Distance-regular graphs of valency 10

No. of verticesGraphIntersection Array
16Complement of Clebsch graph$\{10,3;1,6\}$
21$J(7,2)$$\{10,4;1,4\}$
21$K(7,2)$$\{10,6;1,6\}$
22$K_{11,11}-I$$\{10,9,1;1,9,10\}$
26Paulus graphs$\{10,6;1,4\}$
27Complement of Schläfli graph$\{10,8;1,5\}$
32Incidence graphs of $(16,10,6)$-designs$\{10,9,4;1,6,10\}$
36$H(2,6)$$\{10,5;1,2\}$
56Gewirtz graph$\{10,9;1,2\}$
63Conway-Smith graph$\{10,6,4,1;1,2,6,10\}$
65Hall graph$\{10,6,4;1,2,5\}$
112Doubled Gewirtz graph$\{10,9,8,2,1;1,2,8,9,10\}$
182Incidence graph of $PG(2,9)$$\{10,9,9;1,1,10\}$
243$H(5,3)$$\{10,8,6,4,2;1,2,3,4,5\}$
315Hall-Janko near octagon from $J_2.2$$\{10,8,8,2;1,1,4,5\}$
512Folded 10-cube$\{10,9,8,7,6;1,2,3,4,10\}$
102410-cube $Q_{10} \cong H(10,2)$$\{10,9,8,7,6,5,4,3,2,1;1,2,3,4,5,6,7,8,9,10\}$

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Last updated: 22 March 2024