A Family of Non-quasiprimitive Graphs Admitting a Quasiprimitive 2-arc Transitive Group Action

Abstract

Let Γ be a simple graph and let G be a group of automorphisms of Γ. The graph is (G, 2)-arc transitive if G is transitive on the set of the 2-arcs ofΓ . In this paper we construct a new family of (PSU(3, q2), 2)-arc transitive graphs Γ of valency 9 such that AutΓ=Z3.G , for some almost simple group G with socle PSU(3, q2). This gives a new infinite family of non-quasiprimitive almost simple graphs.