| No. of vertices | Graph | Intersection Array |
| $6$ | $\text{Octahedron }J(4,2)$ | $\{4,1;1,4\}$ |
| $9$ | $\text{Paley graph }P_9 \cong H(2,3)$ | $\{4,2;1,2\}$ |
| $10$ | $K_{5,5}-I$ | $\{4,3,1;1,3,4\}$ |
| $14$ | $\text{Distance-3 graph of Heawood graph}$ | $\{4,3,2;1,2,4\}$ |
| $15$ | $\text{Line graph of Petersen graph}$ | $\{4,2,1;1,1,4\}$ |
| $16$ | $\text{4-cube }Q_4 \cong H(4,2)$ | $\{4,3,2,1;1,2,3,4\}$ |
| $21$ | $\text{Line graph of Heawood graph}$ | $\{4,2,2;1,1,2\}$ |
| $26$ | $\text{Incidence graph of PG(2,3)}$ | $\{4,3,3;1,1,4\}$ |
| $32$ | $\text{Incidence graph of }AG(2,4) \text{ minus a parallel class}$ | $\{4,3,3,1;1,1,3,4\}$ |
| $35$ | $\text{Odd graph }O_4$ | $\{4,3,3;1,1,2\}$ |
| $45$ | $\text{Line graph of Tutte's 8-cage}$ | $\{4,3,3;1,1,2\}$ |
| $70$ | $\text{Doubled Odd Graph }D(O_4)$ | $\{4,3,3,2,2,1,1;1,1,2,2,3,3,4\}$ |
| $80$ | $\text{Incidence graph of }GQ(3,3)$ | $\{4,3,3,3;1,1,1,4\}$ |
| $189$ | $\text{Line graph of Tutte's 12-cage}$ | $\{4,2,2,2,2,2;1,1,1,1,1,2\}$ |
| $728$ | $\text{Incidence graph of }GH(3,3)$ | $\{4,3,3,3,3,3;1,1,1,1,1,4\}$ |
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Last updated: 21 February 2017