Let R be a commutative ring with nonzero identity. In this paper we intro- duce the coannihilator graph of R, which is a dual of the annihilator graph AG(R), denoted by AG0(R). AG0(R) is a graph with the vertex set W(R), where W(R) is the set of all nonzero and nonunit elements of R, and two distinct vertices x and y are adjacent if and only if x /2 xyR or y /2 xyR, where for z 2 R, zR is the principal ideal generated by z. We study the interplay between the ring-theoretic properties of R and graph-theoretic properties of AG(R).

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