Circulants and the Characterization of Vertex-Transitive Graphs
نویسندگان
چکیده
In this paper, we extend the notion of a circulant to a broader class of vertex.transitive graphs, which we call multidimensional circulants. This new class of graphs is shown to consist precisely of those vertextransitive graphs with an automorphism group containing a regular abelian subgroup. The result is proved using a theorem of Sabidussi which shows how to recover any vertex-transitive graph from any transitive subgroup of its automorphism group. The approach also allows a short proof of Turner's theorem that every vertex-transitive graph on a prime number of nodes is a circulant.
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