| No. of vertices | Intersection Array | Parameters $(n,k,\lambda,\mu)$ | Graph |
| 5 | $\{2,1;1,1\}$ | $(5,2,0,1)$ | Paley graph $P_5$ |
| 6 | $\{4,1;1,4\}$ | $(6,4,2,4)$ | Octahedron |
| 9 | $\{4,2;1,2\}$ | $(9,4,1,2)$ | Paley graph $P_9$ |
| 10 | $\{3,2;1,1\}$ | $(10,3,0,1)$ | Petersen graph |
| 10 | $\{6,2;1,4\}$ | $(10,6,3,4)$ | $J(5,2)$ |
| 13 | $\{6,3;1,3\}$ | $(13,6,2,3)$ | Paley graph $P_{13}$ |
| 15 | $\{8,3;1,4\}$ | $(15,8,4,4)$ | $J(6,2)$ |
| 15 | $\{6,4;1,3\}$ | $(15,6,1,3)$ | $K(6,2) \cong \mathrm{NO}_4^-(3)$ graph $\cong \mathrm{O}_5(2)$ graph $\cong \mathrm{Sp}_4(2)$ graph |
| 16 | $\{5,4;1,2\}$ | $(16,5,0,2)$ | Clebsch graph |
| 16 | $\{6,3;1,2\}$ | $(16,6,2,2)$ | Shrikhande graph |
| 16 | $\{9,4;1,6\}$ | $(16,9,4,6)$ | Complement of Shrikhande graph |
| 16 | $\{6,3;1,2\}$ | $(16,6,2,2)$ | $H(2,4)$ |
| 16 | $\{9,4;1,6\}$ | $(16,9,4,6)$ | $\mathrm{VO}_4^+(2)$ graph $\cong$ Bilinear forms graph $\mathrm{H}_2(2,2) \cong$ Complement of $H(2,4)$ |
| 16 | $\{10,3;1,6\}$ | $(16,10,6,6)$ | Complement of Clebsch graph |
| 17 | $\{8,4; 1,4\}$ | $(17,8,3,4)$ | Paley graph $P_{17}$ |
| 21 | $\{10,4;1,4\}$ | $(21,10,5,4)$ | $J(7,2)$ |
| 21 | $\{10,6;1,6\}$ | $(21,10,3,6)$ | $\mathrm{K}(7,2)$ |
| 25 | $\{8,4;1,2\}$ | $(25,8,3,2)$ | $H(2,5)$ |
| 25 | $\{12,6; 1,6\}$ | $(25,12,5,6)$ | Paley graph $P_{25}$ |
| 25 | $\{12,6;1,6\}$ | $(25,12,5,6)$ | Paulus graphs on 25 vertices |
| 26 | $\{10,6;1,4\}$ | $(26,10,3,4)$ | Paulus graphs on 26 vertices |
| 26 | $\{15,6;1,9\}$ | $(26,15,8,9)$ | Complements of Paulus graphs on 26 vertices |
| 27 | $\{10,8;1,5\}$ | $(27,10,1,5)$ | Complement of Schläfli graph |
| 27 | $\{16,5;1,8\}$ | $(27,16,10,8)$ | Schläfli graph |
| 28 | $\{12,5;1,4\}$ | $(28,12,6,4)$ | $J(8,2)$ |
| 28 | $\{15,8;1,10\}$ | $(28,15,6,10)$ | $K(8,2) \cong \mathrm{NO}_6^+(2)$ graph |
| 28 | $\{12,5;1,4\}$ | $(28,12,6,4)$ | Chang graphs |
| 28 | $\{15,8;1,10\}$ | $(28,15,6,10)$ | Complement of Chang graphs |
| 29 | $\{14,7; 1,7\}$ | $(29,14,6,7)$ | Paley graph $P_{29}$ |
| 29 | $\{14,7; 1,7\}$ | $(29,14,6,7)$ | 40 (non-Paley) $\mathrm{SRG}(29,14,6,7)$s |
| 35 | $\{16,9;1,8\}$ | $(35,16,6,8)$ | Folded Johnson graph $J(8,4) \cong$ Merged Johnson graph $J(7,3)$ |
| 35 | $\{18,8;1,9\}$ | $(35,18,9,9)$ | Grassmann graph $J_2(4,2) \cong \mathrm{O}_6^+(2)$ graph |
| 36 | $\{14,9;1,6\}$ | $(36,14,4,6)$ | $\mathrm{G}_2(2)$ graph |
| 36 | $\{14,6;1,4\}$ | $(36,14,7,4)$ | $J(9,2)$ |
| 36 | $\{21,10;1,15\}$ | $(36,21,10,15)$ | $K(9,2)$ |
| 36 | $\{10,5;1,2\}$ | $(36,10,4,2)$ | $H(2,6)$ |
| 36 | $\{15,8;1,6\}$ | $(36,15,6,6)$ | $\mathrm{NO}_6^-(2)$ graph $\cong \mathrm{NO}_5^{- \perp}(3)$ graph |
| 37 | $\{18,9; 1,9\}$ | $(37,18,8,9)$ | Paley graph $P_{37}$ |
| 40 | $\{12,9;1,4\}$ | $(40,12,2,4)$ | Point graphs of $GQ(3,3)$s |
| 41 | $\{20,10; 1,10\}$ | $(41,20,9,10)$ | Paley graph $P_{41}$ |
| 45 | $\{12,8;1,3\}$ | $(45,12,3,3)$ | Point graph of $GQ(4,2)$ |
| 45 | $\{16,7;1,4\}$ | $(45,16,8,4)$ | $J(10,2)$ |
| 45 | $\{28,12;1,21\}$ | $(45,28,15,21)$ | $K(10,2)$ |
| 49 | $\{24,12; 1,12\}$ | $(49,24,11,12)$ | Paley graph $P_{49}$ |
| 49 | $\{24,12; 1,12\}$ | $(49,24,11,12)$ | Peisert graph on 49 vertices |
| 49 | $\{12,6;1,2\}$ | $(49,12,5,2)$ | $H(2,7)$ |
| 50 | $\{7,6;1,1\}$ | $(50,7,0,1)$ | Hoffman-Singleton graph |
| 53 | $\{26,13; 1,13\}$ | $(53,26,12,13)$ | Paley graph $P_{53}$ |
| 55 | $\{18,8; 1,4\}$ | $(55,18,9,4)$ | $J(11,2)$ |
| 55 | $\{36,14;1,28\}$ | $(55,36,21,28)$ | $\mathrm{K}(11,2)$ |
| 56 | $\{10,9;1,2\}$ | $(56,10,0,2)$ | Gewirtz graph |
| 61 | $\{30,15; 1,15\}$ | $(61,30,14,15)$ | Paley graph $P_{61}$ |
| 63 | $\{30,16; 1,15\}$ | $(63,30,13,15)$ | $\mathrm{Sp}_6(2)$ graph $\cong \mathrm{O}_7(2)$ graph |
| 64 | $\{14,7;1,2\}$ | $(64,14,6,2)$ | $H(2,8)$ |
| 64 | $\{21,12;1,6\}$ | $(64,21,8,6)$ | Bilinear forms graph $\mathrm{H}_2(2,3) \cong$ Van Lint–Schrijver graph on 64 vertices |
| 64 | $\{28,15;1,12\}$ | $(64,28,12,12)$ | Halved folded 8-cube |
| 64 | $\{18,15;1,6\}$ | $(64,18,2,6)$ | Point graph of $GQ(3,5)$ |
| 64 | $\{27,16;1,12\}$ | $(64,27,10,12)$ | $\mathrm{VO}_6^-(2)$ graph |
| 64 | $\{35,16;1,20\}$ | $(64,35,18,20)$ | $\mathrm{VO}_6^+(2)$ graph |
| 65 | $\{32,16;1,16\}$ | $(65,32,15,16)$ | Gritsenko graph |
| 66 | $\{20,9;1,4\}$ | $(66,20,10,4)$ | $J(12,2)$ |
| 66 | $\{45,16;1,36\}$ | $(66,45,28,36)$ | $\mathrm{K}(12,2)$ |
| 73 | $\{36,18; 1,18\}$ | $(73,36,17,18)$ | Paley graph $P_{73}$ |
| 77 | $\{16,15;1,4\}$ | $(77,16,0,4)$ | $\mathrm{M}_{22}$ graph |
| 78 | $\{22,10;1,4\}$ | $(78,22,11,4)$ | $J(13,2)$ |
| 78 | $\{55,18;1,45\}$ | $(78,55,36,45)$ | $\mathrm{K}(13,2)$ |
| 81 | $\{20,18;1,6\}$ | $(81,20,1,6)$ | Brouwer–Haemers graph $\cong \mathrm{VO}_4^-(3)$ graph |
| 81 | $\{16,8;1,2\}$ | $(81,16,7,2)$ | $H(2,9)$ |
| 81 | $\{40,20;1,20\}$ | $(81,40,19,20)$ | Paley graph $P_{81}$ |
| 81 | $\{40,20;1,20\}$ | $(81,40,19,20)$ | Peisert graph on 81 vertices |
| 81 | $\{30,20;1,12\}$ | $(81,30,9,12)$ | $\mathrm{VNO}_4^-(3)$ graph |
| 81 | $\{32,18;1,12\}$ | $(81,32,13,12)$ | $\mathrm{VO}_4^+(3)$ graph $\cong$ Bilinear forms graph $\mathrm{H}_3(2,2)$ |
| 85 | $\{20,16;1,5\}$ | $(85,20,3,5)$ | Point graph of $GQ(4,4)$ |
| 89 | $\{44,22; 1,22\}$ | $(89,44,21,22)$ | Paley graph $P_{89}$ |
| 91 | $\{24,11; 1,4\}$ | $(91,24,12,4)$ | $J(14,2)$ |
| 91 | $\{66,20;1,55\}$ | $(91,66,45,55)$ | $\mathrm{K}(14,2)$ |
| 97 | $\{48,24; 1,24\}$ | $(97,48,23,24)$ | Paley graph $P_{97}$ |
| 100 | $\{18,9;1,2\}$ | $(100,18,8,2)$ | $H(2,10)$ |
| 100 | $\{22,21;1,6\}$ | $(100,22,0,6)$ | Higman-Sims graph |
| 100 | $\{36,21;1,12\}$ | $(100,36,14,12)$ | Hall-Janko graph |
| 101 | $\{50,25; 1,25\}$ | $(101,50,24,25)$ | Paley graph $P_{101}$ |
| 105 | $\{32,27;1,12\}$ | $(105,32,4,12)$ | Goethals-Seidel graph |
| 105 | $\{26,12;1,4\}$ | $(105,26,13,4)$ | $J(15,2)$ |
| 105 | $\{78,22;1,66\}$ | $(105,78,55,66)$ | $\mathrm{K}(15,2)$ |
| 109 | $\{54,27;1,27\}$ | $(109,54,26,27)$ | Paley graph $P_{109}$ |
| 112 | $\{30,27;1,10\}$ | $(112,30,2,10)$ | 1st subconstituent of McLaughlin graph |
| 113 | $\{56,28;1,28\}$ | $(113,56,27,28)$ | Paley graph $P_{113}$ |
| 117 | $\{36,20;1,9\}$ | $(117,36,15,9)$ | $\mathrm{NO}_6^+(3)$ graph |
| 119 | $\{54,32;1,27\}$ | $(119,54,21,27)$ | $\mathrm{O}_8^-(2)$ graph |
| 120 | $\{28,13;1,4\}$ | $(120,28,14,4)$ | $J(16,2)$ |
| 120 | $\{91,24;1,78\}$ | $(120,91,66,78)$ | $\mathrm{K}(16,2)$ |
| 120 | $\{42,33;1,18\}$ | $(120,42,8,18)$ | $\mathrm{L}_3(4).2^2$ graph |
| 120 | $\{56,27;1,24\}$ | $(120,56,28,24)$ | Merged Johnson graph $J(10,3)$ |
| 120 | $\{51,32;1,24\}$ | $(120,51,18,24)$ | $\mathrm{NO}_5^-(4)$ graph |
| 120 | $\{63,32;1,36\}$ | $(120,63,30,36)$ | $\mathrm{NO}_8^+(2)$ graph |
| 120 | $\{56,27;1,24\}$ | $(120,56,28,24)$ | $\overline{\mathrm{NO}_8^+(2)}$ graph |
| 121 | $\{20,10;1,2\}$ | $(121,20,9,2)$ | $H(2,11)$ |
| 121 | $\{60,30;1,30\}$ | $(121,60,29,30)$ | Paley graph $P_{121}$ |
| 121 | $\{60,30;1,30\}$ | $(121,60,29,30)$ | Peisert graph on 121 vertices |
| 121 | $\{40,24;1,12\}$ | $(121,40,15,12)$ | Van Lint–Schrijver graph on 121 vertices |
| 125 | $\{62,31;1,31\}$ | $(125,62,30,31)$ | Paley graph $P_{125}$ |
| 126 | $\{25,16;1,4\}$ | $(126,25,8,4)$ | Folded Johnson graph $J(10,5) \cong$ Merged Johnson graph $J(9,4)$ |
| 126 | $\{50,36;1,24\}$ | $(126,50,13,24)$ | Goethals graph |
| 126 | $\{45,32;1,18\}$ | $(126,45,12,18)$ | Zara graph on 126 vertices $\cong \mathrm{NO}_6^-(3)$ graph |
| 130 | $\{48,27;1,16\}$ | $(130,48,20,16)$ | Grassmann graph $J_3(4,2)$ |
| 135 | $\{64,35;1,32\}$ | $(135,64,28,32)$ | $\overline{\mathrm{O}_8^+(2)}$ graph |
| 135 | $\{70,32;1,35\}$ | $(135,70,37,35)$ | $\mathrm{O}_8^+(2)$ graph |
| 136 | $\{30,14;1,4\}$ | $(136,30,15,4)$ | $J(17,2)$ |
| 136 | $\{105,26;1,91\}$ | $(136,105,78,91)$ | $\mathrm{K}(17,2)$ |
| 136 | $\{75,32;1,40\}$ | $(136,75,42,40)$ | $\mathrm{NO}_5^+(4)$ graph |
| 136 | $\{60,35;1,28\}$ | $(136,60,24,28)$ | $\overline{\mathrm{NO}_5^+(4)}$ graph |
| 136 | $\{63,32;1,28\}$ | $(136,63,30,28)$ | $\mathrm{NO}_8^-(2)$ graph |
| 137 | $\{68,34;1,34\}$ | $(137,68,33,34)$ | Paley graph $P_{137}$ |
| 144 | $\{39,32;1,12\}$ | $(144,39,6,12)$ | Faradžev–Klin–Muzychuk graph from $\mathrm{L}_3(3)$ |
| 144 | $\{66,35;1,30\}$ | $(144,66,30,30)$ | Halved Leonard graph |
| 144 | $\{22,11;1,2\}$ | $(144,22,10,2)$ | $H(2,12)$ |
| 149 | $\{74,37;1,37\}$ | $(149,74,36,37)$ | Paley graph $P_{149}$ |
| 153 | $\{32,15;1,4\}$ | $(153,32,16,4)$ | $J(18,2)$ |
| 153 | $\{120,28;1,105\}$ | $(153,120,91,105)$ | $\mathrm{K}(18,2)$ |
| 155 | $\{42,24;1,9\}$ | $(155,42,17,9)$ | Grassmann graph $J_2(5,2)$ |
| 156 | $\{30,25;1,6\}$ | $(156,30,4,6)$ | Point graphs of $\mathrm{GQ}(5,5)$s |
| 157 | $\{78,39;1,39\}$ | $(157,78,38,39)$ | Paley graph $P_{157}$ |
| 162 | $\{56,45;1,24\}$ | $(162,56,10,24)$ | 2nd subconstituent of McLaughlin graph |
| 162 | $\{105,32;1,60\}$ | $(162,105,72,60)$ | Complement of the 2nd sub– constituent of McLaughlin graph |
| 165 | $\{36,32;1,9\}$ | $(165,36,3,9)$ | Point graph of $\mathrm{GQ}(4,8) \cong \mathrm{U}(5,2)$ graph |
| 169 | $\{24,12;1,2\}$ | $(169,24,11,2)$ | $H(2,13)$ |
| 169 | $\{84,42;1,42\}$ | $(169,84,41,42)$ | Paley graph $P_{169}$ |
| 169 | $\{72,40;1,30\}$ | $(169,72,31,30)$ | Rank-3 $\mathrm{SRG}(169,72,31,30)$ |
| 171 | $\{34,16;1,4\}$ | $(171,34,17,4)$ | $J(19,2)$ |
| 171 | $\{136,30;1,120\}$ | $(171,136,105,120)$ | $\mathrm{K}(19,2)$ |
| 173 | $\{86,43;1,43\}$ | $(173,86,42,43)$ | Paley graph $P_{173}$ |
| 175 | $\{72,51;1,36\}$ | $(175,72,20,36)$ | Distance-2 graph of line graph of Hoffman-Singleton graph |
| 176 | $\{40,27;1,8\}$ | $(176,40,12,8)$ | $\overline{\mathrm{NU}_5(2)}$ graph |
| 176 | $\{135,32;1,108\}$ | $(176,135,102,108)$ | $\mathrm{NU}_5(2)$ graph |
| 176 | $\{70,51;1,34\}$ | $(176,70,18,34)$ | $\mathrm{SRG}(176,70,18,34)$ |
| 176 | $\{105,36;1,54\}$ | $(176,105,68,54)$ | $\mathrm{SRG}(176,105,68,54)$ |
| 181 | $\{90,45;1,45\}$ | $(181,90,44,45)$ | Paley graph $P_{181}$ |
| 190 | $\{36,17;1,4\}$ | $(190,36,18,4)$ | $J(20,2)$ |
| 190 | $\{153,32;1,136\}$ | $(190,153,120,136)$ | $\mathrm{K}(20,2)$ |
| 196 | $\{26,13;1,2\}$ | $(196,26,12,2)$ | $H(2,14)$ |
| 208 | $\{75,44;1,25\}$ | $(208,75,30,25)$ | $\mathrm{NU}_3(4)$ graph |
| 210 | $\{38,18;1,4\}$ | $(210,38,19,4)$ | $J(21,2)$ |
| 210 | $\{171,34;1,153\}$ | $(210,171,136,153)$ | $\mathrm{K}(21,2)$ |
| 216 | $\{40,35;1,8\}$ | $(216,40,4,8)$ | Rijeka graph |
| 225 | $\{28,14;1,2\}$ | $(225,28,13,2)$ | $H(2,15)$ |
| 231 | $\{30,20;1,3\}$ | $(231,30,9,3)$ | Cameron graph |
| 231 | $\{40,19;1,4\}$ | $(231,40,20,4)$ | $J(22,2)$ |
| 231 | $\{190,36;1,171\}$ | $(231,190,153,171)$ | $\mathrm{K}(22,2)$ |
| 243 | $\{22,20;1,2\}$ | $(243,22,1,2)$ | Berlekamp-van Lint-Seidel graph |
| 243 | $\{110,72;1,60\}$ | $(243,110,37,60)$ | Delsarte graph |
| 253 | $\{42,20;1,4\}$ | $(253,42,21,4)$ | $J(23,2)$ |
| 253 | $\{210,38;1,190\}$ | $(253,210,171,190)$ | $\mathrm{K}(23,2)$ |
| 253 | $\{112,75;1,60\}$ | $(253,112,36,60)$ | $\mathrm{M}_{23}$ graph |
| 255 | $\{126,64;1,63\}$ | $(255,126,61,63)$ | $\mathrm{Sp}_8(2)$ graph $\cong \mathrm{O}_9(2)$ graph |
| 256 | $\{30,15;1,2\}$ | $(256,30,14,2)$ | $H(2,16)$ |
| 256 | $\{45,28;1,6\}$ | $(256,45,16,6)$ | $\mathrm{H}_2(4,2)$ graph |
| 256 | $\{45,28;1,6\}$ | $(256,45,16,6)$ | Halved folded 10-cube |
| 256 | $\{102,63;1,42\}$ | $(256,102,38,42)$ | $2^8.\mathrm{L}_2(17)$ graph |
| 256 | $\{85,60;1,30\}$ | $(256,85,24,30)$ | Van Lint–Schrijver graph on 256 vertices |
| 256 | $\{51,48;1,12\}$ | $(256,51,2,12)$ | $\mathrm{VO}_4^-(4)$ graph |
| 256 | $\{75,48;1,20\}$ | $(256,75,26,20)$ | $\mathrm{VO}_4^+(4)$ graph $\cong \mathrm{H}_4(2,2)$ graph |
| 256 | $\{119,64;1,56\}$ | $(256,119,54,56)$ | $\mathrm{VO}_8^-(2)$ graph |
| 256 | $\{135,64;1,72\}$ | $(256,135,70,72)$ | $\mathrm{VO}_8^+(2)$ graph |
| 275 | $\{112,81;1,56\}$ | $(275,112,30,56)$ | McLaughlin graph |
| 276 | $\{44,21;1,4\}$ | $(276,44,22,4)$ | $J(24,2)$ |
| 276 | $\{231,40;1,210\}$ | $(276,231,190,210)$ | $\mathrm{K}(24,2)$ |
| 280 | $\{36,27;1,4\}$ | $(280,36,8,4)$ | Cocliques in Hall–Janko graph (Graph with valency 36) |
| 280 | $\{135,64;1,60\}$ | $(280,135,70,60)$ | Cocliques in Hall–Janko graph (Graph with valency 135) |
| 280 | $\{117,72;1,52\}$ | $(280,117,44,52)$ | Mathon–Rosa graph |
| 280 | $\{36,27;1,4\}$ | $(280,36,8,4)$ | Point graph of $GQ(9,3)$ |
| 289 | $\{32,16;1,2\}$ | $(289,32,15,2)$ | $H(2,17)$ |
| 289 | $\{144,72;1,72\}$ | $(289,144,71,72)$ | Paley graph $P_{289}$ |
| 289 | $\{96,60;1,30\}$ | $(289,96,35,30)$ | Van Lint–Schrijver graph on 289 vertices |
| 297 | $\{40,32;1,5\}$ | $(297,40,7,5)$ | Point graph of $\mathrm{GQ}(8,4) \cong$ Dual polar graph $\phantom{.}^2 \mathrm{A}_4(2)$ |
| 300 | $\{46,22;1,4\}$ | $(300,46,23,4)$ | $J(25,2)$ |
| 300 | $\{253,42;1,231\}$ | $(300,253,210,231)$ | $\mathrm{K}(25,2)$ |
| 300 | $\{104,75;1,40\}$ | $(300,104,28,40)$ | $\mathrm{NO}_5^-(5)$ graph |
| 300 | $\{65,54;1,15\}$ | $(300,65,10,15)$ | $\mathrm{NO}_5^{- \perp}(5)$ graph |
| 324 | $\{34,17;1,2\}$ | $(324,34,16,2)$ | $H(2,18)$ |
| 325 | $\{48,23;1,4\}$ | $(325,48,24,4)$ | $J(26,2)$ |
| 325 | $\{276,44;1,253\}$ | $(325,276,231,253)$ | $\mathrm{K}(26,2)$ |
| 325 | $\{144,75;1,60\}$ | $(325,144,68,60)$ | $\mathrm{NO}_5^+(5)$ graph |
| 325 | $\{60,44;1,10\}$ | $(325,60,15,10)$ | $\mathrm{NO}_5^{+ \perp}(5)$ graph |
| 325 | $\{68,64;1,17\}$ | $(325,68,3,17)$ | Point graph of $\mathrm{GQ}(4,16) \cong \mathrm{O}_6^-(4)$ graph |
| 330 | $\{63,38;1,9\}$ | $(330,63,24,9)$ | Merged Johnson graph $J(11,4)$ |
| 351 | $\{50,24;1,4\}$ | $(351,50,25,4)$ | $J(27,2)$ |
| 351 | $\{300,46;1,276\}$ | $(351,300,253,276)$ | $\mathrm{K}(27,2)$ |
| 351 | $\{126,80;1,45\}$ | $(351,126,45,45)$ | $\mathrm{NO}_7^{- \perp}(3)$ graph |
| 357 | $\{100,64;1,25\}$ | $(357,100,35,25)$ | $\mathrm{O}_6^+(4)$ graph |
| 361 | $\{36,18;1,2\}$ | $(361,36,17,2)$ | $H(2,19)$ |
| 361 | $\{180,90;1,90\}$ | $(361,180,89,90)$ | Paley graph $P_{361}$ |
| 361 | $\{180,90;1,90\}$ | $(361,180,89,90)$ | Peisert graph on 361 vertices |
| 361 | $\{144,84;1,56\}$ | $(361,144,59,56)$ | Rank-3 $\mathrm{SRG}(361,144,59,56)$ |
| 364 | $\{120,81;1,40\}$ | $(364,120,38,40)$ | $\mathrm{O}_7(3)$ graph |
| 364 | $\{120,81;1,40\}$ | $(364,120,38,40)$ | $\mathrm{Sp}_6(3)$ graph |
| 378 | $\{52,25;1,4\}$ | $(378,52,26,4)$ | $J(28,2)$ |
| 378 | $\{325,48;1,300\}$ | $(378,325,276,300)$ | $\mathrm{K}(28,2)$ |
| 378 | $\{117,80;1,36\}$ | $(378,117,36,36)$ | $\mathrm{NO}_7^{+ \perp}(3)$ graph |
| 400 | $\{38,19;1,2\}$ | $(400,38,18,2)$ | $H(2,20)$ |
| 400 | $\{56,49;1,8\}$ | $(400,56,6,8)$ | Point graphs of $\mathrm{GQ}(7,7)$s |
| 406 | $\{54,26;1,4\}$ | $(406,54,27,4)$ | $J(29,2)$ |
| 406 | $\{351,50;1,325\}$ | $(406,351,300,325)$ | $\mathrm{K}(29,2)$ |
| 416 | $\{100,63;1,20\}$ | $(416,100,36,20)$ | $\mathrm{G}_2(4)$ graph |
| 435 | $\{56,27;1,4\}$ | $(435,56,28,4)$ | $J(30,2)$ |
| 435 | $\{378,52;1,351\}$ | $(435,378,325,351)$ | $\mathrm{K}(30,2)$ |
| 441 | $\{40,20;1,2\}$ | $(441,40,19,2)$ | $H(2,21)$ |
| 465 | $\{58,28;1,4\}$ | $(465,58,29,4)$ | $J(31,2)$ |
| 465 | $\{406,54;1,378\}$ | $(465,406,351,378)$ | $\mathrm{K}(31,2)$ |
| 484 | $\{42,21;1,2\}$ | $(484,42,20,2)$ | $H(2,22)$ |
| 495 | $\{238,128;1,119\}$ | $(495,238,109,119)$ | $\mathrm{O}_{10}^-(2)$ graph |
| 496 | $\{60,29;1,4\}$ | $(496,60,30,4)$ | $J(32,2)$ |
| 496 | $\{435,56;1,406\}$ | $(496,435,378,406)$ | $\mathrm{K}(32,2)$ |
| 496 | $\{255,128;1,136\}$ | $(496,255,126,136)$ | $\mathrm{NO}_{10}^+(2)$ graph |
| 496 | $\{240,119;1,112\}$ | $(496,240,120,112)$ | $\overline{\mathrm{NO}_{10}^+(2)}$ graph |
| 525 | $\{144,95;1,36\}$ | $(525,144,48,36)$ | $\mathrm{NU}_3(5)$ graph |
| 527 | $\{270,128;1,135\}$ | $(527,270,141,135)$ | $\mathrm{O}_{10}^+(2)$ graph |
| 528 | $\{62,30;1,4\}$ | $(528,62,31,4)$ | $\mathrm{J}(33,2)$ |
| 528 | $\{465,58;1,435\}$ | $(528,465,406,435)$ | $\mathrm{K}(33,2)$ |
| 528 | $\{255,128;1,120\}$ | $(528,255,126,120)$ | $\mathrm{NO}_{10}^-(2)$ graph |
| 529 | $\{44,22;1,2\}$ | $(529,44,21,2)$ | $H(2,23)$ |
| 529 | $\{264,132;1,132\}$ | $(529,264,131,132)$ | Paley graph $P_{529}$ |
| 529 | $\{264,132;1,132\}$ | $(529,264,131,132)$ | Peisert graph on 529 vertices |
| 529 | $\{264,132;1,132\}$ | $(529,264,131,132)$ | Sporadic Peisert graph on 529 vertices |
| 529 | $\{176,112;1,56\}$ | $(529,176,63,56)$ | Van Lint–Schrijver graph on 529 vertices |
| 540 | $\{224,135;1,96\}$ | $(540,224,88,96)$ | $\mathrm{NU}_4(3)$ graph |
| 540 | $\{187,128;1,68\}$ | $(540,187,58,68)$ | Trsat graphs |
| 560 | $\{208,135;1,80\}$ | $(560,208,72,80)$ | $\mathrm{Aut(Sz(8))}$ graph |
| 561 | $\{64,31;1,4\}$ | $(561,64,32,4)$ | $\mathrm{J}(34,2)$ |
| 561 | $\{496,60;1,465\}$ | $(561,496,435,465)$ | $\mathrm{K}(34,2)$ |
| 576 | $\{46,23;1,2\}$ | $(576,46,22,2)$ | $H(2,24)$ |
| 585 | $\{72,64;1,9\}$ | $(585,72,7,9)$ | Point graph of $\mathrm{GQ}(8,8)$ |
| 595 | $\{66,32;1,4\}$ | $(595,66,33,4)$ | $\mathrm{J}(35,2)$ |
| 595 | $\{528,62;1,496\}$ | $(595,528,465,496)$ | $\mathrm{K}(35,2)$ |
| 625 | $\{144,100;1,30\}$ | $(625,144,43,30)$ | Rank-3 graph on 625 vertices with valency 144 |
| 625 | $\{240,144;1,90\}$ | $(625,240,95,90)$ | Rank-3 graph on 625 vertices with valency 240 |
| 625 | $\{48,24;1,2\}$ | $(625,48,23,2)$ | $H(2,25)$ |
| 625 | $\{312,156;1,156\}$ | $(625,312,155,156)$ | Paley graph $P_{625}$ |
| 625 | $\{208,144;1,72\}$ | $(625,208,63,72)$ | Van Lint–Schrijver graph on 625 vertices |
| 625 | $\{260,154;1,110\}$ | $(625,260,105,110)$ | $\mathrm{VNO}_4^-(5)$ graph |
| 625 | $\{104,100;1,20\}$ | $(625,104,3,20)$ | $\mathrm{VO}_4^-(5)$ graph |
| 625 | $\{144,100;1,30\}$ | $(625,144,43,30)$ | $\mathrm{VO}_4^+(5)$ graph $\cong \mathrm{H}_5(2,2)$ graph |
| 630 | $\{68,33;1,4\}$ | $(630,68,34,4)$ | $\mathrm{J}(36,2)$ |
| 630 | $\{561,64;1,528\}$ | $(630,561,496,528)$ | $\mathrm{K}(36,2)$ |
| 651 | $\{90,56;1,9\}$ | $(651,90,33,9)$ | Grassmann graph $J_2(6,2)$ |
| 666 | $\{70,34;1,4\}$ | $(666,70,35,4)$ | $\mathrm{J}(37,2)$ |
| 666 | $\{595,66;1,561\}$ | $(666,595,528,561)$ | $\mathrm{K}(37,2)$ |
| 672 | $\{495,128;1,360\}$ | $(672,495,366,360)$ | $\mathrm{NU}_6(2)$ graph |
| 672 | $\{176,135;1,48\}$ | $(672,176,40,48)$ | $\overline{\mathrm{NU}_6(2)}$ graph |
| 676 | $\{50,25;1,2\}$ | $(676,50,24,2)$ | $H(2,26)$ |
| 693 | $\{180,128;1,45\}$ | $(693,180,51,45)$ | $\mathrm{U}_6(2)$ polar graph |
| 703 | $\{72,35;1,4\}$ | $(703,72,36,4)$ | $\mathrm{J}(38,2)$ |
| 703 | $\{630,68;1,595\}$ | $(703,630,561,595)$ | $\mathrm{K}(38,2)$ |
| 729 | $\{112,110;1,20\}$ | $(729,112,1,20)$ | Games graph |
| 729 | $\{52,26;1,2\}$ | $(729,52,25,2)$ | $H(2,27)$ |
| 729 | $\{104,72;1,12\}$ | $(729,104,31,12)$ | $\mathrm{H}_3(2,3)$ graph |
| 729 | $\{364,182;1,182\}$ | $(729,364,181,182)$ | Paley graph $P_{729}$ |
| 729 | $\{364,182;1,182\}$ | $(729,364,181,182)$ | Peisert graph on 729 vertices |
| 729 | $\{224,162;1,72\}$ | $(729,224,61,72)$ | $\mathrm{VO}_6^-(3)$ graph |
| 729 | $\{260,162;1,90\}$ | $(729,260,97,90)$ | $\mathrm{VO}_6^+(3)$ graph |
| 741 | $\{74,36;1,4\}$ | $(741,74,37,4)$ | $\mathrm{J}(39,2)$ |
| 741 | $\{666,70;1,630\}$ | $(741,666,595,630)$ | $\mathrm{K}(39,2)$ |
| 756 | $\{130,125;1,26\}$ | $(756,130,4,26)$ | Point graph of $\mathrm{GQ}(5,25) \cong \mathrm{O}_6^-(5)$ graph |
| 780 | $\{76,37;1,4\}$ | $(780,76,38,4)$ | $\mathrm{J}(40,2)$ |
| 780 | $\{703,72;1,666\}$ | $(780,703,630,666)$ | $\mathrm{K}(40,2)$ |
| 784 | $\{54,27;1,2\}$ | $(784,54,26,2)$ | $H(2,28)$ |
| 806 | $\{180,125;1,36\}$ | $(806,180,54,36)$ | $\mathrm{O}_6^+(5)$ graph |
| 820 | $\{78,38;1,4\}$ | $(820,78,39,4)$ | $\mathrm{J}(41,2)$ |
| 820 | $\{741,74;1,703\}$ | $(820,741,666,703)$ | $\mathrm{K}(41,2)$ |
| 820 | $\{90,81;1,10\}$ | $(820,90,8,10)$ | Point graphs of $\mathrm{GQ}(9,9)$s |
| 841 | $\{56,28;1,2\}$ | $(841,56,27,2)$ | $H(2,29)$ |
| 841 | $\{420,210;1,210\}$ | $(841,420,209,210)$ | Paley graph $P_{841}$ |
| 841 | $\{168,120;1,30\}$ | $(841,168,47,30)$ | Rank-3 $\mathrm{SRG}(841,168,47,30)$ |
| 841 | $\{280,180;1,90\}$ | $(841,280,99,90)$ | Van Lint–Schrijver graph on 841 vertices |
| 861 | $\{80,39;1,4\}$ | $(861,80,40,4)$ | $\mathrm{J}(42,2)$ |
| 861 | $\{780,76;1,741\}$ | $(861,780,703,741)$ | $\mathrm{K}(42,2)$ |
| 900 | $\{58,29;1,2\}$ | $(900,58,28,2)$ | $H(2,30)$ |
| 903 | $\{82,40;1,4\}$ | $(903,82,41,4)$ | $\mathrm{J}(43,2)$ |
| 903 | $\{820,78;1,780\}$ | $(903,820,741,780)$ | $\mathrm{K}(43,2)$ |
| 946 | $\{84,41;1,4\}$ | $(946,84,42,4)$ | $\mathrm{J}(44,2)$ |
| 946 | $\{861,80;1,820\}$ | $(946,861,780,820)$ | $\mathrm{K}(44,2)$ |
| 961 | $\{60,30;1,2\}$ | $(961,60,29,2)$ | $H(2,31)$ |
| 961 | $\{480,240;1,240\}$ | $(961,480,239,240)$ | Paley graph $P_{961}$ |
| 961 | $\{480,240;1,240\}$ | $(961,480,239,240)$ | Peisert graph on 961 vertices |
| 961 | $\{240,168;1,56\}$ | $(961,240,71,56)$ | Rank-3 $\mathrm{SRG}(961,240,71,56)$ |
| 961 | $\{360,220;1,132\}$ | $(961,360,139,132)$ | Rank-3 $\mathrm{SRG}(961,360,139,132)$ |
| 977 | $\{488,244;1,244\}$ | $(977,488,243,244)$ | Paley graph $P_{977}$ |
| 990 | $\{86,42;1,4\}$ | $(990,86,43,4)$ | $\mathrm{J}(45,2)$ |
| 990 | $\{903,82;1,861\}$ | $(990,903,820,861)$ | $\mathrm{K}(45,2)$ |
| 997 | $\{498,249;1,249\}$ | $(997,498,248,249)$ | Paley graph $P_{997}$ |
| 1009 | $\{504,252;1,252\}$ | $(1009,504,251,252)$ | Paley graph $P_{1009}$ |
| 1013 | $\{506,253;1,253\}$ | $(1013,506,252,253)$ | Paley graph $P_{1013}$ |
| 1021 | $\{510,255;1,255\}$ | $(1021,510,254,255)$ | Paley graph $P_{1021}$ |
| 1023 | $\{510,256;1,255\}$ | $(1023,510,253,255)$ | $\mathrm{Sp}_{10}(2)$ graph $\cong \mathrm{O}_{11}(2)$ graph |
| 1024 | $\{62,31;1,2\}$ | $(1024,62,30,2)$ | $H(2,32)$ |
| 1024 | $\{93,60;1,6\}$ | $(1024,93,32,6)$ | $\mathrm{H}_2(2,5)$ graph |
| 1024 | $\{155,112;1,20\}$ | $(1024,155,42,20)$ | Rank-3 $\mathrm{SRG}(1024,155,42,20)$ |
| 1024 | $\{341,220;1,110\}$ | $(1024,341,120,110)$ | Van Lint–Schrijver graph on 1024 vertices |
| 1024 | $\{495,256;1,240\}$ | $(1024,495,238,240)$ | $\mathrm{VO}_{10}^-(2)$ graph |
| 1024 | $\{527,256;1,272\}$ | $(1024,527,270,272)$ | $\mathrm{VO}_{10}^+(2)$ graph |
| 1024 | $\{496,255;1,240\}$ | $(1024,496,240,240)$ | $\overline{\mathrm{VO}_{10}^+(2)}$ graph |
| 1066 | $\{336,243;1,112\}$ | $(1066,336,92,112)$ | $\mathrm{O}_8^-(3)$ graph |
| 1080 | $\{351,224;1,108\}$ | $(1080,351,126,108)$ | $\mathrm{NO}_8^+(3)$ graph |
| 1089 | $\{64,32;1,2\}$ | $(1089,64,31,2)$ | $H(2,33)$ |
| 1107 | $\{378,260;1,135\}$ | $(1107,378,117,135)$ | $\mathrm{NO}_8^-(3)$ graph |
| 1120 | $\{390,243;1,130\}$ | $(1120,390,146,130)$ | $\mathrm{O}_8^+(3)$ graph |
| 1156 | $\{66,33;1,2\}$ | $(1156,66,32,2)$ | $H(2,34)$ |
| 1176 | $\{300,245;1,84\}$ | $(1176,300,54,84)$ | $\mathrm{NO}_5^-(7)$ graph |
| 1210 | $\{156,108;1,16\}$ | $(1210,156,47,16)$ | Grassmann graph $\mathrm{J}_3(5,2)$ |
| 1225 | $\{68,34;1,2\}$ | $(1225,68,33,2)$ | $H(2,35)$ |
| 1225 | $\{384,245;1,112\}$ | $(1225,384,138,112)$ | $\mathrm{NO}_5^+(7)$ graph |
| 1288 | $\{495,288;1,180\}$ | $(1288,495,206,180)$ | Complement of the Dodecad graph |
| 1288 | $\{792,315;1,504\}$ | $(1288,792,476,504)$ | Dodecad graph |
| 1296 | $\{70,35;1,2\}$ | $(1296,70,34,2)$ | $H(2,36)$ |
| 1369 | $\{72,36;1,2\}$ | $(1369,72,35,2)$ | $H(2,37)$ |
| 1408 | $\{567,320;1,216\}$ | $(1408,567,246,216)$ | Conway graph on 1408 vertices |
| 1444 | $\{74,37;1,2\}$ | $(1444,74,36,2)$ | $H(2,38)$ |
| 1521 | $\{76,38;1,2\}$ | $(1521,76,37,2)$ | $H(2,39)$ |
| 1600 | $\{78,39;1,2\}$ | $(1600,78,38,2)$ | $H(2,40)$ |
| 1600 | $\{351,256;1,72\}$ | $(1600,351,94,72)$ | $\mathrm{SRG}(1600,351,94,72)$ from Tits group $\phantom{.}^2 F_4(2)'$ |
| 1681 | $\{80,40;1,2\}$ | $(1681,80,39,2)$ | $H(2,41)$ |
| 1716 | $\{882,425;1,450\}$ | $(1716,882,456,450)$ | Merged Johnson graph $J(13,6)$ |
| 1764 | $\{82,41;1,2\}$ | $(1764,82,40,2)$ | $H(2,42)$ |
| 1782 | $\{416,315;1,96\}$ | $(1782,416,100,96)$ | Suzuki graph |
| 1849 | $\{84,42;1,2\}$ | $(1849,84,41,2)$ | $H(2,43)$ |
| 1936 | $\{86,43;1,2\}$ | $(1936,86,42,2)$ | $H(2,44)$ |
| 2016 | $\{455,384;1,112\}$ | $(2016,455,70,112)$ | $\mathrm{NO}_5^-(8)$ graph |
| 2016 | $\{975,512;1,480\}$ | $(2016,975,462,480)$ | $\mathrm{NO}_7^-(4)$ graph |
| 2016 | $\{1023,512;1,528\}$ | $(2016,1023,510,528)$ | $\mathrm{NO}_{12}^+(2)$ graph |
| 2025 | $\{88,44;1,2\}$ | $(2025,88,43,2)$ | $H(2,45)$ |
| 2048 | $\{276,231;1,36\}$ | $(2048,276,44,36)$ | $2^{11}.\mathrm{M}_{24}$ graph on 2048 vertices with valency 276 |
| 2048 | $\{759,448;1,264\}$ | $(2048,759,310,264)$ | $2^{11}.\mathrm{M}_{24}$ graph on 2048 vertices with valency 759 |
| 2048 | $\{1288,495;1,840\}$ | $(2048,1288,759,840)$ | $2^{11}.\mathrm{M}_{24}$ graph on 2048 vertices with valency 1288 |
| 2079 | $\{1054,512;1,527\}$ | $(2079,1054,541,527)$ | $\mathrm{O}_{12}^+(2)$ graph |
| 2080 | $\{567,384;1,144\}$ | $(2080,567,182,144)$ | $\mathrm{NO}_5^+(8)$ graph |
| 2080 | $\{1071,512;1,544\}$ | $(2080,1071,558,544)$ | $\mathrm{NO}_7^+(4)$ graph |
| 2080 | $\{1023,512;1,496\}$ | $(2080,1023,510,496)$ | $\mathrm{NO}_{12}^-(2)$ graph |
| 2107 | $\{384,287;1,64\}$ | $(2107,384,96,64)$ | $\mathrm{NU}_3(7)$ graph |
| 2116 | $\{90,45;1,2\}$ | $(2116,90,44,2)$ | $H(2,46)$ |
| 2197 | $\{1098,549;1,549\}$ | $(2197,1098,548,549)$ | Paley graph $P_{2197}$ |
| 2209 | $\{92,46;1,2\}$ | $(2209,92,45,2)$ | $H(2,47)$ |
| 2209 | $\{1104,552;1,552\}$ | $(2209,1104,551,552)$ | Paley graph $P_{2209}$ |
| 2209 | $\{1104,552;1,552\}$ | $(2209,1104,551,552)$ | Peisert graph on 2209 vertices |
| 2209 | $\{1104,552;1,552\}$ | $(2209,1104,551,552)$ | Rank-3 $\mathrm{SRG}(2209,1104,551,552)$ |
| 2209 | $\{736,480;1,240\}$ | $(2209,736,255,240)$ | Van Lint–Schrijver graph on 2209 vertices |
| 2295 | $\{310,224;1,35\}$ | $(2295,310,85,35)$ | Half dual polar graph $\mathrm{D}_{5,5}(2)$ |
| 2300 | $\{891,512;1,324\}$ | $(2300,891,378,324)$ | Conway graph on 2300 vertices |
| 2304 | $\{94,47;1,2\}$ | $(2304,94,46,2)$ | $H(2,48)$ |
| 2401 | $\{96,48;1,2\}$ | $(2401,96,47,2)$ | $H(2,49)$ |
| 2401 | $\{1200,600;1,600\}$ | $(2401,1200,599,600)$ | Paley graph $P_{2401}$ |
| 2401 | $\{1200,600;1,600\}$ | $(2401,1200,599,600)$ | Peisert graph on 2401 vertices |
| 2401 | $\{240,180;1,20\}$ | $(2401,240,59,20)$ | Rank-3 $\mathrm{SRG}(2401,240,59,20)$ |
| 2401 | $\{480,360;1,90\}$ | $(2401,480,119,90)$ | Rank-3 $\mathrm{SRG}(2401,480,119,90)$ |
| 2401 | $\{720,490;1,210\}$ | $(2401,720,229,210)$ | Rank-3 $\mathrm{SRG}(2401,720,229,210)$ |
| 2401 | $\{960,570;1,380\}$ | $(2401,960,389,380)$ | Rank-3 $\mathrm{SRG}(2401,960,389,380)$ |
| 2401 | $\{480,360;1,90\}$ | $(2401,480,119,90)$ | Van Lint–Schrijver graph on 2401 vertices |
| 2401 | $\{300,294;1,42\}$ | $(2401,300,5,42)$ | $\mathrm{VO}_4^-(7)$ graph |
| 2401 | $\{384,294;1,56\}$ | $(2401,384,89,56)$ | $\mathrm{VO}_4^+(7)$ graph $\cong \mathrm{H}_7(2,2)$ graph |
| 2440 | $\{252,243;1,28\}$ | $(2440,252,8,28)$ | Point graph of $\mathrm{GQ}(9,27)$ |
| 2500 | $\{98,49;1,2\}$ | $(2500,98,48,2)$ | $H(2,50)$ |
| 2667 | $\{186,120;1,9\}$ | $(2667,186,65,9)$ | Grassmann graph $\mathrm{J}_2(7,2)$ |
| 2752 | $\{350,343;1,50\}$ | $(2752,350,6,50)$ | Dual polar graph $\phantom{.}^2 \mathrm{A}_3(7)$ |
| 2752 | $\{2079,512;1,1584\}$ | $(2752,2079,1566,1584)$ | $\mathrm{NU}_7(2)$ graph |
| 3240 | $\{656,567;1,144\}$ | $(3240,656,88,144)$ | $\mathrm{NO}_5^-(9)$ graph |
| 3240 | $\{2132,729;1,1404\}$ | $(3240,2132,1402,1404)$ | $\mathrm{NO}_9^-(3)$ graph |
| 3264 | $\{975,704;1,300\}$ | $(3264,975,270,300)$ | $\mathrm{NU}_4(4)$ graph |
| 3280 | $\{1092,729;1,364\}$ | $(3280,1092,362,364)$ | $\mathrm{O}_9(3)$ graph |
| 3280 | $\{1092,729;1,364\}$ | $(3280,1092,362,364)$ | $\mathrm{Sp}_8(3)$ graph |
| 3321 | $\{800,567;1,180\}$ | $(3321,800,232,180)$ | $\mathrm{NO}_5^+(9)$ graph |
| 3321 | $\{2240,729;1,1512\}$ | $(3321,2240,1510,1512)$ | $\mathrm{NO}_9^+(3)$ graph |
| 3510 | $\{693,512;1,126\}$ | $(3510,693,180,126)$ | $\mathrm{Fi}_{22}$ graph |
| 3648 | $\{567,440;1,81\}$ | $(3648,567,126,81)$ | $\mathrm{NU}_3(8)$ graph |
| 3906 | $\{780,625;1,156\}$ | $(3906,780,154,156)$ | $\mathrm{O}_7(5)$ graph |
| 3906 | $\{780,625;1,156\}$ | $(3906,780,154,156)$ | $\mathrm{Sp}_6(5)$ graph |
| 4060 | $\{1755,1024;1,780\}$ | $(4060,1755,730,780)$ | Rudvalis graph |
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Last updated: 13 August 2024