Zero-Annihilator Graphs of Commutative Rings

Abstract

Assume that $R$ is a commutative ring with nonzero identity. In this paper, we introduce and investigate zero-annihilator graph of $R$ denoted by $\mathtt{ZA}(R)$. It is the graph whose vertex set is the set of all nonzero nonunit elements of $R$ and two distinct vertices $x$ and $y$ are adjacent whenever ${\mathrm{Ann}}_R(x)\cap {\mathrm{Ann}}_R(y)=\{0\}$.

arXiv comment8 pages