Isomorphisms of generalized Cayley graphs

被引：5
|
作者：
Yang, Xu [1 ,2 ]
Liu, Weijun [2 ]
Feng, Lihua [2 ]
机构：
[1] Shanghai Lixin Univ Accounting & Finance, Sch Math & Stat, Shanghai 201209, Peoples R China
[2] Cent South Univ, Sch Math & Stat, Changsha 410083, Hunan, Peoples R China
来源：
ARS MATHEMATICA CONTEMPORANEA | 2018年 / 15卷 / 02期
关键词：
Generalized Cayley graph; natural isomorphism; GCI-group; Cayley regression; INVOLUTORY AUTOMORPHISMS; ADAMS CONJECTURE;
D O I：
10.26493/1855-3974.1345.ae6
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we investigate the isomorphism problems of the generalized Cayley graphs, which are generalizations of the traditional Cayley graphs. We find that there are two types of natural isomorphisms for the generalized Cayley graphs. We also study the GCI-groups among the generalized Cayley graphs, and the Cayley regressions of some groups. We mainly showed that, for an odd prime power n, Z(2)(n) (resp. D-2n) is a restricted GCI-group if D-2(n) (resp. Z(2n)) is a CI-group. We also obtain that the cyclic group of order 2(n) is a 4-quasi-Cayley regression if and only if n = 3.
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页码：407 / 424
页数：18
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