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A census of 4-valent half-arc-transitive graphs and arc-transitive digraphs of valence two. (English) Zbl 1317.05191
Summary: 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.

05E18 Group actions on combinatorial structures
20B25 Finite automorphism groups of algebraic, geometric, or combinatorial structures
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