A Novel Mathematical Model for Radio Mean Square Labeling Problem

Table 3

Comparison between standard radio mean square number, algorithm, and integer linear programming for the upper bound of radio mean square number for the cycle graph.

Cycle graph
N	Standard RMS	Proposed algorithm		Integer linear programming
		rmsn (Cn)	CPU time	rmsn (Cn)	CPU time
1	—	—	—	—	—
2	—	—	—	—	—
3	3	3	0.0002946	3	0.0121703
4	4	4	0.0006198	4	0.0128697
5	5	5	0.0013164	5	0.0130696
6	6	6	0.0017746	6	0.0134300
7	7	7	0.0023419	7	0.0137379
8	8	9	0.0037564	15	0.0137439
9	10	10	0.0050932	17	0.0140673
10	10	11	0.0060342	19	0.0143174
11	11	12	0.0088211	21	0.0143427
12	12	13	0.0148844	23	0.0147269
13	13	14	0.0172248	25	0.0147985
14	14	15	0.0203240	27	0.0149231
15	15	16	0.0251720	29	0.0151018
16	17	17	0.0323380	31	0.0151929
17	18	18	0.0397318	33	0.0155649
18	19	20	0.0492787	52	0.0156036
19	20	21	0.0612156	55	0.0156856
20	21	22	0.0765414	58	0.0157774
21	22	23	0.0898619	61	0.0160212
22	23	24	0.1191102	64	0.0162420
23	24	25	0.1328831	67	0.0163022
24	25	26	0.1583415	70	0.0165312
25	26	27	0.1758159	73	0.0165648
26	27	28	0.2122978	76	0.0165116
27	28	29	0.2491384	79	0.0166234
28	30	30	0.2822584	82	0.0167352
29	31	31	0.3290932	85	0.0168470
30	32	32	0.3655289	88	0.0171844
50	53	54	3.0468593	246	0.0250638