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Vietnam Journal of Mathematics 33:3 (2005) 309-318

 Cayley Graphs of Abelian Groups Which Are Not Normal Edge-Transitive

Mehdi Alaeiyan, Hamid Tavallaee, and Ali A. Talebi

Abstract.  For a group G, and a subset S of G such that 1_G S, let Γ = Cay(G, S) be the corresponding Cayley graph. Then Γ is said to be normal edge transitive, if N_Aut(Γ)(G) is transitive on edges. In this paper we determine all connected, undirected edge-transitive Cayley graphs of finite abelian groups with valency at most five, which are not normal edge transitive. This is a partial answer to a question of Praeger.

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