A classification result about basic 2-arc-transitive graphs

Abstract

A connected graph $\Gamma =(V,E)$ is called a basic 2-arc-transitive graph if its full automorphism group has a 2-arc-transitive subgroup G, and every minimal normal subgroup of G has at most two orbits on V. In 1993, Praeger proved that every finite 2-arc-transitive connected graph is a cover of some basic 2-arc-transitive graph, and proposed the classification problem of finite basic 2-arc-transitive graphs. In this paper, a classification is given for basic 2-arc-transitive non-bipartite graphs of order $r^a{s}^b$ and basic 2-arc-transitive bipartite graphs of order $2r^a{s}^b$, where r and s are distinct primes.