Abstract
For a group G ,a nd as ubsetS of G such that 1GS ,l etX = Cay(G, S) be the corresponding Cayley graph. Then X is said to be normal edge transitive if NAut(X)(G) is transitive on edges. In this paper, we determine all connected directed Cayley graphs of finite abelian groups with valency at most 3 which are normal edge transitive but not normal.
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