Affine Distance-transitive Graphs with Sporadic Stabilizer

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 andGis 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 subgroupVinGwhich acts regularly on the vertex set of Γ and the stabilizerG0of a vertex (which is a complement toVinG) 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.