Groups with a (<i>B, N</i>)–pair and locally transitive graphs

Abstract

Let Γ be an undirected graph and G a subgroup of aut ( Γ ). We denote by ∂(x, y ) the distance between two vertices x and y , by E(Γ ) the edge set of Γ , by V(Γ ) the vertex set of Γ , by Γ(x ) the set of neighbors of the vertex x and by G(x) Γ(x) the permutation group induced by the stabilizer G(x ) on Γ(x ).