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.
@article{559,
title = {A census of 4-valent half-arc-transitive graphs and arc-transitive digraphs of valence two},
journal = {ARS MATHEMATICA CONTEMPORANEA},
volume = {9},
year = {2014},
doi = {10.26493/1855-3974.559.c6c},
language = {EN},
url = {http://dml.mathdoc.fr/item/559}
}
Potočnik, Primož; Spiga, Pablo; Verret, Gabriel. A census of 4-valent half-arc-transitive graphs and arc-transitive digraphs of valence two. ARS MATHEMATICA CONTEMPORANEA, Tome 9 (2014) . doi : 10.26493/1855-3974.559.c6c. http://gdmltest.u-ga.fr/item/559/