This paper is a contribution to the programme to classify finite distance-transitive graphs and their automorphism groups. We classify pairs ( , G) where is a graph and G is an automorphism group of acting distance-transitively and primitively on the vertex set of , subject to the condition that there is a normal elementary abelian subgroup V in G which acts regularly on the vertex set of and the stabilizer G 0 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 , all known for a long time.
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