Vertices 266 Radius 4 Girth 5 | Edges 1463 Diameter 4 Automorphisms 175560 (J1) | |
In the mathematical field of graph theory, the Livingstone graph is a distance-transitive graph with 266 vertices and 1463 edges. It is the largest distance-transitive graph with degree 11.
Algebraic properties
The automorphism group of the Livingstone graph is the sporadic simple group J1, and the stabiliser of a point is PSL(2,11). As the stabiliser is maximal in J1, it acts primitively on the graph.
As the Livingstone graph is distance-transitive, PSL(2,11) acts transitively on the set of 11 vertices adjacent to a reference vertex v, and also on the set of 12 vertices at distance 4 from v. The second action is equivalent to the standard action of PSL(2,11) on the projective line over F11; the first is equivalent to an exceptional action on 11 points, related to the Paley biplane.