$\text{Diameter-5 distance-regular graphs}$

No. of verticesIntersection ArrayGraph
$20$$\{3,2,1,1,1;1,1,1,2,3\}$$\text{Dodecahedron}$
$20$$\{3,2,2,1,1;1,1,2,2,3\}$$\text{Desargues graph }D(O_3)$
$32$$\{5,4,3,2,1; 1,2,3,4,5\}$$\text{5-cube }Q_5 \cong H(5,2)$
$100$$\{7,6,6,1,1;1,1,6,6,7\}$$\text{Doubled Hoffman-Singleton graph}$
$112$$\{10,9,8,2,1;1,2,8,9,10\}$$\text{Doubled Gewirtz graph}$
$154$$\{16,15,12,4,1;1,4,12,15,16\}$$\text{Doubled }M_{22} \text{ graph}$
$200$$\{22,21,16,6,1;1,6,16,21,22\}$$\text{Doubled Higman-Sims graph}$
$243$$\{10,8,6,4,2;1,2,3,4,5\}$$H(5,3)$
$462$$\{6,5,5,4,4;1,1,2,2,3\}$$\text{Odd graph }O_6$
$512$$\{10,9,8,7,6;1,2,3,4\}$$\text{Folded 10-cube}$
$512$$\{45,28,15,6,1;1,6,15,28,45\}$$\text{Halved 10-cube}$

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Last updated: 21 February 2017