Affine distance-transitive graphs with sporadic stabilizer

Abstract

This paper is a contribution to the programme to classify finite distance-transitive graphs and their automorphism groups. We classify pairs (Γ, G) where Γ is a graph and G is an automorphism group of Γ acting distance-transitively and primitively on the vertex set of Γ, subject to the condition that there is a normal elementary abelian subgroup V in G which acts regularly on the vertex set of Γ and the stabilizer G0 of a vertex (which is a complement to V in G) has a unique non-abelian composition factor isomorphic to one of the 26 sporadic simple groups. There are exactly 10 examples of Γ, all known for a long time. © 1999 Academic Press.