On Edge Transitive Circulant Graphs
Copyright policy )On Edge Transitive Circulant Graphs
This paper classifies those circulant graphs for which both the graph and its complement are edge-transitive. The author shows that such a graph must be either a disjoint union of copies of a complete graph, or the complement of such a disjoint union, or a Paley graph on a prime number of vertices. The proof is short, using a result of Schur on Burnside groups and a result of Chao on symmetric graphs with prime order. A digraph version of the result is also given.
Paley graph, Directed graphs (digraphs), tournaments, complement, symmetric graphs, circulant graphs, digraph, Graphs and abstract algebra (groups, rings, fields, etc.)
Paley graph, Directed graphs (digraphs), tournaments, complement, symmetric graphs, circulant graphs, digraph, Graphs and abstract algebra (groups, rings, fields, etc.)
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