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.

- Graphs of order 4 to 300 (18 MB)
- Graphs of order 302 to 500 (66 MB)
- Graphs of order 502 to 600 (69 MB)
- Graphs of order 602 to 700 (84 MB)
- Graphs of order 702 to 800 (114 MB)
- Graphs of order 802 to 900 (147 MB)
- Graphs of order 902 to 1000 (183 MB)
- Graphs of order 1002 to 1050 (164 MB)
- Graphs of order 1052 to 1100 (113 MB)
- Graphs of order 1102 to 1150 (103 MB)
- Graphs of order 1152 to 1200 (234 MB)
- Graphs of order 1202 to 1250 (137 MB)
- Graphs of order 1252 to 1280 (131 MB)

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,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.Bounding the order of the vertex-stabiliser in 3-valent vertex-transitive and 4-valent arc-transitive graphs,arXiv:1010.2546v1 [math.CO].

by Primož Potočnik, Pablo Spiga and Gabriel Verret, last modified September 2014.