| No. of vertices | Intersection Array | Graph |
| 16 | $\{4,3,2,1; 1,2,3,4\}$ | 4-cube $Q_4 \cong H(4,2)$ |
| 18 | $\{3,2,2,1;1,1,2,3\}$ | Pappus graph |
| 28 | $\{3,2,2,1;1,1,1,2\}$ | Coxeter graph |
| 30 | $\{3,2,2,2;1,1,1,3\}$ | Tutte's 8-cage |
| 32 | $\{4,3,3,1;1,1,3,4\}$ | Incidence graph of $AG(2,4)$ minus a parallel class |
| 32 | $\{5,4,1,1;1,1,4,5\}$ | Armanios–Wells graph |
| 32 | $\{8,7,4,1;1,4,7,8\}$ | Hadamard graph on 32 vertices |
| 36 | $\{6,5,4,1;1,2,5,6\}$ | Hexacode graph |
| 45 | $\{4,2,2,2;1,1,1,2\}$ | Line graph of Tutte's 8-cage |
| 45 | $\{6,4,2,1;1,1,4,6\}$ | Halved Foster graph |
| 48 | $\{12,11,6,1;1,6,11,12\}$ | Hadamard graph on 48 vertices |
| 50 | $\{5,4,4,1;1,1,4,5\}$ | Incidence graph of $AG(2,5)$ minus a parallel class |
| 54 | $\{9,8,6,1;1,3,8,9\}$ | Incidence graph of $\mathrm{STD}_3[9;3]$ |
| 63 | $\{10,6,4,1;1,2,6,10\}$ | Conway–Smith graph |
| 64 | $\{8,7,6,1;1,2,7,8\}$ | Incidence graph of $\mathrm{STD}_2[8;4]$ |
| 72 | $\{12,11,8,1;1,4,11,12\}$ | Suetake graph |
| 80 | $\{4,3,3,3;1,1,1,4\}$ | Incidence graph of $GQ(3,3)$ |
| 81 | $\{8,6,4,2;1,2,3,4\}$ | $H(4,3)$ |
| 98 | $\{7,6,6,1;1,1,6,7\}$ | Incidence graph of $AG(2,7)$ minus a parallel class |
| 100 | $\{15,14,10,3;1,5,12,15\}$ | Cocliques in Hoffman–Singleton graph |
| 126 | $\{5,4,4,3;1,1,2,2\}$ | Odd graph $O_5$ |
| 128 | $\{8,7,7,1;1,1,7,8\}$ | Incidence graph of $AG(2,8)$ minus a parallel class |
| 128 | $\{8,7,6,5;1,2,3,8\}$ | Folded 8-cube |
| 128 | $\{28,15,6,1;1,6,15,28\}$ | Halved 8-cube |
| 160 | $\{6,3,3,3;1,1,1,2\}$ | Flag graph of $GQ(3,3)$ |
| 162 | $\{6,5,5,4;1,1,2,6\}$ | van Lint–Schrijver graph |
| 162 | $\{9,8,8,1;1,1,8,9\}$ | Incidence graph of $AG(2,9)$ minus a parallel class |
| 170 | $\{5,4,4,4;1,1,1,5\}$ | Incidence graph of $GQ(4,4)$ |
| 256 | $\{12,9,6,3;1,2,3,4\}$ | $H(4,4)$ |
| 256 | $\{9,8,7,6;1,2,3,4\}$ | Folded 9-cube |
| 256 | $\{36,21,10,3;1,6,15,28\}$ | Halved 9-cube |
| 266 | $\{11,10,6,1;1,1,5,11\}$ | Livingstone graph |
| 280 | $\{9,8,6,3;1,1,3,8\}$ | Unitals in $PG(2,4)$ |
| 288 | $\{12,11,10,7;1,2,5,12\}$ | Leonard graph |
| 315 | $\{10,8,8,2;1,1,4,5\}$ | Hall–Janko/Cohen–Tits near octagon from $J_2.2$ |
| 315 | $\{32,27,8,1;1,4,27,32\}$ | Soicher's 3rd graph |
| 330 | $\{7,6,4,4;1,1,1,6\}$ | Doubly truncated Witt graph |
| 378 | $\{45,32,12,1;1,6,32,45\}$ | Antipodal 3-cover of Zara graph |
| 425 | $\{8,4,4,4;1,1,1,2\}$ | Flag graph of $GQ(4,4)$ |
| 486 | $\{45,44,36,5;1,9,40,45\}$ | Koolen–Riebeek graph |
| 486 | $\{56,45,16,1;1,8,45,56\}$ | Soicher's 2nd graph |
| 1134 | $\{117,80,24,1;1,12,80,117\}$ | Norton–Smith graph |
| 1344 | $\{176,135,29,1;1,24,135,176\}$ | Meixner double-cover of $U_6(2)$ graph |
| 1755 | $\{\}$ | Ree-Tits Generalized Octagon, $GO(2,4)$ |
| 2688 | $\{176,135,36,1;1,12,135,176\}$ | Meixner quadruple cover of $U_6(2)$ graph |
| 5346 | $\{416,315,64,1;1,32,315,416\}$ | Soicher's 1st graph |
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Last updated: 1 March 2024