Arc-transitive groups of automorphisms of antipodal distance-regular graphs of diameter 3 in affine case

摘要

In this paper, we describe pairs (Γ, G), where Γ is an antipodal distance-regular graph of diameter 3 that possesses an arc-transitive group of automorphisms G such that G induces an affine 2-transitive permutation group on the set of its antipodal classes. As a corollary, we revise and specify a list of necessary conditions for existence of such pairs, and find several new additional necessary conditions in one-dimensional subcase.