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

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

机构地区：[1]Department of Mathematics, Beijing Jiaotong University, Beijing 100044, China

出　　处：《Science China Mathematics》2018年第6期1153-1162,共10页中国科学：数学（英文版）

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)

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.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 12p, 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.

关 键 词：Cayley graphs vertex-transitive graphs automorphism groups 

分 类 号：O157.5[理学—数学] O121.5[理学—基础数学]