Finite normal edge-transitive Cayley graphs

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    Abstract

    An approach to analysing the family of Cayley graphs for a finite group G is given which identifies normal edge-transitive Cayley graphs as a sub-family of central importance. These are the Cayley graphs for G for which a subgroup of automorphisms exists which both normalises G and acts transitively on edges. It is shown that, for a nontrivial group G, each normal edge-transitive Cayley graph for G has at least one homomorphic image which is a normal edge-transitive Cayley graph for a characteristically simple quotient group of G. Moreover, given a, normal edge-transitive Cayley graph Gamma(H) for a quotient group G/H, necessary and sufficient conditions are obtained for the existence of a normal edge-transitive Cayley graph Gamma for G which has Gamma(H) as a homomorphic image, and a method for obtaining all such graphs Gamma is given.
    Original languageEnglish
    Pages (from-to)207-220
    JournalBulletin of the Australian Mathematical Society
    Volume60
    DOIs
    Publication statusPublished - 1999

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