$\text{Graphs from Golay codes and Witt designs}$

No. of verticesGraphIntersection Array
$81$$\text{Brouwer-Haemers graph}$$\{16,15;1,4\}$
$144$$\text{Halved Leonard graphs}$$\{66,35;1,30\}$
$162$$\text{van Lint-Schrijver graph}$$\{6,5,5,4;1,1,2,6\}$
$176$$\text{SRG(176,70,18,34)}$$\{70,51;1,34\}$
$176$$\text{SRG(176,105,68,54)}$$\{105,36;1,54\}$
$231$$\text{Cameron graph}$$\{30,20;1,3\}$
$243$$\text{Berlekamp-van Lint-Seidel graph}$$\{22,20;1,2\}$
$243$$\text{Delsarte graph}$$\{110,72;1,60\}$
$243$$\text{Coset graph of shortened ternary Golay code}$$\{20,18,4,1;1,2,18,20\}$
$280$$\text{Unitals in }PG(2,4)$$\{9,8,6,3;1,1,3,8\}$
$288$$\text{Leonard graph}$$\{12,11,10,7;1,2,5,12\}$
$288$$\text{Incidence graphs of Leonard semibiplanes}$$\{66,65,36;1,30,66\}$
$315$$\text{Soicher's } 3^{\text{rd}}\text{ graph}$$\{32,27,8,1;1,4,27,32\}$
$330$$\text{Doubly truncated Witt graph}$$\{7,6,4,4;1,1,1,6\}$
$352$$\text{Incidence graph of Higman's symmetric design}$$\{50,49,36;1,14,50\}$
$352$$\text{Taylor graph from Higman-Sims group}$$\{175,102,1;1,102,175\}$
$352$$\text{Taylor graph from Higman-Sims group}$$\{175,72,1;1,72,175\}$
$486$$\text{Koolen-Riebeek graph}$$\{45,44,36,5;1,9,40,45\}$
$486$$\text{Soicher's } 2^{\text{nd}}\text{ graph}$$\{56,45,16,1;1,8,45,56\}$
$506$$\text{Truncated Witt graph}$$\{15,14,12;1,1,9\}$
$512$$\text{Coset graph of doubly truncated binary Golay code}$$\{21,20,16;1,2,12\}$
$552$$\text{Taylor graph from }Co_3$$\{275,112,1;1,112,275\}$
$552$$\text{Taylor graph from }Co_3$$\{275,162,1;1,162,275\}$
$672$$\text{Moscow-Soicher graph}$$\{110,81,12;1,18,90\}$
$672$$\text{Distance-2 graph of Moscow-Soicher graph}$$\{495,128;1,360\}$
$729$$\text{Coset graph of extended ternary Golay code}$$\{24,22,20;1,2,12\}$
$729$$\text{Coset graph of shortened extended ternary Golay code}$$\{22,20,18,2,1;1,2,9,20,22\}$
$759$$\text{Witt graph}$$\{30,28,24;1,3,15\}$
$990$$\text{Ivanov-Ivanov-Faradjev graph}$$\{7,6,4,4,4,1,1,1;1,1,1,2,4,4,6,7\}$
$1024$$\text{Coset graph of truncated binary Golay code}$$\{22,21,20;1,2,6\}$
$1024$$\text{Distance-2 graph of coset graph of truncated binary Golay code}$$\{231,160,6;1,48,210\}$

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Last updated: 29 August 2019