Leonard Graph

The Leonard graph is a distance-regular graph on 288 vertices (Brouwer et al. 1989, p. 369) with intersection array {12,11,10,7;1,2,5,12}. It is however not distance-transitive. It has graph spectrum (-12)^1(-2sqrt(6))^(66)0^(154)(2sqrt(6))^(66)12^1.

The Leonard graph is implemented in the Wolfram Language as GraphData["LeonardGraph"].

The two halved Leonard graphs are also distance-regular, both with intersection array {66,35;1,30}.

See also

Doubly Truncated Witt Graph, Large Witt Graph, Truncated Witt Graph, Witt Design

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Brouwer, A. E. "On the Uniqueness of a Regular Thin Near Octagon on 2888 Vertices (or the Semibiplane belonging to the Mathieu Group M_(12)." Math. Centre Report ZW196. Amsterdam, Netherlands, Jul. 1983.Brouwer, A. E.; Cohen, A. M.; and Neumaier, A. "The Leonard Graph-M_(12)·2 over PGL(2,11)." §11.4F in Distance Regular Graphs. New York: Springer-Verlag, p. 371, "Halved Leonard Graphs (2 Graphs)." "Leonard Graph.", D. A. Ph.D. thesis. Ohio State University, 1979.

Referenced on Wolfram|Alpha

Leonard Graph

Cite this as:

Weisstein, Eric W. "Leonard Graph." From MathWorld--A Wolfram Web Resource.

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