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

References

[1] Akbari, S. and Mohammadian, A., Zero-divisor graphs of non-commutative rings. J. Algebra 296(2006), no. 2, 462–479. http://dx.doi.org/10.1016/j.jalgebra.2005.07.007 Google Scholar
[2] Anderson, D. F., Axtell, M. C. and Stickles, J. A. Jr., Zero-divisor graphs in commutative rings. In: Commutative Algebra, Noetherian and Non-Noetherian Perspectives. Springer-Verlag, New York, 2011, 23–45.Google Scholar
[3] Anderson, D. F. and Livingston, P. S., The zero-divisor graph of a commutative ring. J. Algebra 217(1999), no. 2, 434–447. http://dx.doi.org/10.1006/jabr.1998.7840 Google Scholar
[4] Haynes, T.W., Hedetniemi, S. T., and Slater, P. J.. Fundamentals of Domination in Graphs. Monographs and Textbooks in Pure and Applied Mathematics 208. Marcel Dekker, New York, 1998.Google Scholar
[5] Redmond, S. P., The zero-divisor graph of a non-commutative ring. In: Commutative rings, Nova Sci. Publ., Hauppauge, NY, 2002, pp. 39–47. Google Scholar