|
| 摘要: |
| 设R为含幺的有限交换环, 本文引入了环 R 的 U-clean 图 U-Cl(R) 的概念, 研究了 U-Cl(R) 的基本性质. 设p, q 为素数, m, n 为正整数, 给出了U-Cl(Zp × Zq)的结构, 证明了U-Cl(Zpm × Zqn)是欧拉图当且仅当pm =2, qn=2, 并探究了一些特殊环的U-clean图的团数以及点染色数. |
| 关键词: U-clean 图 欧拉图 可逆元 |
| DOI： |
| 分类号:O153.3 ; O157.6 |
| 基金项目:安徽省自然科学基金项目；安徽省教育厅重点研究项目 |
|
| THE U-CLEAN GRAPHS OF FINITE COMMUTATIVE RINGS |
|
huxue,YIN Xiao-bin,程智,崔建
|
| Abstract: |
| Let R be a finite commutative ring with identity 1. The U-clean graph of R, denoted by U-Cl(R), is a graph with vertices in form (e, u), where e is a nonzero idempotent of R and u is a unit of R. In this paper, some basic properties of U-Cl(R) and the explicit structures of U-Cl(Zp × Zq) are given, where p, q are primes. We prove that U-Cl(Zpm × Zqn) is Eulerlian if and only if pm =2, qn=2, where m, n are positive integers. Moreover, the clique number, the chromatic number of the U-clean graphs for some classes of rings are determined. |
| Key words: U-clean graph Eulerlian unit |
