|
| 摘要: |
| 设G是一个有限非交换群,群G上的交换图Γ(G)具有顶点集G\Z(G),这里Z(G)表示群G的中心,两个顶点a和b相邻当且仅当ab=ba.一个图Γ的顶点集V(Γ)的子集C是Γ的一个完备码,如果C是V(Γ)的一个独立集,且V(Γ)\C的每个顶点恰好与C中的一个顶点相邻.判断交换图上完备码存在性以及构造完备码的问题是一个重要的研究课题,本文给出了一些有限非交换群上交换图的完备码. |
| 关键词: 非交换群 交换图 完备码 半二面体群 |
| DOI： |
| 分类号:O152.1 |
| 基金项目:重庆市自然科学基金项目(CSTB2022NSCQ-MSX0831,cstc2021jcyj-msxmX0575);重庆理工大学研究生教育高质量发展行动计划资助成果(gzljg2022319,gzlcx20253353,gzlcx20253360);重庆理工大学教育教学改革项目(2023YB115,2023YB132);重庆理工大学高等教育研究项目(2024YB08). |
|
| PERFECT CODES IN COMMUTING GRAPHS ON SEVERAL FINITE NON-ABELIAN GROUPS |
|
HUO Li-jun,YI Guang-li,LI Ming-dan
|
| Abstract: |
| Let G be a flnite non-abelian group. The commuting graph Γ(G) on group G has vertex set G\Z(G), and two vertices a and b are adjacent if and only if ab = ba, where Z(G) denotes the center of the group G. A subset C of the vertex set V (Γ) in graph Γ is a perfect code if C is an independent set of V (Γ) and each vertex in V (Γ)\C is adjacent to exactly one vertex in C. The problem of determining the existence of perfect codes and constructing such codes on commuting graphs is an important research topic. This paper presents some perfect codes of commuting graphs on some non-abelian groups. |
| Key words: non-abelian group commuting graph perfect code semidihedral group |
