On the Cozero-Divisor Graphs of Commutative Rings and Their Complements

Let R be a commutative ring with non-zero identity. The cozero-divisor graph of R, denoted by Γ′(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∉bR and b∉aR. In this paper, we characterize all commutative rings whose cozero-divisor graphs are forest, star, double-star or unicyclic.