Automorphism groups of connected cubic Cayley graphs of order 4p

作者：Zhou Chuixiang^*; Feng Yan Quan

来源：Algebra Colloquium, 2007, 14(2): 351-359.

• Cayley graph
• symmetric graph
• normal Cayley graph

For a prime p, let D-4p be the dihedral group (a, b\a(2p) = b(2) = 1, b(-1)ab = a(-1)) of order 4p, and Cay(G, S) a connected cubic Cayley graph of order 4p. In this paper, it is shown that the automorphism group Aut(Cay(G, S)) of Cay(G, S) is the semiproduct R(G) X Aut(G, S), where R(G) is the right regular representation of G and Aut(G, S) = {alpha is an element of Aut(G)\S-alpha = S}, except either G = D-4p (p >= 3), S-beta = {b, ab, a(p)b} for some beta is an element of Aut(D-4p) and Aut(Cay(D-4p, S)) congruent to Z(2)(p) X D-2p, or Cay(G, S) is isomorphic to the three-dimensional hypercube Q(3) (Aut(Q(3)) congruent to Z(2)(3) x S-3) and G = Z(4) X Z(2) or D-8.

• 出版日期2007-6
• 单位北京交通大学