Cubic vertex-transitive non-Cayley graphs of order 12p

作     者：Wei-Juan Zhang Yan-Quan Feng Jin-Xin Zhou 

作者机构：Department of Mathematics Beijing Jiaotong University Beijing 100044 China 

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

年 卷 期：2018年第61卷第6期

页      面：1153-1162页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 070101[理学-基础数学] 

基　　金：supported by National Natural Science Foundation of China(Grant Nos.11671030,11171020 and 11231008) the Fundamental Research Funds for the Central Universities(Grant No.2015JBM110) 

主　　题：Cayley graphs vertex-transitive graphs automorphism groups 

摘      要：A graph is said to be vertex-transitive non-Cayley if its full automorphism group acts transitively on its vertices and contains no subgroups acting regularly on its vertices. In this paper, a complete classification of cubic vertex-transitive non-Cayley graphs of order 12 p, where p is a prime, is given. As a result, there are 11 sporadic and one infinite family of such graphs, of which the sporadic ones occur when p equals 5, 7 or 17, and the infinite family exists if and only if p ≡ 1(mod 4), and in this family there is a unique graph for a given order.