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

Published online by Cambridge University Press:  20 November 2018

Sima Kiani ,
Hamid Reza Maimani  and
Reza Nikandish
Sima Kiani
Affiliation:
Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran e-mail: s.kiani@srbiau.ac.ir
Hamid Reza Maimani
Affiliation:
Mathematics Section, Department of Basic Sciences, Shahid Rajaee Teacher Training University, Tehran, Iran and School of Mathematics, Institute for Research in Fundamental Sciences (IPM), Tehran, Iran e-mail: maimani@ipm.ir
Reza Nikandish
Affiliation:
Department of Mathematics, Jundi-Shapur University of Technology, Dezful, Iran and School of Mathematics, Institute for Research in Fundamental Sciences (IPM), Tehran, Iran e-mail: r.nikandish@ipm.ir
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Abstract

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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 $\Gamma \left( {R}/{I}\; \right)$ and ${{\Gamma }_{1}}\left( R \right)$, and the domination numbers of $\Gamma \left( R \right)$ and $\Gamma \left( R\left[ x,\,\alpha ,\,\delta \right] \right)$, where $R\left[ x,\,\alpha ,\,\delta \right]$ is the Ore extension of $R$, are studied.

Keywords

05C7513H10zero-divisor graphdomination number
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 57 , Issue 3 , 01 September 2014 , pp. 573 - 578
Copyright
Copyright © Canadian Mathematical Society 2014

References

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