Graphs of degree <24, which are limit graphs for minimal vertex-primitive graphs of type HA

Abstract

Throughout the paper, by a graph we mean an undirected graph without loops or multiple edges. The vertex set and edge set of a graph Γ are denoted by V(Γ) and E(Γ). By an automorphism of graph Γ we mean a permutation on the set V(Γ) preserving the adjacency relation. A graph is called a vertexprimitive graph if it admits a primitive on its vertex set group of automor� phisms. We denote the class of connected vertexprim� itive graphs by (here and below by a class of some graphs we mean a set of isomorphic types of these graphs). Each primitive permutation group can be realized as an edgetransitive automorphism group of some connected graph. Here the most natural realiza� tions are obtained via graphs of minimal degree. A connected graph is called a graph of minimal degree for a primitive permutation group of automorphisms G on the set V if it has a minimal degree among all con� nected graphs Γ, with V(Γ) = V and G ≤ Aut(Γ). The subclass of the class consisting of all graphs of minimal degree for finite primitive permutation groups is denoted by .