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On Domination in Zero-Divisor Graphs

Published online by Cambridge University Press:  20 November 2018

Nader Jafari Rad,
Sayyed Heidar Jafari and
Doost Ali Mojdeh
Nader Jafari Rad
Affiliation:
Department of Mathematics, Shahrood University of Technology, Shahrood, Iran e-mail: n.jafarirad@shahroodut.ac.ir shjafari55@gmail.com
Sayyed Heidar Jafari
Affiliation:
Department of Mathematics, University of Tafresh, Tafresh, Iran e-mail: damojdeh@yahoo.com
Doost Ali Mojdeh
Affiliation:
Department of Mathematics, University of Tafresh, Tafresh, Iran and School of Mathematics, Institute for Research in Fundamental Sciences (IPM), Tehran, Iran e-mail: damojdeh@yahoo.com
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Abstract

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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

13AXX05C69zero-divisor graphdomination

Information

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 56 , Issue 2 , 01 June 2013, pp. 407 - 411
Copyright
Copyright © Canadian Mathematical Society 2013

References

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