id	sid	eid	entity	type
ejpam-4963	1	1	european journal	ORG
ejpam-4963	2	1	17	CARDINAL
ejpam-4963	2	2	2	CARDINAL
ejpam-4963	2	3	2024	DATE
ejpam-4963	2	4	969	CARDINAL
ejpam-4963	2	5	new york	GPE
ejpam-4963	2	6	mark l. caay1,∗	PERSON
ejpam-4963	2	7	andrew c. hernandez1	PERSON
ejpam-4963	3	1	1	CARDINAL
ejpam-4963	3	2	science	ORG
ejpam-4963	3	3	polytechnic university of the philippines	ORG
ejpam-4963	3	4	sta	PERSON
ejpam-4963	4	1	mesa	ORG
ejpam-4963	4	2	manila city	GPE
ejpam-4963	4	3	1016	CARDINAL
ejpam-4963	4	4	manila	GPE
ejpam-4963	4	5	philippines	GPE
ejpam-4963	5	1	⊆	CARDINAL
ejpam-4963	5	2	γpe0(g	CARDINAL
ejpam-4963	6	1	two	CARDINAL
ejpam-4963	8	1	2020	DATE
ejpam-4963	8	2	05c69	CARDINAL
ejpam-4963	8	3	05c76	CARDINAL
ejpam-4963	8	4	1	CARDINAL
ejpam-4963	9	1	one	CARDINAL
ejpam-4963	9	2	claude berge	PERSON
ejpam-4963	9	3	1958	DATE
ejpam-4963	9	4	today	DATE
ejpam-4963	9	5	2	CARDINAL
ejpam-4963	11	1	livingston	GPE
ejpam-4963	12	1	16	CARDINAL
ejpam-4963	12	2	15	CARDINAL
ejpam-4963	13	1	years	DATE
ejpam-4963	14	1	caay	GPE
ejpam-4963	15	1	6	CARDINAL
ejpam-4963	17	1	https://doi.org/10.29020/nybg.ejpam.v17i2.4963	GPE
ejpam-4963	17	2	m. caay	GPE
ejpam-4963	17	3	andrew.hernndez@pup.edu.ph (a. hernandez	ORG
ejpam-4963	18	1	969	CARDINAL
ejpam-4963	19	1	2024	CARDINAL
ejpam-4963	20	1	m. caay	PERSON
ejpam-4963	20	2	a. hernandez	PERSON
ejpam-4963	21	1	j. pure	PERSON
ejpam-4963	21	2	17	CARDINAL
ejpam-4963	21	3	2	CARDINAL
ejpam-4963	21	4	2024	CARDINAL
ejpam-4963	21	5	969-978	CARDINAL
ejpam-4963	21	6	16	CARDINAL
ejpam-4963	21	7	10	CARDINAL
ejpam-4963	22	1	11	CARDINAL
ejpam-4963	24	1	a. anitha	PERSON
ejpam-4963	25	1	8	CARDINAL
ejpam-4963	25	2	g. deepak	PERSON
ejpam-4963	26	1	9	CARDINAL
ejpam-4963	27	1	5	CARDINAL
ejpam-4963	28	1	caay	GPE
ejpam-4963	28	2	4	CARDINAL
ejpam-4963	29	1	2024	DATE
ejpam-4963	29	2	3	CARDINAL
ejpam-4963	30	1	2013	DATE
ejpam-4963	30	2	hamid	PERSON
ejpam-4963	30	3	13	CARDINAL
ejpam-4963	32	1	armada	ORG
ejpam-4963	32	2	hamja	PERSON
ejpam-4963	32	3	1	CARDINAL
ejpam-4963	33	1	17	CARDINAL
ejpam-4963	35	1	⊆	CARDINAL
ejpam-4963	36	1	section 2	LAW
ejpam-4963	38	1	two	CARDINAL
ejpam-4963	39	1	section 3	LAW
ejpam-4963	40	1	2	CARDINAL
ejpam-4963	44	1	∈	ORG
ejpam-4963	45	1	∈	ORG
ejpam-4963	45	2	∈	ORG
ejpam-4963	46	1	⊆	CARDINAL
ejpam-4963	47	1	⋃	DATE
ejpam-4963	49	1	⋃ n(d	PERSON
ejpam-4963	51	1	kn	PERSON
ejpam-4963	52	1	1	CARDINAL
ejpam-4963	53	1	two	CARDINAL
ejpam-4963	54	1	m. caay	PERSON
ejpam-4963	54	2	a. hernandez	PERSON
ejpam-4963	55	1	j. pure	PERSON
ejpam-4963	55	2	17	CARDINAL
ejpam-4963	55	3	2	CARDINAL
ejpam-4963	55	4	2024	CARDINAL
ejpam-4963	55	5	969-978 971	QUANTITY
ejpam-4963	55	6	1	CARDINAL
ejpam-4963	57	1	1	CARDINAL
ejpam-4963	58	1	cartesian	NORP
ejpam-4963	59	1	2	CARDINAL
ejpam-4963	60	1	14	CARDINAL
ejpam-4963	60	2	two	CARDINAL
ejpam-4963	61	1	∈	ORG
ejpam-4963	62	1	3	CARDINAL
ejpam-4963	63	1	12	CARDINAL
ejpam-4963	63	2	two	CARDINAL
ejpam-4963	63	3	one	CARDINAL
ejpam-4963	63	4	2	CARDINAL
ejpam-4963	63	5	∈	PERSON
ejpam-4963	63	6	∈	ORG
ejpam-4963	65	1	γ(g	NORP
ejpam-4963	66	1	16	CARDINAL
ejpam-4963	66	2	∈	ORG
ejpam-4963	67	1	one	CARDINAL
ejpam-4963	67	2	∈ s.	PERSON
ejpam-4963	68	1	8	CARDINAL
ejpam-4963	68	2	9	CARDINAL
ejpam-4963	68	3	∈	ORG
ejpam-4963	68	4	|deg(u)−	ORG
ejpam-4963	70	1	g. caay	GPE
ejpam-4963	70	2	4	CARDINAL
ejpam-4963	73	1	13	CARDINAL
ejpam-4963	73	2	⊆	CARDINAL
ejpam-4963	73	3	∈	PERSON
ejpam-4963	74	1	g. m. caay	PERSON
ejpam-4963	74	2	a. hernandez	PERSON
ejpam-4963	75	1	j. pure	PERSON
ejpam-4963	75	2	17	CARDINAL
ejpam-4963	75	3	2	CARDINAL
ejpam-4963	75	4	2024	CARDINAL
ejpam-4963	75	5	969	CARDINAL
ejpam-4963	75	6	2	CARDINAL
ejpam-4963	76	1	13	CARDINAL
ejpam-4963	77	1	3	CARDINAL
ejpam-4963	78	1	16	CARDINAL
ejpam-4963	78	2	1	CARDINAL
ejpam-4963	79	1	1	CARDINAL
ejpam-4963	80	1	g. theorem 4	ORG
ejpam-4963	81	1	4	CARDINAL
ejpam-4963	81	2	3	CARDINAL
ejpam-4963	82	1	3	CARDINAL
ejpam-4963	84	1	one	CARDINAL
ejpam-4963	87	1	5	CARDINAL
ejpam-4963	89	1	integer k	PERSON
ejpam-4963	89	2	γpe0(g	CARDINAL
ejpam-4963	90	1	integer k	PERSON
ejpam-4963	90	2	∈	ORG
ejpam-4963	90	3	\s	ORG
ejpam-4963	90	4	one	CARDINAL
ejpam-4963	90	5	∈	ORG
ejpam-4963	91	1	∈	ORG
ejpam-4963	92	1	|deg(u)−	ORG
ejpam-4963	92	2	γpe0(g	DATE
ejpam-4963	93	1	k. theorems 5	PERSON
ejpam-4963	93	2	6	CARDINAL
ejpam-4963	95	1	4	CARDINAL
ejpam-4963	96	1	⊆	CARDINAL
ejpam-4963	97	1	γpe0(g	CARDINAL
ejpam-4963	98	1	∈	ORG
ejpam-4963	98	2	∈	ORG
ejpam-4963	99	1	2	CARDINAL
ejpam-4963	99	2	1	CARDINAL
ejpam-4963	99	3	u8	CARDINAL
ejpam-4963	100	1	u7	ORG
ejpam-4963	100	2	u8	CARDINAL
ejpam-4963	103	1	1 |deg(u4)− deg(u2)|	QUANTITY
ejpam-4963	103	2	1 |deg(u4)− deg(u3)|	QUANTITY
ejpam-4963	103	3	m. caay	PERSON
ejpam-4963	103	4	a. hernandez	PERSON
ejpam-4963	104	1	j. pure	PERSON
ejpam-4963	104	2	17	CARDINAL
ejpam-4963	104	3	2	CARDINAL
ejpam-4963	104	4	2024	CARDINAL
ejpam-4963	104	5	969	CARDINAL
ejpam-4963	108	1	u8	CARDINAL
ejpam-4963	110	1	u8	CARDINAL
ejpam-4963	111	1	1 |deg(u8)− deg(u6)| ≤ 1 |deg(u8)− deg(u7)|	QUANTITY
ejpam-4963	112	1	u8	CARDINAL
ejpam-4963	114	1	u8	CARDINAL
ejpam-4963	115	1	u8	CARDINAL
ejpam-4963	116	1	γpe0(g	DATE
ejpam-4963	116	2	2	CARDINAL
ejpam-4963	116	3	1	CARDINAL
ejpam-4963	117	1	4	CARDINAL
ejpam-4963	119	1	∩	PERSON
ejpam-4963	120	1	∈	ORG
ejpam-4963	120	2	|deg(u)−	ORG
ejpam-4963	120	3	deg(v)|	ORG
ejpam-4963	120	4	1	CARDINAL
ejpam-4963	120	5	2	CARDINAL
ejpam-4963	121	1	1	CARDINAL
ejpam-4963	122	1	1	CARDINAL
ejpam-4963	122	2	γpe0(g	DATE
ejpam-4963	123	1	1	CARDINAL
ejpam-4963	123	2	3	CARDINAL
ejpam-4963	123	3	peid	ORG
ejpam-4963	124	1	8	CARDINAL
ejpam-4963	124	2	m. caay	GPE
ejpam-4963	124	3	a. hernandez	PERSON
ejpam-4963	125	1	j. pure	PERSON
ejpam-4963	125	2	17	CARDINAL
ejpam-4963	125	3	2	CARDINAL
ejpam-4963	125	4	2024	CARDINAL
ejpam-4963	125	5	969	CARDINAL
ejpam-4963	126	1	4	CARDINAL
ejpam-4963	126	2	16	CARDINAL
ejpam-4963	126	3	at least one	CARDINAL
ejpam-4963	126	4	13	CARDINAL
ejpam-4963	127	1	3	CARDINAL
ejpam-4963	127	2	3	CARDINAL
ejpam-4963	129	1	4	CARDINAL
ejpam-4963	129	2	1	CARDINAL
ejpam-4963	130	1	c5	GPE
ejpam-4963	132	1	n ≥ 2	ORG
ejpam-4963	133	1	γpe0(g	DATE
ejpam-4963	133	2	1	CARDINAL
ejpam-4963	134	1	1	CARDINAL
ejpam-4963	135	1	1 and δ(g	DATE
ejpam-4963	135	2	2	CARDINAL
ejpam-4963	135	3	γpe0(g	DATE
ejpam-4963	136	1	1	CARDINAL
ejpam-4963	137	1	1	CARDINAL
ejpam-4963	139	1	∈	ORG
ejpam-4963	140	1	∈ s. hence	PERSON
ejpam-4963	148	1	∈	ORG
ejpam-4963	149	1	1	CARDINAL
ejpam-4963	149	2	2	CARDINAL
ejpam-4963	151	1	2	CARDINAL
ejpam-4963	151	2	n ≥ 3	DATE
ejpam-4963	152	1	1	CARDINAL
ejpam-4963	153	1	bipartite	NORP
ejpam-4963	155	1	2	CARDINAL
ejpam-4963	157	1	bipartite	NORP
ejpam-4963	157	2	1	CARDINAL
ejpam-4963	158	1	∈	ORG
ejpam-4963	158	2	j = 1	WORK_OF_ART
ejpam-4963	158	3	m.	PERSON
ejpam-4963	158	4	1	CARDINAL
ejpam-4963	158	5	m. since	PERSON
ejpam-4963	158	6	∈	ORG
ejpam-4963	162	1	∈	ORG
ejpam-4963	162	2	j = 1	WORK_OF_ART
ejpam-4963	164	1	one	CARDINAL
ejpam-4963	164	2	one	CARDINAL
ejpam-4963	164	3	∈	ORG
ejpam-4963	165	1	j.	PERSON
ejpam-4963	165	2	j. however	PERSON
ejpam-4963	168	1	2	CARDINAL
ejpam-4963	169	1	8	CARDINAL
ejpam-4963	170	1	g = gp1	PERSON
ejpam-4963	170	2	k-partite	ORG
ejpam-4963	171	1	1	CARDINAL
ejpam-4963	171	2	γpe0(g	DATE
ejpam-4963	171	3	1	CARDINAL
ejpam-4963	171	4	m. caay	PERSON
ejpam-4963	171	5	a. hernandez	PERSON
ejpam-4963	172	1	j. pure	PERSON
ejpam-4963	172	2	17	CARDINAL
ejpam-4963	172	3	2	CARDINAL
ejpam-4963	172	4	2024	CARDINAL
ejpam-4963	172	5	969	CARDINAL
ejpam-4963	173	1	1	CARDINAL
ejpam-4963	174	1	|pi|	CARDINAL
ejpam-4963	174	2	1	CARDINAL
ejpam-4963	174	3	|pi|	CARDINAL
ejpam-4963	174	4	2	CARDINAL
ejpam-4963	176	1	|deg(v)− deg(u)| ≤ 1	PERSON
ejpam-4963	179	1	2	CARDINAL
ejpam-4963	179	2	γpe0(g	DATE
ejpam-4963	179	3	1	CARDINAL
ejpam-4963	179	4	9	CARDINAL
ejpam-4963	180	1	1	CARDINAL
ejpam-4963	180	2	k. proof	PERSON
ejpam-4963	181	1	pk	PERSON
ejpam-4963	181	2	∈	PERSON
ejpam-4963	181	3	kth vertex-partition	PERSON
ejpam-4963	181	4	dominates vi	PERSON
ejpam-4963	181	5	∈	ORG
ejpam-4963	182	1	∈	ORG
ejpam-4963	182	2	/∈ s.	PERSON
ejpam-4963	182	3	∈	ORG
ejpam-4963	184	1	/∈ s	ORG
ejpam-4963	186	1	1	CARDINAL
ejpam-4963	186	2	k. 4	PERSON
ejpam-4963	186	3	peid	ORG
ejpam-4963	187	1	5	CARDINAL
ejpam-4963	188	1	i. wheel graph	PERSON
ejpam-4963	189	1	+kn−1	GPE
ejpam-4963	189	2	4 iii	QUANTITY
ejpam-4963	189	3	pn−1	GPE
ejpam-4963	189	4	n ≥ 5	DATE
ejpam-4963	189	5	2	CARDINAL
ejpam-4963	189	6	3	CARDINAL
ejpam-4963	189	7	10	CARDINAL
ejpam-4963	192	1	1	CARDINAL
ejpam-4963	192	2	1	CARDINAL
ejpam-4963	192	3	γpe0(g + h	DATE
ejpam-4963	192	4	1	CARDINAL
ejpam-4963	193	1	2	CARDINAL
ejpam-4963	193	2	∈	ORG
ejpam-4963	193	3	deg(y	GPE
ejpam-4963	193	4	2	CARDINAL
ejpam-4963	195	1	γpe0(g + h	DATE
ejpam-4963	196	1	1	CARDINAL
ejpam-4963	197	1	⊆	CARDINAL
ejpam-4963	197	2	1	CARDINAL
ejpam-4963	198	1	m. caay	GPE
ejpam-4963	198	2	a. hernandez	PERSON
ejpam-4963	199	1	j. pure	PERSON
ejpam-4963	199	2	17	CARDINAL
ejpam-4963	199	3	2	CARDINAL
ejpam-4963	199	4	2024	CARDINAL
ejpam-4963	199	5	969-978	CARDINAL
ejpam-4963	199	6	1|	CARDINAL
ejpam-4963	200	1	deg(v)|	PERSON
ejpam-4963	201	1	∈	ORG
ejpam-4963	202	1	⊆	CARDINAL
ejpam-4963	202	2	deg(y	GPE
ejpam-4963	203	1	2	CARDINAL
ejpam-4963	203	2	∈	ORG
ejpam-4963	208	1	2	CARDINAL
ejpam-4963	208	2	2 + n	DATE
ejpam-4963	208	3	g+h	PRODUCT
ejpam-4963	209	1	|deg(u)−	ORG
ejpam-4963	210	1	m−	NORP
ejpam-4963	210	2	1	CARDINAL
ejpam-4963	210	3	γpe0(g + h	DATE
ejpam-4963	211	1	1	CARDINAL
ejpam-4963	212	1	10	CARDINAL
ejpam-4963	212	2	3	CARDINAL
ejpam-4963	215	1	δ(g	PERSON
ejpam-4963	215	2	2	CARDINAL
ejpam-4963	215	3	2	CARDINAL
ejpam-4963	215	4	∈	ORG
ejpam-4963	216	1	1	CARDINAL
ejpam-4963	216	2	11	CARDINAL
ejpam-4963	218	1	1	CARDINAL
ejpam-4963	219	1	g+h	ORG
ejpam-4963	219	2	g+h	ORG
ejpam-4963	222	1	∈	ORG
ejpam-4963	222	2	vi ∈	PERSON
ejpam-4963	223	1	∈	ORG
ejpam-4963	223	2	xy ∈	ORG
ejpam-4963	223	3	∈	ORG
ejpam-4963	224	1	{vi, yj	PERSON
ejpam-4963	224	2	vi ∈ s1	PERSON
ejpam-4963	224	3	∈	ORG
ejpam-4963	224	4	⊆	CARDINAL
ejpam-4963	226	1	∈	ORG
ejpam-4963	227	1	g+h	PRODUCT
ejpam-4963	228	1	vi ∈	PERSON
ejpam-4963	228	2	∈	ORG
ejpam-4963	229	1	∈	ORG
ejpam-4963	229	2	vkuj ∈	PERSON
ejpam-4963	231	1	vi ̸= vk	PERSON
ejpam-4963	232	1	vi	PERSON
ejpam-4963	233	1	vi	PERSON
ejpam-4963	234	1	g+h	ORG
ejpam-4963	235	1	one	CARDINAL
ejpam-4963	235	2	wj ∈ s2	ORG
ejpam-4963	236	1	g+h	ORG
ejpam-4963	238	1	1	CARDINAL
ejpam-4963	239	1	g+h	PRODUCT
ejpam-4963	239	2	11	CARDINAL
ejpam-4963	240	1	977 5	DATE
ejpam-4963	241	1	peid	ORG
ejpam-4963	241	2	12	CARDINAL
ejpam-4963	242	1	h. proof	PERSON
ejpam-4963	243	1	⊆	CARDINAL
ejpam-4963	243	2	⊆	CARDINAL
ejpam-4963	244	1	⊆	CARDINAL
ejpam-4963	244	2	∈ s.	PERSON
ejpam-4963	245	1	deg(u	GPE
ejpam-4963	245	2	1	CARDINAL
ejpam-4963	245	3	deg(u	PERSON
ejpam-4963	247	1	∈	ORG
ejpam-4963	247	2	1 degree	QUANTITY
ejpam-4963	248	1	1	CARDINAL
ejpam-4963	249	1	⊆	CARDINAL
ejpam-4963	249	2	w ∈ s.	PERSON
ejpam-4963	249	3	w ∈	ORG
ejpam-4963	250	1	deg(w	GPE
ejpam-4963	250	2	1	CARDINAL
ejpam-4963	250	3	deg(w	GPE
ejpam-4963	252	1	1	CARDINAL
ejpam-4963	253	1	⊆	CARDINAL
ejpam-4963	254	1	u2 ∈	PERSON
ejpam-4963	254	2	∈	ORG
ejpam-4963	257	1	13	CARDINAL
ejpam-4963	259	1	g+h	ORG
ejpam-4963	262	1	e(g ◦	GPE
ejpam-4963	262	2	e(g ◦	GPE
ejpam-4963	262	3	∈	ORG
ejpam-4963	263	1	12	CARDINAL
ejpam-4963	267	1	2	CARDINAL
ejpam-4963	268	1	13	CARDINAL
ejpam-4963	269	1	6	CARDINAL
ejpam-4963	271	1	γpe0(g	DATE
ejpam-4963	271	2	1	CARDINAL
ejpam-4963	272	1	adamson university center for research and	ORG
ejpam-4963	273	1	1	CARDINAL
ejpam-4963	273	2	j hamja	PERSON
ejpam-4963	275	1	european journal	ORG
ejpam-4963	275	2	2023	CARDINAL
ejpam-4963	276	1	2	CARDINAL
ejpam-4963	278	1	greenwood press	ORG
ejpam-4963	278	2	1982	DATE
ejpam-4963	279	1	978	CARDINAL
ejpam-4963	280	1	3	CARDINAL
ejpam-4963	282	1	algebraic systems	ORG
ejpam-4963	282	2	2024	DATE
ejpam-4963	283	1	4	CARDINAL
ejpam-4963	285	1	2017	DATE
ejpam-4963	286	1	5	CARDINAL
ejpam-4963	288	1	gulf journal of mathematics	ORG
ejpam-4963	288	2	2021	CARDINAL
ejpam-4963	289	1	6	CARDINAL
ejpam-4963	291	1	12(2):600–607	ORG
ejpam-4963	291	2	2022	CARDINAL
ejpam-4963	292	1	7	CARDINAL
ejpam-4963	294	1	dover	GPE
ejpam-4963	294	2	1984	DATE
ejpam-4963	295	1	8	CARDINAL
ejpam-4963	297	1	3(3):1726–1732, 2011	DATE
ejpam-4963	298	1	9	CARDINAL
ejpam-4963	298	2	g deepak et.al	PERSON
ejpam-4963	300	1	12(18):209–212, 2011	DATE
ejpam-4963	301	1	10	CARDINAL
ejpam-4963	303	1	12(13):635–649, 2002	DATE
ejpam-4963	304	1	11	CARDINAL
ejpam-4963	306	1	algebraic	PERSON
ejpam-4963	307	1	90th	ORDINAL
ejpam-4963	307	2	125–140	CARDINAL
ejpam-4963	307	3	2017	DATE
ejpam-4963	308	1	12	CARDINAL
ejpam-4963	309	1	two	CARDINAL
ejpam-4963	310	1	aequationes mathematicae	PERSON
ejpam-4963	310	2	4:322–325, 1970	DATE
ejpam-4963	311	1	13	CARDINAL
ejpam-4963	311	2	s. balamurugan	PERSON
ejpam-4963	313	1	arab journal of mathematical sciences	ORG
ejpam-4963	313	2	22(2):232–242	CARDINAL
ejpam-4963	313	3	2015	DATE
ejpam-4963	314	1	14	CARDINAL
ejpam-4963	316	1	addison-wesley	PERSON
ejpam-4963	316	2	1994	DATE
ejpam-4963	317	1	15	CARDINAL
ejpam-4963	319	1	b.n.	GPE
ejpam-4963	319	2	petrox	GPE
ejpam-4963	319	3	f. csaki	PERSON
ejpam-4963	320	1	3rd	ORDINAL
ejpam-4963	321	1	222–231	CARDINAL
ejpam-4963	321	2	acm	ORG
ejpam-4963	321	3	1988	DATE
ejpam-4963	322	1	16	CARDINAL
ejpam-4963	324	1	79(5):187–203	GPE
ejpam-4963	324	2	1990	DATE
ejpam-4963	325	1	17	CARDINAL
ejpam-4963	325	2	kani bala	PERSON
ejpam-4963	327	1	1732	CARDINAL
ejpam-4963	327	2	2021	DATE