id	sid	eid	entity	type
ejpam-4744	1	1	european journal	ORG
ejpam-4744	2	1	16	CARDINAL
ejpam-4744	2	2	2	CARDINAL
ejpam-4744	2	3	2023	CARDINAL
ejpam-4744	2	4	1318	CARDINAL
ejpam-4744	2	5	1307-5543	DATE
ejpam-4744	2	6	new york	GPE
ejpam-4744	2	7	b. palco1,∗	PERSON
ejpam-4744	2	8	rolando n. paluga2	PERSON
ejpam-4744	3	1	allied sciences	ORG
ejpam-4744	3	2	mindanao state university	ORG
ejpam-4744	3	3	9023	DATE
ejpam-4744	3	4	philippines 2 department	ORG
ejpam-4744	3	5	caraga state university	ORG
ejpam-4744	3	6	8600	CARDINAL
ejpam-4744	3	7	philippines	GPE
ejpam-4744	5	1	kn ◦g	ORG
ejpam-4744	6	1	2020	DATE
ejpam-4744	6	2	05c69	CARDINAL
ejpam-4744	6	3	1	CARDINAL
ejpam-4744	7	1	nonempty	ORG
ejpam-4744	9	1	ω(g	ORG
ejpam-4744	9	2	1	CARDINAL
ejpam-4744	11	1	2	CARDINAL
ejpam-4744	11	2	frank harary	PERSON
ejpam-4744	14	1	3	CARDINAL
ejpam-4744	16	1	kn	PERSON
ejpam-4744	17	1	1	CARDINAL
ejpam-4744	17	2	2	DATE
ejpam-4744	17	3	3	DATE
ejpam-4744	17	4	ω(g	ORG
ejpam-4744	20	1	b. palco	ORG
ejpam-4744	20	2	rnpaluga@carsu.edu.ph	GPE
ejpam-4744	20	3	rolando n. paluga	ORG
ejpam-4744	21	1	2023	CARDINAL
ejpam-4744	22	1	j. b. palco	PERSON
ejpam-4744	22	2	r. n. paluga	PERSON
ejpam-4744	23	1	j. pure	PERSON
ejpam-4744	23	2	16	CARDINAL
ejpam-4744	23	3	2	CARDINAL
ejpam-4744	23	4	2023	CARDINAL
ejpam-4744	23	5	1318	CARDINAL
ejpam-4744	23	6	two	CARDINAL
ejpam-4744	25	1	∈	ORG
ejpam-4744	25	2	∈	ORG
ejpam-4744	26	1	1	CARDINAL
ejpam-4744	30	1	nonempty	ORG
ejpam-4744	31	1	ω(h	ORG
ejpam-4744	32	1	m. let s2	PERSON
ejpam-4744	32	2	1	CARDINAL
ejpam-4744	32	3	2	DATE
ejpam-4744	34	1	ϕ(x	ORG
ejpam-4744	35	1	ϕ1(x)×	PERSON
ejpam-4744	35	2	∈	ORG
ejpam-4744	35	3	∈	ORG
ejpam-4744	39	1	1	CARDINAL
ejpam-4744	45	1	2	CARDINAL
ejpam-4744	55	1	∈	ORG
ejpam-4744	55	2	⊆	CARDINAL
ejpam-4744	55	3	ϕ(x	LOC
ejpam-4744	58	1	∈	ORG
ejpam-4744	59	1	⊆	CARDINAL
ejpam-4744	59	2	ϕ(x	ORG
ejpam-4744	61	1	g+h	ORG
ejpam-4744	62	1	1	CARDINAL
ejpam-4744	63	1	s2	PERSON
ejpam-4744	66	1	ω(f	GPE
ejpam-4744	67	1	2	CARDINAL
ejpam-4744	71	1	∩	PERSON
ejpam-4744	72	1	∩	PERSON
ejpam-4744	73	1	j. b. palco	PERSON
ejpam-4744	73	2	r. n. paluga	PERSON
ejpam-4744	74	1	j. pure	PERSON
ejpam-4744	74	2	16	CARDINAL
ejpam-4744	74	3	2	CARDINAL
ejpam-4744	74	4	2023	CARDINAL
ejpam-4744	74	5	1318	CARDINAL
ejpam-4744	76	1	3	CARDINAL
ejpam-4744	84	1	ϕ2(x2	ORG
ejpam-4744	84	2	⊆	CARDINAL
ejpam-4744	85	1	⊆	CARDINAL
ejpam-4744	87	1	∈	ORG
ejpam-4744	89	1	∈	ORG
ejpam-4744	90	1	∈	ORG
ejpam-4744	91	1	g+h	ORG
ejpam-4744	92	1	∈	ORG
ejpam-4744	97	1	ϕ(y2	PERSON
ejpam-4744	102	1	ω(f	PERSON
ejpam-4744	107	1	∈	ORG
ejpam-4744	107	2	ζ(g))|	NORP
ejpam-4744	108	1	2	CARDINAL
ejpam-4744	109	1	kn	PERSON
ejpam-4744	111	1	1	CARDINAL
ejpam-4744	111	2	n ≥ 1 (ii	DATE
ejpam-4744	112	1	1	CARDINAL
ejpam-4744	113	1	1	CARDINAL
ejpam-4744	113	2	two	CARDINAL
ejpam-4744	113	3	∈	ORG
ejpam-4744	113	4	a. j. b. palco	PERSON
ejpam-4744	113	5	r. n. paluga	PERSON
ejpam-4744	114	1	j. pure	PERSON
ejpam-4744	114	2	16	CARDINAL
ejpam-4744	114	3	2	CARDINAL
ejpam-4744	114	4	2023	CARDINAL
ejpam-4744	114	5	1318	CARDINAL
ejpam-4744	114	6	3	CARDINAL
ejpam-4744	116	1	ω(g ◦h	ORG
ejpam-4744	120	1	bco(g	ORG
ejpam-4744	121	1	1	CARDINAL
ejpam-4744	121	2	2	DATE
ejpam-4744	121	3	1 ≤ j ≤ ω(h	QUANTITY
ejpam-4744	121	4	hai	GPE
ejpam-4744	122	1	1	CARDINAL
ejpam-4744	122	2	2	DATE
ejpam-4744	123	1	1 ≤ j ≤	QUANTITY
ejpam-4744	123	2	⋃n i=0 si.	PERSON
ejpam-4744	124	1	1	CARDINAL
ejpam-4744	124	2	2	DATE
ejpam-4744	124	3	∈	ORG
ejpam-4744	125	1	⋃n i=1 fi	PERSON
ejpam-4744	125	2	⋃	DATE
ejpam-4744	125	3	1 ≤ i ≤ n	QUANTITY
ejpam-4744	126	1	ϕ(x	ORG
ejpam-4744	126	2	∈	ORG
ejpam-4744	127	1	i.	PERSON
ejpam-4744	128	1	i.	PERSON
ejpam-4744	128	2	j.	PERSON
ejpam-4744	128	3	0	CARDINAL
ejpam-4744	129	1	⊆	CARDINAL
ejpam-4744	133	1	1	CARDINAL
ejpam-4744	138	1	1	CARDINAL
ejpam-4744	138	2	⊆	CARDINAL
ejpam-4744	139	1	1	CARDINAL
ejpam-4744	139	2	j, 1	WORK_OF_ART
ejpam-4744	139	3	2	DATE
ejpam-4744	139	4	j, ω(h	WORK_OF_ART
ejpam-4744	140	1	j.	PERSON
ejpam-4744	141	1	2	CARDINAL
ejpam-4744	143	1	∩	PERSON
ejpam-4744	143	2	⊆	CARDINAL
ejpam-4744	144	1	j. consequently	PERSON
ejpam-4744	147	1	i.	PERSON
ejpam-4744	147	2	hai	GPE
ejpam-4744	147	3	ϕ(x	LOC
ejpam-4744	148	1	i.	PERSON
ejpam-4744	148	2	ϕ(x	LOC
ejpam-4744	149	1	1	CARDINAL
ejpam-4744	153	1	aj	PERSON
ejpam-4744	153	2	aj ∈	PERSON
ejpam-4744	156	1	ω(f	GPE
ejpam-4744	157	1	2	CARDINAL
ejpam-4744	157	2	hai	GPE
ejpam-4744	157	3	i.	PERSON
ejpam-4744	160	1	∩	PERSON
ejpam-4744	160	2	ω(f	GPE
ejpam-4744	161	1	3	CARDINAL
ejpam-4744	163	1	⊆	CARDINAL
ejpam-4744	163	2	ω(f	GPE
ejpam-4744	164	1	ω(f	GPE
ejpam-4744	165	1	∈	ORG
ejpam-4744	167	1	1	CARDINAL
ejpam-4744	167	2	i.	PERSON
ejpam-4744	168	1	hai	GPE
ejpam-4744	169	1	x1 j. b. palco	PERSON
ejpam-4744	169	2	r. n. paluga	PERSON
ejpam-4744	170	1	j. pure	PERSON
ejpam-4744	170	2	16	CARDINAL
ejpam-4744	170	3	2	CARDINAL
ejpam-4744	170	4	2023	CARDINAL
ejpam-4744	170	5	1318-1325 1322	DATE
ejpam-4744	170	6	hai	GPE
ejpam-4744	171	1	2	CARDINAL
ejpam-4744	171	2	1	CARDINAL
ejpam-4744	171	3	2	DATE
ejpam-4744	171	4	3	DATE
ejpam-4744	173	1	∈	ORG
ejpam-4744	174	1	0	CARDINAL
ejpam-4744	174	2	∈	ORG
ejpam-4744	174	3	0	CARDINAL
ejpam-4744	174	4	aj ∈	PERSON
ejpam-4744	175	1	aj ∈	PERSON
ejpam-4744	176	1	aj	PERSON
ejpam-4744	176	2	aj	PERSON
ejpam-4744	176	3	3	CARDINAL
ejpam-4744	176	4	∈	ORG
ejpam-4744	176	5	j.	PERSON
ejpam-4744	177	1	∈	ORG
ejpam-4744	178	1	a∩b ̸=	ORG
ejpam-4744	178	2	⊆	CARDINAL
ejpam-4744	178	3	⊆	CARDINAL
ejpam-4744	178	4	⊆	CARDINAL
ejpam-4744	179	1	j. consequently	PERSON
ejpam-4744	179	2	∈	ORG
ejpam-4744	180	1	aj	PERSON
ejpam-4744	181	1	ω(f	PERSON
ejpam-4744	181	2	ω(g ◦h	ORG
ejpam-4744	182	1	n∑ i=1	PERSON
ejpam-4744	186	1	ω(g ◦h	ORG
ejpam-4744	189	1	n ≥ 2.	ORG
ejpam-4744	190	1	1 + n	QUANTITY
ejpam-4744	192	1	3	CARDINAL
ejpam-4744	192	2	co(kn)+|v	NORP
ejpam-4744	193	1	2	CARDINAL
ejpam-4744	193	2	1	CARDINAL
ejpam-4744	194	1	1 + n	QUANTITY
ejpam-4744	196	1	1 ≤	QUANTITY
ejpam-4744	197	1	1	CARDINAL
ejpam-4744	197	2	2	DATE
ejpam-4744	197	3	3	DATE
ejpam-4744	198	1	1 ≤	QUANTITY
ejpam-4744	198	2	ϕ(x	LOC
ejpam-4744	199	1	∈	ORG
ejpam-4744	201	1	∈	ORG
ejpam-4744	201	2	j. b. palco	PERSON
ejpam-4744	201	3	r. n. paluga	PERSON
ejpam-4744	202	1	j. pure	PERSON
ejpam-4744	202	2	16	CARDINAL
ejpam-4744	202	3	2	CARDINAL
ejpam-4744	202	4	2023	CARDINAL
ejpam-4744	202	5	1318-1325 1323	CARDINAL
ejpam-4744	202	6	ab /∈	PERSON
ejpam-4744	204	1	∪n	CARDINAL
ejpam-4744	209	1	∪n	CARDINAL
ejpam-4744	209	2	1 + n	QUANTITY
ejpam-4744	211	1	1	CARDINAL
ejpam-4744	211	2	∪n	CARDINAL
ejpam-4744	211	3	0	CARDINAL
ejpam-4744	215	1	t ∈ ϕ(a2	ORG
ejpam-4744	216	1	∈	ORG
ejpam-4744	216	2	r.	NORP
ejpam-4744	216	3	t ∈ ϕ(x	DATE
ejpam-4744	219	1	1 + n	QUANTITY
ejpam-4744	220	1	2	CARDINAL
ejpam-4744	221	1	n ≥ 2.	ORG
ejpam-4744	225	1	3	CARDINAL
ejpam-4744	226	1	ω(g	ORG
ejpam-4744	227	1	2	CARDINAL
ejpam-4744	227	2	1	CARDINAL
ejpam-4744	229	1	1	CARDINAL
ejpam-4744	230	1	1	CARDINAL
ejpam-4744	231	1	1 ≤ i ≤ n − 1	QUANTITY
ejpam-4744	231	2	1 ≤	QUANTITY
ejpam-4744	232	1	1	CARDINAL
ejpam-4744	232	2	2	DATE
ejpam-4744	232	3	3	DATE
ejpam-4744	233	1	1 ≤	QUANTITY
ejpam-4744	233	2	ϕ(x	LOC
ejpam-4744	234	1	∈	ORG
ejpam-4744	236	1	∈	ORG
ejpam-4744	236	2	ab /∈	ORG
ejpam-4744	238	1	∪n	CARDINAL
ejpam-4744	241	1	j. b. palco	PERSON
ejpam-4744	241	2	r. n. paluga	PERSON
ejpam-4744	242	1	j. pure	PERSON
ejpam-4744	242	2	16	CARDINAL
ejpam-4744	242	3	2	CARDINAL
ejpam-4744	242	4	2023	CARDINAL
ejpam-4744	242	5	1318	CARDINAL
ejpam-4744	245	1	∪n	CARDINAL
ejpam-4744	245	2	1	CARDINAL
ejpam-4744	246	1	1	CARDINAL
ejpam-4744	247	1	∩	PERSON
ejpam-4744	247	2	1 ≤	QUANTITY
ejpam-4744	248	1	∩	PERSON
ejpam-4744	248	2	1 ≤	QUANTITY
ejpam-4744	249	1	∪n	CARDINAL
ejpam-4744	249	2	ai ∩ aj ̸=	ORG
ejpam-4744	249	3	∩ aj	PERSON
ejpam-4744	251	1	∈	ORG
ejpam-4744	255	1	1	CARDINAL
ejpam-4744	256	1	3	CARDINAL
ejpam-4744	258	1	ω(cn	CARDINAL
ejpam-4744	258	2	1 + 3ω(g	CARDINAL
ejpam-4744	258	3	3	CARDINAL
ejpam-4744	258	4	n ≥ 4	DATE
ejpam-4744	260	1	3	CARDINAL
ejpam-4744	262	1	2	CARDINAL
ejpam-4744	262	2	co(cn	ORG
ejpam-4744	262	3	1	CARDINAL
ejpam-4744	262	4	4	CARDINAL
ejpam-4744	262	5	3	CARDINAL
ejpam-4744	262	6	1	CARDINAL
ejpam-4744	262	7	n ≥ 4	DATE
ejpam-4744	264	1	ω(cn	CARDINAL
ejpam-4744	265	1	1 ≤ i ≤ n − 1	QUANTITY
ejpam-4744	265	2	1 ≤	QUANTITY
ejpam-4744	266	1	1	CARDINAL
ejpam-4744	266	2	2	DATE
ejpam-4744	266	3	3	DATE
ejpam-4744	268	1	1 ≤	QUANTITY
ejpam-4744	268	2	ϕ(x	LOC
ejpam-4744	269	1	∈	ORG
ejpam-4744	271	1	∈	ORG
ejpam-4744	272	1	ab /∈	PERSON
ejpam-4744	273	1	∪n	CARDINAL
ejpam-4744	274	1	i=1 |ei|	GPE
ejpam-4744	274	2	1325	CARDINAL
ejpam-4744	277	1	∪n	CARDINAL
ejpam-4744	278	1	∩	PERSON
ejpam-4744	278	2	1 ≤	QUANTITY
ejpam-4744	278	3	1 ≤	QUANTITY
ejpam-4744	278	4	∪n	CARDINAL
ejpam-4744	278	5	ai ∩ aj ̸=	ORG
ejpam-4744	278	6	∩ aj	PERSON
ejpam-4744	280	1	∈	ORG
ejpam-4744	284	1	4	CARDINAL
ejpam-4744	285	1	n ≥ 3	DATE
ejpam-4744	286	1	ω(crn	CARDINAL
ejpam-4744	286	2	4	CARDINAL
ejpam-4744	286	3	3 2n	DATE
ejpam-4744	286	4	n ≥ 4	DATE
ejpam-4744	288	1	3	CARDINAL
ejpam-4744	289	1	mindanao	LOC
ejpam-4744	290	1	1	CARDINAL
ejpam-4744	290	2	paul erdos	PERSON
ejpam-4744	290	3	goodman	ORG
ejpam-4744	290	4	louis posa	PERSON
ejpam-4744	292	1	canadian	NORP
ejpam-4744	292	2	18:106–112, 1966	DATE
ejpam-4744	293	1	2	CARDINAL
ejpam-4744	295	1	addison-wesly	PERSON
ejpam-4744	295	2	massachusetts	GPE
ejpam-4744	295	3	1972	DATE
ejpam-4744	296	1	3	CARDINAL
ejpam-4744	296	2	r.	NORP
ejpam-4744	297	1	the mindanawan journal of mathematics	ORG
ejpam-4744	297	2	3:63–75, 2012	DATE