| No. of vertices | Intersection Array | Graph |
| 8 | $\{3,2,1;1,2,3\}$ | 3-cube $Q_3 \cong H(3,2)$ |
| 10 | $\{4,3,1; 1,3,4\}$ | $K_{5,5}-I$ |
| 12 | $\{5,4,1; 1,4,5\}$ | $K_{6,6}-I$ |
| 12 | $\{5,2,1;1,2,5\}$ | Icosahedron |
| 14 | $\{3,2,2;1,1,3\}$ | Heawood graph (Incidence graph of $PG(2,2)$) |
| 14 | $\{4,3,2;1,2,4\}$ | Distance-3 graph of Heawood graph (Non-incidence graph of $PG(2,2)$) |
| 14 | $\{6,5,1; 1,5,6\}$ | $K_{7,7}-I$ |
| 15 | $\{4,2,1;1,1,4\}$ | Line graph of Petersen graph |
| 16 | $\{7,6,1; 1,6,7\}$ | $K_{8,8}-I$ |
| 18 | $\{8,7,1; 1,7,8\}$ | $K_{9,9}-I$ |
| 20 | $\{9,4,1;1,4,9\}$ | $J(6,3)$ |
| 20 | $\{9,8,1; 1,8,9\}$ | $K_{10,10}-I$ |
| 21 | $\{4,2,2;1,1,2\}$ | Line graph of Heawood graph (Flag graph of $PG(2,2)$) |
| 22 | $\{5,4,3;1,2,5\}$ | Incidence graph of biplane on 11 points |
| 22 | $\{6,5,3;1,3,6\}$ | Incidence graph of $(11,6,3)$-design |
| 22 | $\{10,9,1; 1,9,10\}$ | $K_{11,11}-I$ |
| 24 | $\{7,4,1;1,2,7\}$ | Klein graph |
| 24 | $\{11,10,1; 1,10,11\}$ | $K_{12,12}-I$ |
| 26 | $\{4,3,3;1,1,4\}$ | Incidence graph of $PG(2,3)$ |
| 26 | $\{9,8,3;1,6,9\}$ | Incidence graph of $(13,9,3)$-design |
| 26 | $\{12,11,1; 1,11,12\}$ | $K_{13,13}-I$ |
| 27 | $\{6,4,2;1,2,3\}$ | $H(3,3)$ |
| 27 | $\{8,6,1;1,3,8\}$ | $GQ(2,4)$ minus spread (2 graphs) |
| 28 | $\{13,16,1;1,6,13\}$ | Taylor graph from $P_{13}$ |
| 28 | $\{13,12,1; 1,12,13\}$ | $K_{14,14}-I$ |
| 30 | $\{7,6,4;1,3,7\}$ | Incidence graph of $PG(3,2)$ |
| 30 | $\{7,6,4;1,3,7\}$ | Incidence graphs of Hadamard $(15,7,3)$-designs |
| 30 | $\{8,7,4;1,4,8\}$ | Incidence graph of complement of $PG(3,2)$ |
| $30$ | $\{8,7,4;1,4,8\}$ | Incidence graphs of $(15,8,4)$-designs (N=4) |
| 30 | $\{14,13,1; 1,13,14\}$ | $K_{15,15}-I$ |
| 32 | $\{6,5,4;1,2,6\}$ | Folded 6-cube |
| 32 | $\{6,5,4;1,2,6\}$ | Incidence graphs of biplanes on 16 points |
| 32 | $\{8,7,4;1,4,8\}$ | Incidence graphs of $(16,10,6)$-designs |
| 32 | $\{15,6,1; 1,6,15\}$ | Taylor graph from $J(6,2) \cong$ Halved 6-cube |
| 32 | $\{15,8,1; 1,8,15\}$ | Taylor graph from $K(6,2)$ |
| 32 | $\{15,14,1; 1,14,15\}$ | $K_{16,16}-I$ |
| 34 | $\{16,15,1; 1,15,16\}$ | $K_{17,17}-I$ |
| 35 | $\{4,3,3;1,1,2\}$ | Odd graph $O_4$ |
| 35 | $\{12,6,2;1,4,9\}$ | $J(7,3)$ |
| 36 | $\{5,4,2;1,1,4\}$ | Sylvester graph |
| 36 | $\{17,8,1;1,8,17\}$ | Taylor graph from $P_{17}$ |
| 38 | $\{9,8,5;1,4,9\}$ | Incidence graphs of Hadamard $(19,9,4)$-designs |
| 42 | $\{13,8,1;1,4,13\}$ | Coolsaet-Degraer 3-cover of $K_{14}$ |
| 42 | $\{5,4,4;1,1,5\}$ | Incidence graph of $PG(2,4)$ |
| 42 | $\{13,8,1;1,4,13\}$ | Symplectic 3-cover of $K_{14}$ |
| 42 | $\{6,5,1;1,1,6\}$ | 2nd subconstituent of Hoffman-Singleton graph |
| 51 | $\{16,10,1;1,5,16\}$ | Symplectic 3-cover of $K_{17}$ |
| 52 | $\{6,3,3;1,1,2\}$ | Flag graph of $PG(2,3)$ |
| 56 | $\{15,8,3;1,4,9\}$ | $J(8,3)$ |
| 56 | $\{27,10,1;1,10,27\}$ | Gosset graph |
| 56 | $\{27,16,1;1,16,27\}$ | Distance-2 graph of Gosset graph |
| 57 | $\{6,5,2;1,1,3\}$ | Perkel graph |
| 60 | $\{11,8,1;1,2,11\}$ | Symplectic 5-cover of $K_{12}$ |
| 62 | $\{6,5,5;1,1,6\}$ | Incidence graph of $PG(2,5)$ |
| 62 | $\{15,14,8;1,7,15\}$ | Incidence graph of $PG(4,2)$ |
| 63 | $\{6,4,4;1,1,3\}$ | Point graphs of $GH(2,2)$ and its dual |
| 63 | $\{8,6,1;1,1,8\}$ | Symplectic 7-cover of $K_9$ |
| 64 | $\{9,6,3;1,2,3\}$ | $H(3,4)$ |
| 64 | $\{7,6,5;1,2,3\}$ | Folded 7-cube |
| 64 | $\{21,10,3;1,6,15\}$ | Halved 7-cube |
| 65 | $\{10,6,4;1,2,5\}$ | Hall graph |
| 68 | $\{12,10,3;1,3,8\}$ | Doro graph |
| 80 | $\{13,12,9;1,4,13\}$ | Incidence graph of $PG(3,3)$ |
| 84 | $\{18,10,4;1,4,9\}$ | $J(9,3)$ |
| 85 | $\{16,12,1;1,3,16\}$ | Symplectic 5-cover of $K_{17}$ |
| 105 | $\{8,4,4;1,1,2\}$ | Flag graph of $PG(2,4)$ |
| 114 | $\{8,7,7;1,1,8\}$ | Incidence graph of $PG(2,7)$ |
| 120 | $\{21,12,5;1,4,9\}$ | $J(10,3)$ |
| 125 | $\{12,8,4;1,2,3\}$ | $H(3,5)$ |
| 146 | $\{9,8,8;1,1,9\}$ | Incidence graph of $PG(2,8)$ |
| 175 | $\{12,6,5;1,1,4\}$ | Line graph of Hoffman-Singleton graph |
| 182 | $\{10,9,9;1,1,10\}$ | Incidence graph of $PG(2,9)$ |
| 186 | $\{10,5,5;1,1,2\}$ | Flag graph of $PG(2,5)$ |
| 208 | $\{12,10,5;1,1,8\}$ | Unitary graph from $\mathrm{P} \Gamma \mathrm{U}(3,4)$ |
| 266 | $\{12,11,11;1,1,12\}$ | Incidence graph of $PG(2,11)$ |
| 288 | $\{66,65,36;1,30,66\}$ | Incidence graphs of Leonard semibiplanes |
| 352 | $\{175,102,1;1,102,175\}$ | Taylor graph from Higman-Sims group (a) |
| 352 | $\{175,72,1;1,72,175\}$ | Taylor graph from Higman-Sims group (b) |
| 352 | $\{50,49,36;1,14,50\}$ | Incidence graph of Higman's symmetric design |
| 364 | $\{12,9,9;1,1,4\}$ | Point graph of $GH(3,3)$ |
| 462 | $\{36,25,16;1,4,18\}$ | Folded Johnson graph $J(12,6)$ |
| 506 | $\{15,14,12;1,1,9\}$ | Truncated Witt graph |
| 512 | $\{21,20,16;1,2,12\}$ | Coset graph of doubly truncated binary Golay code |
| 525 | $\{20,18,6;1,1,15\}$ | Unitary graph from $\mathrm{P} \Gamma \mathrm{U}(3,5)$ |
| 552 | $\{275,112,1;1,112,275\}$ | Taylor graph from $Co_3$ (a) |
| 552 | $\{275,162,1;1,162,275\}$ | Taylor graph from $Co_3$ (b) |
| 672 | $\{110,81,12;1,18,90\}$ | Moscow-Soicher graph |
| 729 | $\{24,22,20;1,2,12\}$ | Coset graph of extended ternary Golay code |
| 759 | $\{30,28,24;1,3,15\}$ | Witt graph |
| 1024 | $\{22,21,20;1,2,6\}$ | Coset graph of truncated binary Golay code |
| 1024 | $\{231,160,6;1,48,210\}$ | Distance-2 graph of coset graph of truncated binary Golay code |
| 1024 | $\{33,30,15;1,2,15\}$ | Shi-Krotov-Solé graph |
| 1395 | $\{98,72,32;1,9,49\}$ | Grassmann graph $J_2(6,3)$ |