Potočnik, Primož; Spiga, Pablo; Verret, Gabriel A census of 4-valent half-arc-transitive graphs and arc-transitive digraphs of valence two. (English) Zbl 1317.05191 Ars Math. Contemp. 8, No. 1, 133-148 (2015). 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. Cited in 21 Documents MSC: 05E18 Group actions on combinatorial structures 20B25 Finite automorphism groups of algebraic, geometric, or combinatorial structures Keywords:digraph; edge-transitive graphs; vertex-transitive graphs; arc-transitive digraphs; half-arc-transitive graphs PDF BibTeX XML Cite \textit{P. Potočnik} et al., Ars Math. Contemp. 8, No. 1, 133--148 (2015; Zbl 1317.05191) Full Text: DOI