Automorphism Groups of Connected Cubic Cayley Graphs of Order 4p

• 来源期刊: 代数集刊（英文版）
• 关键词: Cayley graph symmetric graph normal Cayley graph
• 年，卷（期）: 2007,（2）
• 页码范围: 351-359
• 页数: 9页
• 语种: 英文

摘要

For a prime p, let D4p be the dihedral group <a, b | a2p = b2 = 1, b-lab=a-1>of order 4p, and Cay(G, S) a connected cubic Cayley graph of order 4pIn this paper, it is shown that the automorphism group Aut(Cay(G, S)) of Cay(G, S) is the semiproduct R(G)×Aut(G, S), where R(G) is the right regular representation of G and Aut(G, S) ={αε Aut(G) |Sαα = S}, except either G = D4p (p ≥ 3), Sβ = {b, ab, aPb} for some E Aut(D4p) and Aut(Cay(D4p, S)) ≌Zp2×D2p, or Cay(G,S) is isomorphic to the three-dimensional hypercube Q3 (Aut(Q3)≌Z23×S3) and G = Z4× Z2 or De.