| 摘要: |
| 设~$\Gamma$ 是一个图. 顶点集~$V(\Gamma)$ 的一个独立集~$C$ 是图~$\Gamma$ 的一个完备码，如果~$V(\Gamma)\backslash C$ 中的每个顶点都与~$C$ 中的一个顶点相邻. 称非空子集~$C$ 为~$\Gamma$ 的完全完备码，如果~$\Gamma$ 的每个顶点在~$C$ 中恰好有一个点与之相邻. 本文给出了有限群的正规子群作为完备码或完全完备码的若干充分或必要条件. |
| 关键词: 完备码 完全完备码 正规子群 有限群 |
| DOI： |
| 分类号:O157.6 |
| 基金项目:重庆市自然科学基金 |
|
| Perfect Codes and Total Perfect Codes of Finite Groups |
|
Huo Lijun
|
|
Chongqing University of Technology
|
| Abstract: |
| Let $\Gamma$ be graph, a subset $C$ of $V(\Gamma)$ is called a perfect code in $\Gamma$ if every vertex of $\Gamma$ is at distance no more than one to exactly one vertex in $C$, and a subset $C$ of $V(\Gamma)$ is called a total perfect code in $\Gamma$ if every vertex of $\Gamma$ is adjacent
to exactly one vertex in $C$. This paper provides several sufficient or necessary conditions for a normal subgroup of a finite group to be a perfect code or total perfect code. |
| Key words: Perfect code Total perfect code Normal subgroup Finite group. |
