Leonard Graph

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 .

Explore with Wolfram|Alpha

More things to try:

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)." https://www.math.mun.ca/distanceregular/graphs/halved-leonard.html.DistanceRegular.org. "Leonard Graph." https://www.math.mun.ca/distanceregular/graphs/leonard.html.Leonard, D. A. Ph.D. thesis. Ohio State University, 1979.