Diameter-4 distance-regular graphs

No. of verticesIntersection ArrayGraph
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 $\mathrm{STD}_2[8;4]$
70$\{16,9,4,1;1,4,9,16\}$$J(8,4)$
72$\{12,11,8,1;1,4,11,12\}$Suetake graph
80$\{4,3,3,3;1,1,1,4\}$Incidence graph of $GQ(3,3)$
81$\{8,6,4,2;1,2,3,4\}$$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$\{20,12,6,2;1,4,9,16\}$$J(9,4)$
126$\{5,4,4,3;1,1,2,2\}$Odd graph $O_5$
128$\{8,7,7,1;1,1,7,8\}$Incidence graph of $AG(2,8)$ minus a parallel class
128$\{8,7,6,5;1,2,3,8\}$Folded 8-cube
128$\{28,15,6,1;1,6,15,28\}$Halved 8-cube
160$\{6,3,3,3;1,1,1,2\}$Flag graph of $GQ(3,3)$
162$\{6,5,5,4;1,1,2,6\}$Van Lint–Schrijver graph on 162 vertices
162$\{9,8,8,1;1,1,8,9\}$Incidence graph of $AG(2,9)$ minus a parallel class
170$\{5,4,4,4;1,1,1,5\}$Incidence graph of $GQ(4,4)$
210$\{24,15,8,3;1,4,9,16\}$$J(10,4)$
242$\{11,10,10,1;1,1,10,11\}$Incidence graph of $AG(2,11)$ minus a parallel class
243$\{20,18,4,1;1,2,18,20\}$Coset graph of shortened ternary Golay code
256$\{12,9,6,3;1,2,3,4\}$$H(4,4)$
256$\{9,8,7,6;1,2,3,4\}$Folded 9-cube
256$\{36,21,10,3;1,6,15,28\}$Halved 9-cube
266$\{11,10,6,1;1,1,5,11\}$Livingstone graph
280$\{9,8,6,3;1,1,3,8\}$Unitals in $PG(2,4)$
288$\{12,11,10,7;1,2,5,12\}$Leonard graph
315$\{10,8,8,2;1,1,4,5\}$Hall–Janko/Cohen–Tits near octagon from $J_2.2$
315$\{32,27,8,1;1,4,27,32\}$Soicher's 3rd graph
330$\{7,6,4,4;1,1,1,6\}$Doubly truncated Witt graph
330$\{28,18,10,4;1,4,9,16\}$$J(11,4)$
338$\{13,12,12,1;1,1,12,13\}$Incidence graph of $AG(2,13)$ minus a parallel class
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
495$\{32,21,12,5;1,4,9,16\}$$J(12,4)$
625$\{16,12,8,4,2;1,2,3,4\}$$H(4,5)$
715$\{36,24,14,6;1,4,9,16\}$$J(13,4)$
1001$\{40,27,16,7;1,4,9,16\}$$J(14,4)$
1134$\{117,80,24,1;1,12,80,117\}$Norton–Smith graph
1296$\{20,15,10,5;1,2,3,4\}$$H(4,6)$
1344$\{176,135,29,1;1,24,135,176\}$Meixner double-cover of $U_6(2)$ graph
1365$\{44,30,18,8;1,4,9,16\}$$J(15,4)$
1755$\{10,8,8,8;1,1,1,5\}$Ree-Tits Generalized Octagon, $GO(2,4)$
1820$\{48,33,20,9;1,4,9,16\}$$J(16,4)$
2295$\{30,28,24,16;1,3,7,15\}$Dual polar graph $\mathrm{B}_4(2) \cong$ Dual polar graph $\mathrm{C}_4(2)$
2380$\{52,36,22,10;1,4,9,16\}$$J(17,4)$
2401$\{24,18,12,6;1,2,3,4\}$$H(4,7)$
2688$\{176,135,36,1;1,12,135,176\}$Meixner quadruple cover of $U_6(2)$ graph
3060$\{56,39,24,11;1,4,9,16\}$$J(18,4)$
3876$\{60,42,26,12;1,4,9,16\}$$J(19,4)$
5346$\{416,315,64,1;1,32,315,416\}$Soicher's 1st graph

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Last updated: 8 August 2024