Automorphisms of a Family of Cubic Graphs

作者：Zhou Jin Xin; Ghasemi Mohsen^*

来源：Algebra Colloquium, 2013, 20(3): 495-506.

• Cayley graphs
• vertex-transitive graphs
• automorphism groups

A Cayley graph Cay(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 Cay(G, S). For a positive integer n, let Gamma(n), be a graph with vertex set {x(i), y(i) vertical bar Z(2n)} edge set {{x(i), x(i+1)}, {y(i), y(i+1)}, {x(2i), y(2i+1)}, {x(2i) , y(2i+1)} vertical bar i is an element of Z(2n)}. In this paper, it is shown that Gamma(r), is a Cayley graph and its full automorphism group is isomorphic to Z(2)(3) x S-3 for n = 2, and to Z(2)(n) x D-2n, for n > 2. Furthermore, we determine all pairs of G and S such that Gamma(n) = Cay(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.

• 出版日期2013-9
• 单位北京交通大学