Cubic vertex-transitive graphs on up to 1280 vertices. (English) Zbl 1256.05102

Potočnik, Primož; Spiga, Pablo; Verret, Gabriel

J. Symb. Comput. 50, 465-477 (2013).

Summary: 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.

MSC:

05C25

Graphs and abstract algebra (groups, rings, fields, etc.)

Keywords:

cubic graphs; tetravalent graphs; valency 3; valency 4; vertex-transitive graphs; arc-transitive graphs; automorphism group; computer calculations; cubic vertex-transitive graphs; tetravalent arc-transitive graphs