Journal of Mathematics / 2022 / Article / Tab 2 / Research Article
A Novel Mathematical Model for Radio Mean Square Labeling Problem Table 2 Comparison between standard radio mean square number, algorithm, and integer linear programming for the upper bound of radio mean square number for the path graph.
Path graph N Standard RMS Proposed algorithm Integer linear programming rmsn (P n ) CPU time rmsn (P n ) CPU time 1 1 — — — — 2 2 2 0.0001565 2 0.0135961 3 3 3 0.0007495 3 0.0137607 4 4 4 0.0009242 4 0.0142838 5 5 6 0.0009259 9 0.0148360 6 6 7 0.0011930 11 0.0149701 7 7 8 0.0028154 13 0.0151607 8 8 9 0.0031659 15 0.0153437 9 9 10 0.0086583 17 0.0153530 10 10 12 0.0092995 28 0.0153602 11 11 13 0.0178153 31 0.0154630 12 12 14 0.0179739 34 0.0158122 13 13 15 0.0195242 37 0.0159264 14 14 16 0.0214671 40 0.0160664 15 15 17 0.0323685 43 0.0165312 16 17 18 0.0397062 46 0.0165756 17 18 20 0.0488390 65 0.0166756 18 19 21 0.0521773 69 0.0168593 19 20 22 0.0635412 73 0.0168673 20 21 23 0.0773853 77 0.0173017 21 22 24 0.0926470 81 0.0173982 22 23 25 0.1082337 85 0.0174649 23 25 26 0.1321028 89 0.0176519 24 26 27 0.1680530 93 0.0178209 25 27 28 0.1819503 97 0.0178319 26 28 30 0.2174177 126 0.0178408 27 29 31 0.2423215 131 0.0178502 28 30 32 0.2838989 135 0.0179323 29 31 33 0.3306090 142 0.0181244 30 32 34 0.3907487 146 0.0182150 50 54 56 3.3044964 344 0.0295531