Constructing 4-Valent 12-Transitive Graphs with a Nonsolvable Automorphism Group

A graph is said to be 12-transitive if its automorphism group acts transitively on vertices and edges but not on arcs. For eachn⩾11, a 12-transitive graph of valency 4 and girth 6, with the automorphism group isomorphic toAn×Z2, is given.