id	sid	eid	entity	type
ejpam-4069	1	1	european journal	ORG
ejpam-4069	2	1	14	DATE
ejpam-4069	2	2	4	CARDINAL
ejpam-4069	2	3	2021	DATE
ejpam-4069	2	4	1226	CARDINAL
ejpam-4069	2	5	1307-5543	DATE
ejpam-4069	2	6	new york	GPE
ejpam-4069	2	7	sandra a. nanding1,∗	PERSON
ejpam-4069	2	8	helen m. rara2	PERSON
ejpam-4069	3	1	1	CARDINAL
ejpam-4069	3	2	mindanao state university-iligan institute of technology	ORG
ejpam-4069	3	3	9200	CARDINAL
ejpam-4069	3	4	iligan city	GPE
ejpam-4069	3	5	philippines 2 department	ORG
ejpam-4069	3	6	mindanao state university-iligan institute of technology	ORG
ejpam-4069	3	7	9200	CARDINAL
ejpam-4069	3	8	iligan city	GPE
ejpam-4069	3	9	philippines	GPE
ejpam-4069	5	1	∈	ORG
ejpam-4069	6	1	2	CARDINAL
ejpam-4069	6	2	two	CARDINAL
ejpam-4069	8	1	2020	DATE
ejpam-4069	8	2	05c69	CARDINAL
ejpam-4069	8	3	1	CARDINAL
ejpam-4069	8	4	the late 1950’s	DATE
ejpam-4069	8	5	1960	DATE
ejpam-4069	9	1	1	CARDINAL
ejpam-4069	9	2	1958	DATE
ejpam-4069	11	1	one	CARDINAL
ejpam-4069	11	2	b. gayathri	PERSON
ejpam-4069	11	3	s. kaspar	PERSON
ejpam-4069	11	4	2010	DATE
ejpam-4069	11	5	3	CARDINAL
ejpam-4069	12	1	2	CARDINAL
ejpam-4069	12	2	6	DATE
ejpam-4069	12	3	12	CARDINAL
ejpam-4069	13	1	years later	DATE
ejpam-4069	13	2	natarajan	PERSON
ejpam-4069	13	3	8	CARDINAL
ejpam-4069	14	1	7	CARDINAL
ejpam-4069	14	2	9–11	CARDINAL
ejpam-4069	14	3	13	CARDINAL
ejpam-4069	16	1	s. nanding	PERSON
ejpam-4069	16	2	helen.rara@g.msuiit.edu.ph	GPE
ejpam-4069	16	3	h. rara	PERSON
ejpam-4069	16	4	1226	CARDINAL
ejpam-4069	16	5	2021	CARDINAL
ejpam-4069	17	1	s. nanding	PERSON
ejpam-4069	17	2	h. rara	PERSON
ejpam-4069	18	1	j. pure	PERSON
ejpam-4069	18	2	14	CARDINAL
ejpam-4069	18	3	4	CARDINAL
ejpam-4069	18	4	2021	CARDINAL
ejpam-4069	18	5	1226	CARDINAL
ejpam-4069	18	6	1236 1227	CARDINAL
ejpam-4069	20	1	5	CARDINAL
ejpam-4069	20	2	haynes	ORG
ejpam-4069	20	3	henning	PERSON
ejpam-4069	28	1	two	CARDINAL
ejpam-4069	28	2	two	CARDINAL
ejpam-4069	36	1	4	CARDINAL
ejpam-4069	37	1	two	CARDINAL
ejpam-4069	38	1	⊆	CARDINAL
ejpam-4069	38	2	⊆	CARDINAL
ejpam-4069	42	1	⊆	CARDINAL
ejpam-4069	42	2	∈	PERSON
ejpam-4069	43	1	2	CARDINAL
ejpam-4069	45	1	2	CARDINAL
ejpam-4069	46	1	2	CARDINAL
ejpam-4069	46	2	∈	ORG
ejpam-4069	46	3	2	CARDINAL
ejpam-4069	46	4	ng[u	DATE
ejpam-4069	46	5	2	CARDINAL
ejpam-4069	46	6	2	CARDINAL
ejpam-4069	47	1	⊆	CARDINAL
ejpam-4069	47	2	2	CARDINAL
ejpam-4069	47	3	⋃	PERSON
ejpam-4069	47	4	2	CARDINAL
ejpam-4069	48	1	2	CARDINAL
ejpam-4069	48	2	2	CARDINAL
ejpam-4069	49	1	∈	ORG
ejpam-4069	50	1	s. nanding	PERSON
ejpam-4069	50	2	h. rara	PERSON
ejpam-4069	51	1	j. pure	PERSON
ejpam-4069	51	2	14	CARDINAL
ejpam-4069	51	3	4	CARDINAL
ejpam-4069	51	4	2021	CARDINAL
ejpam-4069	51	5	1226-1236 1228	CARDINAL
ejpam-4069	51	6	sci(g	PERSON
ejpam-4069	51	7	= sci(g	PERSON
ejpam-4069	52	1	⊆	CARDINAL
ejpam-4069	53	1	2	CARDINAL
ejpam-4069	54	1	1	CARDINAL
ejpam-4069	57	1	2	CARDINAL
ejpam-4069	59	1	1 ≤	QUANTITY
ejpam-4069	60	1	1	CARDINAL
ejpam-4069	61	1	1	CARDINAL
ejpam-4069	63	1	1	CARDINAL
ejpam-4069	63	2	1 2	CARDINAL
ejpam-4069	63	3	2	CARDINAL
ejpam-4069	63	4	3	CARDINAL
ejpam-4069	63	5	2	CARDINAL
ejpam-4069	63	6	3	CARDINAL
ejpam-4069	63	7	3	CARDINAL
ejpam-4069	63	8	1	CARDINAL
ejpam-4069	63	9	4	CARDINAL
ejpam-4069	63	10	3	CARDINAL
ejpam-4069	64	1	1	CARDINAL
ejpam-4069	66	1	2	CARDINAL
ejpam-4069	70	1	2	CARDINAL
ejpam-4069	72	1	∈	ORG
ejpam-4069	72	2	2)∪ng(y	DATE
ejpam-4069	72	3	2	CARDINAL
ejpam-4069	73	1	∈	ORG
ejpam-4069	73	2	2	CARDINAL
ejpam-4069	77	1	2	CARDINAL
ejpam-4069	78	1	∈	ORG
ejpam-4069	78	2	2	CARDINAL
ejpam-4069	78	3	2	CARDINAL
ejpam-4069	81	1	xy ∈	PERSON
ejpam-4069	84	1	xy ∈	PERSON
ejpam-4069	84	2	2	CARDINAL
ejpam-4069	85	1	2	CARDINAL
ejpam-4069	89	1	2	CARDINAL
ejpam-4069	92	1	2	CARDINAL
ejpam-4069	92	2	s. nanding	PERSON
ejpam-4069	92	3	h. rara	PERSON
ejpam-4069	93	1	j. pure	PERSON
ejpam-4069	93	2	14	CARDINAL
ejpam-4069	93	3	4	CARDINAL
ejpam-4069	93	4	2021	CARDINAL
ejpam-4069	93	5	1226	CARDINAL
ejpam-4069	93	6	1236 1229	CARDINAL
ejpam-4069	93	7	2	CARDINAL
ejpam-4069	94	1	n ≥ 2	ORG
ejpam-4069	100	1	∈	ORG
ejpam-4069	100	2	2	CARDINAL
ejpam-4069	101	1	1	CARDINAL
ejpam-4069	103	1	3	CARDINAL
ejpam-4069	103	2	3	CARDINAL
ejpam-4069	104	1	two	CARDINAL
ejpam-4069	108	1	∈	ORG
ejpam-4069	109	1	3	CARDINAL
ejpam-4069	111	1	two	CARDINAL
ejpam-4069	112	1	⊆	CARDINAL
ejpam-4069	112	2	g+h	ORG
ejpam-4069	113	1	one	CARDINAL
ejpam-4069	113	2	h. (ii	LAW
ejpam-4069	114	1	sg	GPE
ejpam-4069	116	1	g+h	ORG
ejpam-4069	118	1	h)\sh	PERSON
ejpam-4069	119	1	h)\sh	PERSON
ejpam-4069	120	1	∈	ORG
ejpam-4069	121	1	w ∈ s	PERSON
ejpam-4069	121	2	2	CARDINAL
ejpam-4069	124	1	sg	GPE
ejpam-4069	125	1	sg	PERSON
ejpam-4069	126	1	∈	ORG
ejpam-4069	128	1	1	CARDINAL
ejpam-4069	130	1	∈	ORG
ejpam-4069	130	2	h)\sh	PERSON
ejpam-4069	131	1	w ∈	PERSON
ejpam-4069	132	1	w ∈ s	PERSON
ejpam-4069	132	2	2	CARDINAL
ejpam-4069	132	3	2	CARDINAL
ejpam-4069	133	1	∈	ORG
ejpam-4069	135	1	2	CARDINAL
ejpam-4069	135	2	g+h	ORG
ejpam-4069	136	1	h)\sh	PERSON
ejpam-4069	138	1	g+h	ORG
ejpam-4069	139	1	s. nanding	PERSON
ejpam-4069	139	2	h. rara	PERSON
ejpam-4069	140	1	j. pure	PERSON
ejpam-4069	140	2	14	CARDINAL
ejpam-4069	140	3	4	CARDINAL
ejpam-4069	140	4	2021	CARDINAL
ejpam-4069	140	5	1226	CARDINAL
ejpam-4069	140	6	1	CARDINAL
ejpam-4069	141	1	two	CARDINAL
ejpam-4069	144	1	⊆	CARDINAL
ejpam-4069	144	2	⊆	CARDINAL
ejpam-4069	144	3	3	CARDINAL
ejpam-4069	148	1	3	CARDINAL
ejpam-4069	148	2	g+h	ORG
ejpam-4069	149	1	sci(g	PERSON
ejpam-4069	151	1	4.	CARDINAL
ejpam-4069	151	2	two	CARDINAL
ejpam-4069	151	3	g◦h	ORG
ejpam-4069	151	4	one	CARDINAL
ejpam-4069	151	5	∈	ORG
ejpam-4069	151	6	one	CARDINAL
ejpam-4069	151	7	∈	ORG
ejpam-4069	152	1	4	CARDINAL
ejpam-4069	154	1	⊆	CARDINAL
ejpam-4069	155	1	⋃	PRODUCT
ejpam-4069	155	2	sv ⊆	ORG
ejpam-4069	157	1	sv ⊆	ORG
ejpam-4069	158	1	⋃ v∈v	PERSON
ejpam-4069	160	1	⋃ v∈v	PERSON
ejpam-4069	160	2	s. nanding	PERSON
ejpam-4069	160	3	h. rara	PERSON
ejpam-4069	161	1	j. pure	PERSON
ejpam-4069	161	2	14	CARDINAL
ejpam-4069	161	3	4	CARDINAL
ejpam-4069	161	4	2021	CARDINAL
ejpam-4069	161	5	1226-1236 1231	DATE
ejpam-4069	162	1	⋃	PRODUCT
ejpam-4069	162	2	sv ⊆	ORG
ejpam-4069	164	1	w ∈	PERSON
ejpam-4069	165	1	w ∈	PERSON
ejpam-4069	167	1	h(w	PRODUCT
ejpam-4069	167	2	2	CARDINAL
ejpam-4069	168	1	⋃ v∈v	PERSON
ejpam-4069	169	1	2	CARDINAL
ejpam-4069	171	1	m.	PERSON
ejpam-4069	171	2	coi(g ◦h	ORG
ejpam-4069	172	1	n(1 +m− β(h	PERSON
ejpam-4069	174	1	4	CARDINAL
ejpam-4069	174	2	⋃ v∈v	PERSON
ejpam-4069	175	1	coi(g ◦h	ORG
ejpam-4069	175	2	⋃	DATE
ejpam-4069	175	3	∑ v∈v	PERSON
ejpam-4069	176	1	∑ v∈v	PERSON
ejpam-4069	176	2	hv)|	CARDINAL
ejpam-4069	176	3	hv)|	DATE
ejpam-4069	176	4	− β(h	PERSON
ejpam-4069	177	1	n(m− β(h	PERSON
ejpam-4069	180	1	coi(g ◦h	ORG
ejpam-4069	181	1	dv ⊆	ORG
ejpam-4069	182	1	⋃ v∈v	PERSON
ejpam-4069	182	2	4	CARDINAL
ejpam-4069	183	1	coi(g ◦h	ORG
ejpam-4069	183	2	⋃	PRODUCT
ejpam-4069	184	1	∑ v∈v	PERSON
ejpam-4069	185	1	hv)|	DATE
ejpam-4069	185	2	hv)|	DATE
ejpam-4069	185	3	− β(h	PERSON
ejpam-4069	186	1	n(m− β(h	PERSON
ejpam-4069	189	1	s. nanding	PERSON
ejpam-4069	189	2	h. rara	PERSON
ejpam-4069	190	1	j. pure	PERSON
ejpam-4069	190	2	14	CARDINAL
ejpam-4069	190	3	4	CARDINAL
ejpam-4069	190	4	2021	CARDINAL
ejpam-4069	190	5	1226	CARDINAL
ejpam-4069	190	6	coi(g ◦h	ORG
ejpam-4069	193	1	coi(g ◦h	ORG
ejpam-4069	193	2	n(1 +m− β(h	PERSON
ejpam-4069	194	1	5	CARDINAL
ejpam-4069	194	2	two	CARDINAL
ejpam-4069	194	3	g[h	ORG
ejpam-4069	194	4	∈	ORG
ejpam-4069	195	1	5	CARDINAL
ejpam-4069	197	1	⋃	PERSON
ejpam-4069	197	2	⊆	CARDINAL
ejpam-4069	197	3	tx	ORG
ejpam-4069	197	4	⊆	PRODUCT
ejpam-4069	198	1	tx ̸=	ORG
ejpam-4069	198	2	h)\tx	ORG
ejpam-4069	198	3	tx	ORG
ejpam-4069	198	4	g[h	ORG
ejpam-4069	199	1	∈	ORG
ejpam-4069	205	1	tx ̸=	ORG
ejpam-4069	206	1	h)\tx	ORG
ejpam-4069	207	1	w ∈	PERSON
ejpam-4069	207	2	h)\tx	ORG
ejpam-4069	207	3	̸= w.	PERSON
ejpam-4069	207	4	∈	ORG
ejpam-4069	207	5	u)(x	GPE
ejpam-4069	207	6	w	GPE
ejpam-4069	210	1	h)\tx	ORG
ejpam-4069	213	1	̸=	ORG
ejpam-4069	215	1	∈	ORG
ejpam-4069	215	2	p)(x	ORG
ejpam-4069	215	3	∈	ORG
ejpam-4069	218	1	xa ∈	PERSON
ejpam-4069	219	1	∈	ORG
ejpam-4069	220	1	̸= tx	PERSON
ejpam-4069	220	2	∈	ORG
ejpam-4069	220	3	h)\tx	ORG
ejpam-4069	222	1	b)(a	GPE
ejpam-4069	222	2	∈	ORG
ejpam-4069	222	3	tx	ORG
ejpam-4069	223	1	2	CARDINAL
ejpam-4069	223	2	2	CARDINAL
ejpam-4069	224	1	∩ tx ̸= tx	PERSON
ejpam-4069	224	2	tx	ORG
ejpam-4069	225	1	⋃	PERSON
ejpam-4069	226	1	first	ORDINAL
ejpam-4069	227	1	two	CARDINAL
ejpam-4069	230	1	1	CARDINAL
ejpam-4069	232	1	̸=	ORG
ejpam-4069	232	2	ab /∈ e(h	ORG
ejpam-4069	233	1	∈	ORG
ejpam-4069	234	1	w	ORG
ejpam-4069	235	1	w	GPE
ejpam-4069	235	2	2	CARDINAL
ejpam-4069	236	1	2	CARDINAL
ejpam-4069	237	1	1	CARDINAL
ejpam-4069	237	2	2	DATE
ejpam-4069	238	1	s. nanding	PERSON
ejpam-4069	238	2	h. rara	PERSON
ejpam-4069	239	1	j. pure	PERSON
ejpam-4069	239	2	14	CARDINAL
ejpam-4069	239	3	4	CARDINAL
ejpam-4069	239	4	2021	CARDINAL
ejpam-4069	239	5	1226	CARDINAL
ejpam-4069	239	6	1236 1233	CARDINAL
ejpam-4069	239	7	un	ORG
ejpam-4069	241	1	w	ORG
ejpam-4069	243	1	1	CARDINAL
ejpam-4069	243	2	w	ORG
ejpam-4069	247	1	v)(w	PERSON
ejpam-4069	248	1	2	CARDINAL
ejpam-4069	249	1	tu ̸=	PERSON
ejpam-4069	249	2	tw ̸=	PERSON
ejpam-4069	251	1	v)(w	PERSON
ejpam-4069	255	1	y /∈	PERSON
ejpam-4069	256	1	1	CARDINAL
ejpam-4069	257	1	tx	ORG
ejpam-4069	257	2	y /∈	PERSON
ejpam-4069	258	1	∩ tx ̸= tx	PERSON
ejpam-4069	259	1	∈	ORG
ejpam-4069	259	2	tx	ORG
ejpam-4069	260	1	2	CARDINAL
ejpam-4069	261	1	2	CARDINAL
ejpam-4069	264	1	2	CARDINAL
ejpam-4069	266	1	2	CARDINAL
ejpam-4069	266	2	g[h	ORG
ejpam-4069	267	1	g[h	ORG
ejpam-4069	268	1	3	CARDINAL
ejpam-4069	269	1	β(h	ORG
ejpam-4069	272	1	β(h	ORG
ejpam-4069	274	1	d0 ⊆	ORG
ejpam-4069	274	2	g)\d0	PERSON
ejpam-4069	275	1	tx	ORG
ejpam-4069	275	2	g)\d0	PERSON
ejpam-4069	278	1	⋃	PERSON
ejpam-4069	278	2	 ⋃	PERSON
ejpam-4069	278	3	x∈v	PERSON
ejpam-4069	278	4	g)\d0	PERSON
ejpam-4069	278	5	g[h	ORG
ejpam-4069	278	6	5	CARDINAL
ejpam-4069	280	1	m−	NORP
ejpam-4069	282	1	+ r(g)β(h	GPE
ejpam-4069	282	2	+ r(g)β(h	PERCENT
ejpam-4069	282	3	β(h	ORG
ejpam-4069	283	1	+ r(g)β(h	PERCENT
ejpam-4069	284	1	+ r(g)β(h	PERCENT
ejpam-4069	285	1	s. nanding	PERSON
ejpam-4069	285	2	h. rara	PERSON
ejpam-4069	286	1	j. pure	PERSON
ejpam-4069	286	2	14	CARDINAL
ejpam-4069	286	3	4	CARDINAL
ejpam-4069	286	4	2021	CARDINAL
ejpam-4069	286	5	1226-1236 1234	CARDINAL
ejpam-4069	287	1	g[h	ORG
ejpam-4069	289	1	⋃ x∈d	PERSON
ejpam-4069	289	2	 ⋃	PERSON
ejpam-4069	289	3	x∈v (g)\d tx 	PERSON
ejpam-4069	291	1	h)\tx	ORG
ejpam-4069	294	1	m−	NORP
ejpam-4069	295	1	β(h	ORG
ejpam-4069	296	1	β(h	ORG
ejpam-4069	297	1	+ r(g)β(h	PERCENT
ejpam-4069	298	1	+ r(g)β(h	PERCENT
ejpam-4069	298	2	β(h	ORG
ejpam-4069	299	1	+ r(g)β(h	PERCENT
ejpam-4069	300	1	4	CARDINAL
ejpam-4069	302	1	coi(kn[h	GPE
ejpam-4069	302	2	1	CARDINAL
ejpam-4069	303	1	∈	ORG
ejpam-4069	304	1	5	CARDINAL
ejpam-4069	304	2	y∈v	DATE
ejpam-4069	304	3	kn)\{v	PERSON
ejpam-4069	305	1	kn)\{v	PERSON
ejpam-4069	306	1	coi(kn[h	GPE
ejpam-4069	306	2	1)|ty|+	CARDINAL
ejpam-4069	306	3	1)m+ |t	TIME
ejpam-4069	306	4	1)m+	CARDINAL
ejpam-4069	308	1	5	CARDINAL
ejpam-4069	309	1	coi(kn[h	GPE
ejpam-4069	309	2	|co|	CARDINAL
ejpam-4069	309	3	1235	CARDINAL
ejpam-4069	309	4	1)|rx|	CARDINAL
ejpam-4069	309	5	1)|v	CARDINAL
ejpam-4069	310	1	1)m	CARDINAL
ejpam-4069	311	1	coi(kn[h	GPE
ejpam-4069	311	2	1	CARDINAL
ejpam-4069	312	1	the department of science and technology	ORG
ejpam-4069	312	2	philippines	GPE
ejpam-4069	313	1	1	CARDINAL
ejpam-4069	314	1	theorie des graphes	ORG
ejpam-4069	315	1	wiley	GPE
ejpam-4069	315	2	london	GPE
ejpam-4069	315	3	new york	GPE
ejpam-4069	315	4	1962	DATE
ejpam-4069	316	1	2	CARDINAL
ejpam-4069	316	2	r. detalla	PERSON
ejpam-4069	316	3	h. rara	PERSON
ejpam-4069	318	1	2019	DATE
ejpam-4069	319	1	3	CARDINAL
ejpam-4069	319	2	b. gayathri	PERSON
ejpam-4069	319	3	s. kaspar	PERSON
ejpam-4069	322	1	6:423–429, 2011	DATE
ejpam-4069	323	1	4	CARDINAL
ejpam-4069	323	2	f. harary	PERSON
ejpam-4069	325	1	addison-wesley publishing company, usa, 1969	ORG
ejpam-4069	326	1	5	CARDINAL
ejpam-4069	326	2	w. desormeaux	PERSON
ejpam-4069	326	3	m.a. henning	ORG
ejpam-4069	328	1	2016	DATE
ejpam-4069	329	1	6	CARDINAL
ejpam-4069	329	2	i. aniversario m. bonsocan	PERSON
ejpam-4069	331	1	2018	DATE
ejpam-4069	332	1	7	CARDINAL
ejpam-4069	332	2	s. canoy	PERSON
ejpam-4069	332	3	r. mollejon	PERSON
ejpam-4069	332	4	j. canoy	PERSON
ejpam-4069	334	1	european journal	ORG
ejpam-4069	334	2	12(4):1455–1463,	DATE
ejpam-4069	334	3	2019	DATE
ejpam-4069	335	1	8	CARDINAL
ejpam-4069	335	2	c. natarajan	PERSON
ejpam-4069	335	3	s. ayyaswamy	ORG
ejpam-4069	336	1	versita	PERSON
ejpam-4069	336	2	23(2):187	CARDINAL
ejpam-4069	336	3	199	CARDINAL
ejpam-4069	336	4	2015	DATE
ejpam-4069	337	1	9	CARDINAL
ejpam-4069	337	2	c. natarajan	PERSON
ejpam-4069	339	1	2018	DATE
ejpam-4069	340	1	10	CARDINAL
ejpam-4069	340	2	h. rara	PERSON
ejpam-4069	342	1	2017	DATE
ejpam-4069	343	1	11	CARDINAL
ejpam-4069	343	2	h. rara	PERSON
ejpam-4069	345	1	asian-european journal of mathematics, 2018.	ORG
ejpam-4069	346	1	1236	CARDINAL
ejpam-4069	346	2	12	CARDINAL
ejpam-4069	346	3	m. perocho and	PERSON
ejpam-4069	346	4	h. rara	PERSON
ejpam-4069	348	1	2020	DATE
ejpam-4069	349	1	13	CARDINAL
ejpam-4069	349	2	g. salasalan	PERSON
ejpam-4069	349	3	s. canoy jr.	PERSON
ejpam-4069	351	1	2021	CARDINAL