The Leonard graph is a distance-regular graph on 288 vertices (Brouwer et al. 1989, p. 369) with intersection
array
.
It is however not distance-transitive.
It has graph spectrum
.
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
.
See also
Doubly Truncated Witt Graph,
Large Witt Graph,
Truncated
Witt Graph,
Witt Design
Explore with Wolfram|Alpha
References
Brouwer, A. E. "On the Uniqueness of a Regular Thin Near Octagon on 2888 Vertices (or the Semibiplane belonging to the Mathieu Group
." Math. Centre Report ZW196.
Amsterdam, Netherlands, Jul. 1983.Brouwer, A. E.; Cohen, A. M.;
and Neumaier, A. "The Leonard Graph-
over
." §11.4F in Distance
Regular Graphs. New York: Springer-Verlag, p. 371, 1989.DistanceRegular.org.
"Halved Leonard Graphs (2 Graphs)." http://www.distanceregular.org/graphs/halved-leonard.html.DistanceRegular.org.
"Leonard Graph." http://www.distanceregular.org/graphs/leonard.html.Leonard,
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. https://mathworld.wolfram.com/LeonardGraph.html
Subject classifications