The Basic Locally Primitive Graphs of Order Twice a Prime Square

Abstract

A graph Γ is called G-basic if G is quasiprimitive or bi-quasiprimitive on the vertex set of Γ, where G⩽Aut(Γ). It is known that locally primitive vertex-transitive graphs are normal covers of basic ones. In this paper, a complete classification of the basic locally primitive vertex-transitive graph of order 2p2 is given, where p is an odd prime.