发表机构
Birla Institute of Technology and Science Pilani（比拉理工学院皮拉尼分校）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究交换环的弱零因子图WΓ(R)，证明当R为阿廷环或既约环时，WΓ(R)的顶点连通性等于其最小度，并刻画了该图的所有最小度顶点。
AI 中文摘要
交换环R的弱零因子图WΓ(R)是简单无向图，其顶点为R的非零零因子，两个不同顶点x、y相邻当且仅当存在w∈ann(x)和z∈ann(y)使得wz=0。本文中，我们得到了R为阿廷环或既约环时WΓ(R)的顶点连通性，证明这类环的WΓ(R)顶点连通性等于其最小度，还刻画了WΓ(R)所有最小度顶点。
英文摘要
The weakly zero-divisor graph $WΓ(R)$ of a commutative ring $R$ is the simple undirected graph whose vertices are nonzero zero-divisors of $R$, and two distinct vertices $x$, $y$ are adjacent if and only if there exists $w\in {\rm ann}(x)$ and $ z\in {\rm ann}(y)$ such that $wz =0$. In this paper, first we prove that the vertex connectivity of $WΓ(R)$ is equal to its minimum degree, where $R$ is either an Artinian ring or reduced ring. For any finite ring $R$, we obtain the vertex connectivity of $WΓ(R)$. Moreover, this paper characterizes all the vertices that attain the minimum degree of $WΓ(R)$.
