Name
Abstract | ||
|---|---|---|
A graph @C is symmetric if its automorphism group acts transitively on the arcs of @C, and s-regular if its automorphism group acts regularly on the set of s-arcs of @C. Tutte [W.T. Tutte, A family of cubical graphs, Proc. Cambridge Philos. Soc. 43 (1947) 459-474; W.T. Tutte, On the symmetry of cubic graphs, Canad. J. Math. 11 (1959) 621-624] showed that every cubic finite symmetric cubic graph is s-regular for some s= in the case g=8. All the 3-transitive cubic graphs and exceptional 1- and 2-regular cubic graphs of girth at most 9 appear in the list of cubic symmetric graphs up to 768 vertices produced by Conder and Dobcsanyi [M. Conder, P. Dobcsanyi, Trivalent symmetric graphs up to 768 vertices, J. Combin. Math. Combin. Comput. 40 (2002) 41-63]; the largest is the 3-regular graph F570 of order 570 (and girth 9). The proofs of the main results are computer-assisted. |
Year | DOI | Venue |
|---|---|---|
2007 | 10.1016/j.jctb.2007.01.001 | J. Comb. Theory, Ser. B |
Keywords | Field | DocType |
small girth,arc-transitive graph,girth,cubic graph,regular map,cubical graph,c. tutte,automorphism group,triangle group,finite symmetric cubic graph,s-regular graph,cubic symmetric graph,2-regular cubic graph,3-regular graph,s -regular graph,3-transitive cubic graph,trivalent symmetric graph,regular graph | Discrete mathematics,Odd graph,Combinatorics,Vertex-transitive graph,Chordal graph,Polyhedral graph,Foster graph,Nowhere-zero flow,Symmetric graph,Triangle-free graph,Mathematics | Journal |
Volume | Issue | ISSN |
97 | 5 | Journal of Combinatorial Theory, Series B |
Citations | PageRank | References |
5 | 0.50 | 6 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Marston D. E. Conder | 1 | 233 | 34.35 |
| Roman Nedela | 2 | 392 | 47.78 |