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# Some Results on the Domination Number of a Zero-divisor Graph

Published:2014-06-09
Printed: Sep 2014
• Sima Kiani,
Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran
• Hamid Reza Maimani,
Mathematics Section, Department of Basic Sciences, Shahid Rajaee Teacher Training University, Tehran, Iran,
• Reza Nikandish,
Department of Mathematics, Jundi-Shapur University of Technology, Dezful,Iran
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## Abstract

In this paper, we investigate the domination, total domination and semi-total domination numbers of a zero-divisor graph of a commutative Noetherian ring. Also, some relations between the domination numbers of $\Gamma(R/I)$ and $\Gamma_I(R)$, and the domination numbers of $\Gamma(R)$ and $\Gamma(R[x,\alpha,\delta])$, where $R[x,\alpha,\delta]$ is the Ore extension of $R$, are studied.
 Keywords: zero-divisor graph, domination number
 MSC Classifications: 05C75 - Structural characterization of families of graphs 13H10 - Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.) [See also 14M05]

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