Geodesic
A census of 4-valent half-arc-transitive graphs and arc-transitive digraphs of valence two
Ars Mathematica Contemporanea, Tome 8 (2015) no. 1, pp. 133-148.

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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.
DOI : 10.26493/1855-3974.559.c6c
Keywords: Graph, digraph, edge-transitive, vertex-transitive, arc-transitive, half-arc-transitive 
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Primož Potočnik; Pablo Spiga; Gabriel Verret. A census of 4-valent half-arc-transitive graphs and arc-transitive digraphs of valence two. Ars Mathematica Contemporanea, Tome 8 (2015) no. 1, pp. 133-148. doi : 10.26493/1855-3974.559.c6c. http://geodesic.mathdoc.fr/articles/10.26493/1855-3974.559.c6c/

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