$\text{Diameter-4 distance-regular graphs}$

No. of verticesIntersection ArrayGraph
$16$$\{4,3,2,1; 1,2,3,4\}$$\text{4-cube }Q_4 \cong H(4,2)$
$18$$\{3,2,2,1;1,1,2,3\}$$\text{Pappus graph}$
$28$$\{3,2,2,1;1,1,1,2\}$$\text{Coxeter graph}$
$30$$\{3,2,2,2;1,1,1,3\}$$\text{Tutte's 8-cage}$
$32$$\{4,3,3,1;1,1,3,4\}$$\text{Incidence graph of }AG(2,4) \text{ minus a parallel class}$
$32$$\{5,4,1,1;1,1,4,5\}$$\text{Armanios-Wells graph}$
$32$$\{8,7,4,1;1,4,7,8\}$$\text{Hadamard graph on 32 vertices}$
$36$$\{6,5,4,1;1,2,5,6\}$$\text{Hexacode graph}$
$45$$\{4,2,2,2;1,1,1,2\}$$\text{Line graph of Tutte's 8-cage}$
$45$$\{6,4,2,1;1,1,4,6\}$$\text{Halved Foster graph}$
$48$$\{12,11,6,1;1,6,11,12\}$$\text{Hadamard graph on 48 vertices}$
$50$$\{5,4,4,1;1,1,4,5\}$$\text{Incidence graph of }AG(2,5)\text{ minus a parallel class }$
$54$$\{9,8,6,1;1,3,8,9\}$$\text{Incidence graph of }\mathrm{STD}_3[9;3]$
$63$$\{10,6,4,1;1,2,6,10\}$$\text{Conway-Smith graph}$
$64$$\{8,7,6,1;1,2,7,8\}$$\text{Incidence graph of }\mathrm{STD}_2[8;4]$
$72$$\{12,11,8,1;1,4,11,12\}$$\text{Suetake graph}$
$80$$\{4,3,3,3;1,1,1,4\}$$\text{Incidence graph of }GQ(3,3)$
$81$$\{8,6,4,2;1,2,3,4\}$$H(4,3)$
$98$$\{7,6,6,1;1,1,6,7\}$$\text{Incidence graph of }AG(2,7) \text{ minus a parallel class}$
$100$$\{15,14,10,3;1,5,12,15\}$$\text{Cocliques in Hoffman-Singleton graph}$
$126$$\{5,4,4,3;1,1,2,2\}$$\text{Odd graph }O_5$
$128$$\{8,7,7,1;1,1,7,8\}$$\text{Incidence graph of }AG(2,8) \text{ minus a parallel class}$
$128$$\{8,7,6,5;1,2,3,8\}$$\text{Folded 8-cube}$
$128$$\{28,15,6,1;1,6,15,28\}$$\text{Halved 8-cube}$
$162$$\{6,5,5,4;1,1,2,6\}$$\text{van Lint-Schrijver graph}$
$162$$\{9,8,8,1;1,1,8,9\}$$\text{Incidence graph of }AG(2,9) \text{ minus a parallel class}$
$170$$\{5,4,4,4;1,1,1,5\}$$\text{Incidence graph of }GQ(4,4)$
$256$$\{12,9,6,3;1,2,3,4\}$$H(4,4)$
$256$$\{9,8,7,6;1,2,3,4\}$$\text{Folded 9-cube}$
$256$$\{36,21,10,3;1,6,15,28\}$$\text{Halved 9-cube}$
$266$$\{11,10,6,1;1,1,5,11\}$$\text{Livingstone graph}$
$280$$\{9,8,6,3;1,1,3,8\}$$\text{Unitals in }PG(2,4)$
$288$$\{12,11,10,7;1,2,5,12\}$$\text{Leonard graph}$
$315$$\{10,8,8,2;1,1,4,5\}$$\text{Hall--Janko/Cohen--Tits near octagon from }J_2.2$
$330$$\{7,6,4,4;1,1,1,6\}$$\text{Doubly truncated Witt graph}$

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Last updated: 25 July 2017