Normal Edge-Transitive Cayley Graphs of the Group U6n

Abstract

A Cayley graph of a group G is called normal edge-transitive if the normalizer of the right representation of the group in the automorphism of the Cayley graph acts transitively on the set of edges of the graph. In this paper, we determine all connected normal edge-transitive Cayley graphs of the group U6n.

Tetravalent normal edge-transitive Cayley graphs on a certaingroup of order $6n$

“…In fact, in the general case of determining vertex-transitive Cayley graphs, the special case reduces to the determination of the normal edge-transitive Cayley graphs, in which case the full automorphism group of this graph is completely known. In [1] the author found normal edge-transitive Cayley graphs of abelian groups and in [2] the same group G of order 6n was considered and it was shown that in general if S is a subset of G with 1 / ∈ S , S = S −1 and if Cay(G, S) is normal edge-transitive, then |S| is even.…”