University of IsfahanTransactions on Combinatorics2251-86576120170301On annihilator graph of a finite commutative ring1112036010.22108/toc.2017.20360ENSanghitaDuttaNorth eastern Hill UniversityChanlemkiLanongNorth Eastern Hill UniversityJournal Article20150702The 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 $gamma (AG(R))in {1,2}$ 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.https://toc.ui.ac.ir/article_20360_56c78d48b767dab5eff9143a4cf11336.pdf