The automorphisms of bi-Cayley graphs

被引：71
|
作者：
Zhou, Jin-Xin [1 ]
Feng, Yan-Quan [1 ]
机构：
[1] Beijing Jiaotong Univ, Math, Beijing 100044, Peoples R China
来源：
JOURNAL OF COMBINATORIAL THEORY SERIES B | 2016年 / 116卷
基金：
中国国家自然科学基金;
关键词：
Bi-Cayley graph; Edge-transitive; Automorphism group; Cayley graph; ABELIAN-GROUPS; SYMMETRIC GRAPHS; DIGRAPHS; ORDER; CONNECTIVITY; BICIRCULANTS; PRIME;
D O I：
10.1016/j.jctb.2015.10.004
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
A bi-Cayley graph Gamma is a graph which admits a semiregular group H of automorphisms with two orbits. In this paper, the normalizer of H in the full automorphism group of Gamma is determined. Applying this, a characterization of cubic edge-transitive graphs of order a 2-power is given. As byproducts, we answer a problem proposed in Godsil (1983) [16] regarding the existence of arc-regular non-normal Cayley graphs of order a 2-power, and construct the first known family of cubic semisymmetric graphs of order a 2-power. (C) 2015 Elsevier Inc. All rights reserved.
引用
收藏
页码：504 / 532
页数：29
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