On annihilator graph 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) \cup ann(y) \neq 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 \gamma (AG(R))\in \{۱,۲\} and we also characterize the rings for which AG(R) has a cut vertex‎. ‎Finally we find the clique number of a finite reduced ring and characterize the rings for which AG(R) is a planar graph‎.

Keywords:

‎Annihilator‎ , ‎Clique number‎ , ‎Domination Number