@article {
author = {Dutta, Sanghita and Lanong, Chanlemki},
title = {On annihilator graph of a finite commutative ring},
journal = {Transactions on Combinatorics},
volume = {6},
number = {1},
pages = {1-11},
year = {2017},
publisher = {University of Isfahan},
issn = {2251-8657},
eissn = {2251-8665},
doi = {10.22108/toc.2017.20360},
abstract = {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.},
keywords = {Annihilator,Clique number,Domination Number},
url = {https://toc.ui.ac.ir/article_20360.html},
eprint = {https://toc.ui.ac.ir/article_20360_56c78d48b767dab5eff9143a4cf11336.pdf}
}