ON ANNIHILATOR GRAPHS OF A FINITE COMMUTATIVE RING

The 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). In this paper we give the sufficient condition for a graph AG(R) to be complete. We characterize rings for which AG(R) is a regular graph, we show that (AG(R)) 2 f1; 2g and we also characterize the rings for which AG(R) has a cut vertex. Finally we nd the clique number of a nite reduced ring and characterize the rings for which AG(R) is a planar graph.