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

No. of verticesGraphIntersection 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$$\text{Folded 6-cube}$$\{6,5,4;1,2,6\}$
$32$$\text{Incidence graphs of biplanes on 16 points }(N=3)$$\{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: 4 April 2019