Non-normal one-regular and 4-valent Cayley graphs of dihedral groups D2n

  • Authors:

  • Changqun Wang;Mingyao Xu

  • Affiliations:

  • Department of Mathematics, Zhengzhou University, Zhengzhou, People's Republic of China;Department of Mathematics, Peking University, Beijing, People's Republic of China

  • Venue:
  • European Journal of Combinatorics
  • Year:
  • 2006

Quantified Score

Hi-index 0.01

Visualization

Abstract

A Cayley graph X = Cay(G, S) of group G is said to be normal if R(G) is normal in Aut(X). Let G = «a, b | an = b2 = 1 », S be a generating set of G, |S| = 4. In this paper we show that any one-regular and 4-valent Cayley graph X = Cay(G, S) of dihedral groups G is normal except that n = 4s, and X ≃ Cay(G, {a, a-1, aib, a-ib}), where i2 ≡ ± 1 (mod 2s), 2 ≤ i ≤ 2s - 2.