id	sid	eid	entity	type
ejpam-4316	1	1	european journal	ORG
ejpam-4316	2	1	15	CARDINAL
ejpam-4316	2	2	2	CARDINAL
ejpam-4316	2	3	2022	CARDINAL
ejpam-4316	2	4	602	CARDINAL
ejpam-4316	2	5	new york	GPE
ejpam-4316	2	6	francis joseph h. campeña1	PERSON
ejpam-4316	2	7	ma	PERSON
ejpam-4316	2	8	christine g. egan1,∗	PERSON
ejpam-4316	2	9	john rafael m. antalan1,2	PERSON
ejpam-4316	2	10	1	CARDINAL
ejpam-4316	2	11	de la salle university	ORG
ejpam-4316	2	12	2401	CARDINAL
ejpam-4316	2	13	taft avenue malate	FAC
ejpam-4316	2	14	manila	GPE
ejpam-4316	2	15	philippines	GPE
ejpam-4316	3	1	2	CARDINAL
ejpam-4316	3	2	central luzon state university	ORG
ejpam-4316	3	3	muñoz	ORG
ejpam-4316	3	4	3120	CARDINAL
ejpam-4316	3	5	philippines	GPE
ejpam-4316	5	1	e. sampathkumar	PERSON
ejpam-4316	5	2	1980	DATE
ejpam-4316	7	1	2020	DATE
ejpam-4316	7	2	05c50	CARDINAL
ejpam-4316	7	3	05c09	CARDINAL
ejpam-4316	7	4	1	CARDINAL
ejpam-4316	9	1	one	CARDINAL
ejpam-4316	11	1	topological	ORG
ejpam-4316	11	2	18	CARDINAL
ejpam-4316	12	1	qspr/qsar	ORG
ejpam-4316	13	1	qspr	ORG
ejpam-4316	13	2	1	CARDINAL
ejpam-4316	14	1	13	CARDINAL
ejpam-4316	15	1	qspr	GPE
ejpam-4316	17	1	al	PERSON
ejpam-4316	17	2	13	CARDINAL
ejpam-4316	17	3	20	CARDINAL
ejpam-4316	18	1	hosamani ∗corresponding	PERSON
ejpam-4316	19	1	https://doi.org/10.29020/nybg.ejpam.v15i2.4316	GPE
ejpam-4316	20	1	campeña	PERSON
ejpam-4316	20	2	ma_christine_egan@dlsu.edu.ph	GPE
ejpam-4316	20	3	egan	PERSON
ejpam-4316	20	4	antalan	PERSON
ejpam-4316	20	5	602	CARDINAL
ejpam-4316	21	1	2022	CARDINAL
ejpam-4316	23	1	campeña	PERSON
ejpam-4316	23	2	egan	PERSON
ejpam-4316	24	1	antalan	PERSON
ejpam-4316	25	1	j. pure	PERSON
ejpam-4316	25	2	15	CARDINAL
ejpam-4316	25	3	2	CARDINAL
ejpam-4316	25	4	2022	CARDINAL
ejpam-4316	25	5	602	CARDINAL
ejpam-4316	25	6	3clpro	PRODUCT
ejpam-4316	25	7	10	CARDINAL
ejpam-4316	26	1	topological	ORG
ejpam-4316	27	1	zagreb	ORG
ejpam-4316	29	1	15	CARDINAL
ejpam-4316	30	1	first	ORDINAL
ejpam-4316	30	2	harry wiener	PERSON
ejpam-4316	30	3	1947	DATE
ejpam-4316	31	1	24	CARDINAL
ejpam-4316	32	1	milan randic	ORG
ejpam-4316	32	2	1993	DATE
ejpam-4316	33	1	14	CARDINAL
ejpam-4316	36	1	17	CARDINAL
ejpam-4316	37	1	11	CARDINAL
ejpam-4316	37	2	1993	DATE
ejpam-4316	40	1	2	CARDINAL
ejpam-4316	41	1	first	ORDINAL
ejpam-4316	41	2	first	ORDINAL
ejpam-4316	41	3	zagreb	ORG
ejpam-4316	41	4	two	CARDINAL
ejpam-4316	41	5	3	CARDINAL
ejpam-4316	42	1	gao et	PERSON
ejpam-4316	43	1	topological	ORG
ejpam-4316	43	2	6	CARDINAL
ejpam-4316	45	1	al	ORG
ejpam-4316	45	2	covid-19	PRODUCT
ejpam-4316	45	3	15	CARDINAL
ejpam-4316	46	1	yeh	PERSON
ejpam-4316	46	2	25	CARDINAL
ejpam-4316	47	1	21	CARDINAL
ejpam-4316	48	1	khalifeh et	PERSON
ejpam-4316	49	1	al	PERSON
ejpam-4316	49	2	12	CARDINAL
ejpam-4316	51	1	al	ORG
ejpam-4316	51	2	5	CARDINAL
ejpam-4316	53	1	⊆	CARDINAL
ejpam-4316	55	1	n ≥ 1	DATE
ejpam-4316	55	2	∪{x′|x ∈ s	PERSON
ejpam-4316	56	1	∈	ORG
ejpam-4316	56	2	n(x	GPE
ejpam-4316	57	1	19	CARDINAL
ejpam-4316	58	1	16	CARDINAL
ejpam-4316	59	1	γ(g	ORG
ejpam-4316	59	2	⊆	CARDINAL
ejpam-4316	61	1	section 2	LAW
ejpam-4316	63	1	campeña	PERSON
ejpam-4316	63	2	egan	PERSON
ejpam-4316	64	1	antalan	PERSON
ejpam-4316	65	1	j. pure	PERSON
ejpam-4316	65	2	15	CARDINAL
ejpam-4316	65	3	2	CARDINAL
ejpam-4316	65	4	2022	CARDINAL
ejpam-4316	65	5	602	CARDINAL
ejpam-4316	65	6	γ(g	ORG
ejpam-4316	65	7	section 3	DATE
ejpam-4316	67	1	chapter 4	LAW
ejpam-4316	67	2	γ(g	GPE
ejpam-4316	68	1	2	CARDINAL
ejpam-4316	71	1	two	CARDINAL
ejpam-4316	71	2	xj	ORG
ejpam-4316	71	3	e(g	GPE
ejpam-4316	73	1	three	CARDINAL
ejpam-4316	74	1	a(g	GPE
ejpam-4316	77	1	aij	ORG
ejpam-4316	77	2	1	CARDINAL
ejpam-4316	77	3	xj	ORG
ejpam-4316	77	4	aij	ORG
ejpam-4316	78	1	d(xi	GPE
ejpam-4316	78	2	xj	GPE
ejpam-4316	78	3	two	CARDINAL
ejpam-4316	78	4	xj	ORG
ejpam-4316	78	5	xj	GPE
ejpam-4316	79	1	g. d(g	PERSON
ejpam-4316	80	1	d(xi	GPE
ejpam-4316	80	2	xj	GPE
ejpam-4316	80	3	4	CARDINAL
ejpam-4316	82	1	{vi	PERSON
ejpam-4316	82	2	1 2	CARDINAL
ejpam-4316	83	1	{vi	PERSON
ejpam-4316	83	2	1 2	CARDINAL
ejpam-4316	84	1	1 d(vi	CARDINAL
ejpam-4316	89	1	1	CARDINAL
ejpam-4316	90	1	17	CARDINAL
ejpam-4316	90	2	23	CARDINAL
ejpam-4316	90	3	n ≥ 1	DATE
ejpam-4316	90	4	1 6n(n 2	CARDINAL
ejpam-4316	90	5	1	CARDINAL
ejpam-4316	91	1	1	CARDINAL
ejpam-4316	91	2	2	CARDINAL
ejpam-4316	92	1	17	CARDINAL
ejpam-4316	92	2	23	CARDINAL
ejpam-4316	92	3	n ≥ 3	DATE
ejpam-4316	93	1	1)(n+ 1)n	DATE
ejpam-4316	94	1	campeña	PERSON
ejpam-4316	94	2	egan	PERSON
ejpam-4316	95	1	antalan	PERSON
ejpam-4316	96	1	j. pure	PERSON
ejpam-4316	96	2	15	CARDINAL
ejpam-4316	96	3	2	CARDINAL
ejpam-4316	96	4	2022	CARDINAL
ejpam-4316	96	5	602	CARDINAL
ejpam-4316	96	6	1 2	CARDINAL
ejpam-4316	97	1	3	CARDINAL
ejpam-4316	98	1	22	CARDINAL
ejpam-4316	98	2	23	CARDINAL
ejpam-4316	98	3	n ≥ 1	DATE
ejpam-4316	98	4	1	CARDINAL
ejpam-4316	98	5	2	CARDINAL
ejpam-4316	99	1	4	CARDINAL
ejpam-4316	100	1	22	CARDINAL
ejpam-4316	100	2	23	CARDINAL
ejpam-4316	100	3	n ≥ 1	DATE
ejpam-4316	100	4	w	ORG
ejpam-4316	100	5	sn	ORG
ejpam-4316	100	6	n−	ORG
ejpam-4316	100	7	1)2	PRODUCT
ejpam-4316	100	8	1	CARDINAL
ejpam-4316	101	1	5	CARDINAL
ejpam-4316	102	1	22	CARDINAL
ejpam-4316	102	2	23	CARDINAL
ejpam-4316	102	3	n ≥ 4	DATE
ejpam-4316	104	1	1	CARDINAL
ejpam-4316	105	1	6	CARDINAL
ejpam-4316	106	1	8	CARDINAL
ejpam-4316	106	2	23	CARDINAL
ejpam-4316	106	3	n ≥ 1	DATE
ejpam-4316	106	4	bipartite	NORP
ejpam-4316	106	5	graph km	PERSON
ejpam-4316	106	6	m2+mn+n2−m−n	ORG
ejpam-4316	106	7	h(km,n	ORG
ejpam-4316	107	1	1 4(m	CARDINAL
ejpam-4316	108	1	3	CARDINAL
ejpam-4316	108	2	1980	DATE
ejpam-4316	108	3	19	CARDINAL
ejpam-4316	109	1	3.1	CARDINAL
ejpam-4316	110	1	⊆	CARDINAL
ejpam-4316	111	1	n ≥ 2	DATE
ejpam-4316	111	2	≥ 1	DATE
ejpam-4316	112	1	∈	PRODUCT
ejpam-4316	113	1	x′	DATE
ejpam-4316	113	2	∈	ORG
ejpam-4316	113	3	x.	GPE
ejpam-4316	113	4	γ(g	GPE
ejpam-4316	113	5	19	CARDINAL
ejpam-4316	115	1	1	CARDINAL
ejpam-4316	116	1	2	CARDINAL
ejpam-4316	116	2	1	CARDINAL
ejpam-4316	117	1	γ(g	NORP
ejpam-4316	117	2	∈	PRODUCT
ejpam-4316	118	1	2n	CARDINAL
ejpam-4316	118	2	m. (ii	PERSON
ejpam-4316	118	3	∈	ORG
ejpam-4316	118	4	2degg(v	CARDINAL
ejpam-4316	119	1	∈	ORG
ejpam-4316	121	1	γ(g	GPE
ejpam-4316	123	1	campeña	PERSON
ejpam-4316	123	2	egan	PERSON
ejpam-4316	124	1	antalan	PERSON
ejpam-4316	125	1	j. pure	PERSON
ejpam-4316	125	2	15	CARDINAL
ejpam-4316	125	3	2	CARDINAL
ejpam-4316	125	4	2022	CARDINAL
ejpam-4316	125	5	602	CARDINAL
ejpam-4316	131	1	2|v	CARDINAL
ejpam-4316	132	1	γ(g	GPE
ejpam-4316	132	2	2	CARDINAL
ejpam-4316	135	1	γ	GPE
ejpam-4316	136	1	∈	ORG
ejpam-4316	136	2	2degg(v	CARDINAL
ejpam-4316	139	1	γ	GPE
ejpam-4316	139	2	three	CARDINAL
ejpam-4316	139	3	∈	ORG
ejpam-4316	140	1	x′	DATE
ejpam-4316	140	2	d(x	ORG
ejpam-4316	140	3	2	CARDINAL
ejpam-4316	140	4	2	CARDINAL
ejpam-4316	140	5	d(x	ORG
ejpam-4316	141	1	2	CARDINAL
ejpam-4316	141	2	∈	ORG
ejpam-4316	141	3	6=	CARDINAL
ejpam-4316	149	1	γ	GPE
ejpam-4316	149	2	γ(g	NORP
ejpam-4316	150	1	2	CARDINAL
ejpam-4316	151	1	at least two	CARDINAL
ejpam-4316	152	1	γ(g	PERSON
ejpam-4316	154	1	2	CARDINAL
ejpam-4316	154	2	1	CARDINAL
ejpam-4316	155	1	d(xi	GPE
ejpam-4316	155	2	xj	GPE
ejpam-4316	155	3	xj	PERSON
ejpam-4316	155	4	1 ≤	QUANTITY
ejpam-4316	155	5	6=	CARDINAL
ejpam-4316	156	1	3	CARDINAL
ejpam-4316	156	2	xj	ORG
ejpam-4316	156	3	d(xi	GPE
ejpam-4316	156	4	xj	GPE
ejpam-4316	157	1	xn	ORG
ejpam-4316	159	1	3	CARDINAL
ejpam-4316	160	1	at least two	CARDINAL
ejpam-4316	162	1	2	CARDINAL
ejpam-4316	162	2	1	CARDINAL
ejpam-4316	163	1	d(xi	GPE
ejpam-4316	163	2	xj	GPE
ejpam-4316	163	3	xj	ORG
ejpam-4316	163	4	1 ≤	CARDINAL
ejpam-4316	164	1	6=	CARDINAL
ejpam-4316	164	2	2	CARDINAL
ejpam-4316	164	3	xj	ORG
ejpam-4316	165	1	campeña	PERSON
ejpam-4316	165	2	egan	PERSON
ejpam-4316	166	1	antalan	PERSON
ejpam-4316	167	1	j. pure	PERSON
ejpam-4316	167	2	15	CARDINAL
ejpam-4316	167	3	2	CARDINAL
ejpam-4316	167	4	2022	CARDINAL
ejpam-4316	167	5	602-619 607	CARDINAL
ejpam-4316	167	6	d(xi	GPE
ejpam-4316	167	7	xj	GPE
ejpam-4316	168	1	xn	ORG
ejpam-4316	170	1	2	CARDINAL
ejpam-4316	172	1	d(g	ORG
ejpam-4316	172	2	d(g	ORG
ejpam-4316	172	3	3	CARDINAL
ejpam-4316	173	1	d(g	ORG
ejpam-4316	173	2	d(g	ORG
ejpam-4316	174	1	d(g	ORG
ejpam-4316	174	2	a(g	PERSON
ejpam-4316	174	3	g. theorem 7	ORG
ejpam-4316	178	1	+ 2	DATE
ejpam-4316	178	2	w	ORG
ejpam-4316	179	1	6=	CARDINAL
ejpam-4316	179	2	3	CARDINAL
ejpam-4316	181	1	j d(xi	PERSON
ejpam-4316	181	2	xj	GPE
ejpam-4316	183	1	first	ORDINAL
ejpam-4316	186	1	lemma 2	ORG
ejpam-4316	186	2	3	CARDINAL
ejpam-4316	189	1	w	GPE
ejpam-4316	191	1	first	ORDINAL
ejpam-4316	192	1	1	CARDINAL
ejpam-4316	192	2	xj	ORG
ejpam-4316	192	3	d(g)−a(g	GPE
ejpam-4316	192	4	two	CARDINAL
ejpam-4316	192	5	2	CARDINAL
ejpam-4316	192	6	3	CARDINAL
ejpam-4316	192	7	d(xi	GPE
ejpam-4316	192	8	xj	GPE
ejpam-4316	192	9	two	CARDINAL
ejpam-4316	192	10	v2	PRODUCT
ejpam-4316	194	1	campeña	PERSON
ejpam-4316	194	2	egan	PERSON
ejpam-4316	195	1	antalan	PERSON
ejpam-4316	196	1	j. pure	PERSON
ejpam-4316	196	2	15	CARDINAL
ejpam-4316	196	3	2	CARDINAL
ejpam-4316	196	4	2022	CARDINAL
ejpam-4316	196	5	602	CARDINAL
ejpam-4316	196	6	3	CARDINAL
ejpam-4316	196	7	2	CARDINAL
ejpam-4316	196	8	xj	GPE
ejpam-4316	196	9	v2	GPE
ejpam-4316	196	10	3	CARDINAL
ejpam-4316	197	1	3	CARDINAL
ejpam-4316	197	2	d(g)−a(g	GPE
ejpam-4316	198	1	d(g	ORG
ejpam-4316	198	2	a(g	GPE
ejpam-4316	198	3	1	CARDINAL
ejpam-4316	198	4	6=	CARDINAL
ejpam-4316	198	5	0	CARDINAL
ejpam-4316	198	6	a′′(g	ORG
ejpam-4316	198	7	1	CARDINAL
ejpam-4316	200	1	0	CARDINAL
ejpam-4316	201	1	3.2	CARDINAL
ejpam-4316	201	2	γ(g	GPE
ejpam-4316	201	3	∑ a.	PERSON
ejpam-4316	201	4	∑ a. theorem 8	PERSON
ejpam-4316	203	1	w	ORG
ejpam-4316	204	1	4w	CARDINAL
ejpam-4316	204	2	m. proof	PERSON
ejpam-4316	208	1	d(g	ORG
ejpam-4316	208	2	d(g	ORG
ejpam-4316	208	3	γ	ORG
ejpam-4316	208	4	half	CARDINAL
ejpam-4316	209	1	1 2	CARDINAL
ejpam-4316	209	2	1 2	CARDINAL
ejpam-4316	210	1	+ 4 ∑	DATE
ejpam-4316	211	1	4	CARDINAL
ejpam-4316	212	1	+ 2 ∑	QUANTITY
ejpam-4316	212	2	∑ a(g	PERSON
ejpam-4316	212	3	4w	CARDINAL
ejpam-4316	212	4	4w	CARDINAL
ejpam-4316	212	5	sn	ORG
ejpam-4316	212	6	3	CARDINAL
ejpam-4316	214	1	1	CARDINAL
ejpam-4316	215	1	3	CARDINAL
ejpam-4316	215	2	γ	GPE
ejpam-4316	217	1	+10n−6 3	DATE
ejpam-4316	218	1	campeña	PERSON
ejpam-4316	218	2	egan	PERSON
ejpam-4316	219	1	antalan	PERSON
ejpam-4316	220	1	j. pure	PERSON
ejpam-4316	220	2	15	CARDINAL
ejpam-4316	220	3	2	CARDINAL
ejpam-4316	220	4	2022	CARDINAL
ejpam-4316	220	5	602-619 609	MONEY
ejpam-4316	220	6	γ(sn	ORG
ejpam-4316	222	1	4n+ 2	DATE
ejpam-4316	222	2	γ(cn	ORG
ejpam-4316	225	1	1	CARDINAL
ejpam-4316	225	2	8	CARDINAL
ejpam-4316	225	3	4	CARDINAL
ejpam-4316	225	4	8	CARDINAL
ejpam-4316	225	5	2	CARDINAL
ejpam-4316	225	6	8	CARDINAL
ejpam-4316	226	1	9	CARDINAL
ejpam-4316	227	1	2	CARDINAL
ejpam-4316	227	2	1	CARDINAL
ejpam-4316	227	3	at least one	CARDINAL
ejpam-4316	227	4	w	ORG
ejpam-4316	228	1	4w	CARDINAL
ejpam-4316	232	1	d(g	ORG
ejpam-4316	232	2	d(g	ORG
ejpam-4316	233	1	d(g	ORG
ejpam-4316	233	2	a(g	GPE
ejpam-4316	234	1	1 2	CARDINAL
ejpam-4316	234	2	1 2	CARDINAL
ejpam-4316	234	3	+ 4 ∑	DATE
ejpam-4316	234	4	∑ a(g	PERSON
ejpam-4316	235	1	4	CARDINAL
ejpam-4316	236	1	+ 2 ∑	QUANTITY
ejpam-4316	236	2	+ 1 2 ∑ a(g	QUANTITY
ejpam-4316	236	3	4w	CARDINAL
ejpam-4316	236	4	w	GPE
ejpam-4316	236	5	4w	CARDINAL
ejpam-4316	237	1	4w	CARDINAL
ejpam-4316	238	1	2	CARDINAL
ejpam-4316	239	1	3	CARDINAL
ejpam-4316	239	2	γ	GPE
ejpam-4316	241	1	5n2−n 2	CARDINAL
ejpam-4316	242	1	4n2	CARDINAL
ejpam-4316	243	1	− 8n+ 6	WORK_OF_ART
ejpam-4316	245	1	3	CARDINAL
ejpam-4316	245	2	9	CARDINAL
ejpam-4316	245	3	5	CARDINAL
ejpam-4316	245	4	9	CARDINAL
ejpam-4316	246	1	•	CARDINAL
ejpam-4316	247	1	kn	PERSON
ejpam-4316	247	2	γ(g	NORP
ejpam-4316	249	1	campeña	PERSON
ejpam-4316	249	2	egan	PERSON
ejpam-4316	250	1	antalan	PERSON
ejpam-4316	251	1	j. pure	PERSON
ejpam-4316	251	2	15	CARDINAL
ejpam-4316	251	3	2	CARDINAL
ejpam-4316	251	4	2022	CARDINAL
ejpam-4316	251	5	602	CARDINAL
ejpam-4316	251	6	n ≥ 3	DATE
ejpam-4316	252	1	γ(g	NORP
ejpam-4316	252	2	γ(g	GPE
ejpam-4316	253	1	γ(g	GPE
ejpam-4316	253	2	6=	CARDINAL
ejpam-4316	254	1	bipartite	ORG
ejpam-4316	255	1	lemma	ORG
ejpam-4316	255	2	g. lemma 4	PERSON
ejpam-4316	256	1	v2	PRODUCT
ejpam-4316	257	1	⊆	CARDINAL
ejpam-4316	257	2	γ(g	GPE
ejpam-4316	257	3	10	CARDINAL
ejpam-4316	258	1	g = kn	PERSON
ejpam-4316	258	2	n ≥ 3	DATE
ejpam-4316	258	3	1 ≤	QUANTITY
ejpam-4316	258	4	1	CARDINAL
ejpam-4316	259	1	kn	PERSON
ejpam-4316	271	1	′ 1	DATE
ejpam-4316	271	2	2	CARDINAL
ejpam-4316	272	1	r.	NORP
ejpam-4316	274	1	a(kr)	DATE
ejpam-4316	275	1	2ir	ORDINAL
ejpam-4316	277	1	2ir	ORDINAL
ejpam-4316	277	2	2a(kr) 	DATE
ejpam-4316	277	3	a(kr	DATE
ejpam-4316	277	4	ir	ORG
ejpam-4316	277	5	kn	PERSON
ejpam-4316	277	6	kr	ORG
ejpam-4316	278	1	w	ORG
ejpam-4316	279	1	1 2	CARDINAL
ejpam-4316	279	2	1 2	CARDINAL
ejpam-4316	279	3	+ 4	DATE
ejpam-4316	279	4	∑ ir + ∑	PERSON
ejpam-4316	279	5	1 2	CARDINAL
ejpam-4316	280	1	+ 2 ∑ ir	QUANTITY
ejpam-4316	280	2	+ 1 2 ∑	QUANTITY
ejpam-4316	281	1	+ 1 2 ∑	QUANTITY
ejpam-4316	281	2	jr×n−r = w	PERSON
ejpam-4316	281	3	2|e(kr)|	CARDINAL
ejpam-4316	281	4	+ 1 2 ∑	QUANTITY
ejpam-4316	282	1	+ 1 2 ∑	QUANTITY
ejpam-4316	282	2	jr×n−r =	PERSON
ejpam-4316	282	3	1	CARDINAL
ejpam-4316	282	4	2	CARDINAL
ejpam-4316	283	1	1	CARDINAL
ejpam-4316	284	1	n− r)r	ORG
ejpam-4316	284	2	1	CARDINAL
ejpam-4316	284	3	2	CARDINAL
ejpam-4316	284	4	2r	CARDINAL
ejpam-4316	286	1	2	CARDINAL
ejpam-4316	286	2	11	CARDINAL
ejpam-4316	287	1	3	CARDINAL
ejpam-4316	287	2	∈	ORG
ejpam-4316	289	1	campeña	PERSON
ejpam-4316	289	2	egan	PERSON
ejpam-4316	290	1	antalan	PERSON
ejpam-4316	291	1	j. pure	PERSON
ejpam-4316	291	2	15	CARDINAL
ejpam-4316	291	3	2	CARDINAL
ejpam-4316	291	4	2022	CARDINAL
ejpam-4316	291	5	602-619 611	MONEY
ejpam-4316	291	6	γ(cn	ORG
ejpam-4316	293	1	γ(cn	ORG
ejpam-4316	293	2	8 + k2 + 2	QUANTITY
ejpam-4316	295	1	2k + 1	DATE
ejpam-4316	300	1	x3	GPE
ejpam-4316	300	2	xn−1	GPE
ejpam-4316	301	1	xk+1	GPE
ejpam-4316	301	2	′ 1	DATE
ejpam-4316	302	1	2	CARDINAL
ejpam-4316	302	2	1	DATE
ejpam-4316	302	3	1	CARDINAL
ejpam-4316	302	4	2	DATE
ejpam-4316	302	5	2	DATE
ejpam-4316	302	6	3	DATE
ejpam-4316	302	7	3	CARDINAL
ejpam-4316	307	1	1)(n+ 1	DATE
ejpam-4316	308	1	2	CARDINAL
ejpam-4316	309	1	1)(n+ 1	DATE
ejpam-4316	309	2	1)(n+ 1	DATE
ejpam-4316	310	1	x3	GPE
ejpam-4316	310	2	xn−1	GPE
ejpam-4316	312	1	xk−1	GPE
ejpam-4316	312	2	′ 1	DATE
ejpam-4316	315	1	2	CARDINAL
ejpam-4316	315	2	1	DATE
ejpam-4316	315	3	1	CARDINAL
ejpam-4316	315	4	2	DATE
ejpam-4316	315	5	2	DATE
ejpam-4316	321	1	i=1 i+ k = n3	PERSON
ejpam-4316	321	2	8 + 2 + 2	QUANTITY
ejpam-4316	322	1	8 + 2 + 2	QUANTITY
ejpam-4316	323	1	8 + k2 + 2	QUANTITY
ejpam-4316	323	2	12	CARDINAL
ejpam-4316	327	1	n ≥ 2	DATE
ejpam-4316	327	2	+3n2−4n+12 6	CARDINAL
ejpam-4316	327	3	2 ≤	MONEY
ejpam-4316	327	4	1	CARDINAL
ejpam-4316	328	1	+3n2+2n+6i2−6in−6i+12 6	DATE
ejpam-4316	330	1	campeña	PERSON
ejpam-4316	330	2	egan	PERSON
ejpam-4316	331	1	antalan	PERSON
ejpam-4316	332	1	j. pure	PERSON
ejpam-4316	332	2	15	CARDINAL
ejpam-4316	332	3	2	CARDINAL
ejpam-4316	332	4	2022	CARDINAL
ejpam-4316	332	5	602	CARDINAL
ejpam-4316	337	1	γ(s	PRODUCT
ejpam-4316	339	1	1	CARDINAL
ejpam-4316	339	2	2	CARDINAL
ejpam-4316	339	3	1	DATE
ejpam-4316	339	4	2	CARDINAL
ejpam-4316	343	1	w	ORG
ejpam-4316	345	1	n(n2	DATE
ejpam-4316	345	2	1	CARDINAL
ejpam-4316	346	1	1	CARDINAL
ejpam-4316	346	2	2	CARDINAL
ejpam-4316	346	3	+ 3n2	CARDINAL
ejpam-4316	346	4	4n+ 12 6	DATE
ejpam-4316	347	1	2 ≤	QUANTITY
ejpam-4316	353	1	2	CARDINAL
ejpam-4316	353	2	1	DATE
ejpam-4316	353	3	2	CARDINAL
ejpam-4316	355	1	w	GPE
ejpam-4316	357	1	− 2in+ n−	ORG
ejpam-4316	357	2	2	CARDINAL
ejpam-4316	357	3	n(n2	CARDINAL
ejpam-4316	357	4	1	CARDINAL
ejpam-4316	357	5	− 2in+ n−	ORG
ejpam-4316	357	6	2	CARDINAL
ejpam-4316	357	7	+ 3n2 + 2n+ 6i2	DATE
ejpam-4316	357	8	6in−	CARDINAL
ejpam-4316	358	1	13	CARDINAL
ejpam-4316	359	1	bipartite	NORP
ejpam-4316	359	2	graph km	PERSON
ejpam-4316	360	1	−m− n−	GPE
ejpam-4316	361	1	2nj	ORDINAL
ejpam-4316	362	1	+ 3ij	DATE
ejpam-4316	364	1	campeña	PERSON
ejpam-4316	364	2	egan	PERSON
ejpam-4316	365	1	antalan	PERSON
ejpam-4316	366	1	j. pure	PERSON
ejpam-4316	366	2	15	CARDINAL
ejpam-4316	366	3	2	CARDINAL
ejpam-4316	366	4	2022	CARDINAL
ejpam-4316	366	5	602	CARDINAL
ejpam-4316	369	1	xm	ORG
ejpam-4316	377	1	xm	ORG
ejpam-4316	379	1	′ 1	DATE
ejpam-4316	381	1	′ 1	DATE
ejpam-4316	383	1	2jm	ORDINAL
ejpam-4316	383	2	2im	ORDINAL
ejpam-4316	383	3	2	CARDINAL
ejpam-4316	384	1	2ii 3ji×j jj×m 2jj×n	DATE
ejpam-4316	384	2	2jj	ORDINAL
ejpam-4316	384	3	2ij	CARDINAL
ejpam-4316	384	4	∑ jm −	PERSON
ejpam-4316	384	5	− ii	PERSON
ejpam-4316	384	6	∑ jm×n	PERSON
ejpam-4316	384	7	∑ jn×i	GPE
ejpam-4316	384	8	3	CARDINAL
ejpam-4316	384	9	2	CARDINAL
ejpam-4316	384	10	2	CARDINAL
ejpam-4316	386	1	3.3	CARDINAL
ejpam-4316	387	1	γ(g	GPE
ejpam-4316	387	2	plavšić et al	PERSON
ejpam-4316	388	1	17	CARDINAL
ejpam-4316	389	1	11	CARDINAL
ejpam-4316	392	1	{vi	PERSON
ejpam-4316	392	2	1 2	CARDINAL
ejpam-4316	394	1	γ = γ(g	ORG
ejpam-4316	396	1	zero	CARDINAL
ejpam-4316	398	1	aij	ORG
ejpam-4316	398	2	aij	ORG
ejpam-4316	398	3	0	CARDINAL
ejpam-4316	399	1	0	CARDINAL
ejpam-4316	399	2	1	CARDINAL
ejpam-4316	399	3	∑ a.	PERSON
ejpam-4316	399	4	γ(g	GPE
ejpam-4316	400	1	5	CARDINAL
ejpam-4316	402	1	aij	ORG
ejpam-4316	403	1	at least one	CARDINAL
ejpam-4316	403	2	aij	ORG
ejpam-4316	403	3	bij	ORG
ejpam-4316	403	4	zero	CARDINAL
ejpam-4316	404	1	∑ b. proposition	PERSON
ejpam-4316	404	2	1	CARDINAL
ejpam-4316	407	1	1	CARDINAL
ejpam-4316	409	1	−a+ ∑	PERSON
ejpam-4316	409	2	1)a	CARDINAL
ejpam-4316	410	1	campeña	PERSON
ejpam-4316	410	2	egan	PERSON
ejpam-4316	411	1	antalan	PERSON
ejpam-4316	412	1	j. pure	PERSON
ejpam-4316	412	2	15	CARDINAL
ejpam-4316	412	3	2	CARDINAL
ejpam-4316	412	4	2022	CARDINAL
ejpam-4316	412	5	602	CARDINAL
ejpam-4316	413	1	∑ ci proof	PERSON
ejpam-4316	417	1	aij	ORG
ejpam-4316	418	1	aij	ORG
ejpam-4316	418	2	0	CARDINAL
ejpam-4316	418	3	1	CARDINAL
ejpam-4316	418	4	0 ≤	MONEY
ejpam-4316	418	5	1	CARDINAL
ejpam-4316	418	6	1	CARDINAL
ejpam-4316	418	7	1 aij	QUANTITY
ejpam-4316	418	8	1	CARDINAL
ejpam-4316	418	9	1	CARDINAL
ejpam-4316	418	10	aij	PRODUCT
ejpam-4316	419	1	1	CARDINAL
ejpam-4316	419	2	1)a	CARDINAL
ejpam-4316	419	3	all zero	CARDINAL
ejpam-4316	420	1	zero	CARDINAL
ejpam-4316	421	1	j. furthermore	PERSON
ejpam-4316	421	2	+ 1)a	DATE
ejpam-4316	421	3	zero	CARDINAL
ejpam-4316	421	4	+ 1	DATE
ejpam-4316	422	1	+ 1)a	DATE
ejpam-4316	422	2	5	CARDINAL
ejpam-4316	423	1	−a+ ∑	PERSON
ejpam-4316	423	2	1)a	CARDINAL
ejpam-4316	424	1	all zero	CARDINAL
ejpam-4316	425	1	5	CARDINAL
ejpam-4316	426	1	14	DATE
ejpam-4316	427	1	γ(g	GPE
ejpam-4316	427	2	h(γ	NORP
ejpam-4316	427	3	4h(g	DATE
ejpam-4316	428	1	2 3	CARDINAL
ejpam-4316	428	2	m. proof	PERSON
ejpam-4316	431	1	2×2	CARDINAL
ejpam-4316	433	1	d(g	ORG
ejpam-4316	433	2	d(g	ORG
ejpam-4316	434	1	d(g	ORG
ejpam-4316	434	2	a(g	GPE
ejpam-4316	434	3	γ	ORG
ejpam-4316	434	4	half	CARDINAL
ejpam-4316	434	5	d(γ	GPE
ejpam-4316	435	1	1 2	CARDINAL
ejpam-4316	435	2	1 2	CARDINAL
ejpam-4316	435	3	+ 2	DATE
ejpam-4316	435	4	+ 2	DATE
ejpam-4316	436	1	1 2	CARDINAL
ejpam-4316	437	1	2	CARDINAL
ejpam-4316	438	1	2	CARDINAL
ejpam-4316	438	2	d(g)−a(g	GPE
ejpam-4316	440	1	1 2	CARDINAL
ejpam-4316	440	2	+ 2 ∑ 2	QUANTITY
ejpam-4316	441	1	campeña	PERSON
ejpam-4316	441	2	egan	PERSON
ejpam-4316	442	1	antalan	PERSON
ejpam-4316	443	1	j. pure	PERSON
ejpam-4316	443	2	15	CARDINAL
ejpam-4316	443	3	2	CARDINAL
ejpam-4316	443	4	2022	CARDINAL
ejpam-4316	443	5	602	CARDINAL
ejpam-4316	443	6	4	CARDINAL
ejpam-4316	444	1	2	CARDINAL
ejpam-4316	444	2	1 2 ∑ a(g	QUANTITY
ejpam-4316	444	3	4h(g	DATE
ejpam-4316	445	1	1 2 ∑ a(g	QUANTITY
ejpam-4316	445	2	4h(g	DATE
ejpam-4316	446	1	2	CARDINAL
ejpam-4316	446	2	3	CARDINAL
ejpam-4316	446	3	1 2	CARDINAL
ejpam-4316	446	4	2	CARDINAL
ejpam-4316	446	5	4h(g	DATE
ejpam-4316	447	1	3	CARDINAL
ejpam-4316	447	2	4h(g	DATE
ejpam-4316	448	1	2	CARDINAL
ejpam-4316	448	2	3	CARDINAL
ejpam-4316	450	1	h(γ	ORG
ejpam-4316	450	2	2	CARDINAL
ejpam-4316	451	1	1 6	DATE
ejpam-4316	454	1	h(γ	NORP
ejpam-4316	455	1	25 6	DATE
ejpam-4316	457	1	5	CARDINAL
ejpam-4316	458	1	sn	ORG
ejpam-4316	459	1	sn	ORG
ejpam-4316	459	2	h(γ	ORG
ejpam-4316	459	3	1 6	CARDINAL
ejpam-4316	462	1	15	CARDINAL
ejpam-4316	463	1	2	CARDINAL
ejpam-4316	463	2	1	CARDINAL
ejpam-4316	463	3	γ(g	GPE
ejpam-4316	463	4	h(γ	NORP
ejpam-4316	463	5	4h(g	DATE
ejpam-4316	467	1	d(g	ORG
ejpam-4316	467	2	d(g	ORG
ejpam-4316	468	1	d(g	ORG
ejpam-4316	468	2	a(g	GPE
ejpam-4316	470	1	campeña	PERSON
ejpam-4316	470	2	egan	PERSON
ejpam-4316	471	1	antalan	PERSON
ejpam-4316	472	1	j. pure	PERSON
ejpam-4316	472	2	15	CARDINAL
ejpam-4316	472	3	2	CARDINAL
ejpam-4316	472	4	2022	CARDINAL
ejpam-4316	472	5	602	CARDINAL
ejpam-4316	473	1	1 2	CARDINAL
ejpam-4316	473	2	1 2	CARDINAL
ejpam-4316	473	3	+ 2	DATE
ejpam-4316	473	4	+ 2	DATE
ejpam-4316	474	1	1 2	CARDINAL
ejpam-4316	475	1	2	CARDINAL
ejpam-4316	476	1	2	CARDINAL
ejpam-4316	476	2	d(g)−a(g	GPE
ejpam-4316	476	3	2a(g	TIME
ejpam-4316	478	1	1 2	CARDINAL
ejpam-4316	478	2	+ 2 ∑ 2	QUANTITY
ejpam-4316	479	1	4	CARDINAL
ejpam-4316	480	1	2	CARDINAL
ejpam-4316	480	2	2a(g)− 1 2 ∑	TIME
ejpam-4316	480	3	4h(g	DATE
ejpam-4316	481	1	2a(g)− 1 2 ∑	TIME
ejpam-4316	481	2	h(γ	NORP
ejpam-4316	481	3	4h(g	DATE
ejpam-4316	482	1	2	CARDINAL
ejpam-4316	482	2	2	CARDINAL
ejpam-4316	482	3	1 2	CARDINAL
ejpam-4316	482	4	2	CARDINAL
ejpam-4316	482	5	4h(g	DATE
ejpam-4316	483	1	2	CARDINAL
ejpam-4316	483	2	4h(g	DATE
ejpam-4316	484	1	2	CARDINAL
ejpam-4316	485	1	6	CARDINAL
ejpam-4316	487	1	kn	PERSON
ejpam-4316	487	2	h(γ	ORG
ejpam-4316	487	3	1 4	CARDINAL
ejpam-4316	487	4	5n	CARDINAL
ejpam-4316	490	1	w	ORG
ejpam-4316	491	1	1	CARDINAL
ejpam-4316	492	1	16	CARDINAL
ejpam-4316	493	1	n ≥ 3	DATE
ejpam-4316	493	2	1 ≤	QUANTITY
ejpam-4316	493	3	1	CARDINAL
ejpam-4316	494	1	kn	PERSON
ejpam-4316	496	1	2n2−2n+r2−3r+4nr 4	DATE
ejpam-4316	506	1	′ 1	DATE
ejpam-4316	506	2	2	CARDINAL
ejpam-4316	507	1	r.	NORP
ejpam-4316	509	1	a(kr)	DATE
ejpam-4316	510	1	2ir	ORDINAL
ejpam-4316	512	1	2ir	ORDINAL
ejpam-4316	512	2	2a(kr	CARDINAL
ejpam-4316	513	1	campeña	PERSON
ejpam-4316	513	2	egan	PERSON
ejpam-4316	514	1	antalan	PERSON
ejpam-4316	515	1	j. pure	PERSON
ejpam-4316	515	2	15	CARDINAL
ejpam-4316	515	3	2	CARDINAL
ejpam-4316	515	4	2022	CARDINAL
ejpam-4316	515	5	602-619 617	QUANTITY
ejpam-4316	515	6	a(kr	DATE
ejpam-4316	515	7	ir	ORG
ejpam-4316	515	8	kn	PERSON
ejpam-4316	515	9	kr	ORG
ejpam-4316	516	1	h(γ	ORG
ejpam-4316	517	1	1 2	CARDINAL
ejpam-4316	517	2	1 2	CARDINAL
ejpam-4316	518	1	1 2	CARDINAL
ejpam-4316	520	1	2a(kr	CARDINAL
ejpam-4316	522	1	+ 1 2 ∑	QUANTITY
ejpam-4316	522	2	jr×n−r = h(kn	WORK_OF_ART
ejpam-4316	524	1	2ir	ORDINAL
ejpam-4316	524	2	2a(kr	CARDINAL
ejpam-4316	526	1	+ 1 2 ∑	QUANTITY
ejpam-4316	526	2	jr×n−r =	PERSON
ejpam-4316	526	3	1	CARDINAL
ejpam-4316	526	4	2	CARDINAL
ejpam-4316	527	1	2|e(kr)| 2	DATE
ejpam-4316	527	2	n− r)r	ORG
ejpam-4316	527	3	1	CARDINAL
ejpam-4316	527	4	2	CARDINAL
ejpam-4316	528	1	2	CARDINAL
ejpam-4316	528	2	1	CARDINAL
ejpam-4316	528	3	2	CARDINAL
ejpam-4316	529	1	2 +	CARDINAL
ejpam-4316	529	2	1	CARDINAL
ejpam-4316	529	3	2	CARDINAL
ejpam-4316	530	1	1	CARDINAL
ejpam-4316	530	2	2	CARDINAL
ejpam-4316	531	1	2 +	CARDINAL
ejpam-4316	531	2	1	CARDINAL
ejpam-4316	532	1	5r	CARDINAL
ejpam-4316	533	1	2 +	CARDINAL
ejpam-4316	533	2	2n2	CARDINAL
ejpam-4316	533	3	2n+	CARDINAL
ejpam-4316	533	4	3r	CARDINAL
ejpam-4316	533	5	theorems	GPE
ejpam-4316	533	6	13	CARDINAL
ejpam-4316	534	1	17	CARDINAL
ejpam-4316	535	1	∈	ORG
ejpam-4316	536	1	2k + 1	DATE
ejpam-4316	536	2	h(γ(g	ORG
ejpam-4316	536	3	1 2	CARDINAL
ejpam-4316	536	4	2 +	DATE
ejpam-4316	537	1	h(γ(g	ORG
ejpam-4316	537	2	1 2	CARDINAL
ejpam-4316	537	3	2 +	DATE
ejpam-4316	538	1	18	CARDINAL
ejpam-4316	542	1	n ≥ 2	DATE
ejpam-4316	542	2	1)hn−1	CARDINAL
ejpam-4316	542	3	3 2	CARDINAL
ejpam-4316	542	4	2 ≤	QUANTITY
ejpam-4316	545	1	+ 1 2	DATE
ejpam-4316	546	1	19	CARDINAL
ejpam-4316	547	1	bipartite	NORP
ejpam-4316	547	2	graph km	PERSON
ejpam-4316	548	1	h(γ	NORP
ejpam-4316	548	2	1 4	DATE
ejpam-4316	548	3	−m− n−	GPE
ejpam-4316	549	1	3 + mi	DATE
ejpam-4316	550	1	618	CARDINAL
ejpam-4316	550	2	central luzon state university	ORG
ejpam-4316	550	3	de la salle university	ORG
ejpam-4316	552	1	1	CARDINAL
ejpam-4316	552	2	f. abedin	PERSON
ejpam-4316	552	3	b. roughton	PERSON
ejpam-4316	552	4	p. spencer	PERSON
ejpam-4316	552	5	q. ye	PERSON
ejpam-4316	552	6	k. camarda	PERSON
ejpam-4316	554	1	krist v. gernaey	ORG
ejpam-4316	554	2	jakob k. huusom	PERSON
ejpam-4316	554	3	gani	ORG
ejpam-4316	554	4	12th	ORDINAL
ejpam-4316	554	5	25th	ORDINAL
ejpam-4316	554	6	37	CARDINAL
ejpam-4316	554	7	2081–2086	CARDINAL
ejpam-4316	555	1	2015	DATE
ejpam-4316	556	1	2	CARDINAL
ejpam-4316	557	1	topological	ORG
ejpam-4316	558	1	chemical physics letters	ORG
ejpam-4316	558	2	89(5):399–404	ORG
ejpam-4316	558	3	1982	DATE
ejpam-4316	559	1	3	CARDINAL
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ejpam-4316	560	1	arxiv preprint arxiv:1704.05476, 2017.	ORG
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ejpam-4316	577	1	addison-wesley publishing company, inc.	ORG
ejpam-4316	577	2	1969	DATE
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ejpam-4316	580	1	arxiv preprint arxiv:2008.07350	ORG
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ejpam-4316	584	1	12(1):309–318, 1993	DATE
ejpam-4316	585	1	619	CARDINAL
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ejpam-4316	594	1	34, 1994	DATE
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ejpam-4316	600	1	308:242–254	DATE
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ejpam-4316	603	1	12(1):235–250, 1993	DATE
ejpam-4316	604	1	18	CARDINAL
ejpam-4316	606	1	american	NORP
ejpam-4316	606	2	61(6):729–735, 1973	DATE
ejpam-4316	607	1	19	CARDINAL
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ejpam-4316	608	1	the karnatak university	ORG
ejpam-4316	608	2	25(13):13–16	CARDINAL
ejpam-4316	608	3	1980	DATE
ejpam-4316	609	1	20	CARDINAL
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ejpam-4316	610	1	2020	DATE
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ejpam-4316	613	1	235(1):237–244, 2001	DATE
ejpam-4316	614	1	chech	ORG
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ejpam-4316	615	1	22	CARDINAL
ejpam-4316	616	1	wolfram mathworld	PERSON
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ejpam-4316	620	1	2009	DATE
ejpam-4316	621	1	24	CARDINAL
ejpam-4316	623	1	american	NORP
ejpam-4316	623	2	69(1):17–20, 1947	DATE
ejpam-4316	624	1	20291038	DATE
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ejpam-4316	625	2	yeh	PERSON
ejpam-4316	625	3	i. gutman	PERSON
ejpam-4316	627	1	135(1):359–365, 1994	DATE