Table 1 Upper bounds of \(\pmb{R(G)}\) for graphs generated by \(\pmb{G_{\mathrm{ER}}(n,0.5)}\) 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 | 7 | 0.46 | 1.29 | 1.33 | 4 | 1.55 | 1.62 |
10 | 26 | 0.68 | 1.99 | 1.80 | 8 | 2.02 | 2.08 |
15 | 52 | 0.33 | 3.12 | 2.28 | 10 | 2.33 | 2.44 |
20 | 106 | 0.69 | 3.98 | 2.27 | 16 | 2.71 | 2.74 |
25 | 153 | 0.32 | 3.66 | 2.92 | 16 | 2.94 | 3.00 |
50 | 600 | 0.42 | 5.10 | 3.92 | 31 | 3.98 | 4.04 |
100 | 2,463 | 0.56 | 7.30 | 5.43 | 66 | 5.47 | 5.50 |
250 | 15,358 | 0.49 | 9.67 | 8.32 | 142 | 8.38 | 8.41 |
500 | 62,304 | 0.47 | 13.52 | 11.65 | 289 | 11.67 | 11.68 |
1,000 | 249,556 | 0.50 | 17.92 | 16.29 | 549 | 16.30 | 16.31 |