id	sid	eid	entity	type
ejpam-4978	1	1	european journal	ORG
ejpam-4978	2	1	17	CARDINAL
ejpam-4978	2	2	1	CARDINAL
ejpam-4978	2	3	2024	DATE
ejpam-4978	2	4	93	CARDINAL
ejpam-4978	2	5	new york	GPE
ejpam-4978	2	6	t. bilar1,∗	GPE
ejpam-4978	2	7	maria andrea o. bonsocan1	PERSON
ejpam-4978	2	8	javier a. hassan2	PERSON
ejpam-4978	2	9	susan c. dagondon1	PERSON
ejpam-4978	3	1	msu-iligan institute of technology	ORG
ejpam-4978	3	2	9200	CARDINAL
ejpam-4978	3	3	iligan city	GPE
ejpam-4978	3	4	philippines 2mathematics	ORG
ejpam-4978	3	5	sciences department	ORG
ejpam-4978	3	6	msu tawi-tawi college of technology	ORG
ejpam-4978	3	7	philippines	GPE
ejpam-4978	6	1	two	CARDINAL
ejpam-4978	7	1	2020	DATE
ejpam-4978	7	2	05c69	CARDINAL
ejpam-4978	7	3	1	CARDINAL
ejpam-4978	9	1	claude berge	PERSON
ejpam-4978	10	1	1	CARDINAL
ejpam-4978	10	2	1958	DATE
ejpam-4978	11	1	6	CARDINAL
ejpam-4978	11	2	1962	DATE
ejpam-4978	13	1	first	ORDINAL
ejpam-4978	13	2	natarajan et al	PERSON
ejpam-4978	14	1	5	CARDINAL
ejpam-4978	15	1	2–4	CARDINAL
ejpam-4978	20	1	j. hassan	PERSON
ejpam-4978	20	2	susan.dagondon@g.msuiit.edu.ph	GPE
ejpam-4978	20	3	s.c. dagondon	GPE
ejpam-4978	21	1	93	CARDINAL
ejpam-4978	21	2	2024	CARDINAL
ejpam-4978	22	1	t. bilar et al	ORG
ejpam-4978	23	1	j. pure	PERSON
ejpam-4978	23	2	17	CARDINAL
ejpam-4978	23	3	1	CARDINAL
ejpam-4978	23	4	2024	CARDINAL
ejpam-4978	23	5	93	CARDINAL
ejpam-4978	25	1	α(g	PERSON
ejpam-4978	25	2	α(g	PERSON
ejpam-4978	26	1	2	CARDINAL
ejpam-4978	26	2	n2 g(a	ORG
ejpam-4978	28	1	2	CARDINAL
ejpam-4978	28	2	n2	ORG
ejpam-4978	29	1	⊆	CARDINAL
ejpam-4978	30	1	⋃	DATE
ejpam-4978	30	2	a∈s n2 g(a	PERSON
ejpam-4978	31	1	s.	PERSON
ejpam-4978	31	2	∈	ORG
ejpam-4978	31	3	dg(a	GPE
ejpam-4978	31	4	2	CARDINAL
ejpam-4978	36	1	two	CARDINAL
ejpam-4978	37	1	+ h	GPE
ejpam-4978	37	2	∈	ORG
ejpam-4978	38	1	one	CARDINAL
ejpam-4978	39	1	3	CARDINAL
ejpam-4978	39	2	1	CARDINAL
ejpam-4978	41	1	g. v. t. bilar et al	PERSON
ejpam-4978	42	1	j. pure	PERSON
ejpam-4978	42	2	17	CARDINAL
ejpam-4978	42	3	1	CARDINAL
ejpam-4978	42	4	2024	CARDINAL
ejpam-4978	42	5	93	CARDINAL
ejpam-4978	42	6	95	CARDINAL
ejpam-4978	42	7	1	CARDINAL
ejpam-4978	42	8	1	CARDINAL
ejpam-4978	44	1	one	CARDINAL
ejpam-4978	45	1	2	CARDINAL
ejpam-4978	46	1	4	CARDINAL
ejpam-4978	46	2	1	CARDINAL
ejpam-4978	46	3	4	CARDINAL
ejpam-4978	52	1	2	CARDINAL
ejpam-4978	55	1	at least one	CARDINAL
ejpam-4978	57	1	ga	ORG
ejpam-4978	57	2	2	CARDINAL
ejpam-4978	57	3	1	CARDINAL
ejpam-4978	60	1	t. bilar et al	ORG
ejpam-4978	61	1	j. pure	PERSON
ejpam-4978	61	2	17	CARDINAL
ejpam-4978	61	3	1	CARDINAL
ejpam-4978	61	4	2024	CARDINAL
ejpam-4978	61	5	93	CARDINAL
ejpam-4978	61	6	ae	ORG
ejpam-4978	62	1	2	CARDINAL
ejpam-4978	71	1	2	CARDINAL
ejpam-4978	73	1	3	CARDINAL
ejpam-4978	76	1	3	CARDINAL
ejpam-4978	77	1	3	CARDINAL
ejpam-4978	79	1	3	CARDINAL
ejpam-4978	79	2	3	CARDINAL
ejpam-4978	80	1	3	CARDINAL
ejpam-4978	81	1	1	CARDINAL
ejpam-4978	82	1	1	CARDINAL
ejpam-4978	83	1	1 ≤	QUANTITY
ejpam-4978	83	2	1	CARDINAL
ejpam-4978	84	1	2	CARDINAL
ejpam-4978	84	2	2	CARDINAL
ejpam-4978	85	1	g. v. t. bilar et al	PERSON
ejpam-4978	86	1	j. pure	PERSON
ejpam-4978	86	2	17	CARDINAL
ejpam-4978	86	3	1	CARDINAL
ejpam-4978	86	4	2024	CARDINAL
ejpam-4978	86	5	93	CARDINAL
ejpam-4978	89	1	1 ≤	QUANTITY
ejpam-4978	90	1	1	CARDINAL
ejpam-4978	91	1	2	CARDINAL
ejpam-4978	91	2	2	CARDINAL
ejpam-4978	94	1	1	CARDINAL
ejpam-4978	94	2	2	CARDINAL
ejpam-4978	95	1	2	CARDINAL
ejpam-4978	95	2	2	CARDINAL
ejpam-4978	96	1	2	CARDINAL
ejpam-4978	96	2	dg(a	GPE
ejpam-4978	96	3	1	CARDINAL
ejpam-4978	96	4	2	CARDINAL
ejpam-4978	96	5	2	CARDINAL
ejpam-4978	96	6	2.	DATE
ejpam-4978	97	1	y /∈	PERSON
ejpam-4978	99	1	2	CARDINAL
ejpam-4978	100	1	2	CARDINAL
ejpam-4978	100	2	∈	ORG
ejpam-4978	104	1	1	CARDINAL
ejpam-4978	107	1	1	CARDINAL
ejpam-4978	110	1	2	CARDINAL
ejpam-4978	112	1	g = kn	PERSON
ejpam-4978	113	1	1	CARDINAL
ejpam-4978	115	1	2n	CARDINAL
ejpam-4978	115	2	g = kn	PERSON
ejpam-4978	115	3	g = kn	PERSON
ejpam-4978	117	1	g = kn	PERSON
ejpam-4978	117	2	g = kn	PERSON
ejpam-4978	117	3	2	CARDINAL
ejpam-4978	122	1	g = kn	PERSON
ejpam-4978	123	1	v. t. bilar et al	PERSON
ejpam-4978	124	1	j. pure	PERSON
ejpam-4978	124	2	17	CARDINAL
ejpam-4978	124	3	1	CARDINAL
ejpam-4978	124	4	2024	CARDINAL
ejpam-4978	124	5	93	CARDINAL
ejpam-4978	124	6	4 ≤	QUANTITY
ejpam-4978	126	1	1	CARDINAL
ejpam-4978	126	2	one	CARDINAL
ejpam-4978	127	1	4 ≤	QUANTITY
ejpam-4978	130	1	one	CARDINAL
ejpam-4978	133	1	1(iii	CARDINAL
ejpam-4978	134	1	g = kn	PERSON
ejpam-4978	136	1	one	CARDINAL
ejpam-4978	137	1	1(iii	CARDINAL
ejpam-4978	137	2	1	CARDINAL
ejpam-4978	137	3	1	CARDINAL
ejpam-4978	138	1	2n	CARDINAL
ejpam-4978	138	2	1	CARDINAL
ejpam-4978	139	1	2	CARDINAL
ejpam-4978	139	2	2	CARDINAL
ejpam-4978	139	3	1(i	CARDINAL
ejpam-4978	140	1	4	CARDINAL
ejpam-4978	140	2	4	CARDINAL
ejpam-4978	140	3	4 ≤	QUANTITY
ejpam-4978	141	1	1 and 4 ≤	QUANTITY
ejpam-4978	142	1	3	CARDINAL
ejpam-4978	143	1	2	CARDINAL
ejpam-4978	144	1	2	CARDINAL
ejpam-4978	144	2	2	CARDINAL
ejpam-4978	148	1	2	CARDINAL
ejpam-4978	148	2	2	CARDINAL
ejpam-4978	148	3	2	CARDINAL
ejpam-4978	148	4	n ≥ 2	ORG
ejpam-4978	148	5	2	CARDINAL
ejpam-4978	151	1	2	CARDINAL
ejpam-4978	152	1	γvch(p5	ORG
ejpam-4978	153	1	3	CARDINAL
ejpam-4978	153	2	2	CARDINAL
ejpam-4978	153	3	⊆	CARDINAL
ejpam-4978	154	1	2	CARDINAL
ejpam-4978	154	2	4	CARDINAL
ejpam-4978	156	1	one	CARDINAL
ejpam-4978	157	1	3	CARDINAL
ejpam-4978	158	1	t. bilar et al	ORG
ejpam-4978	159	1	j. pure	PERSON
ejpam-4978	159	2	17	CARDINAL
ejpam-4978	159	3	1	CARDINAL
ejpam-4978	159	4	2024	CARDINAL
ejpam-4978	159	5	93	CARDINAL
ejpam-4978	159	6	4	CARDINAL
ejpam-4978	159	7	3	CARDINAL
ejpam-4978	159	8	3	CARDINAL
ejpam-4978	162	1	1 ≤	CARDINAL
ejpam-4978	163	1	1	CARDINAL
ejpam-4978	168	1	1	CARDINAL
ejpam-4978	169	1	1 ≤	CARDINAL
ejpam-4978	172	1	1	CARDINAL
ejpam-4978	173	1	∈	ORG
ejpam-4978	173	2	ab ∈ e(w	ORG
ejpam-4978	174	1	2	CARDINAL
ejpam-4978	175	1	2	CARDINAL
ejpam-4978	180	1	∈	ORG
ejpam-4978	180	2	⊆	CARDINAL
ejpam-4978	180	3	2	CARDINAL
ejpam-4978	180	4	2	CARDINAL
ejpam-4978	180	5	1	CARDINAL
ejpam-4978	186	1	j. pure	PERSON
ejpam-4978	186	2	17	CARDINAL
ejpam-4978	186	3	1	CARDINAL
ejpam-4978	186	4	2024	CARDINAL
ejpam-4978	186	5	93	CARDINAL
ejpam-4978	188	1	2	CARDINAL
ejpam-4978	188	2	2	CARDINAL
ejpam-4978	188	3	3 3	CARDINAL
ejpam-4978	188	4	5	CARDINAL
ejpam-4978	190	1	3	CARDINAL
ejpam-4978	191	1	4	CARDINAL
ejpam-4978	192	1	10	CARDINAL
ejpam-4978	192	2	two	CARDINAL
ejpam-4978	193	1	⊆	CARDINAL
ejpam-4978	193	2	g+h	ORG
ejpam-4978	195	1	5	CARDINAL
ejpam-4978	196	1	two	CARDINAL
ejpam-4978	198	1	g+h	ORG
ejpam-4978	199	1	one	CARDINAL
ejpam-4978	201	1	⊆	CARDINAL
ejpam-4978	204	1	∈	ORG
ejpam-4978	204	2	∈	ORG
ejpam-4978	206	1	g+h	ORG
ejpam-4978	208	1	g+h	ORG
ejpam-4978	208	2	4	CARDINAL
ejpam-4978	208	3	g+h	ORG
ejpam-4978	211	1	g+h	ORG
ejpam-4978	212	1	4	CARDINAL
ejpam-4978	213	1	g+h	ORG
ejpam-4978	215	1	g+h	ORG
ejpam-4978	216	1	6	CARDINAL
ejpam-4978	217	1	two	CARDINAL
ejpam-4978	221	1	5	CARDINAL
ejpam-4978	221	2	one	CARDINAL
ejpam-4978	222	1	t. bilar et al	ORG
ejpam-4978	223	1	j. pure	PERSON
ejpam-4978	223	2	17	CARDINAL
ejpam-4978	223	3	1	CARDINAL
ejpam-4978	223	4	2024	CARDINAL
ejpam-4978	223	5	93	CARDINAL
ejpam-4978	224	1	|cg|+ |ch	PERSON
ejpam-4978	224	2	|cg|+ |ch	PERSON
ejpam-4978	226	1	g+h	NORP
ejpam-4978	226	2	5	CARDINAL
ejpam-4978	227	1	5	CARDINAL
ejpam-4978	230	1	1	CARDINAL
ejpam-4978	230	2	6	CARDINAL
ejpam-4978	230	3	2	CARDINAL
ejpam-4978	235	1	 n+ 2	CARDINAL
ejpam-4978	235	2	3	CARDINAL
ejpam-4978	235	3	5	CARDINAL
ejpam-4978	236	1	n 2	PRODUCT
ejpam-4978	236	2	n ≥ 5 and odd	DATE
ejpam-4978	238	1	⊆	CARDINAL
ejpam-4978	238	2	g+h	ORG
ejpam-4978	241	1	⊆	CARDINAL
ejpam-4978	242	1	4	CARDINAL
ejpam-4978	243	1	∈	ORG
ejpam-4978	243	2	t. bilar et al	ORG
ejpam-4978	244	1	j. pure	PERSON
ejpam-4978	244	2	17	CARDINAL
ejpam-4978	244	3	1	CARDINAL
ejpam-4978	244	4	2024	CARDINAL
ejpam-4978	244	5	93	CARDINAL
ejpam-4978	245	1	g+h	ORG
ejpam-4978	247	1	g+h	ORG
ejpam-4978	248	1	4	CARDINAL
ejpam-4978	248	2	g+h	ORG
ejpam-4978	249	1	g+h	ORG
ejpam-4978	250	1	8	CARDINAL
ejpam-4978	256	1	g+h	ORG
ejpam-4978	258	1	g)|+ |ch |	PERSON
ejpam-4978	263	1	1	CARDINAL
ejpam-4978	263	2	7	CARDINAL
ejpam-4978	263	3	3	CARDINAL
ejpam-4978	268	1	 n+ 2	CARDINAL
ejpam-4978	268	2	3	CARDINAL
ejpam-4978	268	3	5	CARDINAL
ejpam-4978	268	4	2	CARDINAL
ejpam-4978	268	5	4	CARDINAL
ejpam-4978	270	1	vcpnd(cm	ORG
ejpam-4978	270	2	2	CARDINAL
ejpam-4978	270	3	4	CARDINAL
ejpam-4978	270	4	5	CARDINAL
ejpam-4978	272	1	1 + vcpnd(cm	DATE
ejpam-4978	273	1	1 + m	QUANTITY
ejpam-4978	273	2	2	CARDINAL
ejpam-4978	273	3	4	CARDINAL
ejpam-4978	273	4	1 +	DATE
ejpam-4978	273	5	5	CARDINAL
ejpam-4978	275	1	1 +	CARDINAL
ejpam-4978	275	2	3	CARDINAL
ejpam-4978	275	3	3 4	DATE
ejpam-4978	275	4	5	CARDINAL
ejpam-4978	275	5	1 + m	QUANTITY
ejpam-4978	275	6	2	CARDINAL
ejpam-4978	275	7	4	CARDINAL
ejpam-4978	275	8	1 + ⌊m2	DATE
ejpam-4978	276	1	103	CARDINAL
ejpam-4978	276	2	9	CARDINAL
ejpam-4978	278	1	∪v∈v (g)cv	ORG
ejpam-4978	278	2	cv ⊆	ORG
ejpam-4978	279	1	cv	ORG
ejpam-4978	280	1	cv	ORG
ejpam-4978	281	1	n2 g◦h	ORG
ejpam-4978	283	1	⋃	PRODUCT
ejpam-4978	283	2	cv	PERSON
ejpam-4978	284	1	cv	ORG
ejpam-4978	284	2	∪v∈v (g)cv	ORG
ejpam-4978	288	1	⋃	PRODUCT
ejpam-4978	288	2	cv	ORG
ejpam-4978	288	3	9	CARDINAL
ejpam-4978	289	1	4.	CARDINAL
ejpam-4978	291	1	two	CARDINAL
ejpam-4978	294	1	msu-iligan institute of technology	ORG
ejpam-4978	294	2	msu tawi-tawi college of technology	ORG
ejpam-4978	295	1	1	CARDINAL
ejpam-4978	297	1	104	CARDINAL
ejpam-4978	298	1	2	CARDINAL
ejpam-4978	298	2	s. canoy jr.	PERSON
ejpam-4978	298	3	j. hassan	PERSON
ejpam-4978	301	1	j. pure	PERSON
ejpam-4978	301	2	15(4):1783–1796	CARDINAL
ejpam-4978	301	3	2022	CARDINAL
ejpam-4978	302	1	3	CARDINAL
ejpam-4978	302	2	s. canoy jr.	PERSON
ejpam-4978	302	3	j. hassan	PERSON
ejpam-4978	305	1	j. pure	PERSON
ejpam-4978	305	2	16(2):1196–1211	CARDINAL
ejpam-4978	305	3	2023	CARDINAL
ejpam-4978	306	1	4	CARDINAL
ejpam-4978	306	2	s. canoy jr.	PERSON
ejpam-4978	306	3	g. salasalan	PERSON
ejpam-4978	308	1	kyungpook mathematical journal.	ORG
ejpam-4978	308	2	62:193–204	CARDINAL
ejpam-4978	308	3	2022	CARDINAL
ejpam-4978	309	1	5	CARDINAL
ejpam-4978	309	2	c. natarajan	PERSON
ejpam-4978	309	3	s. ayyaswamy	ORG
ejpam-4978	310	1	versita	PERSON
ejpam-4978	310	2	23(2):187	CARDINAL
ejpam-4978	310	3	199	CARDINAL
ejpam-4978	310	4	2015	DATE
ejpam-4978	311	1	6	CARDINAL
ejpam-4978	312	1	38	CARDINAL
ejpam-4978	313	1	1962	DATE
ejpam-4978	314	1	7	CARDINAL
ejpam-4978	314	2	s. ayyaswamy	PERSON
ejpam-4978	314	3	b. krishnakumari	PERSON
ejpam-4978	316	1	2015	DATE
ejpam-4978	317	1	8	CARDINAL
ejpam-4978	317	2	c. natarajan s.	PERSON
ejpam-4978	317	3	g. sathiamoorphy	PERSON
ejpam-4978	319	1	2018	DATE
ejpam-4978	320	1	9	CARDINAL
ejpam-4978	320	2	j. hassan s. canoy jr.	PERSON
ejpam-4978	320	3	c. j. saromines	PERSON
ejpam-4978	323	1	j. pure	PERSON
ejpam-4978	323	2	16(1):319–335	DATE
ejpam-4978	323	3	2023	CARDINAL
ejpam-4978	324	1	10	CARDINAL
ejpam-4978	324	2	r. mollejon s. canoy jr.	PERSON
ejpam-4978	324	3	j. g. canoy	PERSON
ejpam-4978	327	1	j. pure	PERSON
ejpam-4978	328	1	12(4):1455–1463,	DATE
ejpam-4978	328	2	2019	DATE
ejpam-4978	329	1	11	CARDINAL
ejpam-4978	329	2	g. salasalan	PERSON
ejpam-4978	329	3	s. canoy jr.	PERSON
ejpam-4978	331	1	j. pure	PERSON
ejpam-4978	331	2	14(1):112–125	DATE
ejpam-4978	331	3	2021	DATE