A census of 4-valent half-arc-transitive graphs and arc-transitive digraphs of valence two
Keywords:Graph, digraph, edge-transitive, vertex-transitive, arc-transitive, half-arc-transitive
A complete list of all connected arc-transitive asymmetric digraphs of in-valence and out-valence 2 on up to 1000 vertices is presented. As a byproduct, a complete list of all connected 4-valent graphs admitting a half-arc-transitive group of automorphisms on up to 1000 vertices is obtained. Several graph-theoretical properties of the elements of our census are calculated and discussed.