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On Domination in Zero-Divisor Graphs
  Published:2011-08-03
 Printed: Jun 2013
Canadian Mathematical Bulletin
  • 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
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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 zero-divisor graph, domination
MSC Classifications: 13AXX, 05C69 show english descriptions unknown classification 13AXX
Dominating sets, independent sets, cliques 13AXX - unknown classification 13AXX
05C69 - Dominating sets, independent sets, cliques
 
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