Table 3 Upper bounds of \(\pmb{R(G)}\) for graphs generated by \(\pmb{G_{\mathrm{ER}}(n,0.1)}\) model
From: Bounding the HL-index of a graph: a majorization approach
n | m | R ( G ) | Bound ( 22 ) | Bound ( 1 ) | Bound ( 3 ) | Bound ( 5 ) | |
|---|---|---|---|---|---|---|---|
5 | 4 | 0.00 | 1.26 | 1.25 | 2 | 1.25 | 1.62 |
10 | 11 | 0.33 | 3.09 | 1.46 | 5 | 1.46 | 2.08 |
15 | 17 | 0.00 | 3.51 | 1.49 | 6 | 1.49 | 2.44 |
20 | 25 | 0.12 | 3.07 | 1.57 | 5 | 1.57 | 2.74 |
25 | 40 | 0.00 | 3.18 | 1.76 | 6 | 1.76 | 3.00 |
50 | 112 | 0.04 | 5.07 | 2.09 | 11 | 2.09 | 4.04 |
100 | 501 | 0.09 | 5.23 | 3.08 | 17 | 3.09 | 5.50 |
250 | 3,082 | 0.14 | 7.01 | 4.80 | 36 | 4.80 | 8.41 |
500 | 12,541 | 0.10 | 9.50 | 6.80 | 70 | 6.81 | 11.68 |
1,000 | 49,890 | 0.14 | 12.09 | 9.57 | 126 | 9.57 | 16.31 |