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 not in bR and b not in aR. Also the comaximal graph is a graph with vertices all elements of R and two distinct vertices a and b are adjacent if and only if aR+bR = R. We denote the subgraph of the comaximal graph with vertex-set W∗(R), by Γ2(R). In this note, we study the relations between two graphs Γ\\\'(R) and Γ2(R). Also, we investigate the cozero-divisor graphs of idealizations of commutative rings.

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