id	sid	eid	entity	type
ejpam-5973	1	1	european journal	ORG
ejpam-5973	1	2	2025	DATE
ejpam-5973	1	3	18	CARDINAL
ejpam-5973	1	4	2	CARDINAL
ejpam-5973	1	5	5973	DATE
ejpam-5973	1	6	1307-5543	DATE
ejpam-5973	1	7	new york	GPE
ejpam-5973	1	8	jamil j. hamja1,2	PERSON
ejpam-5973	1	9	seyed mahmoud sheikholeslami3,∗	PERSON
ejpam-5973	1	10	imelda s. aniversario2,4	PERSON
ejpam-5973	2	1	lyster rey	PERSON
ejpam-5973	3	1	1	CARDINAL
ejpam-5973	3	2	msu	ORG
ejpam-5973	3	3	7500	CARDINAL
ejpam-5973	3	4	2	CARDINAL
ejpam-5973	3	5	mindanao state university-iligan institute of technology	ORG
ejpam-5973	3	6	9200	CARDINAL
ejpam-5973	3	7	iligan city	GPE
ejpam-5973	3	8	philippines 3 department	ORG
ejpam-5973	3	9	shahid madani university	PERSON
ejpam-5973	3	10	iran 4	EVENT
ejpam-5973	3	11	institute of science	ORG
ejpam-5973	3	12	mindanao state university-iligan institute of technology	ORG
ejpam-5973	3	13	9200	CARDINAL
ejpam-5973	3	14	iligan city	GPE
ejpam-5973	3	15	philippines	GPE
ejpam-5973	6	1	1	CARDINAL
ejpam-5973	6	2	2	DATE
ejpam-5973	7	1	k}	PERSON
ejpam-5973	8	1	1	CARDINAL
ejpam-5973	8	2	2	DATE
ejpam-5973	8	3	3	DATE
ejpam-5973	9	1	k}	PERSON
ejpam-5973	9	2	∈	ORG
ejpam-5973	9	3	⋃	DATE
ejpam-5973	9	4	1	CARDINAL
ejpam-5973	9	5	2	DATE
ejpam-5973	10	1	n2 g(v	ORG
ejpam-5973	10	2	two	CARDINAL
ejpam-5973	14	1	bipartite	ORG
ejpam-5973	16	1	γhr2(g	CARDINAL
ejpam-5973	16	2	2020	DATE
ejpam-5973	16	3	05c69	CARDINAL
ejpam-5973	17	1	j. j. hamja	PERSON
ejpam-5973	17	2	s. m. sheikholeslami	PERSON
ejpam-5973	17	3	imelda.aniversario@g.msuiit.edu.ph	GPE
ejpam-5973	17	4	i. s. aniversario	PERSON
ejpam-5973	17	5	l. b. cabardo	PERSON
ejpam-5973	17	6	1	CARDINAL
ejpam-5973	18	1	2025	CARDINAL
ejpam-5973	19	1	j. j. hamja	PERSON
ejpam-5973	21	1	j. pure	PERSON
ejpam-5973	21	2	18	CARDINAL
ejpam-5973	21	3	2	CARDINAL
ejpam-5973	21	4	2025	CARDINAL
ejpam-5973	21	5	5973	DATE
ejpam-5973	21	6	2	CARDINAL
ejpam-5973	21	7	17 1	CARDINAL
ejpam-5973	23	1	2020	DATE
ejpam-5973	24	1	1	CARDINAL
ejpam-5973	28	1	2008	DATE
ejpam-5973	28	2	2	CARDINAL
ejpam-5973	30	1	2014	DATE
ejpam-5973	30	2	z. shao	PERSON
ejpam-5973	30	3	integer k	PERSON
ejpam-5973	31	1	3	CARDINAL
ejpam-5973	35	1	natarajan et al	PERSON
ejpam-5973	36	1	2015	DATE
ejpam-5973	36	2	10	CARDINAL
ejpam-5973	37	1	11–14	CARDINAL
ejpam-5973	38	1	2	CARDINAL
ejpam-5973	39	1	∈	ORG
ejpam-5973	39	2	∈	ORG
ejpam-5973	40	1	s. the degree of	PERSON
ejpam-5973	42	1	two	CARDINAL
ejpam-5973	42	2	kn	PERSON
ejpam-5973	42	3	bipartite	NORP
ejpam-5973	42	4	kp	ORG
ejpam-5973	42	5	q.	PERSON
ejpam-5973	42	6	15	CARDINAL
ejpam-5973	43	1	n ℓ g(u	FAC
ejpam-5973	44	1	∈	ORG
ejpam-5973	44	2	n ℓ g[u	PERSON
ejpam-5973	44	3	n ℓ g(u	PERSON
ejpam-5973	45	1	⊆	CARDINAL
ejpam-5973	46	1	⋃	PERSON
ejpam-5973	46	2	n ℓ g(u	PERSON
ejpam-5973	47	1	j. j. hamja	PERSON
ejpam-5973	49	1	j. pure	PERSON
ejpam-5973	49	2	18	CARDINAL
ejpam-5973	49	3	2	CARDINAL
ejpam-5973	49	4	2025	CARDINAL
ejpam-5973	49	5	5973 3 of 17	DATE
ejpam-5973	50	1	⊆	CARDINAL
ejpam-5973	52	1	γ(g	NORP
ejpam-5973	52	2	γ(g	GPE
ejpam-5973	53	1	⊆	CARDINAL
ejpam-5973	54	1	∈	PERSON
ejpam-5973	54	2	2	CARDINAL
ejpam-5973	54	3	natarajan et al	PERSON
ejpam-5973	55	1	10	CARDINAL
ejpam-5973	57	1	2	CARDINAL
ejpam-5973	57	2	2	CARDINAL
ejpam-5973	57	3	n2 g(u	PRODUCT
ejpam-5973	58	1	2-degree	QUANTITY
ejpam-5973	58	2	deg2(v	ORG
ejpam-5973	59	1	shabani et al	PERSON
ejpam-5973	60	1	16	CARDINAL
ejpam-5973	61	1	0	CARDINAL
ejpam-5973	61	2	1	DATE
ejpam-5973	61	3	2	CARDINAL
ejpam-5973	61	4	∈	ORG
ejpam-5973	62	1	0	CARDINAL
ejpam-5973	62	2	at least one	CARDINAL
ejpam-5973	62	3	2	CARDINAL
ejpam-5973	62	4	e. j. cockayne	PERSON
ejpam-5973	62	5	17	CARDINAL
ejpam-5973	63	1	0	CARDINAL
ejpam-5973	63	2	1	DATE
ejpam-5973	63	3	2	CARDINAL
ejpam-5973	64	1	g(u	PRODUCT
ejpam-5973	65	1	g(w	ORG
ejpam-5973	65	2	2	CARDINAL
ejpam-5973	65	3	d(u	PERSON
ejpam-5973	65	4	2	CARDINAL
ejpam-5973	65	5	hrd	ORG
ejpam-5973	65	6	16	CARDINAL
ejpam-5973	66	1	1	CARDINAL
ejpam-5973	66	2	2	DATE
ejpam-5973	66	3	3	DATE
ejpam-5973	68	1	k}	PERSON
ejpam-5973	69	1	1	CARDINAL
ejpam-5973	69	2	2	DATE
ejpam-5973	69	3	3	DATE
ejpam-5973	70	1	k}	PERSON
ejpam-5973	71	1	∈	ORG
ejpam-5973	71	2	⋃ u∈ng(v	PERSON
ejpam-5973	72	1	1	CARDINAL
ejpam-5973	72	2	2	DATE
ejpam-5973	72	3	3	DATE
ejpam-5973	74	1	k}	PERSON
ejpam-5973	74	2	ω(f	PERSON
ejpam-5973	75	1	∑ v∈v	PERSON
ejpam-5973	75	2	g)|f(v)|	ORG
ejpam-5973	77	1	2	CARDINAL
ejpam-5973	79	1	1	CARDINAL
ejpam-5973	79	2	2	DATE
ejpam-5973	80	1	k}	PERSON
ejpam-5973	80	2	∈	ORG
ejpam-5973	80	3	⋃	DATE
ejpam-5973	80	4	1	CARDINAL
ejpam-5973	80	5	2	DATE
ejpam-5973	84	1	∑ v∈v	PERSON
ejpam-5973	86	1	1	CARDINAL
ejpam-5973	86	2	γh1r(g	GPE
ejpam-5973	87	1	j. j. hamja et al	PERSON
ejpam-5973	88	1	j. pure	PERSON
ejpam-5973	88	2	18	CARDINAL
ejpam-5973	88	3	2	CARDINAL
ejpam-5973	88	4	2025	CARDINAL
ejpam-5973	88	5	5973	DATE
ejpam-5973	88	6	4	CARDINAL
ejpam-5973	88	7	17	CARDINAL
ejpam-5973	88	8	1	CARDINAL
ejpam-5973	88	9	1	CARDINAL
ejpam-5973	89	1	v2, v5	GPE
ejpam-5973	89	2	1	CARDINAL
ejpam-5973	89	3	2	CARDINAL
ejpam-5973	89	4	f(v1	DATE
ejpam-5973	90	1	2	CARDINAL
ejpam-5973	90	2	1	CARDINAL
ejpam-5973	90	3	2	CARDINAL
ejpam-5973	90	4	dg(v4	PERSON
ejpam-5973	91	1	2	CARDINAL
ejpam-5973	92	1	⋃ u1∈n2 g(v3	PERCENT
ejpam-5973	92	2	1	CARDINAL
ejpam-5973	92	3	2	CARDINAL
ejpam-5973	92	4	⋃	DATE
ejpam-5973	92	5	g(v4	ORG
ejpam-5973	93	1	1	CARDINAL
ejpam-5973	93	2	2	CARDINAL
ejpam-5973	94	1	2	CARDINAL
ejpam-5973	96	1	1 + 1 + 0	DATE
ejpam-5973	98	1	6	CARDINAL
ejpam-5973	98	2	v1 v2 v3 v4 v5 v6 v7 v8	PERSON
ejpam-5973	98	3	1	CARDINAL
ejpam-5973	98	4	8	CARDINAL
ejpam-5973	98	5	2	CARDINAL
ejpam-5973	98	6	6	CARDINAL
ejpam-5973	98	7	3	CARDINAL
ejpam-5973	98	8	1	CARDINAL
ejpam-5973	103	1	np vertices	ORG
ejpam-5973	105	1	i=1 γhrk(gi	PERSON
ejpam-5973	108	1	ni vertices	PERSON
ejpam-5973	109	1	first	ORDINAL
ejpam-5973	109	2	1	CARDINAL
ejpam-5973	109	3	2	DATE
ejpam-5973	112	1	p({1	DATE
ejpam-5973	112	2	2	CARDINAL
ejpam-5973	114	1	k}	PERSON
ejpam-5973	114	2	∈	ORG
ejpam-5973	114	3	1	CARDINAL
ejpam-5973	114	4	2	DATE
ejpam-5973	117	1	g1	ORG
ejpam-5973	119	1	i=1 ω(fi	GPE
ejpam-5973	122	1	i=1 γhrk(gi	PERSON
ejpam-5973	123	1	j. j. hamja et al	PERSON
ejpam-5973	124	1	j. pure	PERSON
ejpam-5973	124	2	18	CARDINAL
ejpam-5973	124	3	2	CARDINAL
ejpam-5973	124	4	2025	CARDINAL
ejpam-5973	124	5	5973 5	DATE
ejpam-5973	124	6	17	CARDINAL
ejpam-5973	129	1	γhrk(gi	GPE
ejpam-5973	136	1	i=1 γhrk(gi	FAC
ejpam-5973	137	1	two	CARDINAL
ejpam-5973	138	1	i=1 γhrk(gi	PERSON
ejpam-5973	141	1	0	CARDINAL
ejpam-5973	141	2	1	CARDINAL
ejpam-5973	144	1	2	CARDINAL
ejpam-5973	144	2	1	CARDINAL
ejpam-5973	144	3	2	CARDINAL
ejpam-5973	144	4	2	CARDINAL
ejpam-5973	145	1	1	CARDINAL
ejpam-5973	147	1	1	CARDINAL
ejpam-5973	147	2	v2, v5	GPE
ejpam-5973	147	3	2	CARDINAL
ejpam-5973	147	4	two	CARDINAL
ejpam-5973	147	5	2	CARDINAL
ejpam-5973	149	1	1	CARDINAL
ejpam-5973	151	1	2	CARDINAL
ejpam-5973	152	1	2	CARDINAL
ejpam-5973	153	1	1	CARDINAL
ejpam-5973	160	1	1)|v	CARDINAL
ejpam-5973	162	1	1	CARDINAL
ejpam-5973	163	1	∈	ORG
ejpam-5973	164	1	0	CARDINAL
ejpam-5973	164	2	1	CARDINAL
ejpam-5973	170	1	ω(f	PERSON
ejpam-5973	170	2	∑ v∈v	PERSON
ejpam-5973	175	1	⋃	DATE
ejpam-5973	176	1	j. j. hamja et al	PERSON
ejpam-5973	177	1	j. pure	PERSON
ejpam-5973	177	2	18	CARDINAL
ejpam-5973	177	3	2	CARDINAL
ejpam-5973	177	4	2025	CARDINAL
ejpam-5973	177	5	6	CARDINAL
ejpam-5973	177	6	17	CARDINAL
ejpam-5973	177	7	1	CARDINAL
ejpam-5973	177	8	2	DATE
ejpam-5973	179	1	0	CARDINAL
ejpam-5973	179	2	f j for j ≥ 2	ORG
ejpam-5973	180	1	at least one	CARDINAL
ejpam-5973	182	1	1)|v	CARDINAL
ejpam-5973	185	1	2	CARDINAL
ejpam-5973	187	1	+np	PERSON
ejpam-5973	190	1	= kr	PERSON
ejpam-5973	190	2	1	CARDINAL
ejpam-5973	190	3	1	CARDINAL
ejpam-5973	194	1	i=1 γhrk(gi	PERSON
ejpam-5973	196	1	2	CARDINAL
ejpam-5973	196	2	1	CARDINAL
ejpam-5973	199	1	3	CARDINAL
ejpam-5973	200	1	2	CARDINAL
ejpam-5973	206	1	0	CARDINAL
ejpam-5973	206	2	at least one	CARDINAL
ejpam-5973	207	1	n ≥ k	GPE
ejpam-5973	208	1	2	CARDINAL
ejpam-5973	208	2	2	CARDINAL
ejpam-5973	209	1	0	CARDINAL
ejpam-5973	213	1	4	CARDINAL
ejpam-5973	214	1	1	CARDINAL
ejpam-5973	215	1	k + 1	PRODUCT
ejpam-5973	215	2	1 ≤ n ≤	QUANTITY
ejpam-5973	219	1	3	CARDINAL
ejpam-5973	221	1	0	CARDINAL
ejpam-5973	221	2	⋃	DATE
ejpam-5973	222	1	1	CARDINAL
ejpam-5973	222	2	2	DATE
ejpam-5973	223	1	k}	PERSON
ejpam-5973	223	2	g(v	PERSON
ejpam-5973	223	3	j. j. hamja	PERSON
ejpam-5973	225	1	j. pure	PERSON
ejpam-5973	225	2	18	CARDINAL
ejpam-5973	225	3	2	CARDINAL
ejpam-5973	225	4	2025	CARDINAL
ejpam-5973	225	5	7	CARDINAL
ejpam-5973	226	1	2	CARDINAL
ejpam-5973	231	1	k + 1	PRODUCT
ejpam-5973	232	1	p({1	DATE
ejpam-5973	232	2	2	CARDINAL
ejpam-5973	234	1	k}	PERSON
ejpam-5973	235	1	1	CARDINAL
ejpam-5973	235	2	∈	ORG
ejpam-5973	237	1	1	CARDINAL
ejpam-5973	238	1	2	CARDINAL
ejpam-5973	247	1	1	CARDINAL
ejpam-5973	247	2	2	DATE
ejpam-5973	250	1	2	CARDINAL
ejpam-5973	250	2	1	CARDINAL
ejpam-5973	250	3	y ∈ n2 g(x	PERSON
ejpam-5973	251	1	1	CARDINAL
ejpam-5973	251	2	2	DATE
ejpam-5973	254	1	1	CARDINAL
ejpam-5973	254	2	g(z	PERSON
ejpam-5973	254	3	0	CARDINAL
ejpam-5973	258	1	5	CARDINAL
ejpam-5973	259	1	k ≥ 2	ORG
ejpam-5973	263	1	∈	ORG
ejpam-5973	264	1	∈	PRODUCT
ejpam-5973	264	2	⋃ x∈n2 g(v	PERSON
ejpam-5973	264	3	1	CARDINAL
ejpam-5973	264	4	2	DATE
ejpam-5973	268	1	1	CARDINAL
ejpam-5973	268	2	2	DATE
ejpam-5973	270	1	⊆	CARDINAL
ejpam-5973	273	1	2	CARDINAL
ejpam-5973	273	2	p({1	DATE
ejpam-5973	273	3	2	CARDINAL
ejpam-5973	275	1	k}	PERSON
ejpam-5973	275	2	1	CARDINAL
ejpam-5973	275	3	2	DATE
ejpam-5973	278	1	deg2(x	PERSON
ejpam-5973	279	1	1	CARDINAL
ejpam-5973	281	1	deg2(x	PERSON
ejpam-5973	282	1	0	CARDINAL
ejpam-5973	286	1	5	CARDINAL
ejpam-5973	286	2	2	CARDINAL
ejpam-5973	286	3	6	DATE
ejpam-5973	287	1	1	CARDINAL
ejpam-5973	289	1	j. j. hamja et al	PERSON
ejpam-5973	290	1	j. pure	PERSON
ejpam-5973	290	2	18	CARDINAL
ejpam-5973	290	3	2	CARDINAL
ejpam-5973	290	4	2025	CARDINAL
ejpam-5973	290	5	5973 8	DATE
ejpam-5973	290	6	17	CARDINAL
ejpam-5973	291	1	ω(g	NORP
ejpam-5973	292	1	0	CARDINAL
ejpam-5973	294	1	n2 g(x	PRODUCT
ejpam-5973	295	1	0	CARDINAL
ejpam-5973	297	1	0	CARDINAL
ejpam-5973	297	2	kγhrk(g	GPE
ejpam-5973	298	1	0	CARDINAL
ejpam-5973	299	1	0 | ≤ ∆hγhrk(g	QUANTITY
ejpam-5973	299	2	≥ kn	PERSON
ejpam-5973	304	1	2	CARDINAL
ejpam-5973	305	1	18	CARDINAL
ejpam-5973	306	1	3	CARDINAL
ejpam-5973	307	1	k ≥ 1 and m ≤ n. then γhrk(km,n	ORG
ejpam-5973	309	1	2k	CARDINAL
ejpam-5973	309	2	≥ k	PERSON
ejpam-5973	311	1	kn	PERSON
ejpam-5973	312	1	2	CARDINAL
ejpam-5973	312	2	γrk(ks	ORG
ejpam-5973	314	1	1	CARDINAL
ejpam-5973	315	1	2	CARDINAL
ejpam-5973	315	2	m}+min{k	GPE
ejpam-5973	318	1	2	CARDINAL
ejpam-5973	318	2	10	CARDINAL
ejpam-5973	319	1	7	CARDINAL
ejpam-5973	320	1	2	CARDINAL
ejpam-5973	320	2	≥ k.	PERSON
ejpam-5973	324	1	first	ORDINAL
ejpam-5973	325	1	∈	ORG
ejpam-5973	326	1	∑ v∈v	PERSON
ejpam-5973	326	2	1	CARDINAL
ejpam-5973	326	3	∈	ORG
ejpam-5973	326	4	ω(f	PERSON
ejpam-5973	331	1	p({1	DATE
ejpam-5973	331	2	2	CARDINAL
ejpam-5973	333	1	k}	PERSON
ejpam-5973	334	1	1	CARDINAL
ejpam-5973	334	2	2	DATE
ejpam-5973	335	1	∈	ORG
ejpam-5973	336	1	∈	ORG
ejpam-5973	336	2	d(u	PERSON
ejpam-5973	336	3	2	CARDINAL
ejpam-5973	337	1	1	CARDINAL
ejpam-5973	337	2	2	DATE
ejpam-5973	338	1	⋃	PRODUCT
ejpam-5973	338	2	1	CARDINAL
ejpam-5973	338	3	2	DATE
ejpam-5973	340	1	k} j. j. hamja	PERSON
ejpam-5973	342	1	j. pure	PERSON
ejpam-5973	342	2	18	CARDINAL
ejpam-5973	342	3	2	CARDINAL
ejpam-5973	342	4	2025	CARDINAL
ejpam-5973	342	5	5973 9	DATE
ejpam-5973	342	6	17	DATE
ejpam-5973	342	7	∈	ORG
ejpam-5973	346	1	1	CARDINAL
ejpam-5973	348	1	≥ k.	PERSON
ejpam-5973	348	2	3	CARDINAL
ejpam-5973	349	1	2k	CARDINAL
ejpam-5973	350	1	4	CARDINAL
ejpam-5973	350	2	k ∈	ORG
ejpam-5973	350	3	2	CARDINAL
ejpam-5973	350	4	3	CARDINAL
ejpam-5973	351	1	8	CARDINAL
ejpam-5973	352	1	3	CARDINAL
ejpam-5973	353	1	2 ⌋ + 1	DATE
ejpam-5973	353	2	n ≥ 3	DATE
ejpam-5973	354	1	2 ⌋ +	DATE
ejpam-5973	355	1	n ≥ 5	DATE
ejpam-5973	356	1	3n 4 ⌉ + 1	DATE
ejpam-5973	356	2	n ≡ 0	ORG
ejpam-5973	356	3	2	DATE
ejpam-5973	356	4	3	CARDINAL
ejpam-5973	357	1	n ≥ 5	DATE
ejpam-5973	359	1	3n 4	DATE
ejpam-5973	360	1	8	CARDINAL
ejpam-5973	360	2	k ∈	ORG
ejpam-5973	360	3	2	CARDINAL
ejpam-5973	360	4	3	CARDINAL
ejpam-5973	360	5	9	CARDINAL
ejpam-5973	363	1	4	CARDINAL
ejpam-5973	364	1	n ≡ 1,	ORG
ejpam-5973	364	2	3	DATE
ejpam-5973	364	3	2	CARDINAL
ejpam-5973	364	4	n ≡ 0	ORG
ejpam-5973	364	5	2	CARDINAL
ejpam-5973	366	1	2	CARDINAL
ejpam-5973	366	2	3n 8 ⌉ + 2	DATE
ejpam-5973	366	3	n ≡ 0	ORG
ejpam-5973	367	1	8	CARDINAL
ejpam-5973	367	2	8	CARDINAL
ejpam-5973	367	3	n ≡ 1, 7	ORG
ejpam-5973	367	4	2	CARDINAL
ejpam-5973	367	5	3n 8	DATE
ejpam-5973	367	6	n ≡ 2,	ORG
ejpam-5973	367	7	4	DATE
ejpam-5973	367	8	6	DATE
ejpam-5973	367	9	8	CARDINAL
ejpam-5973	367	10	8	CARDINAL
ejpam-5973	367	11	n ≡ 3, 5	ORG
ejpam-5973	368	1	n ≥ 4	DATE
ejpam-5973	369	1	2 ⌋ +	DATE
ejpam-5973	369	2	n ≡ 1	ORG
ejpam-5973	369	3	2	CARDINAL
ejpam-5973	370	1	n ≥ 5	DATE
ejpam-5973	371	1	3n 4	DATE
ejpam-5973	371	2	n ≡ 1	ORG
ejpam-5973	371	3	2	CARDINAL
ejpam-5973	371	4	3n 8	DATE
ejpam-5973	372	1	j. j. hamja et al	PERSON
ejpam-5973	373	1	j. pure	PERSON
ejpam-5973	373	2	18	CARDINAL
ejpam-5973	373	3	2	CARDINAL
ejpam-5973	373	4	2025	CARDINAL
ejpam-5973	373	5	5973	DATE
ejpam-5973	373	6	10	CARDINAL
ejpam-5973	373	7	17	CARDINAL
ejpam-5973	377	1	4	CARDINAL
ejpam-5973	377	2	1	CARDINAL
ejpam-5973	377	3	2	DATE
ejpam-5973	377	4	3	DATE
ejpam-5973	377	5	4	CARDINAL
ejpam-5973	378	1	n ≥ 5	DATE
ejpam-5973	379	1	two	CARDINAL
ejpam-5973	386	1	two	CARDINAL
ejpam-5973	392	1	n/2 vertices	ORG
ejpam-5973	393	1	n/2	ORG
ejpam-5973	393	2	2	CARDINAL
ejpam-5973	393	3	1	CARDINAL
ejpam-5973	395	1	1	CARDINAL
ejpam-5973	396	1	1	CARDINAL
ejpam-5973	398	1	2	CARDINAL
ejpam-5973	398	2	4	CARDINAL
ejpam-5973	398	3	2	CARDINAL
ejpam-5973	398	4	4	CARDINAL
ejpam-5973	400	1	2	CARDINAL
ejpam-5973	400	2	2	CARDINAL
ejpam-5973	402	1	2	CARDINAL
ejpam-5973	402	2	4 ⌋ + 1	DATE
ejpam-5973	403	1	4	CARDINAL
ejpam-5973	403	2	1	CARDINAL
ejpam-5973	405	1	1 4 ⌋ + 1	DATE
ejpam-5973	405	2	1 4 ⌋ + 1	DATE
ejpam-5973	407	1	1 4	DATE
ejpam-5973	407	2	1 4	DATE
ejpam-5973	407	3	4	CARDINAL
ejpam-5973	407	4	4	CARDINAL
ejpam-5973	408	1	n ≡ 0	ORG
ejpam-5973	409	1	n 2	ORG
ejpam-5973	409	2	0	CARDINAL
ejpam-5973	409	3	2	CARDINAL
ejpam-5973	409	4	0	CARDINAL
ejpam-5973	409	5	1	CARDINAL
ejpam-5973	409	6	8-(iii	CARDINAL
ejpam-5973	409	7	2 n	QUANTITY
ejpam-5973	410	1	2	CARDINAL
ejpam-5973	410	2	2	CARDINAL
ejpam-5973	410	3	3n 8 ⌉ + 1	DATE
ejpam-5973	411	1	n ≡ 1	ORG
ejpam-5973	411	2	n ≡ 7	ORG
ejpam-5973	411	3	2	CARDINAL
ejpam-5973	411	4	1	CARDINAL
ejpam-5973	411	5	2	CARDINAL
ejpam-5973	411	6	0	CARDINAL
ejpam-5973	413	1	1	CARDINAL
ejpam-5973	413	2	8-(iii	CARDINAL
ejpam-5973	415	1	3n+1 2 4	DATE
ejpam-5973	415	2	j. j. hamja et al	PERSON
ejpam-5973	416	1	j. pure	PERSON
ejpam-5973	416	2	18	CARDINAL
ejpam-5973	416	3	2	CARDINAL
ejpam-5973	416	4	2025	CARDINAL
ejpam-5973	416	5	5973 11	DATE
ejpam-5973	416	6	17	CARDINAL
ejpam-5973	416	7	1	CARDINAL
ejpam-5973	416	8	8	CARDINAL
ejpam-5973	416	9	8	CARDINAL
ejpam-5973	417	1	n ≡ 3	ORG
ejpam-5973	417	2	n ≡ 5	ORG
ejpam-5973	418	1	2	CARDINAL
ejpam-5973	418	2	2	CARDINAL
ejpam-5973	418	3	2	CARDINAL
ejpam-5973	418	4	1	CARDINAL
ejpam-5973	419	1	1	CARDINAL
ejpam-5973	419	2	8-(iii	CARDINAL
ejpam-5973	421	1	3n+1 2 4	DATE
ejpam-5973	421	2	1	CARDINAL
ejpam-5973	421	3	8	CARDINAL
ejpam-5973	421	4	8	CARDINAL
ejpam-5973	422	1	n ≡ 2,	ORG
ejpam-5973	422	2	4	DATE
ejpam-5973	422	3	6	DATE
ejpam-5973	422	4	2	CARDINAL
ejpam-5973	424	1	8-(iii	CARDINAL
ejpam-5973	425	1	2 n	QUANTITY
ejpam-5973	427	1	2 ⌈	PERCENT
ejpam-5973	427	2	3n 2 4	DATE
ejpam-5973	427	3	2 ⌈	PERCENT
ejpam-5973	427	4	3n 8	DATE
ejpam-5973	431	1	4	CARDINAL
ejpam-5973	431	2	1	CARDINAL
ejpam-5973	432	1	3 and	CARDINAL
ejpam-5973	433	1	4	CARDINAL
ejpam-5973	433	2	n ≥ 5	DATE
ejpam-5973	434	1	two	CARDINAL
ejpam-5973	440	1	n 2	ORG
ejpam-5973	441	1	1	CARDINAL
ejpam-5973	443	1	2	CARDINAL
ejpam-5973	444	1	2	CARDINAL
ejpam-5973	444	2	4	CARDINAL
ejpam-5973	444	3	8	CARDINAL
ejpam-5973	444	4	8	CARDINAL
ejpam-5973	447	1	2	CARDINAL
ejpam-5973	447	2	4	CARDINAL
ejpam-5973	447	3	4	CARDINAL
ejpam-5973	452	1	4	CARDINAL
ejpam-5973	452	2	1	CARDINAL
ejpam-5973	453	1	γr3(c 2 n	PRODUCT
ejpam-5973	454	1	n ≥ 5	DATE
ejpam-5973	458	1	γr3(c 2 n	PRODUCT
ejpam-5973	459	1	8(iv	CARDINAL
ejpam-5973	461	1	3n 4	DATE
ejpam-5973	461	2	j. j. hamja et al	PERSON
ejpam-5973	462	1	j. pure	PERSON
ejpam-5973	462	2	18	CARDINAL
ejpam-5973	462	3	2	CARDINAL
ejpam-5973	462	4	2025	CARDINAL
ejpam-5973	462	5	5973 12	DATE
ejpam-5973	464	1	two	CARDINAL
ejpam-5973	472	1	γr3(c 2 n	PRODUCT
ejpam-5973	473	1	n 2	ORG
ejpam-5973	473	2	8-(iv	CARDINAL
ejpam-5973	474	1	3n 2 4	DATE
ejpam-5973	474	2	3n 8	DATE
ejpam-5973	476	1	3n 8	DATE
ejpam-5973	478	1	3n 8 ⌉ + ⌈ 3n 8	DATE
ejpam-5973	478	2	2 ⌈	PERCENT
ejpam-5973	478	3	3n 8	DATE
ejpam-5973	479	1	9	CARDINAL
ejpam-5973	479	2	3	CARDINAL
ejpam-5973	480	1	3	CARDINAL
ejpam-5973	482	1	2	CARDINAL
ejpam-5973	482	2	0	CARDINAL
ejpam-5973	483	1	1− diam(g)	TIME
ejpam-5973	483	2	2	CARDINAL
ejpam-5973	483	3	2	CARDINAL
ejpam-5973	483	4	1− diam(g)+1 2	PERCENT
ejpam-5973	483	5	1	CARDINAL
ejpam-5973	483	6	1 + 1−diam(g	DATE
ejpam-5973	483	7	2	DATE
ejpam-5973	483	8	3	CARDINAL
ejpam-5973	485	1	8	CARDINAL
ejpam-5973	485	2	0	CARDINAL
ejpam-5973	485	3	6	CARDINAL
ejpam-5973	485	4	1− diam(g	TIME
ejpam-5973	486	1	+ 2 ⌈ 3diam(g)+3 8	DATE
ejpam-5973	486	2	1	CARDINAL
ejpam-5973	486	3	3	DATE
ejpam-5973	486	4	5	CARDINAL
ejpam-5973	486	5	1− diam(g	TIME
ejpam-5973	487	1	8	CARDINAL
ejpam-5973	487	2	2	CARDINAL
ejpam-5973	487	3	4	DATE
ejpam-5973	487	4	1 + 3−diam(g	CARDINAL
ejpam-5973	487	5	4	DATE
ejpam-5973	487	6	7	CARDINAL
ejpam-5973	490	1	+ 1	DATE
ejpam-5973	493	1	2	CARDINAL
ejpam-5973	493	2	3	CARDINAL
ejpam-5973	496	1	1	CARDINAL
ejpam-5973	507	1	2	CARDINAL
ejpam-5973	507	2	9	CARDINAL
ejpam-5973	508	1	4	CARDINAL
ejpam-5973	511	1	1	CARDINAL
ejpam-5973	511	2	2	CARDINAL
ejpam-5973	512	1	3	CARDINAL
ejpam-5973	513	1	2	CARDINAL
ejpam-5973	513	2	+ 1	DATE
ejpam-5973	513	3	γhr2(c4m+1	NORP
ejpam-5973	513	4	2	CARDINAL
ejpam-5973	513	5	+ 1	DATE
ejpam-5973	513	6	2	CARDINAL
ejpam-5973	513	7	2	CARDINAL
ejpam-5973	515	1	2	CARDINAL
ejpam-5973	515	2	= a. j. j.	PERSON
ejpam-5973	517	1	j. pure	PERSON
ejpam-5973	517	2	18	CARDINAL
ejpam-5973	517	3	2	CARDINAL
ejpam-5973	517	4	2025	CARDINAL
ejpam-5973	517	5	5973 13	DATE
ejpam-5973	517	6	17	CARDINAL
ejpam-5973	517	7	4	CARDINAL
ejpam-5973	518	1	γr2(g)− γhr2(g	ORG
ejpam-5973	520	1	2a	CARDINAL
ejpam-5973	520	2	+ 8	DATE
ejpam-5973	521	1	γr2(g)− γhr2(g	ORG
ejpam-5973	521	2	5	CARDINAL
ejpam-5973	523	1	k1,a+1	PERSON
ejpam-5973	523	2	first	ORDINAL
ejpam-5973	524	1	2(a+	CARDINAL
ejpam-5973	524	2	4	CARDINAL
ejpam-5973	525	1	3	CARDINAL
ejpam-5973	529	1	4	CARDINAL
ejpam-5973	530	1	γr2(g ′	LAW
ejpam-5973	530	2	γhr2(g	CARDINAL
ejpam-5973	531	1	5	CARDINAL
ejpam-5973	531	2	g′′	PERSON
ejpam-5973	531	3	γhr2(g	CARDINAL
ejpam-5973	531	4	′′	ORG
ejpam-5973	531	5	′′	ORG
ejpam-5973	532	1	γhr2(g	CARDINAL
ejpam-5973	533	1	γhr2(g	CARDINAL
ejpam-5973	534	1	5	CARDINAL
ejpam-5973	534	2	γhr2(g	CARDINAL
ejpam-5973	539	1	t ≥ 1	DATE
ejpam-5973	539	2	2	CARDINAL
ejpam-5973	539	3	3	CARDINAL
ejpam-5973	540	1	t ≥ 1	DATE
ejpam-5973	540	2	2	CARDINAL
ejpam-5973	541	1	j. j. hamja et al	PERSON
ejpam-5973	542	1	j. pure	PERSON
ejpam-5973	542	2	18	CARDINAL
ejpam-5973	542	3	2	CARDINAL
ejpam-5973	542	4	2025	CARDINAL
ejpam-5973	542	5	5973	DATE
ejpam-5973	542	6	14	CARDINAL
ejpam-5973	542	7	17	CARDINAL
ejpam-5973	542	8	2	CARDINAL
ejpam-5973	543	1	3	CARDINAL
ejpam-5973	544	1	shabani et al	PERSON
ejpam-5973	545	1	16	CARDINAL
ejpam-5973	545	2	6	CARDINAL
ejpam-5973	546	1	6	CARDINAL
ejpam-5973	547	1	16	CARDINAL
ejpam-5973	549	1	∈	ORG
ejpam-5973	550	1	10	CARDINAL
ejpam-5973	551	1	k ≤ 2	ORG
ejpam-5973	551	2	1	CARDINAL
ejpam-5973	552	1	γhr2(g	CARDINAL
ejpam-5973	553	1	∈	ORG
ejpam-5973	558	1	6	CARDINAL
ejpam-5973	558	2	∈	ORG
ejpam-5973	559	1	∈	ORG
ejpam-5973	560	1	4	CARDINAL
ejpam-5973	561	1	2	CARDINAL
ejpam-5973	561	2	6	CARDINAL
ejpam-5973	563	1	shabani et al	PERSON
ejpam-5973	564	1	16	CARDINAL
ejpam-5973	564	2	n. shabani et al	PERSON
ejpam-5973	565	1	16	CARDINAL
ejpam-5973	567	1	1	CARDINAL
ejpam-5973	568	1	j. j. hamja et al	PERSON
ejpam-5973	569	1	j. pure	PERSON
ejpam-5973	569	2	18	CARDINAL
ejpam-5973	569	3	2	CARDINAL
ejpam-5973	569	4	2025	CARDINAL
ejpam-5973	569	5	5973 15	DATE
ejpam-5973	569	6	17	CARDINAL
ejpam-5973	569	7	1	CARDINAL
ejpam-5973	569	8	1	CARDINAL
ejpam-5973	569	9	2	CARDINAL
ejpam-5973	569	10	integer k ≥ 3	PERSON
ejpam-5973	570	1	3	CARDINAL
ejpam-5973	570	2	integer k ≥ 2	PERSON
ejpam-5973	572	1	first	ORDINAL
ejpam-5973	572	2	0	CARDINAL
ejpam-5973	572	3	0	CARDINAL
ejpam-5973	573	1	1	CARDINAL
ejpam-5973	573	2	vertex vi	PERSON
ejpam-5973	573	3	2	CARDINAL
ejpam-5973	576	1	k+1	TIME
ejpam-5973	577	1	4	CARDINAL
ejpam-5973	579	1	3	CARDINAL
ejpam-5973	580	1	integer k ≥ 2	PERSON
ejpam-5973	582	1	+ 1	DATE
ejpam-5973	582	2	4	CARDINAL
ejpam-5973	582	3	integer k ≥ 1	PERSON
ejpam-5973	582	4	2min{n	CARDINAL
ejpam-5973	584	1	2n	CARDINAL
ejpam-5973	585	1	n ≤ k + 1	FAC
ejpam-5973	586	1	2n	CARDINAL
ejpam-5973	589	1	4	CARDINAL
ejpam-5973	592	1	5	CARDINAL
ejpam-5973	592	2	k ≥ 3. 7	ORG
ejpam-5973	596	1	j. j. hamja et al	PERSON
ejpam-5973	597	1	j. pure	PERSON
ejpam-5973	597	2	18	CARDINAL
ejpam-5973	597	3	2	CARDINAL
ejpam-5973	597	4	2025	CARDINAL
ejpam-5973	597	5	5973	DATE
ejpam-5973	597	6	16	CARDINAL
ejpam-5973	597	7	17	CARDINAL
ejpam-5973	598	1	the department of science and technology	ORG
ejpam-5973	598	2	mindanao state university	ORG
ejpam-5973	598	3	mindanao state university – iligan institute of technology	ORG
ejpam-5973	598	4	msu-iit	ORG
ejpam-5973	599	1	1	CARDINAL
ejpam-5973	599	2	w. haynes	PERSON
ejpam-5973	599	3	s. t. hedetniemi	PERSON
ejpam-5973	599	4	m. a. henning	PERSON
ejpam-5973	600	1	64	CARDINAL
ejpam-5973	601	1	2020	DATE
ejpam-5973	602	1	2	CARDINAL
ejpam-5973	602	2	m. a. henning	PERSON
ejpam-5973	602	3	d. f. rall	PERSON
ejpam-5973	604	1	taiwanese	NORP
ejpam-5973	604	2	12(1):213–225, 2008	DATE
ejpam-5973	605	1	3	CARDINAL
ejpam-5973	605	2	z. shao	PERSON
ejpam-5973	605	3	m. liang	PERSON
ejpam-5973	605	4	c. yin	PERSON
ejpam-5973	605	5	x. xu	PERSON
ejpam-5973	607	1	254:225–234, 2014	DATE
ejpam-5973	608	1	4	CARDINAL
ejpam-5973	608	2	h. abdollahzadeh	PERSON
ejpam-5973	608	3	j. amjadi	PERSON
ejpam-5973	608	4	n. jafari rad	PERSON
ejpam-5973	608	5	d. samodivkin	PERSON
ejpam-5973	610	1	3(1):37–50	DATE
ejpam-5973	610	2	2018	DATE
ejpam-5973	611	1	5	CARDINAL
ejpam-5973	611	2	t. k.	PERSON
ejpam-5973	612	1	2	CARDINAL
ejpam-5973	613	1	155(17):2394–2400,	DATE
ejpam-5973	613	2	2007	DATE
ejpam-5973	614	1	6	CARDINAL
ejpam-5973	615	1	2	CARDINAL
ejpam-5973	616	1	155:2394–2400, 2007	DATE
ejpam-5973	617	1	7	CARDINAL
ejpam-5973	617	2	a. mahmoodi	PERSON
ejpam-5973	617	3	l. volkmann	PERSON
ejpam-5973	618	1	2	CARDINAL
ejpam-5973	619	1	8(2):431–444	CARDINAL
ejpam-5973	619	2	2023	CARDINAL
ejpam-5973	620	1	8	CARDINAL
ejpam-5973	620	2	r. y. salkhori	PERSON
ejpam-5973	620	3	e. vatandoost	PERSON
ejpam-5973	620	4	a. behtoei	PERSON
ejpam-5973	621	1	2	CARDINAL
ejpam-5973	622	1	2023	CARDINAL
ejpam-5973	624	1	9	CARDINAL
ejpam-5973	624	2	n. jafari rad. bounds	PERSON
ejpam-5973	624	3	2	CARDINAL
ejpam-5973	625	1	29(4):1125–1133, 2013	DATE
ejpam-5973	626	1	10	CARDINAL
ejpam-5973	626	2	c. natarajan	PERSON
ejpam-5973	626	3	s. k.	PERSON
ejpam-5973	628	1	ovidius constanţa	PERSON
ejpam-5973	628	2	seria matematică	PERSON
ejpam-5973	628	3	23(2):187–199	DATE
ejpam-5973	628	4	2015	DATE
ejpam-5973	629	1	11	CARDINAL
ejpam-5973	629	2	j. john	PERSON
ejpam-5973	629	3	s. joseph robin	PERSON
ejpam-5973	631	1	11(3):483–489	ORG
ejpam-5973	631	2	2021	CARDINAL
ejpam-5973	632	1	12	CARDINAL
ejpam-5973	632	2	s. joseph robin	PERSON
ejpam-5973	632	3	j. john	PERSON
ejpam-5973	634	1	boletim da	PERSON
ejpam-5973	634	2	de matemática	ORG
ejpam-5973	634	3	42:1–12	CARDINAL
ejpam-5973	634	4	2024	DATE
ejpam-5973	635	1	13	CARDINAL
ejpam-5973	635	2	s. k. ayyaswamy	PERSON
ejpam-5973	635	3	c. natarajan	PERSON
ejpam-5973	635	4	g. sathiamoorthy	PERSON
ejpam-5973	637	1	2018	DATE
ejpam-5973	638	1	j. j. hamja et al	PERSON
ejpam-5973	639	1	j. pure	PERSON
ejpam-5973	639	2	18	CARDINAL
ejpam-5973	639	3	2	CARDINAL
ejpam-5973	639	4	2025	CARDINAL
ejpam-5973	639	5	5973 17	DATE
ejpam-5973	639	6	14	CARDINAL
ejpam-5973	639	7	a. e. hassan	PERSON
ejpam-5973	639	8	a. e. gamorez	PERSON
ejpam-5973	639	9	e. c. ahmad	PERSON
ejpam-5973	639	10	j. j. hamja	PERSON
ejpam-5973	641	1	19(4):1105	CARDINAL
ejpam-5973	641	2	1110	DATE
ejpam-5973	641	3	2024	DATE
ejpam-5973	642	1	15	CARDINAL
ejpam-5973	642	2	f. harary	PERSON
ejpam-5973	644	1	addison-wesley publishing company	ORG
ejpam-5973	644	2	massachusetts	GPE
ejpam-5973	644	3	1969	DATE
ejpam-5973	645	1	16	CARDINAL
ejpam-5973	645	2	e. shabani	PERSON
ejpam-5973	645	3	n. jafari rad	PERSON
ejpam-5973	645	4	a. poureidi	PERSON
ejpam-5973	647	1	moldova	ORG
ejpam-5973	647	2	27(1):3–22	CARDINAL
ejpam-5973	647	3	2019	DATE
ejpam-5973	648	1	17	CARDINAL
ejpam-5973	648	2	e. j. cockayne	PERSON
ejpam-5973	648	3	m. dreyer jr.	PERSON
ejpam-5973	648	4	s. m. hedetniemi	PERSON
ejpam-5973	648	5	s. t. hedetniemi	PERSON
ejpam-5973	650	1	278(1	CARDINAL
ejpam-5973	650	2	2004	DATE
ejpam-5973	651	1	18	CARDINAL
ejpam-5973	651	2	d. a. mojdeh	PERSON
ejpam-5973	651	3	z. mansouri	PERSON
ejpam-5973	653	1	combinatorics	ORG
ejpam-5973	653	2	7(4):99–106	DATE
ejpam-5973	653	3	2018	DATE
ejpam-5973	653	4	3rd	ORDINAL