## $\text{Distance-regular graphs of valency 6}$

$\text{Folded 6-cube}$$\text{Incidence graphs of biplanes on 16 points }(N=3)$
 No. of vertices Graph Intersection Array $10$ $J(5,2)$ $\{6,2;1,4\}$ $13$ $\text{Paley graph }P_{13}$ $\{6,3;1,3\}$ $14$ $K_{7,7}-I$ $\{6,5,1;1,5,6\}$ $15$ $K(6,2)$ $\{6,4;1,3\}$ $16$ $H(2,4)$ $\{6,3;1,2\}$ $16$ $\text{Shrikhande graph}$ $\{6,3;1,2\}$ $22$ $\text{Incidence graph of }(11,6,3)\text{-design}$ $\{6,5,3;1,3,6\}$ $27$ $H(3,3)$ $\{6,4,2;1,2,3\}$ $32$ $\{6,5,4;1,2,6\}$ $32$ $\{6,5,4;1,2,6\}$ $36$ $\text{Hexacode graph}$ $\{6,5,4,1;1,2,5,6\}$ $42$ $2^{\text{nd}}\text{ subconstituent of Hoffman-Singleton graph}$ $\{6,5,1;1,1,6\}$ $45$ $\text{Halved Foster graph}$ $\{6,4,2,1;1,1,4,6\}$ $52$ $\text{Flag graph of PG(2,3)}$ $\{6,3,3;1,1,2\}$ $57$ $\text{Perkel graph}$ $\{6,5,2;1,1,3\}$ $62$ $\text{Incidence graph of PG(2,5)}$ $\{6,5,5;1,1,6\}$ $63$ $\text{Point graphs of }GH(2,2) \text{ and its dual}$ $\{6,4,4;1,1,3\}$ $64$ $\text{6-cube }Q_6 \cong H(6,2)$ $\{6,5,4,3,2,1;1,2,3,4,5,6\}$ $162$ $\text{van Lint-Schrijver graph}$ $\{6,5,5,4;1,1,2,6\}$ $462$ $\text{Odd graph }O_6$ $\{6,5,5,4,4;1,1,2,2,3\}$

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Last updated: 21 February 2017