Automorphisms of a Family of Cubic Graphs.

A Cayley graph (G,S) on a group G with respect to a Cayley subset S is said to be normal if the right regular representation R(G) of G is normal in the full automorphism group of (G,S). For a positive integer n, let Γn be a graph with vertex set {xi,yi|i ∈ ℤ2n} and edge set {{xi,xi+1}, {yi,yi+1}, {x2i,y2i+1}, {y2i,x2i+1}|i ∈ ℤ2n}. In this paper, it is shown that Γn is a Cayley graph and its full automorphism group is isomorphic to for n=2, and to for n > 2. Furthermore, we determine all pairs of G and S such that Γn=(G,S) is non-normal for G. Using this, all connected cubic non-normal Cayley graphs of order 8p are constructed explicitly for each prime p. [ABSTRACT FROM AUTHOR]