Let R be a commutative ring with nonzero identity. We denote by AG(R) the annihilator graph of R,whose vertex set consists of the set of nonzero zero-divisors of R, and two distint vertices x and y are adjacent if and only if ann(x) ∪ ann(y)\not equal ann(xy), where for t ∈ R, we set ann(t) := {r ∈ R | rt = 0}. In this paper, we define the annihiator-ideal graph of R, which is denoted by AI (R), as an undirected graph with vertex set A_*(R), and two distinct vertices I and J are adjacent if and only if ann(I ) ∪ ann(J ) \not= ann(I J). We study some basic properties of AI (R) such as connectivity, diameter and girth. Also we investigate the situations under which the graphs AG(R) and AI (R) are coincide. Moreover, we examin the planarity of the graph AI (R).

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