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# On Domination in Zero-Divisor Graphs

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Published:2011-08-03
Printed: Jun 2013
• Nader Jafari Rad,
Department of Mathematics, Shahrood University of Technology, Shahrood, Iran
• Sayyed Heidar Jafari,
Department of Mathematics, Shahrood University of Technology, Shahrood, Iran
• Doost Ali Mojdeh,
Department of Mathematics, University of Tafresh, Tafresh, Iran
 Format: LaTeX MathJax PDF

## Abstract

We first determine the domination number for the zero-divisor graph of the product of two commutative rings with $1$. We then calculate the domination number for the zero-divisor graph of any commutative artinian ring. Finally, we extend some of the results to non-commutative rings in which an element is a left zero-divisor if and only if it is a right zero-divisor.
 Keywords: zero-divisor graph, domination
 MSC Classifications: 13AXX - unknown classification 13AXX05C69 - Dominating sets, independent sets, cliques

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