Topological graph theory
The MAGMA algebra system I: the user language
Journal of Symbolic Computation - Special issue on computational algebra and number theory: proceedings of the first MAGMA conference
Group actions, coverings and lifts of automorphisms
Discrete Mathematics - Special issue on Graph theory
Lifting graph automorphisms by voltage assignments
European Journal of Combinatorics
s-Regular cyclic coverings of the three-dimensional hypercube Q3
European Journal of Combinatorics
2-Arc-transitive regular covers of complete graphs Having the covering transformation group Zp3
Journal of Combinatorial Theory Series B
Cubic symmetric graphs of order a small number times a prime or a prime square
Journal of Combinatorial Theory Series B
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A graph X is said to be an m-Cayley graph on a group G (|G|1) if its automorphism group contains a semiregular subgroup isomorphic to G having m orbits on the vertex set of X. If G is cyclic and m=1,2,3,4, or 5 then X is said to be a circulant, a bicirculant, a tricirculant, a tetracirculant, or a pentacirculant, respectively. A graph is said to be symmetric if its automorphism group acts transitively on the set of its arcs. All cubic symmetric circulants, bicirculants and tricirculants are known, and in this paper we give complete classifications of cubic symmetric tetracirculants and pentacirculants. In particular, it is shown that there are infinitely many connected cubic symmetric tetracirculants whereas there are only two connected cubic symmetric pentacirculants.