Cubic vertex-transitive graphs on up to 1280 vertices

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.