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Finite normal edge-transitive Cayley graphs

  • Cheryl E. Praeger (a1)
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 ΓH for a quotient group G/H, necessary and sufficient conditions are obtained for the existence of a normal edge-transitive Cayley graph Γ for G which has ΓH as a homomorphic image, and a method for obtaining all such graphs Γ is given.

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[3]C.Y. Chao , ‘On the classification of symmetric graphs with a prime number of vertices’, Trans. Amer. Math. Soc. 158 (1971), 247256.

[12]M.Y. Xu , ‘Automorphism groups and isomorphisms of Cayley graphs’, Discrete Math. 182 (1998), 309319.

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Bulletin of the Australian Mathematical Society
  • ISSN: 0004-9727
  • EISSN: 1755-1633
  • URL: /core/journals/bulletin-of-the-australian-mathematical-society
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