%0 Journal Article
%T On annihilator graph of a finite commutative ring
%J Transactions on Combinatorics
%I University of Isfahan
%Z 2251-8657
%A Dutta, Sanghita
%A Lanong, Chanlemki
%D 2017
%\ 03/01/2017
%V 6
%N 1
%P 1-11
%! On annihilator graph of a finite commutative ring
%K Annihilator
%K Clique number
%K Domination Number
%R 10.22108/toc.2017.20360
%X 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 $gamma (AG(R))in {1,2}$ 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.
%U https://toc.ui.ac.ir/article_20360_56c78d48b767dab5eff9143a4cf11336.pdf