This page contains a complete census of all connected cubic vertex-transitive graphs of order at most 1280. We encourage all users to report any bugs, comments or contributions by e-mail here. (For basic definitions, see terminology.)
The following plain text files (which are also magma-readable) contain the graphs themselves, grouped by order.
One of the step in our census was to construct all connected locally-imprimitive 4-valent arc-transitive graphs on up to 640 vertices. Combined with the list of small 2-arc-transitive 4-valent graphs due to Primož Potočnik, this yields a census of all connected 4-valent arc-transitive graphs on up to 640 vertices (39 MB).
We present some interesting overall data which can be extracted from the census.
We also have a table table containing more detailed information about graphs of each order.
This census is a joint project by Primož Potočnik (University of Ljubljana), Pablo Spiga (University of Milano-Bicocca), and Gabriel Verret (University of Western Australia). If you find this data useful in your research or other endeavour, please acknowledge our contribution by citing:
P. Potočnik, P. Spiga, G. Verret, Cubic vertex-transitive graphs on up to 1280 vertices, Journal of Symbolic Computation 50 (2013), 465-477.
P. Potočnik, P. Spiga, G. Verret, Bounding the order of the vertex-stabiliser in 3-valent vertex-transitive and 4-valent arc-transitive graphs, arXiv:1010.2546v1 [math.CO].The first paper describes the methods used to obtain the census while the second provides the theoretical tools necessary to have the algorithms run efficiently.