A family of non-quasiprimitive graphs admitting a quasiprimitive 2-arc transitive group action (Q1306932)

A permutation group on a set \(\Omega\) is said to be quasiprimitive if each of its non-trivial normal subgroups is transitive on \(\Omega\). A fundamental problem to classify 2-arc-transitive graphs is classifying quasiprimitive 2-arc-transitive graphs. A graph \(\Gamma\) is called \((G,2)\)-arc-transitive if \(G\) is transitive on the 2-arcs of \(\Gamma\). In this paper a family of \((\text{PSU}(3, q^2),2)\)-arc-transitive graphs \(\Gamma\) of valency 9 is constructed such that \(\Aut\Gamma= Z_3\times G\), for some almost simple group with socle \(\text{PSU}(3, q^2)\).