Normal edge-transitive Cayley graphs on a class of non-abelian groups

Abstract

Let Γ=Cay(G, S) be the Cayley graph of a group G with respect to its subset S. The graph Γ is said to be normal edge-transitive if the normalizer of G in the automorphism group Aut(Γ) of Γ acts transitively on the edge set of Γ. In this paper, we study the structure of normal edge-transitive Cayley graphs on a class of non-abelian groups with order 2p² (p refers to an odd prime). The structure and automorphism groups of the non-abelian groups are first presented, and then the tetravalent normal edge-transitive Cayley graphs on such groups are investigated. Finally, the normal edge-transitive Cayley graphs on group G are characterized and classified.

Keywords

Cayley graph / symmetric graph / normal edge-transitivity

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