On annihilator graph of a finite commutative ring

ýThe annihilator graph AG(R) of a commutative ring R is a simple undirected graph with the vertex set Z(R)∗ and two distinct vertices are adjacent if and only if ann(x)∪ann(y) ≠ ann(xy)ý. ýIn this paper we give the sufficient condition for a graph AG(R) to be completeý. ýWe characterize rings for which AG(R) is a regular graphý, ýwe show that γ(AG(R))∈{1,2} and we also characterize the rings for which AG(R) has a cut vertexý. ýFinally we find the clique number of a finite reduced ring and characterize the rings for which AG(R)is a planar graphý.