@article {
author = {Pirzada, Shariefuddin and Altaf, Aaqib},
title = {Cliques in the extended zero-divisor graph of finite commutative rings},
journal = {Communications in Combinatorics and Optimization},
volume = {},
number = {},
pages = {-},
year = {2023},
publisher = {Azarbaijan Shahid Madani University},
issn = {2538-2128},
eissn = {2538-2136},
doi = {10.22049/cco.2023.28740.1693},
abstract = {Let $R$ be a finite commutative ring with or without unity and $\Gamma_{e}(R)$ be its extended zero-divisor graph with vertex set $Z^{*}(R)=Z(R)\setminus \lbrace0\rbrace$ and two distinct vertices $x,y$ are adjacent if and only if $x.y=0$ or $x+y\in Z^{*}(R)$. In this paper, we characterize finite commutative rings whose extended zero-divisor graph have clique number $1 ~ \text{or}~ 2$. We completely characterize the rings of the form $R\cong R_1\times R_2 $, where $R_1$ and $R_2$ are local, having clique number $3,~4~\text{or}~5$. Further we determine the rings of the form $R\cong R_1\times R_2 \times R_3$, where $R_1$,$R_2$ and $R_3$ are local rings, to have clique number equal to six.},
keywords = {Zero-divisor graph,Extended zero-divisor graph,finite commutative rings,clique number},
url = {https://comb-opt.azaruniv.ac.ir/article_14651.html},
eprint = {https://comb-opt.azaruniv.ac.ir/article_14651_e70cc7687ea0a7593283a2693d0f51f1.pdf}
}