v15i3.4440	PERSON
ejpam-4440	21	2	helyn.sumaoy@g.msuiit.edu.ph (h. sumaoy	ORG
ejpam-4440	21	3	helen.rara@g.msuiit.edu.ph	GPE
ejpam-4440	21	4	h. rara	PERSON
ejpam-4440	22	1	2022	CARDINAL
ejpam-4440	23	1	h. sumaoy	PERSON
ejpam-4440	23	2	h. rara	PERSON
ejpam-4440	24	1	j. pure	PERSON
ejpam-4440	24	2	15	CARDINAL
ejpam-4440	24	3	3	CARDINAL
ejpam-4440	24	4	2022	CARDINAL
ejpam-4440	24	5	1201-1210	DATE
ejpam-4440	25	1	slater	PERSON
ejpam-4440	25	2	the united states	GPE
ejpam-4440	27	1	12	CARDINAL
ejpam-4440	28	1	9	CARDINAL
ejpam-4440	29	1	13	CARDINAL
ejpam-4440	30	1	3	CARDINAL
ejpam-4440	30	2	2	CARDINAL
ejpam-4440	30	3	5	CARDINAL
ejpam-4440	30	4	8	CARDINAL
ejpam-4440	34	1	∈	ORG
ejpam-4440	34	2	∈	ORG
ejpam-4440	35	1	⊆	CARDINAL
ejpam-4440	35	2	⋃	PERSON
ejpam-4440	37	1	⊆	CARDINAL
ejpam-4440	37	2	∈	ORG
ejpam-4440	37	3	w ∈	PERSON
ejpam-4440	38	1	w ∈	ORG
ejpam-4440	38	2	w ∈	ORG
ejpam-4440	39	1	|c∗|	GPE
ejpam-4440	39	2	∈	ORG
ejpam-4440	40	1	∈	ORG
ejpam-4440	41	1	ωds(g	CARDINAL
ejpam-4440	43	1	two	CARDINAL
ejpam-4440	44	1	⊆	CARDINAL
ejpam-4440	44	2	w	GPE
ejpam-4440	45	1	w	ORG
ejpam-4440	46	1	two	CARDINAL
ejpam-4440	46	2	w	GPE
ejpam-4440	47	1	dim(g	ORG
ejpam-4440	47	2	cardinality dim(g	ORG
ejpam-4440	48	1	⊆	CARDINAL
ejpam-4440	49	1	at least one	CARDINAL
ejpam-4440	49	2	∈	ORG
ejpam-4440	50	1	γ(g	NORP
ejpam-4440	50	2	γ(g	NORP
ejpam-4440	52	1	⊆	CARDINAL
ejpam-4440	52	2	∈	ORG
ejpam-4440	52	3	∈	ORG
ejpam-4440	52	4	∈	ORG
ejpam-4440	52	5	ig[u	ORG
ejpam-4440	52	6	w	ORG
ejpam-4440	54	1	cardinality γsr(g	ORG
ejpam-4440	54	2	g. h. sumaoy	PERSON
ejpam-4440	54	3	h. rara	PERSON
ejpam-4440	55	1	j. pure	PERSON
ejpam-4440	55	2	15	CARDINAL
ejpam-4440	55	3	3	CARDINAL
ejpam-4440	55	4	2022	CARDINAL
ejpam-4440	55	5	1201-1210 1203	DATE
ejpam-4440	55	6	⊆	CARDINAL
ejpam-4440	55	7	1-movable	QUANTITY
ejpam-4440	55	8	∈	ORG
ejpam-4440	55	9	∈	ORG
ejpam-4440	55	10	1-movable	QUANTITY
ejpam-4440	55	11	γ1m(g	PERSON
ejpam-4440	55	12	1-movable	QUANTITY
ejpam-4440	55	13	1-movable	QUANTITY
ejpam-4440	55	14	γ1m(g	PERSON
ejpam-4440	55	15	1-movable	QUANTITY
ejpam-4440	55	16	∈	ORG
ejpam-4440	55	17	∈	ORG
ejpam-4440	55	18	1-movable	QUANTITY
ejpam-4440	55	19	γ1mr(g	ORG
ejpam-4440	55	20	1-movable	QUANTITY
ejpam-4440	55	21	1-movable	QUANTITY
ejpam-4440	55	22	γ1mr(g	ORG
ejpam-4440	55	23	two	CARDINAL
ejpam-4440	58	1	∈	ORG
ejpam-4440	59	1	two	CARDINAL
ejpam-4440	59	2	g ◦ h	ORG
ejpam-4440	59	3	one	CARDINAL
ejpam-4440	59	4	∈	ORG
ejpam-4440	59	5	one	CARDINAL
ejpam-4440	59	6	⟨{v}⟩ +	GPE
ejpam-4440	59	7	∈	ORG
ejpam-4440	60	1	two	CARDINAL
ejpam-4440	60	2	g[h	ORG
ejpam-4440	60	3	∈	ORG
ejpam-4440	61	1	2	CARDINAL
ejpam-4440	63	1	1	CARDINAL
ejpam-4440	64	1	1	CARDINAL
ejpam-4440	65	1	1	CARDINAL
ejpam-4440	66	1	10	CARDINAL
ejpam-4440	70	1	1	CARDINAL
ejpam-4440	71	1	1	CARDINAL
ejpam-4440	71	2	1	CARDINAL
ejpam-4440	72	1	⊆	CARDINAL
ejpam-4440	72	2	k1+g	GPE
ejpam-4440	72	3	k1+g	GPE
ejpam-4440	72	4	1	CARDINAL
ejpam-4440	72	5	c∗	PERSON
ejpam-4440	72	6	2	CARDINAL
ejpam-4440	73	1	1	CARDINAL
ejpam-4440	73	2	⊆	CARDINAL
ejpam-4440	73	3	k1+g	GPE
ejpam-4440	73	4	k1+g	GPE
ejpam-4440	75	1	3	CARDINAL
ejpam-4440	76	1	1	CARDINAL
ejpam-4440	76	2	1	CARDINAL
ejpam-4440	76	3	2	DATE
ejpam-4440	77	1	m.	PERSON
ejpam-4440	77	2	h. sumaoy	PERSON
ejpam-4440	77	3	h. rara	PERSON
ejpam-4440	78	1	j. pure	PERSON
ejpam-4440	78	2	15	CARDINAL
ejpam-4440	78	3	3	CARDINAL
ejpam-4440	78	4	2022	CARDINAL
ejpam-4440	78	5	1201-1210 1204	DATE
ejpam-4440	78	6	ci	PERSON
ejpam-4440	78	7	1	CARDINAL
ejpam-4440	78	8	2	DATE
ejpam-4440	80	1	2	CARDINAL
ejpam-4440	81	1	g. hence	GPE
ejpam-4440	82	1	3	CARDINAL
ejpam-4440	83	1	2	CARDINAL
ejpam-4440	87	1	1	CARDINAL
ejpam-4440	91	1	1	CARDINAL
ejpam-4440	94	1	∩	WORK_OF_ART
ejpam-4440	94	2	1	CARDINAL
ejpam-4440	95	1	∃y ∈	PERSON
ejpam-4440	95	2	⊆	CARDINAL
ejpam-4440	96	1	2	CARDINAL
ejpam-4440	99	1	n ≥ 1	DATE
ejpam-4440	99	2	⊆	CARDINAL
ejpam-4440	105	1	2	CARDINAL
ejpam-4440	108	1	∈	ORG
ejpam-4440	110	1	lemma 1	ORG
ejpam-4440	111	1	h. sumaoy	PERSON
ejpam-4440	111	2	h. rara	PERSON
ejpam-4440	112	1	j. pure	PERSON
ejpam-4440	112	2	15	CARDINAL
ejpam-4440	112	3	3	CARDINAL
ejpam-4440	112	4	2022	CARDINAL
ejpam-4440	112	5	1201-1210	DATE
ejpam-4440	113	1	1	CARDINAL
ejpam-4440	114	1	∈	ORG
ejpam-4440	114	2	∩	ORG
ejpam-4440	115	1	∈	ORG
ejpam-4440	115	2	x})∪	GPE
ejpam-4440	115	3	g. lemma 3	PERSON
ejpam-4440	116	1	⊆	CARDINAL
ejpam-4440	116	2	∈	ORG
ejpam-4440	116	3	{x	PERSON
ejpam-4440	117	1	1	CARDINAL
ejpam-4440	117	2	∈	PRODUCT
ejpam-4440	118	1	1	CARDINAL
ejpam-4440	119	1	∈	ORG
ejpam-4440	121	1	∈	ORG
ejpam-4440	122	1	∈	ORG
ejpam-4440	124	1	1	CARDINAL
ejpam-4440	124	2	∈	ORG
ejpam-4440	124	3	∈	ORG
ejpam-4440	124	4	g)\ng(v	PERSON
ejpam-4440	127	1	x}⟩	ORG
ejpam-4440	127	2	lemma 2	ORG
ejpam-4440	127	3	3	CARDINAL
ejpam-4440	128	1	4	CARDINAL
ejpam-4440	133	1	1	CARDINAL
ejpam-4440	133	2	3	CARDINAL
ejpam-4440	134	1	5	CARDINAL
ejpam-4440	135	1	1	CARDINAL
ejpam-4440	136	1	⊆	CARDINAL
ejpam-4440	139	1	1	CARDINAL
ejpam-4440	140	1	1	CARDINAL
ejpam-4440	140	2	h. sumaoy	PERSON
ejpam-4440	140	3	h. rara	PERSON
ejpam-4440	141	1	j. pure	PERSON
ejpam-4440	141	2	15	CARDINAL
ejpam-4440	141	3	3	CARDINAL
ejpam-4440	141	4	2022	CARDINAL
ejpam-4440	141	5	1201-1210 1206	DATE
ejpam-4440	141	6	c∗	PERSON
ejpam-4440	141	7	2	CARDINAL
ejpam-4440	141	8	3	CARDINAL
ejpam-4440	143	1	1	CARDINAL
ejpam-4440	143	2	k1+g	GPE
ejpam-4440	144	1	2	CARDINAL
ejpam-4440	144	2	3	CARDINAL
ejpam-4440	144	3	1	CARDINAL
ejpam-4440	145	1	k1+g	GPE
ejpam-4440	145	2	lemma 2	ORG
ejpam-4440	145	3	3	CARDINAL
ejpam-4440	145	4	1	CARDINAL
ejpam-4440	145	5	6	CARDINAL
ejpam-4440	147	1	⊆	CARDINAL
ejpam-4440	147	2	k1+g	GPE
ejpam-4440	150	1	k1+g	GPE
ejpam-4440	151	1	2	CARDINAL
ejpam-4440	151	2	k1+g	GPE
ejpam-4440	151	3	lemma 2	ORG
ejpam-4440	151	4	3	CARDINAL
ejpam-4440	151	5	2	CARDINAL
ejpam-4440	151	6	k1+g	GPE
ejpam-4440	156	1	ofk1+g	ORG
ejpam-4440	157	1	1	CARDINAL
ejpam-4440	157	2	k1+g)\c	PERSON
ejpam-4440	159	1	1− 1 = n.	TIME
ejpam-4440	160	1	γmsr(k1	PERSON
ejpam-4440	160	2	1	CARDINAL
ejpam-4440	160	3	2	DATE
ejpam-4440	162	1	m.	PERSON
ejpam-4440	162	2	k1+g	GPE
ejpam-4440	163	1	ci	PERSON
ejpam-4440	163	2	1	CARDINAL
ejpam-4440	163	3	1	CARDINAL
ejpam-4440	163	4	2	DATE
ejpam-4440	166	1	3	CARDINAL
ejpam-4440	166	2	ci	PERSON
ejpam-4440	166	3	1	CARDINAL
ejpam-4440	166	4	2	DATE
ejpam-4440	170	1	1	CARDINAL
ejpam-4440	170	2	lemma 2	ORG
ejpam-4440	170	3	3	CARDINAL
ejpam-4440	170	4	ci	PERSON
ejpam-4440	171	1	1	CARDINAL
ejpam-4440	171	2	2	DATE
ejpam-4440	173	1	1.2	CARDINAL
ejpam-4440	175	1	lemma 2	ORG
ejpam-4440	175	2	3	CARDINAL
ejpam-4440	175	3	6	CARDINAL
ejpam-4440	175	4	h. sumaoy	PERSON
ejpam-4440	175	5	h. rara	PERSON
ejpam-4440	176	1	j. pure	PERSON
ejpam-4440	176	2	15	CARDINAL
ejpam-4440	176	3	3	CARDINAL
ejpam-4440	176	4	2022	CARDINAL
ejpam-4440	176	5	1201	CARDINAL
ejpam-4440	177	1	ci	PERSON
ejpam-4440	177	2	1	CARDINAL
ejpam-4440	177	3	1	CARDINAL
ejpam-4440	177	4	2	DATE
ejpam-4440	180	1	3	CARDINAL
ejpam-4440	180	2	lemma 2	ORG
ejpam-4440	180	3	3	CARDINAL
ejpam-4440	180	4	5	DATE
ejpam-4440	180	5	2	CARDINAL
ejpam-4440	181	1	1	CARDINAL
ejpam-4440	181	2	2	DATE
ejpam-4440	185	1	8	CARDINAL
ejpam-4440	188	1	at least one	CARDINAL
ejpam-4440	190	1	1.	CARDINAL
ejpam-4440	190	2	γ(h	ORG
ejpam-4440	191	1	1	CARDINAL
ejpam-4440	192	1	g+h	ORG
ejpam-4440	193	1	10	CARDINAL
ejpam-4440	193	2	2	CARDINAL
ejpam-4440	193	3	3	CARDINAL
ejpam-4440	194	1	10	CARDINAL
ejpam-4440	194	2	2	CARDINAL
ejpam-4440	194	3	3	CARDINAL
ejpam-4440	194	4	3	CARDINAL
ejpam-4440	198	1	m+	CARDINAL
ejpam-4440	198	2	1	CARDINAL
ejpam-4440	198	3	4	CARDINAL
ejpam-4440	199	1	9	CARDINAL
ejpam-4440	202	1	hu	PERSON
ejpam-4440	202	2	⊆	CARDINAL
ejpam-4440	204	1	g ◦ h (i	ORG
ejpam-4440	204	2	10	CARDINAL
ejpam-4440	205	1	hu	PERSON
ejpam-4440	205	2	⊆	CARDINAL
ejpam-4440	207	1	∈	ORG
ejpam-4440	208	1	hu	PERSON
ejpam-4440	209	1	⋃	PERSON
ejpam-4440	209	2	⋃	DATE
ejpam-4440	209	3	10	CARDINAL
ejpam-4440	210	1	hu	PERSON
ejpam-4440	210	2	⊆	CARDINAL
ejpam-4440	211	1	h. sumaoy	PERSON
ejpam-4440	211	2	h. rara	PERSON
ejpam-4440	212	1	j. pure	PERSON
ejpam-4440	212	2	15	CARDINAL
ejpam-4440	212	3	3	CARDINAL
ejpam-4440	212	4	2022	CARDINAL
ejpam-4440	212	5	1201-1210 1208	DATE
ejpam-4440	212	6	hu	PERSON
ejpam-4440	213	1	10	CARDINAL
ejpam-4440	214	1	hu	PERSON
ejpam-4440	215	1	hu	PERSON
ejpam-4440	215	2	∈	ORG
ejpam-4440	215	3	hu	PERSON
ejpam-4440	215	4	hu	PERSON
ejpam-4440	217	1	1	CARDINAL
ejpam-4440	218	1	hu	PERSON
ejpam-4440	218	2	⊆	CARDINAL
ejpam-4440	220	1	∣∣∣∣ ⋃	ORG
ejpam-4440	220	2	hu	PERSON
ejpam-4440	221	1	⋃	DATE
ejpam-4440	221	2	hu	PERSON
ejpam-4440	221	3	9	CARDINAL
ejpam-4440	222	1	|s∗|	PRODUCT
ejpam-4440	223	1	hu	PERSON
ejpam-4440	223	2	5	CARDINAL
ejpam-4440	224	1	h. sumaoy	PERSON
ejpam-4440	224	2	h. rara	PERSON
ejpam-4440	225	1	j. pure	PERSON
ejpam-4440	225	2	15	CARDINAL
ejpam-4440	225	3	3	CARDINAL
ejpam-4440	225	4	2022	CARDINAL
ejpam-4440	225	5	1201	CARDINAL
ejpam-4440	225	6	4	CARDINAL
ejpam-4440	226	1	1	CARDINAL
ejpam-4440	226	2	γ(h	ORG
ejpam-4440	227	1	1	CARDINAL
ejpam-4440	227	2	g[h	ORG
ejpam-4440	228	1	g[h	ORG
ejpam-4440	229	1	g = kn	PERSON
ejpam-4440	229	2	1	CARDINAL
ejpam-4440	229	3	1	CARDINAL
ejpam-4440	231	1	ng[h]((a	GPE
ejpam-4440	232	1	∈	ORG
ejpam-4440	232	2	a×c	ORG
ejpam-4440	232	3	g[h	ORG
ejpam-4440	233	1	a×c	ORG
ejpam-4440	233	2	g[h	ORG
ejpam-4440	236	1	∈	ORG
ejpam-4440	238	1	∈	ORG
ejpam-4440	240	1	1	CARDINAL
ejpam-4440	240	2	∩	NORP
ejpam-4440	242	1	∩ng[h]((a	DATE
ejpam-4440	243	1	g[h	ORG
ejpam-4440	244	1	10	CARDINAL
ejpam-4440	245	1	1	CARDINAL
ejpam-4440	246	1	g[h	ORG
ejpam-4440	247	1	γ(h	ORG
ejpam-4440	248	1	1	CARDINAL
ejpam-4440	249	1	g[h	ORG
ejpam-4440	250	1	2	CARDINAL
ejpam-4440	250	2	4	CARDINAL
ejpam-4440	251	1	g[h	ORG
ejpam-4440	252	1	1	CARDINAL
ejpam-4440	252	2	lemma 4	ORG
ejpam-4440	252	3	γ(h	ORG
ejpam-4440	253	1	1	CARDINAL
ejpam-4440	253	2	g[h])\(a×c	NORP
ejpam-4440	253	3	⊆	CARDINAL
ejpam-4440	253	4	γ(h	ORG
ejpam-4440	254	1	1	CARDINAL
ejpam-4440	255	1	⊆	CARDINAL
ejpam-4440	255	2	g[h	ORG
ejpam-4440	256	1	γ(h	ORG
ejpam-4440	257	1	1	CARDINAL
ejpam-4440	257	2	g[h	ORG
ejpam-4440	258	1	1	CARDINAL
ejpam-4440	258	2	4	CARDINAL
ejpam-4440	259	1	g[h	ORG
ejpam-4440	260	1	10	CARDINAL
ejpam-4440	261	1	5	CARDINAL
ejpam-4440	262	1	1	CARDINAL
ejpam-4440	262	2	m.	PERSON
ejpam-4440	262	3	γ1msr(g[h	PERSON
ejpam-4440	263	1	mn	ORG
ejpam-4440	263	2	1	CARDINAL
ejpam-4440	263	3	γ(h	ORG
ejpam-4440	264	1	1	CARDINAL
ejpam-4440	264	2	the department of science and technology	ORG
ejpam-4440	264	3	philippines	GPE
ejpam-4440	265	1	1210	CARDINAL
ejpam-4440	265	2	1	CARDINAL
ejpam-4440	265	3	h. rara	PERSON
ejpam-4440	267	1	21(1):91–101	DATE
ejpam-4440	267	2	2019	DATE
ejpam-4440	268	1	2	CARDINAL
ejpam-4440	269	1	m. johnson	PERSON
ejpam-4440	271	1	105(13):99–113	CARDINAL
ejpam-4440	272	1	3	CARDINAL
ejpam-4440	272	2	r. bailey	PERSON
ejpam-4440	273	1	43(2	CARDINAL
ejpam-4440	274	1	2011	DATE
ejpam-4440	275	1	4	CARDINAL
ejpam-4440	276	1	theorie des graphes	ORG
ejpam-4440	277	1	wiley	GPE
ejpam-4440	277	2	london	GPE
ejpam-4440	277	3	new york	GPE
ejpam-4440	277	4	1962	DATE
ejpam-4440	278	1	5	CARDINAL
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ejpam-4440	280	1	88:349–366	CARDINAL
ejpam-4440	281	1	6	CARDINAL
ejpam-4440	281	2	hattingh j.s	PERSON
ejpam-4440	281	3	s.t.	PERSON
ejpam-4440	281	4	laskar r.c.	PERSON
ejpam-4440	281	5	markus	PERSON
ejpam-4440	282	1	203	CARDINAL
ejpam-4440	283	1	1999	DATE
ejpam-4440	284	1	7	CARDINAL
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ejpam-4440	285	1	1998	DATE
ejpam-4440	286	1	8	CARDINAL
ejpam-4440	286	2	d. kuziak	PERSON
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ejpam-4440	286	6	2016	DATE
ejpam-4440	287	1	9	CARDINAL
ejpam-4440	287	2	k. liu	PERSON
ejpam-4440	287	3	n. abu-ghazaleh	PERSON
ejpam-4440	290	1	sci.	ORG
ejpam-4440	290	2	4104	DATE
ejpam-4440	290	3	2006	DATE
ejpam-4440	291	1	10	CARDINAL
ejpam-4440	291	2	g. monsanto	PERSON
ejpam-4440	291	3	h. rara	PERSON
ejpam-4440	293	1	european journal	ORG
ejpam-4440	293	2	13(1):170	CARDINAL
ejpam-4440	293	3	179	CARDINAL
ejpam-4440	293	4	2020	DATE
ejpam-4440	294	1	11	CARDINAL
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ejpam-4440	296	1	203:61–69, 1999	DATE
ejpam-4440	297	1	12	CARDINAL
ejpam-4440	297	2	k. samir	PERSON
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ejpam-4440	299	1	1996	DATE
ejpam-4440	300	1	13	CARDINAL
ejpam-4440	300	2	andras	PERSON
ejpam-4440	302	1	29(2):383–393	CARDINAL
ejpam-4440	303	1	14	CARDINAL
ejpam-4440	305	1	22(4):445–455, 1988	DATE