Cubic vertex-transitive graphs on up to 1280 vertices

Authors:
Primo PotočNik;Pablo Spiga;Gabriel Verret
Affiliations:
Faculty of Mathematics and Physics, University of Ljubljana, Jadranska 19, 1000 Ljubljana, Slovenia;University of Milano-Bicocca, Departimento di Matematica Pura e Applicata, Via Cozzi 53, 20126 Milano, Italy;Faculty of Mathematics, Nat. Sci. and Info. Tech., University of Primorska, Glagoljaška 8, 6000 Koper, Slovenia
Venue:
Journal of Symbolic Computation
Year:
2013

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Abstract

A graph is called cubic (respectively tetravalent) if all of its vertices have valency 3 (respectively valency 4). It is called vertex-transitive (respectively arc-transitive) if its automorphism group acts transitively on its vertex-set (respectively arc-set). In this paper, we combine some new theoretical results with computer calculations to determine all cubic vertex-transitive graphs of order at most 1280. In the process, we also determine all tetravalent arc-transitive graphs of order at most 640.