id	sid	eid	entity	type
ejpam-4750	1	1	european journal	ORG
ejpam-4750	2	1	16	CARDINAL
ejpam-4750	2	2	2	CARDINAL
ejpam-4750	2	3	2023	CARDINAL
ejpam-4750	2	4	1068-1083	CARDINAL
ejpam-4750	2	5	1307-5543	DATE
ejpam-4750	2	6	new york	GPE
ejpam-4750	2	7	2-metric	QUANTITY
ejpam-4750	2	8	dennis b. managbanag1,∗	PERSON
ejpam-4750	2	9	helen m. rara2	PERSON
ejpam-4750	3	1	1	CARDINAL
ejpam-4750	3	2	mindanao state university-iligan institute of technology	ORG
ejpam-4750	3	3	9200	CARDINAL
ejpam-4750	3	4	iligan city	GPE
ejpam-4750	3	5	philippines 2 department	ORG
ejpam-4750	3	6	mindanao state university-iligan institute of technology	ORG
ejpam-4750	3	7	9200	CARDINAL
ejpam-4750	3	8	iligan city	GPE
ejpam-4750	3	9	philippines	GPE
ejpam-4750	4	1	2-metric	QUANTITY
ejpam-4750	5	1	2-metric	QUANTITY
ejpam-4750	5	2	2-metric	QUANTITY
ejpam-4750	6	1	2-metric	QUANTITY
ejpam-4750	7	1	2020	DATE
ejpam-4750	7	2	05c69	CARDINAL
ejpam-4750	7	3	2	CARDINAL
ejpam-4750	7	4	2-metric	QUANTITY
ejpam-4750	7	5	2-metric	QUANTITY
ejpam-4750	7	6	1	CARDINAL
ejpam-4750	8	1	blumenthal [3	PERSON
ejpam-4750	8	2	1953	DATE
ejpam-4750	9	1	2	CARDINAL
ejpam-4750	10	1	nearly 20 years	DATE
ejpam-4750	10	2	1976	DATE
ejpam-4750	10	3	5	CARDINAL
ejpam-4750	10	4	11	CARDINAL
ejpam-4750	10	5	12	CARDINAL
ejpam-4750	11	1	2019	DATE
ejpam-4750	11	2	bailey	GPE
ejpam-4750	11	3	1	CARDINAL
ejpam-4750	12	1	2	CARDINAL
ejpam-4750	12	2	j. cabaro	PERSON
ejpam-4750	12	3	h. rara	PERSON
ejpam-4750	13	1	4	CARDINAL
ejpam-4750	13	2	2021	CARDINAL
ejpam-4750	14	1	1987	DATE
ejpam-4750	14	2	klein	PERSON
ejpam-4750	14	3	8	CARDINAL
ejpam-4750	15	1	1991	DATE
ejpam-4750	15	2	∗corresponding	PERSON
ejpam-4750	16	1	d.	NORP
ejpam-4750	16	2	helen.rara@g.msuiit.edu.ph	GPE
ejpam-4750	16	3	h. rara	PERSON
ejpam-4750	16	4	1068	CARDINAL
ejpam-4750	17	1	2023	CARDINAL
ejpam-4750	18	1	d. managbanag	PERSON
ejpam-4750	18	2	h. rara	PERSON
ejpam-4750	19	1	j. pure	PERSON
ejpam-4750	19	2	16	CARDINAL
ejpam-4750	19	3	2	CARDINAL
ejpam-4750	19	4	2023	CARDINAL
ejpam-4750	19	5	1068-1083 1069	CARDINAL
ejpam-4750	20	1	al	PERSON
ejpam-4750	21	1	6	CARDINAL
ejpam-4750	22	1	1999	DATE
ejpam-4750	22	2	chartrand et	ORG
ejpam-4750	23	1	al	PERSON
ejpam-4750	24	1	13	CARDINAL
ejpam-4750	25	1	2	CARDINAL
ejpam-4750	27	1	2	CARDINAL
ejpam-4750	28	1	2.	CARDINAL
ejpam-4750	29	1	1	CARDINAL
ejpam-4750	29	2	4	DATE
ejpam-4750	29	3	9	DATE
ejpam-4750	29	4	10	CARDINAL
ejpam-4750	30	1	⊆	CARDINAL
ejpam-4750	32	1	w.	PERSON
ejpam-4750	32	2	∈	ORG
ejpam-4750	33	1	1	CARDINAL
ejpam-4750	33	2	2	CARDINAL
ejpam-4750	33	3	2	CARDINAL
ejpam-4750	33	4	2	CARDINAL
ejpam-4750	33	5	2-metric	QUANTITY
ejpam-4750	34	1	2-metric	QUANTITY
ejpam-4750	34	2	⊆	CARDINAL
ejpam-4750	35	1	⊆	CARDINAL
ejpam-4750	35	2	2	CARDINAL
ejpam-4750	36	1	2	CARDINAL
ejpam-4750	38	1	∈	ORG
ejpam-4750	39	1	2	CARDINAL
ejpam-4750	39	2	2	CARDINAL
ejpam-4750	39	3	2	CARDINAL
ejpam-4750	39	4	⊆	CARDINAL
ejpam-4750	40	1	2,2)-locating	CARDINAL
ejpam-4750	40	2	2,1)-locating	CARDINAL
ejpam-4750	40	3	2	CARDINAL
ejpam-4750	40	4	1	CARDINAL
ejpam-4750	41	1	2,2)-locating	CARDINAL
ejpam-4750	41	2	2,1)-locating	CARDINAL
ejpam-4750	41	3	ln(2,1)(g	PERSON
ejpam-4750	41	4	2,2)-locating	CARDINAL
ejpam-4750	41	5	2,1)-locating	CARDINAL
ejpam-4750	41	6	2,2)-locating	CARDINAL
ejpam-4750	41	7	2,1)-locating	CARDINAL
ejpam-4750	41	8	ln(2,1)(g	PERSON
ejpam-4750	41	9	2-metric	QUANTITY
ejpam-4750	41	10	w	ORG
ejpam-4750	41	11	w	GPE
ejpam-4750	41	12	2-metric	QUANTITY
ejpam-4750	41	13	2-metric	QUANTITY
ejpam-4750	41	14	w	GPE
ejpam-4750	43	1	2-metric	QUANTITY
ejpam-4750	44	1	2-metric	QUANTITY
ejpam-4750	45	1	d. managbanag	GPE
ejpam-4750	45	2	h. rara	PERSON
ejpam-4750	46	1	j. pure	PERSON
ejpam-4750	46	2	16	CARDINAL
ejpam-4750	46	3	2	CARDINAL
ejpam-4750	46	4	2023	CARDINAL
ejpam-4750	46	5	1068-1083	CARDINAL
ejpam-4750	47	1	w	GPE
ejpam-4750	47	2	2	CARDINAL
ejpam-4750	47	3	w	ORG
ejpam-4750	48	1	2	CARDINAL
ejpam-4750	50	1	w	ORG
ejpam-4750	50	2	w	GPE
ejpam-4750	50	3	2	CARDINAL
ejpam-4750	50	4	w	ORG
ejpam-4750	51	1	2	CARDINAL
ejpam-4750	51	2	min{fln(2,2)(w	PERSON
ejpam-4750	53	1	3	CARDINAL
ejpam-4750	53	2	4	CARDINAL
ejpam-4750	54	1	1	CARDINAL
ejpam-4750	55	1	n ≥ 2	ORG
ejpam-4750	55	2	2 ≤	QUANTITY
ejpam-4750	55	3	n ≥ 2	DATE
ejpam-4750	55	4	1	CARDINAL
ejpam-4750	56	1	2	CARDINAL
ejpam-4750	57	1	1	CARDINAL
ejpam-4750	57	2	2	CARDINAL
ejpam-4750	57	3	n ≥ 2	ORG
ejpam-4750	58	1	1	CARDINAL
ejpam-4750	61	1	1 2	CARDINAL
ejpam-4750	61	2	n ≥ 3	DATE
ejpam-4750	62	1	1 2	CARDINAL
ejpam-4750	62	2	n ≥ 5	DATE
ejpam-4750	63	1	2	CARDINAL
ejpam-4750	63	2	2,2)-locating	CARDINAL
ejpam-4750	65	1	4	CARDINAL
ejpam-4750	65	2	1 2	CARDINAL
ejpam-4750	66	1	n ≥ 8	DATE
ejpam-4750	66	2	1 2	CARDINAL
ejpam-4750	67	1	d. managbanag	PERSON
ejpam-4750	67	2	h. rara	PERSON
ejpam-4750	68	1	j. pure	PERSON
ejpam-4750	68	2	16	CARDINAL
ejpam-4750	68	3	2	CARDINAL
ejpam-4750	68	4	2023	CARDINAL
ejpam-4750	68	5	1068-1083 1071	QUANTITY
ejpam-4750	68	6	2	CARDINAL
ejpam-4750	69	1	⊆	CARDINAL
ejpam-4750	69	2	2	CARDINAL
ejpam-4750	70	1	2,2)-locating	CARDINAL
ejpam-4750	70	2	2,1)-locating	CARDINAL
ejpam-4750	72	1	2	CARDINAL
ejpam-4750	73	1	2	CARDINAL
ejpam-4750	73	2	2,2)-locating	CARDINAL
ejpam-4750	74	1	2,1)-locating	CARDINAL
ejpam-4750	75	1	4	CARDINAL
ejpam-4750	77	1	⊆	CARDINAL
ejpam-4750	77	2	2	CARDINAL
ejpam-4750	78	1	⊆	CARDINAL
ejpam-4750	78	2	⋃	DATE
ejpam-4750	78	3	{sv : sv	PERSON
ejpam-4750	78	4	2	CARDINAL
ejpam-4750	78	5	∈	ORG
ejpam-4750	79	1	2	CARDINAL
ejpam-4750	80	1	⊆	CARDINAL
ejpam-4750	80	2	∈	ORG
ejpam-4750	81	1	1	CARDINAL
ejpam-4750	81	2	∈	ORG
ejpam-4750	81	3	2	CARDINAL
ejpam-4750	82	1	4	CARDINAL
ejpam-4750	82	2	2-metric	QUANTITY
ejpam-4750	82	3	3	CARDINAL
ejpam-4750	84	1	0 ≤	MONEY
ejpam-4750	85	1	4	CARDINAL
ejpam-4750	87	1	0	CARDINAL
ejpam-4750	88	1	2-metric	QUANTITY
ejpam-4750	88	2	1	CARDINAL
ejpam-4750	88	3	at least two	CARDINAL
ejpam-4750	88	4	2-metric	QUANTITY
ejpam-4750	88	5	one	CARDINAL
ejpam-4750	88	6	2-metric	QUANTITY
ejpam-4750	91	1	2-metric	QUANTITY
ejpam-4750	91	2	\d	ORG
ejpam-4750	91	3	2-metric	QUANTITY
ejpam-4750	92	1	2-metric	QUANTITY
ejpam-4750	93	1	∈	ORG
ejpam-4750	93	2	\d	ORG
ejpam-4750	93	3	2-metric	QUANTITY
ejpam-4750	93	4	2-metric	QUANTITY
ejpam-4750	94	1	2-metric	QUANTITY
ejpam-4750	95	1	w /∈ j	PERSON
ejpam-4750	96	1	w ∈ k.	PERSON
ejpam-4750	96	2	vw ∈	ORG
ejpam-4750	96	3	\d	ORG
ejpam-4750	96	4	2-metric	QUANTITY
ejpam-4750	97	1	2-metric	QUANTITY
ejpam-4750	99	1	d. managbanag	PERSON
ejpam-4750	99	2	h. rara	PERSON
ejpam-4750	100	1	j. pure	PERSON
ejpam-4750	100	2	16	CARDINAL
ejpam-4750	100	3	2	CARDINAL
ejpam-4750	100	4	2023	CARDINAL
ejpam-4750	100	5	1068-1083	CARDINAL
ejpam-4750	100	6	2	CARDINAL
ejpam-4750	101	1	1	CARDINAL
ejpam-4750	102	1	kn	PERSON
ejpam-4750	102	2	kn	PERSON
ejpam-4750	102	3	2	CARDINAL
ejpam-4750	102	4	kn	PERSON
ejpam-4750	103	1	4	CARDINAL
ejpam-4750	103	2	0	CARDINAL
ejpam-4750	103	3	3	CARDINAL
ejpam-4750	104	1	n ≥ 2 vertices	ORG
ejpam-4750	108	1	2	CARDINAL
ejpam-4750	108	2	2-metric	QUANTITY
ejpam-4750	108	3	{vi	PERSON
ejpam-4750	108	4	1 ≤	QUANTITY
ejpam-4750	109	1	1	CARDINAL
ejpam-4750	109	2	1	CARDINAL
ejpam-4750	110	1	j = 2	PERSON
ejpam-4750	110	2	0	CARDINAL
ejpam-4750	110	3	1	CARDINAL
ejpam-4750	110	4	2	CARDINAL
ejpam-4750	110	5	1	CARDINAL
ejpam-4750	111	1	2	CARDINAL
ejpam-4750	113	1	2	CARDINAL
ejpam-4750	113	2	j, 1	WORK_OF_ART
ejpam-4750	114	1	2	CARDINAL
ejpam-4750	114	2	1	CARDINAL
ejpam-4750	115	1	+ 1	DATE
ejpam-4750	115	2	0	CARDINAL
ejpam-4750	115	3	1	CARDINAL
ejpam-4750	115	4	2	CARDINAL
ejpam-4750	115	5	1	CARDINAL
ejpam-4750	116	1	1	CARDINAL
ejpam-4750	116	2	2	CARDINAL
ejpam-4750	116	3	1	CARDINAL
ejpam-4750	118	1	+ 1	DATE
ejpam-4750	119	1	1	CARDINAL
ejpam-4750	120	1	1	CARDINAL
ejpam-4750	121	1	1	CARDINAL
ejpam-4750	121	2	2	CARDINAL
ejpam-4750	121	3	2	CARDINAL
ejpam-4750	123	1	4	CARDINAL
ejpam-4750	124	1	2	CARDINAL
ejpam-4750	125	1	4	CARDINAL
ejpam-4750	126	1	3	CARDINAL
ejpam-4750	126	2	0	DATE
ejpam-4750	126	3	3	CARDINAL
ejpam-4750	126	4	n ≥ 5	DATE
ejpam-4750	129	1	un	ORG
ejpam-4750	130	1	3	CARDINAL
ejpam-4750	130	2	4	DATE
ejpam-4750	130	3	2	CARDINAL
ejpam-4750	131	1	4	CARDINAL
ejpam-4750	133	1	n ≥ 5	DATE
ejpam-4750	135	1	2	CARDINAL
ejpam-4750	135	2	2	CARDINAL
ejpam-4750	136	1	3	CARDINAL
ejpam-4750	136	2	ub	ORG
ejpam-4750	136	3	uc	ORG
ejpam-4750	136	4	2-metric	QUANTITY
ejpam-4750	136	5	2-metric	QUANTITY
ejpam-4750	136	6	∈	ORG
ejpam-4750	136	7	\s	ORG
ejpam-4750	136	8	2-metric	QUANTITY
ejpam-4750	136	9	5	CARDINAL
ejpam-4750	137	1	3	CARDINAL
ejpam-4750	137	2	5	CARDINAL
ejpam-4750	138	1	2	CARDINAL
ejpam-4750	138	2	2,2)-locating	CARDINAL
ejpam-4750	138	3	5	CARDINAL
ejpam-4750	140	1	0	CARDINAL
ejpam-4750	141	1	1	CARDINAL
ejpam-4750	141	2	at least two	CARDINAL
ejpam-4750	141	3	one	CARDINAL
ejpam-4750	141	4	g. d. managbanag	PERSON
ejpam-4750	141	5	h. rara	PERSON
ejpam-4750	142	1	j. pure	PERSON
ejpam-4750	142	2	16	CARDINAL
ejpam-4750	142	3	2	CARDINAL
ejpam-4750	142	4	2023	CARDINAL
ejpam-4750	142	5	1068	CARDINAL
ejpam-4750	142	6	6	CARDINAL
ejpam-4750	144	1	2	CARDINAL
ejpam-4750	146	1	∪{vu	ORG
ejpam-4750	147	1	2	CARDINAL
ejpam-4750	149	1	w ∈ i.	PERSON
ejpam-4750	149	2	vw ∈	ORG
ejpam-4750	149	3	\s	ORG
ejpam-4750	149	4	j = h∪t	PERSON
ejpam-4750	151	1	5	CARDINAL
ejpam-4750	153	1	1	CARDINAL
ejpam-4750	153	2	kn	PERSON
ejpam-4750	154	1	5	CARDINAL
ejpam-4750	155	1	0	CARDINAL
ejpam-4750	155	2	6	CARDINAL
ejpam-4750	156	1	2	CARDINAL
ejpam-4750	158	1	un−1	PERSON
ejpam-4750	158	2	un	ORG
ejpam-4750	158	3	n ≥ 2	DATE
ejpam-4750	159	1	un−1	PERSON
ejpam-4750	159	2	un	ORG
ejpam-4750	159	3	∩ s ̸=	WORK_OF_ART
ejpam-4750	159	4	ui+1	ORG
ejpam-4750	159	5	1 ≤	QUANTITY
ejpam-4750	159	6	6	CARDINAL
ejpam-4750	160	1	n ≥ 2 vertices	ORG
ejpam-4750	160	2	2	CARDINAL
ejpam-4750	160	3	3	DATE
ejpam-4750	160	4	1	CARDINAL
ejpam-4750	160	5	5	CARDINAL
ejpam-4750	160	6	2	DATE
ejpam-4750	160	7	3	CARDINAL
ejpam-4750	163	1	un	ORG
ejpam-4750	164	1	1	CARDINAL
ejpam-4750	164	2	2	CARDINAL
ejpam-4750	164	3	3	CARDINAL
ejpam-4750	165	1	5	CARDINAL
ejpam-4750	166	1	0	CARDINAL
ejpam-4750	166	2	5	CARDINAL
ejpam-4750	166	3	1	CARDINAL
ejpam-4750	167	1	3	CARDINAL
ejpam-4750	167	2	6	CARDINAL
ejpam-4750	168	1	5	CARDINAL
ejpam-4750	168	2	1	CARDINAL
ejpam-4750	169	1	6	CARDINAL
ejpam-4750	169	2	u4}	PERSON
ejpam-4750	169	3	u4}	PERSON
ejpam-4750	172	1	3	CARDINAL
ejpam-4750	172	2	6	CARDINAL
ejpam-4750	172	3	6	CARDINAL
ejpam-4750	172	4	d. managbanag	GPE
ejpam-4750	172	5	h. rara	PERSON
ejpam-4750	173	1	j. pure	PERSON
ejpam-4750	173	2	16	CARDINAL
ejpam-4750	173	3	2	CARDINAL
ejpam-4750	173	4	2023	CARDINAL
ejpam-4750	173	5	1068-1083	CARDINAL
ejpam-4750	173	6	u4, u5}	ORG
ejpam-4750	173	7	s5	GPE
ejpam-4750	173	8	u4, u5	ORG
ejpam-4750	173	9	s6	GPE
ejpam-4750	176	1	2	CARDINAL
ejpam-4750	177	1	n ≥ 7 and n	ORG
ejpam-4750	178	1	6	CARDINAL
ejpam-4750	178	2	u5	PERSON
ejpam-4750	180	1	un−2	GPE
ejpam-4750	180	2	un	ORG
ejpam-4750	182	1	0	CARDINAL
ejpam-4750	182	2	5	CARDINAL
ejpam-4750	183	1	n ≥ 8	DATE
ejpam-4750	186	1	un−2	GPE
ejpam-4750	186	2	un	ORG
ejpam-4750	188	1	un−2	GPE
ejpam-4750	188	2	un	ORG
ejpam-4750	188	3	m3	CARDINAL
ejpam-4750	188	4	u5	PERSON
ejpam-4750	190	1	un−2	GPE
ejpam-4750	190	2	u5	PERSON
ejpam-4750	192	1	un−2	GPE
ejpam-4750	192	2	un	ORG
ejpam-4750	192	3	u5	PERSON
ejpam-4750	194	1	un−1	PERSON
ejpam-4750	194	2	un	ORG
ejpam-4750	196	1	un−2	GPE
ejpam-4750	196	2	un	ORG
ejpam-4750	196	3	6	CARDINAL
ejpam-4750	197	1	⊆	CARDINAL
ejpam-4750	197	2	2	CARDINAL
ejpam-4750	197	3	7	CARDINAL
ejpam-4750	198	1	2	CARDINAL
ejpam-4750	200	1	n ≥ 3	DATE
ejpam-4750	201	1	⊆	CARDINAL
ejpam-4750	202	1	∈ w	ORG
ejpam-4750	203	1	1 ≤ j ≤	QUANTITY
ejpam-4750	206	1	3	CARDINAL
ejpam-4750	206	2	3	CARDINAL
ejpam-4750	206	3	4	DATE
ejpam-4750	206	4	1	DATE
ejpam-4750	206	5	2	CARDINAL
ejpam-4750	206	6	n ≥ 7 is odd,	ORG
ejpam-4750	206	7	3	CARDINAL
ejpam-4750	209	1	un	ORG
ejpam-4750	212	1	2	CARDINAL
ejpam-4750	213	1	5	CARDINAL
ejpam-4750	213	2	0	CARDINAL
ejpam-4750	213	3	5	CARDINAL
ejpam-4750	213	4	1	CARDINAL
ejpam-4750	214	1	3	CARDINAL
ejpam-4750	214	2	j = v	PERSON
ejpam-4750	214	3	{vi	PERSON
ejpam-4750	214	4	j ∈	PERSON
ejpam-4750	214	5	1	CARDINAL
ejpam-4750	214	6	2	DATE
ejpam-4750	215	1	5	CARDINAL
ejpam-4750	215	2	c5	ORG
ejpam-4750	216	1	vi ∈	PERSON
ejpam-4750	216	2	{vi	PERSON
ejpam-4750	216	3	k	PERSON
ejpam-4750	216	4	c5	GPE
ejpam-4750	217	1	6, fln2(c5	DATE
ejpam-4750	218	1	3	CARDINAL
ejpam-4750	219	1	n ≥ 6	DATE
ejpam-4750	220	1	1	CARDINAL
ejpam-4750	221	1	2	CARDINAL
ejpam-4750	222	1	u5	PERSON
ejpam-4750	224	1	un−1	PERSON
ejpam-4750	226	1	un	ORG
ejpam-4750	227	1	d1 d. managbanag	ORG
ejpam-4750	227	2	h. rara	PERSON
ejpam-4750	228	1	j. pure	PERSON
ejpam-4750	228	2	16	CARDINAL
ejpam-4750	228	3	2	CARDINAL
ejpam-4750	228	4	2023	CARDINAL
ejpam-4750	228	5	1068-1083 1075	CARDINAL
ejpam-4750	229	1	5	CARDINAL
ejpam-4750	230	1	1	CARDINAL
ejpam-4750	230	2	n ≥ 7 and n	ORG
ejpam-4750	231	1	1	CARDINAL
ejpam-4750	232	1	1 2	CARDINAL
ejpam-4750	233	1	7	CARDINAL
ejpam-4750	233	2	ui	ORG
ejpam-4750	233	3	ui+1	ORG
ejpam-4750	235	1	ui−4	ORG
ejpam-4750	235	2	1 ≤ i ≤	QUANTITY
ejpam-4750	237	1	1	CARDINAL
ejpam-4750	237	2	fln2(si	ORG
ejpam-4750	237	3	2	CARDINAL
ejpam-4750	238	1	8	CARDINAL
ejpam-4750	240	1	0	CARDINAL
ejpam-4750	241	1	1	CARDINAL
ejpam-4750	241	2	at least two	CARDINAL
ejpam-4750	241	3	one	CARDINAL
ejpam-4750	241	4	g. theorem 7	ORG
ejpam-4750	245	1	2	CARDINAL
ejpam-4750	249	1	∪{vu	ORG
ejpam-4750	253	1	w ∈ i.	PERSON
ejpam-4750	253	2	vw ∈	ORG
ejpam-4750	257	1	9	CARDINAL
ejpam-4750	258	1	2,2)-locating	CARDINAL
ejpam-4750	259	1	1	CARDINAL
ejpam-4750	259	2	2,2)-locating	CARDINAL
ejpam-4750	260	1	8	CARDINAL
ejpam-4750	261	1	n ≥ 4 vertices	ORG
ejpam-4750	261	2	2	CARDINAL
ejpam-4750	261	3	n ≥ 8	DATE
ejpam-4750	261	4	3	CARDINAL
ejpam-4750	261	5	6	CARDINAL
ejpam-4750	261	6	4	DATE
ejpam-4750	266	1	8	CARDINAL
ejpam-4750	266	2	0	CARDINAL
ejpam-4750	266	3	5	CARDINAL
ejpam-4750	266	4	2	CARDINAL
ejpam-4750	266	5	4	CARDINAL
ejpam-4750	266	6	d. managbanag	GPE
ejpam-4750	266	7	h. rara	PERSON
ejpam-4750	267	1	j. pure	PERSON
ejpam-4750	267	2	16	CARDINAL
ejpam-4750	267	3	2	CARDINAL
ejpam-4750	267	4	2023	CARDINAL
ejpam-4750	267	5	1068-1083	CARDINAL
ejpam-4750	267	6	q5	ORG
ejpam-4750	268	1	∈	ORG
ejpam-4750	269	1	k ∈	PERSON
ejpam-4750	269	2	1	CARDINAL
ejpam-4750	269	3	2	DATE
ejpam-4750	269	4	3	DATE
ejpam-4750	269	5	4	DATE
ejpam-4750	269	6	5	CARDINAL
ejpam-4750	269	7	2)-set	CARDINAL
ejpam-4750	270	1	7	CARDINAL
ejpam-4750	270	2	4	CARDINAL
ejpam-4750	270	3	6	CARDINAL
ejpam-4750	270	4	2	CARDINAL
ejpam-4750	271	1	4	CARDINAL
ejpam-4750	273	1	fln(2,2)(p6	WORK_OF_ART
ejpam-4750	274	1	3	CARDINAL
ejpam-4750	274	2	n ≥ 7 and n	ORG
ejpam-4750	275	1	2	CARDINAL
ejpam-4750	276	1	1 2	CARDINAL
ejpam-4750	278	1	2)-set	CARDINAL
ejpam-4750	279	1	8	CARDINAL
ejpam-4750	280	1	n ≥ 8	DATE
ejpam-4750	283	1	t3	ORG
ejpam-4750	285	1	vn−3	ORG
ejpam-4750	285	2	vn−2	GPE
ejpam-4750	285	3	t4	PERSON
ejpam-4750	287	1	vn−3	ORG
ejpam-4750	287	2	t5	ORG
ejpam-4750	289	1	vn−1	ORG
ejpam-4750	289	2	t6	ORG
ejpam-4750	291	1	2)-sets	CARDINAL
ejpam-4750	292	1	2)-set	DATE
ejpam-4750	294	1	2	CARDINAL
ejpam-4750	294	2	t3	ORG
ejpam-4750	294	3	t4	GPE
ejpam-4750	294	4	t5	ORG
ejpam-4750	295	1	2	CARDINAL
ejpam-4750	296	1	9	CARDINAL
ejpam-4750	297	1	4	CARDINAL
ejpam-4750	297	2	fln(2,2)(cn	ORG
ejpam-4750	297	3	4	CARDINAL
ejpam-4750	297	4	1	DATE
ejpam-4750	297	5	2	CARDINAL
ejpam-4750	297	6	n ≥ 7 is odd,	ORG
ejpam-4750	297	7	4	DATE
ejpam-4750	297	8	5	CARDINAL
ejpam-4750	297	9	6	DATE
ejpam-4750	300	1	2)-set	CARDINAL
ejpam-4750	301	1	8	CARDINAL
ejpam-4750	302	1	5	CARDINAL
ejpam-4750	302	2	2)-sets	CARDINAL
ejpam-4750	303	1	∈	ORG
ejpam-4750	303	2	k ∈	PERSON
ejpam-4750	303	3	1	CARDINAL
ejpam-4750	303	4	2	DATE
ejpam-4750	303	5	3	DATE
ejpam-4750	303	6	4	DATE
ejpam-4750	303	7	5	CARDINAL
ejpam-4750	303	8	2)-set	CARDINAL
ejpam-4750	303	9	c5	ORG
ejpam-4750	304	1	7	CARDINAL
ejpam-4750	304	2	4	CARDINAL
ejpam-4750	304	3	6	CARDINAL
ejpam-4750	304	4	j = v	PERSON
ejpam-4750	304	5	{vi	PERSON
ejpam-4750	304	6	j ∈	PERSON
ejpam-4750	304	7	1	CARDINAL
ejpam-4750	304	8	2	DATE
ejpam-4750	306	1	6	CARDINAL
ejpam-4750	307	1	vi ∈	PERSON
ejpam-4750	307	2	c6) \ei	ORG
ejpam-4750	307	3	{vi	PERSON
ejpam-4750	307	4	k	PERSON
ejpam-4750	308	1	d. managbanag	GPE
ejpam-4750	308	2	h. rara	PERSON
ejpam-4750	309	1	j. pure	PERSON
ejpam-4750	309	2	16	CARDINAL
ejpam-4750	309	3	2	CARDINAL
ejpam-4750	309	4	2023	CARDINAL
ejpam-4750	309	5	1068-1083 1077	QUANTITY
ejpam-4750	310	1	4	CARDINAL
ejpam-4750	311	1	n ≥ 7 and n	ORG
ejpam-4750	312	1	1	CARDINAL
ejpam-4750	312	2	2	DATE
ejpam-4750	312	3	1 2	CARDINAL
ejpam-4750	313	1	fln(2,2)(cn	ORG
ejpam-4750	313	2	2	CARDINAL
ejpam-4750	313	3	n ≥ 8	DATE
ejpam-4750	314	1	2	CARDINAL
ejpam-4750	315	1	2	CARDINAL
ejpam-4750	317	1	vn−3	ORG
ejpam-4750	319	1	2)-sets	CARDINAL
ejpam-4750	321	1	8(ii	CARDINAL
ejpam-4750	321	2	fln(2,2)(f1	GPE
ejpam-4750	321	3	1	CARDINAL
ejpam-4750	322	1	6	CARDINAL
ejpam-4750	322	2	2-metric	QUANTITY
ejpam-4750	322	3	two	CARDINAL
ejpam-4750	322	4	∈	ORG
ejpam-4750	323	1	2	CARDINAL
ejpam-4750	323	2	8	CARDINAL
ejpam-4750	324	1	2-metric	QUANTITY
ejpam-4750	326	1	g. theorem 9	PERSON
ejpam-4750	330	1	0	DATE
ejpam-4750	332	1	8	CARDINAL
ejpam-4750	332	2	2-metric	QUANTITY
ejpam-4750	332	3	k1+g	GPE
ejpam-4750	333	1	4	CARDINAL
ejpam-4750	333	2	0	CARDINAL
ejpam-4750	334	1	at least two	CARDINAL
ejpam-4750	337	1	8	CARDINAL
ejpam-4750	337	2	2-metric	QUANTITY
ejpam-4750	339	1	2-metric	QUANTITY
ejpam-4750	341	1	8	CARDINAL
ejpam-4750	341	2	s0	ORG
ejpam-4750	342	1	fln(2,2)(s0	ORG
ejpam-4750	345	1	d. managbanag	PERSON
ejpam-4750	345	2	h. rara	PERSON
ejpam-4750	346	1	j. pure	PERSON
ejpam-4750	346	2	16	CARDINAL
ejpam-4750	346	3	2	CARDINAL
ejpam-4750	346	4	2023	CARDINAL
ejpam-4750	346	5	1068	CARDINAL
ejpam-4750	346	6	1083 1078	CARDINAL
ejpam-4750	346	7	3	CARDINAL
ejpam-4750	347	1	1	CARDINAL
ejpam-4750	348	1	n ≥ 2, fdim2(fn	ORG
ejpam-4750	348	2	2	CARDINAL
ejpam-4750	348	3	3	DATE
ejpam-4750	348	4	1	CARDINAL
ejpam-4750	348	5	5	CARDINAL
ejpam-4750	348	6	2	DATE
ejpam-4750	348	7	n ≥ 8	DATE
ejpam-4750	348	8	3	CARDINAL
ejpam-4750	348	9	4	CARDINAL
ejpam-4750	348	10	6	DATE
ejpam-4750	349	1	2	CARDINAL
ejpam-4750	350	1	n ≥ 3	DATE
ejpam-4750	350	2	3	CARDINAL
ejpam-4750	350	3	4	DATE
ejpam-4750	350	4	1	DATE
ejpam-4750	350	5	2	CARDINAL
ejpam-4750	350	6	n ≥ 7 is odd,	ORG
ejpam-4750	350	7	3	CARDINAL
ejpam-4750	350	8	5	CARDINAL
ejpam-4750	350	9	6	DATE
ejpam-4750	351	1	3	CARDINAL
ejpam-4750	353	1	1	CARDINAL
ejpam-4750	354	1	0	CARDINAL
ejpam-4750	355	1	3	CARDINAL
ejpam-4750	356	1	10	CARDINAL
ejpam-4750	359	1	2-metric	QUANTITY
ejpam-4750	361	1	dim2(g+h	NORP
ejpam-4750	362	1	11	CARDINAL
ejpam-4750	363	1	2	CARDINAL
ejpam-4750	364	1	⊆	CARDINAL
ejpam-4750	364	2	2-metric	QUANTITY
ejpam-4750	366	1	dim2(g+h	NORP
ejpam-4750	367	1	12	CARDINAL
ejpam-4750	370	1	+ fln2(h	PERCENT
ejpam-4750	374	1	10	CARDINAL
ejpam-4750	378	1	fh	ORG
ejpam-4750	379	1	|fh	DATE
ejpam-4750	380	1	10	CARDINAL
ejpam-4750	380	2	2-metric	QUANTITY
ejpam-4750	380	3	g+h	ORG
ejpam-4750	381	1	fg ∪ fh	ORG
ejpam-4750	381	2	2-metric	QUANTITY
ejpam-4750	381	3	s′ ̸= s	LAW
ejpam-4750	381	4	10	CARDINAL
ejpam-4750	381	5	h. rara	PERSON
ejpam-4750	382	1	j. pure	PERSON
ejpam-4750	382	2	16	CARDINAL
ejpam-4750	382	3	2	CARDINAL
ejpam-4750	382	4	2023	CARDINAL
ejpam-4750	382	5	1068-1083 1079	DATE
ejpam-4750	382	6	s′	PRODUCT
ejpam-4750	382	7	fg	ORG
ejpam-4750	382	8	fh	ORG
ejpam-4750	383	1	fh	ORG
ejpam-4750	384	1	+ fln2(h	PERCENT
ejpam-4750	385	1	2-metric	QUANTITY
ejpam-4750	385	2	g+h	PRODUCT
ejpam-4750	388	1	10	CARDINAL
ejpam-4750	389	1	⊆	CARDINAL
ejpam-4750	389	2	1	CARDINAL
ejpam-4750	391	1	⊆	CARDINAL
ejpam-4750	392	1	w ′	TIME
ejpam-4750	392	2	g ̸= wg	PERSON
ejpam-4750	395	1	10	CARDINAL
ejpam-4750	395	2	2-metric	QUANTITY
ejpam-4750	395	3	g+h	ORG
ejpam-4750	396	1	2	CARDINAL
ejpam-4750	397	1	⊆	CARDINAL
ejpam-4750	397	2	1	CARDINAL
ejpam-4750	398	1	3	CARDINAL
ejpam-4750	399	1	⊆	CARDINAL
ejpam-4750	399	2	⊆	CARDINAL
ejpam-4750	400	1	g ̸= wg	PERSON
ejpam-4750	400	2	⊆	CARDINAL
ejpam-4750	401	1	2-metric	QUANTITY
ejpam-4750	407	1	|fwg	GPE
ejpam-4750	407	2	+ fln2(h	PERCENT
ejpam-4750	408	1	+ fln2(h	PERCENT
ejpam-4750	413	1	4	CARDINAL
ejpam-4750	413	2	two	CARDINAL
ejpam-4750	414	1	ln(2,2)(c4	ORG
ejpam-4750	414	2	4 = ln(2,1)(c4	QUANTITY
ejpam-4750	414	3	4	CARDINAL
ejpam-4750	417	1	0	CARDINAL
ejpam-4750	417	2	d. managbanag	PERSON
ejpam-4750	417	3	h. rara	PERSON
ejpam-4750	418	1	j. pure	PERSON
ejpam-4750	418	2	16	CARDINAL
ejpam-4750	418	3	2	CARDINAL
ejpam-4750	418	4	2023	CARDINAL
ejpam-4750	418	5	1068-1083 1080	CARDINAL
ejpam-4750	418	6	5	CARDINAL
ejpam-4750	418	7	two	CARDINAL
ejpam-4750	419	1	ln(2,2)(c7	GPE
ejpam-4750	419	2	4	CARDINAL
ejpam-4750	419	3	3	CARDINAL
ejpam-4750	420	1	c7	PERSON
ejpam-4750	420	2	fdim2(c7	GPE
ejpam-4750	423	1	5	CARDINAL
ejpam-4750	423	2	4	CARDINAL
ejpam-4750	423	3	13	CARDINAL
ejpam-4750	424	1	2	CARDINAL
ejpam-4750	426	1	0	CARDINAL
ejpam-4750	430	1	11	DATE
ejpam-4750	430	2	2-metric	QUANTITY
ejpam-4750	430	3	4	CARDINAL
ejpam-4750	431	1	0	CARDINAL
ejpam-4750	435	1	11	DATE
ejpam-4750	435	2	2-metric	QUANTITY
ejpam-4750	435	3	fg	ORG
ejpam-4750	435	4	fh	ORG
ejpam-4750	435	5	fln(2,1)(g	ORG
ejpam-4750	436	1	|fh	DATE
ejpam-4750	437	1	fg ∪ fh	ORG
ejpam-4750	438	1	fh	PERSON
ejpam-4750	438	2	= s.	PERSON
ejpam-4750	438	3	2-metric	QUANTITY
ejpam-4750	438	4	s′ ̸= s	LAW
ejpam-4750	438	5	g + h.	ORG
ejpam-4750	438	6	11	CARDINAL
ejpam-4750	440	1	fh ⊆	ORG
ejpam-4750	440	2	s′	PRODUCT
ejpam-4750	441	1	fg	ORG
ejpam-4750	441	2	fh	ORG
ejpam-4750	442	1	fh	ORG
ejpam-4750	443	1	fln(2,1)(g	ORG
ejpam-4750	444	1	2-metric	QUANTITY
ejpam-4750	445	1	11	CARDINAL
ejpam-4750	446	1	0	CARDINAL
ejpam-4750	446	2	⊆	CARDINAL
ejpam-4750	446	3	⊆	CARDINAL
ejpam-4750	448	1	⊆ d0	QUANTITY
ejpam-4750	448	2	2-metric	QUANTITY
ejpam-4750	448	3	g+h	ORG
ejpam-4750	448	4	f0 ⊆	CARDINAL
ejpam-4750	450	1	s0 h .	ORG
ejpam-4750	454	1	0	CARDINAL
ejpam-4750	457	1	fln(2,1)(g	ORG
ejpam-4750	458	1	fln(2,1)(g	ORG
ejpam-4750	459	1	d. managbanag	PERSON
ejpam-4750	459	2	h. rara	PERSON
ejpam-4750	460	1	j. pure	PERSON
ejpam-4750	460	2	16	CARDINAL
ejpam-4750	460	3	2	CARDINAL
ejpam-4750	460	4	2023	CARDINAL
ejpam-4750	460	5	1068-1083	CARDINAL
ejpam-4750	460	6	6	CARDINAL
ejpam-4750	460	7	two	CARDINAL
ejpam-4750	460	8	2,2)-locating	CARDINAL
ejpam-4750	464	1	w3 =	PERSON
ejpam-4750	466	1	∈	ORG
ejpam-4750	467	1	⊆	CARDINAL
ejpam-4750	467	2	z3	GPE
ejpam-4750	468	1	fln(2,1)(g	ORG
ejpam-4750	468	2	1	CARDINAL
ejpam-4750	468	3	2	CARDINAL
ejpam-4750	468	4	fln(2,1)(g	ORG
ejpam-4750	468	5	1 + 2	CARDINAL
ejpam-4750	468	6	3	CARDINAL
ejpam-4750	469	1	2-metric	QUANTITY
ejpam-4750	469	2	two	CARDINAL
ejpam-4750	469	3	g◦h	ORG
ejpam-4750	469	4	one	CARDINAL
ejpam-4750	469	5	∈	ORG
ejpam-4750	469	6	one	CARDINAL
ejpam-4750	469	7	∈	ORG
ejpam-4750	470	1	⋃ v∈v	PERSON
ejpam-4750	471	1	2	CARDINAL
ejpam-4750	471	2	∈	ORG
ejpam-4750	472	1	rg◦h(q/s	ORG
ejpam-4750	472	2	at least 2	CARDINAL
ejpam-4750	473	1	2	CARDINAL
ejpam-4750	473	2	rhv(p/sv	ORG
ejpam-4750	473	3	at least two	CARDINAL
ejpam-4750	474	1	g ◦ h	ORG
ejpam-4750	474	2	∈	ORG
ejpam-4750	475	1	at least two	CARDINAL
ejpam-4750	476	1	∈	ORG
ejpam-4750	479	1	∈	ORG
ejpam-4750	480	1	w ∈ nhv(p	PRODUCT
ejpam-4750	480	2	w ∈	ORG
ejpam-4750	481	1	sv	ORG
ejpam-4750	481	2	2	CARDINAL
ejpam-4750	482	1	4	CARDINAL
ejpam-4750	483	1	14	DATE
ejpam-4750	485	1	⊆	CARDINAL
ejpam-4750	485	2	2-metric	QUANTITY
ejpam-4750	485	3	g ◦h	ORG
ejpam-4750	486	1	⋃ v∈v	PERSON
ejpam-4750	486	2	sv	ORG
ejpam-4750	486	3	∈	ORG
ejpam-4750	488	1	d. managbanag	PERSON
ejpam-4750	488	2	h. rara	PERSON
ejpam-4750	489	1	j. pure	PERSON
ejpam-4750	489	2	16	CARDINAL
ejpam-4750	489	3	2	CARDINAL
ejpam-4750	489	4	2023	CARDINAL
ejpam-4750	489	5	1068-1083	CARDINAL
ejpam-4750	489	6	15	CARDINAL
ejpam-4750	491	1	0	CARDINAL
ejpam-4750	493	1	∈	ORG
ejpam-4750	493	2	⊆	CARDINAL
ejpam-4750	493	3	15	CARDINAL
ejpam-4750	493	4	⋃ v∈v	PERSON
ejpam-4750	493	5	2-metric	QUANTITY
ejpam-4750	493	6	g◦h.	ORG
ejpam-4750	493	7	4	CARDINAL
ejpam-4750	493	8	0	CARDINAL
ejpam-4750	494	1	∈	ORG
ejpam-4750	494	2	⊆	CARDINAL
ejpam-4750	496	1	⊆	CARDINAL
ejpam-4750	498	1	⋃ v∈v	PERSON
ejpam-4750	498	2	2-metric	QUANTITY
ejpam-4750	498	3	g ◦ h.	ORG
ejpam-4750	498	4	⋃ v∈v	PERSON
ejpam-4750	501	1	2-metric	QUANTITY
ejpam-4750	502	1	fdim2(s ′	DATE
ejpam-4750	503	1	15	CARDINAL
ejpam-4750	503	2	⋃ v∈v	PERSON
ejpam-4750	503	3	rv	GPE
ejpam-4750	503	4	rv	GPE
ejpam-4750	504	1	fdim2(s ′	DATE
ejpam-4750	508	1	∈	ORG
ejpam-4750	509	1	w ∈	PERSON
ejpam-4750	510	1	w	ORG
ejpam-4750	510	2	r′ w ̸=	FAC
ejpam-4750	511	1	⋃ v∈v	PERSON
ejpam-4750	511	2	g)\{w} rv é ∪r′ w	ORG
ejpam-4750	511	3	2-metric	QUANTITY
ejpam-4750	511	4	g ◦h	ORG
ejpam-4750	512	1	cv	ORG
ejpam-4750	512	2	∈	ORG
ejpam-4750	515	1	⋃ v∈v	PERSON
ejpam-4750	515	2	cv	PERSON
ejpam-4750	515	3	∑ v∈v	PERSON
ejpam-4750	515	4	∑ v∈v	PERSON
ejpam-4750	519	1	7	CARDINAL
ejpam-4750	519	2	two	CARDINAL
ejpam-4750	520	1	fdim2(p3 ◦ c4	ORG
ejpam-4750	520	2	3	CARDINAL
ejpam-4750	521	1	0	CARDINAL
ejpam-4750	521	2	8	CARDINAL
ejpam-4750	522	1	two	CARDINAL
ejpam-4750	522	2	c5	ORG
ejpam-4750	523	1	c5	ORG
ejpam-4750	523	2	3	CARDINAL
ejpam-4750	523	3	3	CARDINAL
ejpam-4750	523	4	9	CARDINAL
ejpam-4750	523	5	1083	CARDINAL
ejpam-4750	523	6	the department of science and technology	ORG
ejpam-4750	523	7	philippines	GPE
ejpam-4750	524	1	1	CARDINAL
ejpam-4750	524	2	bailey	PERSON
ejpam-4750	524	3	i. yero	PERSON
ejpam-4750	526	1	discussiones mathematicae	PERSON
ejpam-4750	526	2	39:341–355	CARDINAL
ejpam-4750	526	3	2019	DATE
ejpam-4750	527	1	2	CARDINAL
ejpam-4750	527	2	s. bau	PERSON
ejpam-4750	527	3	a.f.	ORG
ejpam-4750	528	1	beardon	PERSON
ejpam-4750	532	1	13:295–305, 2013	DATE
ejpam-4750	533	1	3	CARDINAL
ejpam-4750	533	2	blumenthal	PERSON
ejpam-4750	535	1	clarendon press	ORG
ejpam-4750	535	2	oxford	NORP
ejpam-4750	535	3	1953	DATE
ejpam-4750	536	1	4	CARDINAL
ejpam-4750	536	2	j. cabaro	PERSON
ejpam-4750	536	3	h. rara	PERSON
ejpam-4750	537	1	2resolving	DATE
ejpam-4750	538	1	european journal	ORG
ejpam-4750	538	2	14(3):773–782	CARDINAL
ejpam-4750	538	3	2021	DATE
ejpam-4750	539	1	5	CARDINAL
ejpam-4750	539	2	f. harary	PERSON
ejpam-4750	539	3	r.a. melter	PERSON
ejpam-4750	540	1	2:191–195	CARDINAL
ejpam-4750	540	2	1976	DATE
ejpam-4750	541	1	6	CARDINAL
ejpam-4750	541	2	zivkovic, f. harary	PERSON
ejpam-4750	541	3	d.j. klein	ORG
ejpam-4750	543	1	j. math	PERSON
ejpam-4750	545	1	6:295–306, 1991	DATE
ejpam-4750	546	1	7	CARDINAL
ejpam-4750	546	2	m. heydarpour	PERSON
ejpam-4750	546	3	s. maghsoudi	PERSON
ejpam-4750	548	1	178:230–235, 2014	DATE
ejpam-4750	549	1	8	CARDINAL
ejpam-4750	549	2	d.j. klein	ORG
ejpam-4750	549	3	m. randic	PERSON
ejpam-4750	550	1	j. comput	PERSON
ejpam-4750	551	1	8:516–521	CARDINAL
ejpam-4750	551	2	1987	DATE
ejpam-4750	552	1	9	CARDINAL
ejpam-4750	552	2	a. estrada-moreno	PERSON
ejpam-4750	552	3	j. rodrıguez-velazquez	PERSON
ejpam-4750	552	4	i. yero	PERSON
ejpam-4750	554	1	9:2829–2840	DATE
ejpam-4750	554	2	2015	DATE
ejpam-4750	555	1	10	CARDINAL
ejpam-4750	555	2	p. zhang	PERSON
ejpam-4750	557	1	australian	NORP
ejpam-4750	557	2	combinatorics	ORG
ejpam-4750	557	3	28:25–37,	DATE
ejpam-4750	557	4	2003	DATE
ejpam-4750	558	1	11	CARDINAL
ejpam-4750	558	2	slater	PERSON
ejpam-4750	560	1	congress	ORG
ejpam-4750	562	1	14:549–559, 1975	DATE
ejpam-4750	563	1	12	CARDINAL
ejpam-4750	563	2	slater	PERSON
ejpam-4750	565	1	j. math	PERSON
ejpam-4750	567	1	sci.	ORG
ejpam-4750	567	2	22:445–455	CARDINAL
ejpam-4750	567	3	1988	DATE
ejpam-4750	568	1	13	CARDINAL
ejpam-4750	568	2	g. chartrand	PERSON
ejpam-4750	568	3	p. zhang	PERSON
ejpam-4750	568	4	kalamazoo	GPE
ejpam-4750	570	1	mathematica bohemica	PERSON
ejpam-4750	570	2	126(4):711–720, 2001	DATE