| No. of vertices | Graph | Intersection Array |
| 16 | $K_{8,8}-I$ | $\{7,6,1;1,6,7\}$ |
| 24 | Klein graph | $\{7,4,1;1,2,7\}$ |
| 30 | Incidence graph of $PG(3,2)$ | $\{7,6,4;1,3,7\}$ |
| 50 | Hoffman-Singleton graph | $\{7,6;1,1\}$ |
| 64 | Folded 7-cube | $\{7,6,5;1,2,3\}$ |
| 98 | Incidence graph of $AG(2,7)$ minus a parallel class | $\{7,6,6,1;1,1,6,7\}$ |
| 100 | Doubled Hoffman-Singleton graph | $\{7,6,6,1,1;1,1,6,6,7\}$ |
| 128 | 7-cube $Q_7 \cong H(7,2)$ | $\{7,6,5,4,3,2,1;1,2,3,4,5,6,7\}$ |
| 310 | Doubled Grassmann graph $\mathrm{DJ}_2(5,2)$ | $\{7,6,6,4,4;1,1,3,3,7\}$ |
| 330 | Doubly truncated Witt graph | $\{7,6,4,4;1,1,1,6\}$ |
| 990 | Ivanov-Ivanov-Faradjev graph | $\{7,6,4,4,4,1,1,1;1,1,1,2,4,4,6,7\}$ |
| 1716 | Odd graph $O_7$ | $\{7,6,6,5,5,4;1,1,2,2,3,3\}$ |
| 3432 | Doubled Odd graph $D(O_7)$ | $\{7,6,6,5,5,4,4,3,3,2,2,1,1;1,1,2,2,3,3,4,4,5,5,6,6,7\}$ |
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Last updated: 9 August 2024