On almost distance-transitive graphs

摘要

We consider undirected graphs without loops or multiple edges. Given a vertex a in a graph Γ, let Γ_i(a) denote the i-neighborhood of a, i.e., the subgraph induced by Γ on the set of all its vertices that are a distance of i away from a. Let [a] = Γ1(a) and a~⊥ = {a} ∪ [a].