Tetravalent half-transitive graphs of order 4p

Authors:
Yan-Quan Feng;Kaishun Wang;Chuixiang Zhou
Affiliations:
Department of Mathematics, Beijing Jiaotong University, Beijing 100044, PR China;Department of Mathematics, Beijing Normal University, Beijing 100875, PR China;Department of Mathematics, Beijing Jiaotong University, Beijing 100044, PR China
Venue:
European Journal of Combinatorics
Year:
2007

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Abstract

A graph is half-transitive if its automorphism group acts transitively on its vertex set and edge set, but not on its arc set. In this paper, the tetravalent half-transitive graphs of order 4p are classified for each prime p. It is shown that there are no tetravalent half-transitive Cayley graphs of order 4p and a tetravalent half-transitive non-Cayley graph of order 4p exists if and only if p-1 is divisible by 8, which is unique for a given order.