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| 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,给出了U-Cl (Zp×Zq)的结构,证明了U-Cl (Zp×Zq)是欧拉图当且仅当p=2,q=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: 关U-clean 欧拉图 可逆元 |
| DOI： |
| 分类号:O153.3;O157.6 |
| 基金项目:Supported by Anhui Provincial Natural Science Foundation (2008085MA06) and the Key Project of Anhui Education Committee (gxyqZD2019009). |
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| THE U-CLEAN GRAPHS OF FINITE COMMUTATIVE RINGS |
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HU Xue,YIN Xiao-bin,CHENG Zhi,CUI Jian
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| 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(Zp×Zq) is Eulerlian if and only if p = 2, q = 2. Moreover, the clique number, the chromatic number of the U-clean graph for some classes of rings are given in this paper. |
| Key words: U-clean graph Eulerlian unit |
