数学杂志2025，Vol.45Issue(5)：385-399,15.
有限交换环的U-clean图
THE U-CLEAN GRAPHS OF FINITE COMMUTATIVE RINGS
摘要
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.关键词
关U-clean/欧拉图/可逆元Key words
U-clean graph/Eulerlian/unit分类
数理科学引用本文复制引用
胡雪,殷晓斌,程智,崔建..有限交换环的U-clean图[J].数学杂志,2025,45(5):385-399,15.基金项目
Supported by Anhui Provincial Natural Science Foundation(2008085MA06)and the Key Project of Anhui Education Committee(gxyqZD2019009). （2008085MA06）
