Let R be a commutative ring with nonzero identity and I be a proper ideal of R. The annihilator graph of R with respect to I, which is denoted by AGI (R), is the undirected graph with vertex-set V(AGI (R)) ={x in R-I : xy in I for some y not in I} and two distinct vertices x and y are adjacent if and only if AI (xy) not= AI (x) UAI (y), where AI (x) = {r in R : rx in I}. In this paper, we study some basic properties of AGI(R), and we characterise when AGI (R) is planar, outerplanar or a ring graph. Also, we study the graph AGI(Zn), where Z-n is the ring of integers modulo n.

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