id	sid	eid	entity	type
ejpam-3657	1	1	european journal	ORG
ejpam-3657	2	1	13	CARDINAL
ejpam-3657	2	2	3, 2020	DATE
ejpam-3657	2	3	701	CARDINAL
ejpam-3657	2	4	1307-5543	CARDINAL
ejpam-3657	2	5	new york	GPE
ejpam-3657	2	6	julius g. caadan1,∗	PERSON
ejpam-3657	2	7	rolando n. paluga2	PERSON
ejpam-3657	3	1	imelda s. aniversario3	PERSON
ejpam-3657	3	2	1	CARDINAL
ejpam-3657	3	3	surigao state college of technology	ORG
ejpam-3657	3	4	8400	CARDINAL
ejpam-3657	3	5	surigao city	GPE
ejpam-3657	3	6	philippines 2 department	ORG
ejpam-3657	3	7	caraga state university	ORG
ejpam-3657	3	8	8600	PRODUCT
ejpam-3657	3	9	butuan city city	GPE
ejpam-3657	3	10	3	CARDINAL
ejpam-3657	3	11	mindanao state university-iligan institute of technology	ORG
ejpam-3657	3	12	9200	CARDINAL
ejpam-3657	3	13	iligan city	GPE
ejpam-3657	3	14	philippines	GPE
ejpam-3657	5	1	nk g(v	PERSON
ejpam-3657	5	2	∈	ORG
ejpam-3657	8	1	two	CARDINAL
ejpam-3657	10	1	2020	DATE
ejpam-3657	10	2	05c12	CARDINAL
ejpam-3657	10	3	1	CARDINAL
ejpam-3657	12	1	1	CARDINAL
ejpam-3657	13	1	⊆	CARDINAL
ejpam-3657	13	2	∈	ORG
ejpam-3657	15	1	∈	ORG
ejpam-3657	16	1	∈	ORG
ejpam-3657	17	1	∈	ORG
ejpam-3657	17	2	∈	ORG
ejpam-3657	19	1	juliusgcaadan@gmail.com	PRODUCT
ejpam-3657	19	2	j. g. caadan	PERSON
ejpam-3657	19	3	rnpaluga@carsu.edu.ph	GPE
ejpam-3657	19	4	r. n. paluga	PERSON
ejpam-3657	19	5	imelda.aniversario@g.msuiit.edu.ph	GPE
ejpam-3657	19	6	i. s. aniversario	PERSON
ejpam-3657	20	1	701	CARDINAL
ejpam-3657	20	2	2020	DATE
ejpam-3657	21	1	j. g. caadan	PERSON
ejpam-3657	21	2	r. n. paluga	PERSON
ejpam-3657	21	3	i. s. aniversario / eur	PERSON
ejpam-3657	22	1	j. pure	PERSON
ejpam-3657	22	2	13	CARDINAL
ejpam-3657	22	3	3	CARDINAL
ejpam-3657	22	4	2020	DATE
ejpam-3657	22	5	701	CARDINAL
ejpam-3657	22	6	709 702	CARDINAL
ejpam-3657	22	7	two	CARDINAL
ejpam-3657	22	8	integer k	PERSON
ejpam-3657	22	9	∈	ORG
ejpam-3657	22	10	nk g(v	PERSON
ejpam-3657	23	1	nk g(v	PERSON
ejpam-3657	26	1	nk g(v	ORG
ejpam-3657	28	1	∈	ORG
ejpam-3657	28	2	∆k(g	PERSON
ejpam-3657	29	1	max{degkg(v	PERSON
ejpam-3657	29	2	∈	ORG
ejpam-3657	30	1	deg1 g(v	PERSON
ejpam-3657	33	1	g and h	ORG
ejpam-3657	33	2	g+h	ORG
ejpam-3657	34	1	∈	ORG
ejpam-3657	35	1	⊆	CARDINAL
ejpam-3657	35	2	s. the δ(g : s	ORG
ejpam-3657	35	3	∈	ORG
ejpam-3657	36	1	⊆	CARDINAL
ejpam-3657	37	1	⊆	CARDINAL
ejpam-3657	37	2	∈ s	ORG
ejpam-3657	38	1	haynes	ORG
ejpam-3657	39	1	5	CARDINAL
ejpam-3657	39	2	al	PERSON
ejpam-3657	40	1	8	CARDINAL
ejpam-3657	41	1	2018	DATE
ejpam-3657	42	1	al	PERSON
ejpam-3657	43	1	2	CARDINAL
ejpam-3657	45	1	2	CARDINAL
ejpam-3657	45	2	4	CARDINAL
ejpam-3657	45	3	3	CARDINAL
ejpam-3657	45	4	6	DATE
ejpam-3657	46	1	two	CARDINAL
ejpam-3657	48	1	2	CARDINAL
ejpam-3657	48	2	1	CARDINAL
ejpam-3657	50	1	⊆	CARDINAL
ejpam-3657	50	2	1	CARDINAL
ejpam-3657	52	1	⊆	CARDINAL
ejpam-3657	53	1	1cost	CARDINAL
ejpam-3657	54	1	1	CARDINAL
ejpam-3657	56	1	kn	PERSON
ejpam-3657	57	1	2	CARDINAL
ejpam-3657	57	2	2	CARDINAL
ejpam-3657	59	1	j. g. caadan	PERSON
ejpam-3657	59	2	r. n. paluga	PERSON
ejpam-3657	59	3	i. s. aniversario / eur	PERSON
ejpam-3657	60	1	j. pure	PERSON
ejpam-3657	60	2	13	CARDINAL
ejpam-3657	60	3	3	CARDINAL
ejpam-3657	60	4	2020	DATE
ejpam-3657	60	5	701	CARDINAL
ejpam-3657	60	6	⊆	CARDINAL
ejpam-3657	60	7	g+h	ORG
ejpam-3657	61	1	⊆	CARDINAL
ejpam-3657	61	2	g+h	ORG
ejpam-3657	62	1	3	CARDINAL
ejpam-3657	65	1	αkce(g+h	ORG
ejpam-3657	67	1	2	CARDINAL
ejpam-3657	67	2	k1,9	PERSON
ejpam-3657	68	1	2	CARDINAL
ejpam-3657	69	1	1	CARDINAL
ejpam-3657	72	1	2	CARDINAL
ejpam-3657	79	1	1	CARDINAL
ejpam-3657	79	2	1− 2|s|	TIME
ejpam-3657	79	3	0	CARDINAL
ejpam-3657	80	1	2	CARDINAL
ejpam-3657	81	1	2	CARDINAL
ejpam-3657	82	1	2|s| ≤	MONEY
ejpam-3657	82	2	∈ s.	PERSON
ejpam-3657	82	3	1	CARDINAL
ejpam-3657	82	4	1− 2|s|	TIME
ejpam-3657	82	5	1−	TIME
ejpam-3657	82	6	0	CARDINAL
ejpam-3657	83	1	g. corollary 1.	PERSON
ejpam-3657	84	1	2	CARDINAL
ejpam-3657	84	2	2	CARDINAL
ejpam-3657	85	1	2	CARDINAL
ejpam-3657	86	1	g+h	ORG
ejpam-3657	87	1	g)|+|v	PERSON
ejpam-3657	87	2	2	CARDINAL
ejpam-3657	87	3	αkce(g+h	ORG
ejpam-3657	88	1	g)|+|v	PERSON
ejpam-3657	88	2	2 c. proof	QUANTITY
ejpam-3657	88	3	1	CARDINAL
ejpam-3657	88	4	2	CARDINAL
ejpam-3657	88	5	4	CARDINAL
ejpam-3657	89	1	integer k ≥ 2	PERSON
ejpam-3657	90	1	j. g. caadan	PERSON
ejpam-3657	90	2	r. n. paluga	PERSON
ejpam-3657	90	3	i. s. aniversario / eur	PERSON
ejpam-3657	91	1	j. pure	PERSON
ejpam-3657	91	2	13	CARDINAL
ejpam-3657	91	3	3	CARDINAL
ejpam-3657	91	4	2020	DATE
ejpam-3657	91	5	701	CARDINAL
ejpam-3657	91	6	2	CARDINAL
ejpam-3657	93	1	⊆	CARDINAL
ejpam-3657	94	1	3	CARDINAL
ejpam-3657	94	2	1	CARDINAL
ejpam-3657	95	1	{v2	PERSON
ejpam-3657	96	1	3	CARDINAL
ejpam-3657	97	1	0	CARDINAL
ejpam-3657	98	1	3	CARDINAL
ejpam-3657	99	1	0	CARDINAL
ejpam-3657	99	2	v1 v2 v3 v4 v5 v6 v7	PERSON
ejpam-3657	99	3	1	CARDINAL
ejpam-3657	99	4	5	CARDINAL
ejpam-3657	99	5	2	CARDINAL
ejpam-3657	99	6	⊆	CARDINAL
ejpam-3657	99	7	2	CARDINAL
ejpam-3657	99	8	1	CARDINAL
ejpam-3657	100	1	⊆	CARDINAL
ejpam-3657	100	2	1	CARDINAL
ejpam-3657	100	3	g(u	PRODUCT
ejpam-3657	101	1	deg〈s〉g(u)− deg〈s〉g(u	PERSON
ejpam-3657	101	2	2deg〈s〉g(u	CARDINAL
ejpam-3657	101	3	0	CARDINAL
ejpam-3657	104	1	2∆(〈s〉g	CARDINAL
ejpam-3657	105	1	2	CARDINAL
ejpam-3657	106	1	2	CARDINAL
ejpam-3657	107	1	3	CARDINAL
ejpam-3657	108	1	n ≥ 2	ORG
ejpam-3657	108	2	⊆	CARDINAL
ejpam-3657	108	3	2	CARDINAL
ejpam-3657	108	4	1	CARDINAL
ejpam-3657	110	1	∈ s.	PERSON
ejpam-3657	111	1	deg〈s〉g(u	NORP
ejpam-3657	111	2	+ n−	GPE
ejpam-3657	111	3	deg〈s〉g(u	NORP
ejpam-3657	112	1	1	CARDINAL
ejpam-3657	116	1	∈ s.	PERSON
ejpam-3657	116	2	2∆(〈s〉g	CARDINAL
ejpam-3657	117	1	2	CARDINAL
ejpam-3657	118	1	j. g. caadan	PERSON
ejpam-3657	118	2	r. n. paluga	PERSON
ejpam-3657	118	3	i. s. aniversario / eur	PERSON
ejpam-3657	119	1	j. pure	PERSON
ejpam-3657	119	2	13	CARDINAL
ejpam-3657	119	3	3	CARDINAL
ejpam-3657	119	4	2020	DATE
ejpam-3657	119	5	701	CARDINAL
ejpam-3657	119	6	709 705	CARDINAL
ejpam-3657	119	7	3	CARDINAL
ejpam-3657	120	1	n ≥ 2	ORG
ejpam-3657	120	2	2	CARDINAL
ejpam-3657	121	1	4	CARDINAL
ejpam-3657	122	1	n ≥ 2	ORG
ejpam-3657	122	2	⊆	CARDINAL
ejpam-3657	123	1	2	CARDINAL
ejpam-3657	123	2	1	CARDINAL
ejpam-3657	123	3	g+h	ORG
ejpam-3657	124	1	2	CARDINAL
ejpam-3657	124	2	2	CARDINAL
ejpam-3657	125	1	2∆(〈s〉g	CARDINAL
ejpam-3657	126	1	∈ s.	PERSON
ejpam-3657	127	1	deg〈s〉g(u	NORP
ejpam-3657	127	2	+ n−	GPE
ejpam-3657	127	3	deg〈s〉g(u	NORP
ejpam-3657	128	1	2∆(〈s〉g	CARDINAL
ejpam-3657	129	1	0	CARDINAL
ejpam-3657	130	1	1	CARDINAL
ejpam-3657	130	2	g+h	ORG
ejpam-3657	132	1	n ≥ 2	ORG
ejpam-3657	132	2	2	CARDINAL
ejpam-3657	133	1	3	CARDINAL
ejpam-3657	133	2	4	CARDINAL
ejpam-3657	133	3	5	CARDINAL
ejpam-3657	133	4	letg	PERSON
ejpam-3657	133	5	n ≥ 2	ORG
ejpam-3657	133	6	bn+∆(g	PERSON
ejpam-3657	133	7	2	CARDINAL
ejpam-3657	134	1	3	CARDINAL
ejpam-3657	135	1	⊆	CARDINAL
ejpam-3657	137	1	∈	ORG
ejpam-3657	138	1	4	CARDINAL
ejpam-3657	138	2	1	CARDINAL
ejpam-3657	139	1	v2, v5	GPE
ejpam-3657	140	1	1	CARDINAL
ejpam-3657	140	2	max{2deg〈s2〉g(u)−	NORP
ejpam-3657	141	1	1	CARDINAL
ejpam-3657	141	2	0	CARDINAL
ejpam-3657	141	3	1	CARDINAL
ejpam-3657	142	1	5	CARDINAL
ejpam-3657	145	1	4	CARDINAL
ejpam-3657	148	1	j. g. caadan	PERSON
ejpam-3657	148	2	r. n. paluga	PERSON
ejpam-3657	148	3	i. s. aniversario / eur	PERSON
ejpam-3657	149	1	j. pure	PERSON
ejpam-3657	149	2	13	CARDINAL
ejpam-3657	149	3	3	CARDINAL
ejpam-3657	149	4	2020	DATE
ejpam-3657	149	5	701	CARDINAL
ejpam-3657	149	6	709 706	CARDINAL
ejpam-3657	149	7	5	CARDINAL
ejpam-3657	149	8	1	CARDINAL
ejpam-3657	149	9	2	CARDINAL
ejpam-3657	149	10	2	CARDINAL
ejpam-3657	150	1	5	CARDINAL
ejpam-3657	150	2	6	CARDINAL
ejpam-3657	150	3	6	CARDINAL
ejpam-3657	152	1	⊆	CARDINAL
ejpam-3657	154	1	6	CARDINAL
ejpam-3657	156	1	1	CARDINAL
ejpam-3657	156	2	g+h	ORG
ejpam-3657	156	3	⊆	CARDINAL
ejpam-3657	156	4	g. (ii	PRODUCT
ejpam-3657	156	5	⊆	CARDINAL
ejpam-3657	156	6	g)∩s	PERSON
ejpam-3657	156	7	1	CARDINAL
ejpam-3657	156	8	1	CARDINAL
ejpam-3657	156	9	⊆	CARDINAL
ejpam-3657	156	10	∈ s.	PERSON
ejpam-3657	157	1	deg〈s〉g(u	NORP
ejpam-3657	157	2	+ n−	GPE
ejpam-3657	157	3	deg〈s〉g(u	NORP
ejpam-3657	159	1	2deg〈s〉g(u)− degg(u	QUANTITY
ejpam-3657	159	2	0	CARDINAL
ejpam-3657	160	1	n −	ORG
ejpam-3657	160	2	0	CARDINAL
ejpam-3657	160	3	∈	ORG
ejpam-3657	160	4	2deg〈s〉g(u)− degg(u	QUANTITY
ejpam-3657	161	1	2	CARDINAL
ejpam-3657	161	2	⊆	CARDINAL
ejpam-3657	161	3	1	CARDINAL
ejpam-3657	162	1	3	CARDINAL
ejpam-3657	162	2	6=	CARDINAL
ejpam-3657	162	3	6=	CARDINAL
ejpam-3657	162	4	∩ s.	PERSON
ejpam-3657	163	1	1 ≤	MONEY
ejpam-3657	165	1	2deg〈v	DATE
ejpam-3657	166	1	2q	CARDINAL
ejpam-3657	167	1	1	CARDINAL
ejpam-3657	169	1	2q	CARDINAL
ejpam-3657	169	2	0	CARDINAL
ejpam-3657	170	1	∈ s.	PERSON
ejpam-3657	170	2	2deg〈v	DATE
ejpam-3657	171	1	g)∩s	PERSON
ejpam-3657	171	2	∩ s.	PERSON
ejpam-3657	172	1	j. g. caadan	PERSON
ejpam-3657	172	2	r. n. paluga	PERSON
ejpam-3657	172	3	i. s. aniversario / eur	PERSON
ejpam-3657	173	1	j. pure	PERSON
ejpam-3657	173	2	13	CARDINAL
ejpam-3657	173	3	3	CARDINAL
ejpam-3657	173	4	2020	DATE
ejpam-3657	173	5	701	CARDINAL
ejpam-3657	173	6	2p+	CARDINAL
ejpam-3657	174	1	2deg〈v	CARDINAL
ejpam-3657	175	1	2deg〈v	CARDINAL
ejpam-3657	175	2	2p	CARDINAL
ejpam-3657	176	1	m−	NORP
ejpam-3657	177	1	∈ s.	PERSON
ejpam-3657	180	1	2deg〈s〉g(u)− degg(u	MONEY
ejpam-3657	182	1	1	CARDINAL
ejpam-3657	182	2	g+h	ORG
ejpam-3657	184	1	∈ s.	PERSON
ejpam-3657	184	2	1	CARDINAL
ejpam-3657	184	3	g+h	ORG
ejpam-3657	186	1	2q	CARDINAL
ejpam-3657	186	2	2p	CARDINAL
ejpam-3657	187	1	∩ s.	PERSON
ejpam-3657	188	1	2deg〈v	DATE
ejpam-3657	189	1	2q	CARDINAL
ejpam-3657	189	2	2q	CARDINAL
ejpam-3657	189	3	2deg〈v	DATE
ejpam-3657	190	1	2q	CARDINAL
ejpam-3657	191	1	2q	CARDINAL
ejpam-3657	191	2	2q	CARDINAL
ejpam-3657	192	1	0	CARDINAL
ejpam-3657	193	1	1	CARDINAL
ejpam-3657	193	2	g+h	ORG
ejpam-3657	194	1	∩ s.	PERSON
ejpam-3657	195	1	2p+	CARDINAL
ejpam-3657	196	1	2deg〈v	CARDINAL
ejpam-3657	198	1	2p−	CARDINAL
ejpam-3657	200	1	2p−	CARDINAL
ejpam-3657	200	2	2p−	CARDINAL
ejpam-3657	200	3	m−	NORP
ejpam-3657	200	4	2p	CARDINAL
ejpam-3657	201	1	0	CARDINAL
ejpam-3657	202	1	1	CARDINAL
ejpam-3657	202	2	g+h	ORG
ejpam-3657	203	1	5	CARDINAL
ejpam-3657	204	1	⊆	CARDINAL
ejpam-3657	204	2	n ≥ 2.	ORG
ejpam-3657	205	1	1	CARDINAL
ejpam-3657	206	1	6	CARDINAL
ejpam-3657	207	1	n ≥ 2	ORG
ejpam-3657	208	1	⊆	CARDINAL
ejpam-3657	208	2	kn	PERSON
ejpam-3657	208	3	1	CARDINAL
ejpam-3657	208	4	2	CARDINAL
ejpam-3657	208	5	708	CARDINAL
ejpam-3657	209	1	+ kn	PERSON
ejpam-3657	209	2	6=	CARDINAL
ejpam-3657	209	3	6=	CARDINAL
ejpam-3657	209	4	1	CARDINAL
ejpam-3657	210	1	2	CARDINAL
ejpam-3657	210	2	1 ≤	MONEY
ejpam-3657	214	1	ρn−2q(g	ORG
ejpam-3657	215	1	1 ≤	MONEY
ejpam-3657	215	2	1 ≤	QUANTITY
ejpam-3657	216	1	1	CARDINAL
ejpam-3657	216	2	g+h	ORG
ejpam-3657	217	1	⊆	CARDINAL
ejpam-3657	218	1	6(i	CARDINAL
ejpam-3657	219	1	⊆	CARDINAL
ejpam-3657	220	1	theorem 6(ii	PERSON
ejpam-3657	221	1	6=	CARDINAL
ejpam-3657	221	2	6=	CARDINAL
ejpam-3657	221	3	6(iii	DATE
ejpam-3657	221	4	ρn−2q(g	ORG
ejpam-3657	222	1	ρn−2q(g	ORG
ejpam-3657	222	2	1 ≤	MONEY
ejpam-3657	222	3	1 ≤	QUANTITY
ejpam-3657	226	1	2	CARDINAL
ejpam-3657	227	1	mindanao state university-iligan institute of technology	ORG
ejpam-3657	228	1	1	CARDINAL
ejpam-3657	228	2	f. buckley	PERSON
ejpam-3657	228	3	f. harary	PERSON
ejpam-3657	230	1	addison-wesley	ORG
ejpam-3657	230	2	redwood city	GPE
ejpam-3657	230	3	1990	DATE
ejpam-3657	231	1	2	CARDINAL
ejpam-3657	231	2	haynes	ORG
ejpam-3657	231	3	m. chellali	PERSON
ejpam-3657	231	4	s.t	PERSON
ejpam-3657	233	1	akce international journal	ORG
ejpam-3657	233	2	15:211–218	CARDINAL
ejpam-3657	233	3	2018	DATE
ejpam-3657	234	1	3	CARDINAL
ejpam-3657	234	2	haynes	ORG
ejpam-3657	234	3	i. vasylieva	PERSON
ejpam-3657	234	4	s.t.	PERSON
ejpam-3657	234	5	hedetniemi	PERSON
ejpam-3657	236	1	akce international journal	ORG
ejpam-3657	236	2	combinatorics	ORG
ejpam-3657	236	3	12:155–160	CARDINAL
ejpam-3657	236	4	2015	DATE
ejpam-3657	237	1	4	CARDINAL
ejpam-3657	237	2	t.w.	GPE
ejpam-3657	237	3	m. henning	PERSON
ejpam-3657	237	4	s.t.	PERSON
ejpam-3657	237	5	hedetniemi	PERSON
ejpam-3657	239	1	j. discrete	PERSON
ejpam-3657	239	2	2000	DATE
ejpam-3657	240	1	5	CARDINAL
ejpam-3657	240	2	hedetniemi	GPE
ejpam-3657	240	3	t.w.	GPE
ejpam-3657	240	4	haynes	ORG
ejpam-3657	240	5	s.t.	PERSON
ejpam-3657	240	6	hedetniemi	PERSON
ejpam-3657	240	7	mccoy	PERSON
ejpam-3657	240	8	i. vasylieva	PERSON
ejpam-3657	243	1	numer	PERSON
ejpam-3657	243	2	211:197–209,	DATE
ejpam-3657	243	3	2012	DATE
ejpam-3657	244	1	709	CARDINAL
ejpam-3657	245	1	6	CARDINAL
ejpam-3657	245	2	f. jamil	PERSON
ejpam-3657	245	3	h. nuenay-maglanque	PERSON
ejpam-3657	247	1	european journal	ORG
ejpam-3657	247	2	12(3):978–998	DATE
ejpam-3657	247	3	2019	DATE
ejpam-3657	248	1	7	CARDINAL
ejpam-3657	248	2	l. lesniaks	PERSON
ejpam-3657	248	3	g. chartrand	PERSON
ejpam-3657	248	4	p. zhang	PERSON
ejpam-3657	248	5	6th	ORDINAL
ejpam-3657	249	1	taylor	PERSON
ejpam-3657	249	2	francis	PERSON
ejpam-3657	249	3	llc crc press	ORG
ejpam-3657	249	4	2016	DATE
ejpam-3657	250	1	8	CARDINAL
ejpam-3657	250	2	k. prikry	PERSON
ejpam-3657	252	1	j. combin	PERSON
ejpam-3657	254	1	50(1):1–10	CARDINAL
ejpam-3657	254	2	1990	DATE
ejpam-3657	255	1	9	CARDINAL
ejpam-3657	255	2	j. palco	PERSON
ejpam-3657	255	3	r. paluga	PERSON
ejpam-3657	255	4	g. malacas	PERSON
ejpam-3657	257	1	far east journal of mathematical sciences	ORG
ejpam-3657	257	2	114(1):55–68	CARDINAL
ejpam-3657	257	3	2019	DATE