Click here to view fulltext PDF

Permanent link:
https://www.ias.ac.in/article/fulltext/pmsc/130/0049

Cozero-divisor graph; von Neumann regular ring; clique number; chromatic number; perfect graph.

Let $R$ be a commutative ring with non-zero identity. The cozero-divisor graph of $R$, denoted by $\Gamma^{\prime }(R)$, is a graph with vertices in $W^*(R)$, which is the set of all non-zero and non-unit elements of $R$, and two distinct vertices $a$ and $b$ in $W^*(R)$ are adjacent if and only if $a\not\in Rb$ and $b\not\in Ra$. In this paper, we show that the cozero-divisor graph of a von Neumann regular ring with finite clique number is not only weakly perfect but also perfect. Also, an explicit formula for the clique number is given.

M BAKHTYIARI¹ R NIKANDISH² M J NIKMEHR¹

1. Faculty of Mathematics, K.N. Toosi Universithy of Technology, P. O. Box 16315-1618, Tehran, Iran
2. Department of Mathematics, Jundi-Shapur University of Technology, P. O. Box 64615-334, Dezful, Iran

Published

12 August 2020

Final version published online

12 August 2020