| No. of vertices | Graph | Intersection Array |
| 10 | $J(5,2)$ | $\{6,2;1,4\}$ |
| 13 | Paley graph $P_{13}$ | $\{6,3;1,3\}$ |
| 14 | $K_{7,7}-I$ | $\{6,5,1;1,5,6\}$ |
| 15 | $K(6,2)$ | $\{6,4;1,3\}$ |
| 16 | $H(2,4)$ | $\{6,3;1,2\}$ |
| 16 | Shrikhande graph | $\{6,3;1,2\}$ |
| 22 | Incidence graph of $(11,6,3)$-design | $\{6,5,3;1,3,6\}$ |
| 27 | $H(3,3)$ | $\{6,4,2;1,2,3\}$ |
| 32 | Folded 6-cube | $\{6,5,4;1,2,6\}$ |
| 32 | Incidence graphs of biplanes on 16 points (N=3) | $\{6,5,4;1,2,6\}$ |
| 36 | Hexacode graph | $\{6,5,4,1;1,2,5,6\}$ |
| 42 | 2nd subconstituent of Hoffman-Singleton graph | $\{6,5,1;1,1,6\}$ |
| 45 | Halved Foster graph | $\{6,4,2,1;1,1,4,6\}$ |
| 52 | Flag graph of $PG(2,3)$ | $\{6,3,3;1,1,2\}$ |
| 57 | Perkel graph | $\{6,5,2;1,1,3\}$ |
| 62 | Incidence graph of $PG(2,5)$ | $\{6,5,5;1,1,6\}$ |
| 63 | Point graphs of $GH(2,2)$ and its dual | $\{6,4,4;1,1,3\}$ |
| 64 | 6-cube $Q_6 \cong H(6,2)$ | $\{6,5,4,3,2,1;1,2,3,4,5,6\}$ |
| 162 | van Lint-Schrijver graph | $\{6,5,5,4;1,1,2,6\}$ |
| 462 | Odd graph $O_6$ | $\{6,5,5,4,4;1,1,2,2,3\}$ |
Back to: Graphs by valency
Last updated: 4 April 2019