Hexavalent half-arc-transitive graphs of order 4p

  • Authors:

  • Xiuyun Wang;Yan-Quan Feng

  • Affiliations:

  • Department of Mathematics, Beijing Jiaotong University, Beijing 100044, PR China;Department of Mathematics, Beijing Jiaotong University, Beijing 100044, PR China

  • Venue:
  • European Journal of Combinatorics
  • Year:
  • 2009

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Abstract

A graph is half-arc-transitive if its automorphism group acts transitively on its vertex set and edge set, but not arc set. It was shown by [Y.-Q. Feng, K.S. Wang, C.X. Zhou, Tetravalent half-transitive graphs of order 4p, European J. Combin. 28 (2007) 726-733] that all tetravalent half-arc-transitive graphs of order 4p for a prime p are non-Cayley and such graphs exist if and only if p-1 is divisible by 8. In this paper, it is proved that each hexavalent half-arc-transitive graph of order 4p is a Cayley graph and such a graph exists if and only if p-1 is divisible by 12, which is unique for a given order. This result contributes to the classification of half-arc-transitive graphs of order 4p of general valencies.