id	sid	eid	entity	type
ejpam-4748	1	1	european journal	ORG
ejpam-4748	2	1	16	CARDINAL
ejpam-4748	2	2	3	CARDINAL
ejpam-4748	2	3	2023	CARDINAL
ejpam-4748	2	4	1685-1694	CARDINAL
ejpam-4748	2	5	1307-5543	CARDINAL
ejpam-4748	2	6	new york	GPE
ejpam-4748	2	7	marivir m. ortega1,∗	PERSON
ejpam-4748	2	8	gina a. malacas1,2	PERSON
ejpam-4748	2	9	sergio r. canoy	PERSON
ejpam-4748	2	10	1	CARDINAL
ejpam-4748	2	11	mindanao state university-iligan institute of technology	ORG
ejpam-4748	2	12	9200	CARDINAL
ejpam-4748	2	13	iligan city	GPE
ejpam-4748	2	14	2	CARDINAL
ejpam-4748	2	15	institute of science	ORG
ejpam-4748	2	16	mindanao state university-iligan institute of technology	ORG
ejpam-4748	2	17	9200	CARDINAL
ejpam-4748	2	18	iligan city	GPE
ejpam-4748	2	19	philippines	GPE
ejpam-4748	5	1	2020	DATE
ejpam-4748	5	2	05c69	CARDINAL
ejpam-4748	5	3	1	CARDINAL
ejpam-4748	6	1	the past decades	DATE
ejpam-4748	8	1	slater	PERSON
ejpam-4748	8	2	10	CARDINAL
ejpam-4748	8	3	11	CARDINAL
ejpam-4748	9	1	7	CARDINAL
ejpam-4748	16	1	1–6	CARDINAL
ejpam-4748	16	2	8	CARDINAL
ejpam-4748	18	1	https://doi.org/10.29020/nybg.ejpam.v16i3.4748	GPE
ejpam-4748	18	2	m. ortega	PERSON
ejpam-4748	18	3	sergio.canoy@g.msuiit.edu.ph	ORG
ejpam-4748	18	4	s. canoy, jr.	PERSON
ejpam-4748	18	5	1685	DATE
ejpam-4748	18	6	2023	CARDINAL
ejpam-4748	19	1	m. ortega	PERSON
ejpam-4748	19	2	g. malacas	PERSON
ejpam-4748	19	3	s. canoy, jr.	PERSON
ejpam-4748	20	1	j. pure	PERSON
ejpam-4748	20	2	16	CARDINAL
ejpam-4748	20	3	3	CARDINAL
ejpam-4748	20	4	2023	CARDINAL
ejpam-4748	20	5	1685-1694	CARDINAL
ejpam-4748	20	6	∈	ORG
ejpam-4748	22	1	∈	ORG
ejpam-4748	23	1	∈	ORG
ejpam-4748	23	2	∈	ORG
ejpam-4748	25	1	1	CARDINAL
ejpam-4748	25	2	annd s(g	PERSON
ejpam-4748	26	1	⊆	CARDINAL
ejpam-4748	27	1	γ(g	NORP
ejpam-4748	27	2	two	CARDINAL
ejpam-4748	27	3	∩ s ̸=	ORG
ejpam-4748	27	4	∩ s.	PERSON
ejpam-4748	27	5	∈	ORG
ejpam-4748	56	1	λs gsl(g	PERSON
ejpam-4748	59	1	m. ortega	PERSON
ejpam-4748	59	2	g. malacas	PERSON
ejpam-4748	59	3	s. canoy, jr.	PERSON
ejpam-4748	60	1	j. pure	PERSON
ejpam-4748	60	2	16	CARDINAL
ejpam-4748	60	3	3	CARDINAL
ejpam-4748	60	4	2023	CARDINAL
ejpam-4748	60	5	1685-1694 1687	CARDINAL
ejpam-4748	61	1	λs gsl(g	PERSON
ejpam-4748	63	1	two	CARDINAL
ejpam-4748	65	1	∈	ORG
ejpam-4748	66	1	one	CARDINAL
ejpam-4748	67	1	one	CARDINAL
ejpam-4748	68	1	∈	ORG
ejpam-4748	71	1	v1)(u2	GPE
ejpam-4748	73	1	3	CARDINAL
ejpam-4748	73	2	first	ORDINAL
ejpam-4748	73	3	1	CARDINAL
ejpam-4748	77	1	2 ≤	CARDINAL
ejpam-4748	78	1	2	CARDINAL
ejpam-4748	79	1	s(g	PERSON
ejpam-4748	79	2	⊆	CARDINAL
ejpam-4748	79	3	s.	PERSON
ejpam-4748	79	4	∈ l(g	ORG
ejpam-4748	79	5	s(g	PERSON
ejpam-4748	79	6	w ∈	PERSON
ejpam-4748	80	1	1	CARDINAL
ejpam-4748	87	1	1	CARDINAL
ejpam-4748	89	1	1	CARDINAL
ejpam-4748	91	1	2	CARDINAL
ejpam-4748	95	1	m. ortega	PERSON
ejpam-4748	95	2	g. malacas	PERSON
ejpam-4748	95	3	s. canoy, jr.	PERSON
ejpam-4748	96	1	j. pure	PERSON
ejpam-4748	96	2	16	CARDINAL
ejpam-4748	96	3	3	CARDINAL
ejpam-4748	96	4	2023	CARDINAL
ejpam-4748	96	5	1685-1694 1688	CARDINAL
ejpam-4748	96	6	2	CARDINAL
ejpam-4748	99	1	1(i	CARDINAL
ejpam-4748	99	2	3	CARDINAL
ejpam-4748	100	1	3	CARDINAL
ejpam-4748	101	1	∈	ORG
ejpam-4748	103	1	2	CARDINAL
ejpam-4748	103	2	∈	ORG
ejpam-4748	104	1	bc	ORG
ejpam-4748	105	1	ac	ORG
ejpam-4748	105	2	bc	ORG
ejpam-4748	115	1	w ∈	PERSON
ejpam-4748	116	1	2	CARDINAL
ejpam-4748	116	2	3	CARDINAL
ejpam-4748	116	3	∩	PERSON
ejpam-4748	117	1	∩	PERSON
ejpam-4748	117	2	∩	PERSON
ejpam-4748	118	1	4	CARDINAL
ejpam-4748	119	1	1	CARDINAL
ejpam-4748	120	1	2	CARDINAL
ejpam-4748	120	2	⊆	CARDINAL
ejpam-4748	121	1	∩ s.	PERSON
ejpam-4748	121	2	3	CARDINAL
ejpam-4748	122	1	n ≥ 4	ORG
ejpam-4748	125	1	3	CARDINAL
ejpam-4748	126	1	1	CARDINAL
ejpam-4748	128	1	4	CARDINAL
ejpam-4748	129	1	5	CARDINAL
ejpam-4748	130	1	2 4 1 5 3	CARDINAL
ejpam-4748	130	2	2 4 1 5 3	CARDINAL
ejpam-4748	130	3	1	CARDINAL
ejpam-4748	130	4	4	CARDINAL
ejpam-4748	130	5	4	CARDINAL
ejpam-4748	131	1	5	CARDINAL
ejpam-4748	132	1	2	CARDINAL
ejpam-4748	133	1	5	CARDINAL
ejpam-4748	134	1	3	CARDINAL
ejpam-4748	139	1	∈	ORG
ejpam-4748	139	2	s(g	PERSON
ejpam-4748	142	1	xz	ORG
ejpam-4748	144	1	s(g	PERSON
ejpam-4748	144	2	2	CARDINAL
ejpam-4748	148	1	sz	GPE
ejpam-4748	148	2	m. ortega	PERSON
ejpam-4748	148	3	g. malacas	PERSON
ejpam-4748	148	4	s. canoy, jr.	PERSON
ejpam-4748	149	1	j. pure	PERSON
ejpam-4748	149	2	16	CARDINAL
ejpam-4748	149	3	3	CARDINAL
ejpam-4748	149	4	2023	CARDINAL
ejpam-4748	149	5	1685-1694	CARDINAL
ejpam-4748	149	6	1	CARDINAL
ejpam-4748	150	1	1	CARDINAL
ejpam-4748	152	1	1	CARDINAL
ejpam-4748	153	1	4	CARDINAL
ejpam-4748	153	2	2	DATE
ejpam-4748	153	3	3	CARDINAL
ejpam-4748	154	1	1	CARDINAL
ejpam-4748	155	1	5	CARDINAL
ejpam-4748	155	2	2	CARDINAL
ejpam-4748	156	1	4	CARDINAL
ejpam-4748	157	1	4	CARDINAL
ejpam-4748	158	1	3	CARDINAL
ejpam-4748	159	1	1	CARDINAL
ejpam-4748	160	1	g+h	ORG
ejpam-4748	160	2	at least one	CARDINAL
ejpam-4748	161	1	3	CARDINAL
ejpam-4748	164	1	⊆	CARDINAL
ejpam-4748	164	2	g+h	ORG
ejpam-4748	166	1	s.	PERSON
ejpam-4748	166	2	g+h	ORG
ejpam-4748	167	1	3	CARDINAL
ejpam-4748	174	1	∪h	PRODUCT
ejpam-4748	175	1	b′	PRODUCT
ejpam-4748	175	2	a′	ORG
ejpam-4748	175	3	b′	PRODUCT
ejpam-4748	176	1	a′	ORG
ejpam-4748	176	2	a′	ORG
ejpam-4748	177	1	b′	PRODUCT
ejpam-4748	177	2	b′	PRODUCT
ejpam-4748	178	1	3	CARDINAL
ejpam-4748	178	2	a′	ORG
ejpam-4748	178	3	b′	PRODUCT
ejpam-4748	178	4	a′	ORG
ejpam-4748	178	5	b′	PRODUCT
ejpam-4748	179	1	g+h	ORG
ejpam-4748	180	1	∈	ORG
ejpam-4748	181	1	a′	ORG
ejpam-4748	181	2	∩	PERSON
ejpam-4748	181	3	ng+h(a	PERSON
ejpam-4748	181	4	ng+h(b)∩ s	ORG
ejpam-4748	181	5	1	CARDINAL
ejpam-4748	181	6	∈	ORG
ejpam-4748	183	1	∪h	PRODUCT
ejpam-4748	184	1	w ∈ s	ORG
ejpam-4748	185	1	w ∈ a′	ORG
ejpam-4748	187	1	∈	ORG
ejpam-4748	187	2	m. ortega	PERSON
ejpam-4748	187	3	g. malacas	PERSON
ejpam-4748	187	4	s. canoy, jr.	PERSON
ejpam-4748	188	1	j. pure	PERSON
ejpam-4748	188	2	16	CARDINAL
ejpam-4748	188	3	3	CARDINAL
ejpam-4748	188	4	2023	CARDINAL
ejpam-4748	188	5	1685-1694 1690	DATE
ejpam-4748	188	6	∈	ORG
ejpam-4748	189	1	∩	PERSON
ejpam-4748	190	1	1	CARDINAL
ejpam-4748	191	1	bw′	LOC
ejpam-4748	191	2	w ∈	GPE
ejpam-4748	193	1	g+h	ORG
ejpam-4748	194	1	3	CARDINAL
ejpam-4748	196	1	g+h	ORG
ejpam-4748	200	1	2	CARDINAL
ejpam-4748	202	1	sg	GPE
ejpam-4748	204	1	m+	CARDINAL
ejpam-4748	207	1	3	CARDINAL
ejpam-4748	207	2	km +g. □ theorem	PRODUCT
ejpam-4748	207	3	4	CARDINAL
ejpam-4748	208	1	4	CARDINAL
ejpam-4748	209	1	g ⋄ h	ORG
ejpam-4748	210	1	⊆	CARDINAL
ejpam-4748	210	2	huv	ORG
ejpam-4748	210	3	huv	ORG
ejpam-4748	210	4	huv	ORG
ejpam-4748	210	5	∈	PRODUCT
ejpam-4748	211	1	∩ l(g	ORG
ejpam-4748	211	2	∈	ORG
ejpam-4748	211	3	∩	WORK_OF_ART
ejpam-4748	211	4	∈	ORG
ejpam-4748	211	5	m. ortega	PERSON
ejpam-4748	211	6	g. malacas	PERSON
ejpam-4748	211	7	s. canoy, jr.	PERSON
ejpam-4748	212	1	j. pure	PERSON
ejpam-4748	212	2	16	CARDINAL
ejpam-4748	212	3	3	CARDINAL
ejpam-4748	212	4	2023	CARDINAL
ejpam-4748	212	5	1685-1694 1691	CARDINAL
ejpam-4748	212	6	2	CARDINAL
ejpam-4748	214	1	γ(g	NORP
ejpam-4748	215	1	1	CARDINAL
ejpam-4748	216	1	1	CARDINAL
ejpam-4748	217	1	γ(g ⋄ h	ORG
ejpam-4748	217	2	1	CARDINAL
ejpam-4748	217	3	g ⋄ h.	ORG
ejpam-4748	218	1	γ(g	NORP
ejpam-4748	218	2	1	CARDINAL
ejpam-4748	218	3	∈	ORG
ejpam-4748	221	1	pq /∈	PERSON
ejpam-4748	222	1	∈	ORG
ejpam-4748	224	1	γ(g	PERSON
ejpam-4748	224	2	1	CARDINAL
ejpam-4748	225	1	1	CARDINAL
ejpam-4748	225	2	∈	ORG
ejpam-4748	226	1	γ(g	PERSON
ejpam-4748	227	1	1	CARDINAL
ejpam-4748	227	2	5	CARDINAL
ejpam-4748	228	1	2	CARDINAL
ejpam-4748	229	1	g ⋄ h	ORG
ejpam-4748	230	1	⊆	CARDINAL
ejpam-4748	235	1	γ(g	NORP
ejpam-4748	235	2	lemma 2.	ORG
ejpam-4748	235	3	γ(g ◦ h	GPE
ejpam-4748	235	4	g ◦ h	ORG
ejpam-4748	237	1	g ⋄ h.	ORG
ejpam-4748	237	2	⊆	CARDINAL
ejpam-4748	237	3	∩ s.	PERSON
ejpam-4748	237	4	4	CARDINAL
ejpam-4748	237	5	g ⋄ h.	ORG
ejpam-4748	238	1	∈	ORG
ejpam-4748	238	2	∈	ORG
ejpam-4748	239	1	∈	ORG
ejpam-4748	240	1	∈	ORG
ejpam-4748	241	1	4 (ii)(a	PERCENT
ejpam-4748	241	2	∈	ORG
ejpam-4748	241	3	∈	ORG
ejpam-4748	241	4	∈	ORG
ejpam-4748	242	1	∈	ORG
ejpam-4748	243	1	xq	ORG
ejpam-4748	243	2	∈	PRODUCT
ejpam-4748	245	1	g ⋄ h	ORG
ejpam-4748	245	2	∩ s. hence	PERSON
ejpam-4748	245	3	1	CARDINAL
ejpam-4748	247	1	w ∈ s	ORG
ejpam-4748	248	1	sw	ORG
ejpam-4748	249	1	sw	ORG
ejpam-4748	250	1	sw	ORG
ejpam-4748	250	2	lemma 1.	ORG
ejpam-4748	252	1	g ⋄ h. consequently	ORG
ejpam-4748	254	1	6	CARDINAL
ejpam-4748	255	1	1	CARDINAL
ejpam-4748	256	1	⊆	CARDINAL
ejpam-4748	257	1	⊆	CARDINAL
ejpam-4748	259	1	1	CARDINAL
ejpam-4748	259	2	m. ortega	PERSON
ejpam-4748	259	3	g. malacas	PERSON
ejpam-4748	259	4	s. canoy, jr.	PERSON
ejpam-4748	260	1	j. pure	PERSON
ejpam-4748	260	2	16	CARDINAL
ejpam-4748	260	3	3	CARDINAL
ejpam-4748	260	4	2023	CARDINAL
ejpam-4748	260	5	1685-1694 1692	CARDINAL
ejpam-4748	262	1	∩a	GPE
ejpam-4748	266	1	⊆	CARDINAL
ejpam-4748	269	1	g ◦ h is connected and	ORG
ejpam-4748	269	2	γ(g ◦ h	GPE
ejpam-4748	269	3	g ◦ h	ORG
ejpam-4748	271	1	⊆	CARDINAL
ejpam-4748	271	2	∩ s.	PERSON
ejpam-4748	271	3	∪v∈v (g)dv	ORG
ejpam-4748	271	4	dv ̸=	ORG
ejpam-4748	271	5	6	CARDINAL
ejpam-4748	272	1	∈	ORG
ejpam-4748	272	2	w ∈	ORG
ejpam-4748	272	3	g)\ng(v	PERSON
ejpam-4748	273	1	dw ̸=	ORG
ejpam-4748	273	2	∈	ORG
ejpam-4748	273	3	∈	ORG
ejpam-4748	274	1	∈	ORG
ejpam-4748	275	1	ng◦h(a	ORG
ejpam-4748	275	2	ng◦h(a	ORG
ejpam-4748	275	3	1	CARDINAL
ejpam-4748	277	1	∈	ORG
ejpam-4748	278	1	7	CARDINAL
ejpam-4748	279	1	4	CARDINAL
ejpam-4748	280	1	2	CARDINAL
ejpam-4748	280	2	⋃	PERSON
ejpam-4748	280	3	⊆	CARDINAL
ejpam-4748	280	4	tx	ORG
ejpam-4748	280	5	⊆	PRODUCT
ejpam-4748	280	6	∈	ORG
ejpam-4748	280	7	g[h	ORG
ejpam-4748	281	1	tx	ORG
ejpam-4748	282	1	tx	ORG
ejpam-4748	283	1	tx	ORG
ejpam-4748	285	1	2	CARDINAL
ejpam-4748	286	1	g[h	ORG
ejpam-4748	287	1	⋃	PERSON
ejpam-4748	287	2	⊆	CARDINAL
ejpam-4748	287	3	g[h	ORG
ejpam-4748	287	4	m. ortega	PERSON
ejpam-4748	287	5	g. malacas	PERSON
ejpam-4748	287	6	s. canoy, jr.	PERSON
ejpam-4748	288	1	j. pure	PERSON
ejpam-4748	288	2	16	CARDINAL
ejpam-4748	288	3	3	CARDINAL
ejpam-4748	288	4	2023	CARDINAL
ejpam-4748	288	5	1685-1694 1693	DATE
ejpam-4748	290	1	∈	ORG
ejpam-4748	292	1	g[h	ORG
ejpam-4748	293	1	g[h	ORG
ejpam-4748	294	1	7	CARDINAL
ejpam-4748	295	1	w ∈	PERSON
ejpam-4748	296	1	∈	ORG
ejpam-4748	296	2	w	GPE
ejpam-4748	296	3	w	GPE
ejpam-4748	296	4	g[h	ORG
ejpam-4748	298	1	g[h	ORG
ejpam-4748	299	1	g[h	ORG
ejpam-4748	300	1	lemma 1	ORG
ejpam-4748	300	2	g[h	ORG
ejpam-4748	301	1	g[h	ORG
ejpam-4748	302	1	g[h	ORG
ejpam-4748	303	1	5	CARDINAL
ejpam-4748	304	1	2	CARDINAL
ejpam-4748	313	1	1694	CARDINAL
ejpam-4748	314	1	the department of science and technology	ORG
ejpam-4748	314	2	mindanao	LOC
ejpam-4748	314	3	institute of technology	ORG
ejpam-4748	315	1	1	CARDINAL
ejpam-4748	315	2	e. ahmad	PERSON
ejpam-4748	315	3	s. canoy jr.	PERSON
ejpam-4748	315	4	g. malacas	PERSON
ejpam-4748	317	1	european journal	ORG
ejpam-4748	317	2	14:638–649	DATE
ejpam-4748	317	3	2021	CARDINAL
ejpam-4748	318	1	2	CARDINAL
ejpam-4748	318	2	m. mora c. hernando	PERSON
ejpam-4748	318	3	i. pelayo	PERSON
ejpam-4748	320	1	ars mathematica contemporanea	PERSON
ejpam-4748	320	2	2015	DATE
ejpam-4748	321	1	3	CARDINAL
ejpam-4748	321	2	m. mora c. hernando	PERSON
ejpam-4748	321	3	i. pelayo	PERSON
ejpam-4748	322	1	bipartite	ORG
ejpam-4748	323	1	1–15	CARDINAL
ejpam-4748	323	2	2017	DATE
ejpam-4748	324	1	4	CARDINAL
ejpam-4748	324	2	s. canoy jr. g. malacas	PERSON
ejpam-4748	324	3	e. chacon	PERSON
ejpam-4748	326	1	european journal	ORG
ejpam-4748	326	2	16:479–490	CARDINAL
ejpam-4748	326	3	2023	CARDINAL
ejpam-4748	327	1	5	CARDINAL
ejpam-4748	327	2	s. canoy jr.	PERSON
ejpam-4748	327	3	g. malacas	PERSON
ejpam-4748	329	1	nrcp research journal	ORG
ejpam-4748	329	2	13:1–8, 2013	DATE
ejpam-4748	330	1	6	CARDINAL
ejpam-4748	330	2	s. canoy jr.	PERSON
ejpam-4748	330	3	g. malacas	PERSON
ejpam-4748	332	1	8:4381–4388	CARDINAL
ejpam-4748	332	2	2013	DATE
ejpam-4748	333	1	7	CARDINAL
ejpam-4748	333	2	c. mynhardt m. frick	PERSON
ejpam-4748	333	3	r. skaggs	PERSON
ejpam-4748	335	1	76:213–227, 2008	DATE
ejpam-4748	336	1	8	CARDINAL
ejpam-4748	336	2	g. malacas	PERSON
ejpam-4748	336	3	a. malnegro	PERSON
ejpam-4748	337	1	cartesian	NORP
ejpam-4748	338	1	21st	ORDINAL
ejpam-4748	338	2	japanese	NORP
ejpam-4748	338	3	36–42,	DATE
ejpam-4748	338	4	2018	DATE
ejpam-4748	339	1	9	CARDINAL
ejpam-4748	339	2	g. malacas	PERSON
ejpam-4748	339	3	a. malnegro	PERSON
ejpam-4748	341	1	20:61–71	DATE
ejpam-4748	341	2	2019	DATE
ejpam-4748	342	1	10	CARDINAL
ejpam-4748	342	2	m. chellal p. slater	PERSON
ejpam-4748	342	3	m. mimouni	PERSON
ejpam-4748	344	1	discussiones mathematicae	PERSON
ejpam-4748	344	2	30:233–235	CARDINAL
ejpam-4748	344	3	2010	DATE
ejpam-4748	345	1	11	CARDINAL
ejpam-4748	347	1	22:445–455	CARDINAL
ejpam-4748	347	2	1988	DATE