ON THE COZERO-DIVISOR GRAPHS AND COMAXIMAL GRAPHS OF COMMUTATIVE RINGS

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 is not an element of bR and b is not an element of 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 Gamma(2)(R). In this note, we study the relations between two graphs Gamma' (R) and Gamma(2) (R). Also, we investigate the cozero-divisor graphs of idealizations of commutative rings.