Volume 35 • Number 4 • 2012   • On the Cozero-Divisor Graphs of Commutative Rings and Their Complements Mojgan Afkhami and Kazem Khashyarmanesh Abstract. Let $R$ be a commutative ring with non-zero identity. The cozero-divisor graph of $R$, denoted by $\Gamma'(R)$, is a graph with vertices in $W^*(R)$, which is the set of all non-zero and non-unit elements of $R$, and two distinct vertices $a$ and $b$ in $W^*(R)$ are adjacent if and only if $a\notin bR$ and $b\notin aR$. In this paper, we characterize all commutative rings whose cozero-divisor graphs are forest, star, double-star or unicyclic. 2010 Mathematics Subject Classification: 05C69, 05C75, 13A15. Full text: PDF