Table 2 Upper bounds of \(\pmb{R(G)}\) for graphs generated by \(\pmb{G_{\mathrm{ER}}(n,0.9)}\) 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 | 9 | 1.00 | 1.41 | 1.17 | 4 | 1.62 | 1.62 |
10 | 43 | 1.00 | 1.61 | 1.15 | 9 | 1.90 | 2.08 |
15 | 102 | 1.00 | 1.57 | 1.13 | 14 | 2.00 | 2.44 |
20 | 176 | 1.00 | 2.19 | 1.22 | 19 | 2.30 | 2.74 |
25 | 284 | 1.00 | 2.09 | 1.19 | 24 | 2.32 | 3.00 |
50 | 1,154 | 1.00 | 2.72 | 1.24 | 49 | 2.79 | 4.04 |
100 | 4,669 | 0.94 | 3.39 | 1.31 | 98 | 3.41 | 5.50 |
250 | 29,507 | 0.96 | 4.63 | 1.42 | 246 | 4.57 | 8.41 |
500 | 118,482 | 0.95 | 6.00 | 1.57 | 488 | 5.91 | 11.68 |
1,000 | 474,713 | 0.96 | 7.96 | 1.79 | 967 | 7.88 | 16.31 |