奇素数与平方因子乘积群的4度Cayley图的正规性  

Tetravalent Normality Cayley Graphs over Groups of Odd Primes and Square Factor Products

作　　者：王丽[1] 林丽青 WANG Li;LIN Liqing(School of Mathematics and Information Science,Henan Polytechnic University,Jiaozuo 454003,China)

机构地区：[1]河南理工大学数学与信息科学学院,河南焦作454003

出　　处：《河南科技大学学报(自然科学版)》2025年第1期88-93,M0007,M0008,共8页Journal of Henan University of Science And Technology:Natural Science

基　　金：国家自然科学基金项目(12126317);河南理工大学骨干教师项目(2023XQG-11);河南理工大学基本科研业务费专项项目(自然科学类)(NSFRF240316)。

摘　　要：群G关于子集S(S■G\{1})的Cayley图X:=Cay(G,S)称为正规的,如果G的右正则表示在Aut(X)中是正规的。图的全自同构群是刻画图对称性的一个重要指标。Cayley图作为具有高度对称性的图,Cayley图的正规性可以很好的反映出图的全自同构群,从而来刻画图的对称性,研究所有pq 2阶群的连通4度Cayley图,其中p,q是素数且p>q>5,并得到这样的Cayley图都是正规的。A Cayley graph X:=Cay G,S on G relative to S(S■G\{1}) is called normal if the right regular representation of the group G is normal in the full automorphism group Aut X of X.The full automorphism group of a graph is an important index to describe the symmetry of a graph.Cayley graph,as a highly symmetrical graph.The normality of Cayley graph can reflect the full automorphism group of the graph well,so as to describe the symmetry of the graph.In this paper,we determine the normality of connected tetravalent Cayley graphs of order pq 2,where p,q are prime and p>q>5.

关 键 词：有限群 非交换群 CAYLEY图 正规性 

分 类 号：O157.5[理学—数学] O152.5[理学—基础数学]