Graphs from Golay codes and Witt designs

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