Cubic one-regular graphs of order twice a square-free integer

作     者：ZHOU JinXin FENG YanQuan 

作者机构：Department of MathematicsBeijing Jiaotong UniversityBeijing 100044China 

出 版 物：《Science China Mathematics》 (中国科学：数学（英文版）)

年 卷 期：2008年第51卷第6期

页      面：1093-1100页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：the National Natural Science Foundation of China(Grant No.10571013) the Key Project of the Chinese Ministry of Education(Grant No.106029) the Specialized Research Fund for the Doctoral Program of High Education in China(Grant No.20060004026) 

主　　题：one-regular graph symmetric graph Cayley graph 05C25 20B25 

摘      要：A graph is one-regular if its automorphism group acts regularly on the set of its arcs. Let n be a square-free integer. In this paper, we show that a cubic one-regular graph of order 2n exists if and only if n = 3 t p 1 p 2···p s ? 13, where t ? 1, s ? 1 and p i ’s are distinct primes such that 3| (p i ? 1). For such an integer n, there are 2 s?1 non-isomorphic cubic one-regular graphs of order 2n, which are all Cayley graphs on the dihedral group of order 2n. As a result, no cubic one-regular graphs of order 4 times an odd square-free integer exist.