Publications de l'Institut Mathématique, Nouvelle SérieVol. 97(111), pp. 225–231 (2015)
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Publications de l'Institut Mathématique, Nouvelle Série Vol. 97(111), pp. 225–231 (2015) |
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DOMINATION NUMBER IN THE ANNIHILATING-IDEAL GRAPHS OF COMMUTATIVE RINGSReza Nikandish, Hamid Reza Maimani, Sima KianiDepartment of Mathematics, Jundi-Shapur University of Technology, Dezful, Iran; Mathematics Section, Department of Basic Sciences, Shahid Rajaee Teacher Training University, Tehran, Iran; School of Mathematics, Institute for Research in Fundamental Sciences (IPM), Tehran, Iran; Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, IranAbstract: Let $R$ be a commutative ring with identity and $\mathbb{A}(R)$ be the set of ideals with nonzero annihilator. The annihilating-ideal graph of $R$ is defined as the graph $\mathbb{AG}(R)$ with the vertex set $\mathbb{A}(R)^{*}=\mathbb{A}(R)\smallsetminus\{0\}$ and two distinct vertices $I$ and $J$ are adjacent if and only if $IJ=0$. In this paper, we study the domination number of $\mathbb{AG}(R)$ and some connections between the domination numbers of annihilating-ideal graphs and zero-divisor graphs are given. Keywords: annihilating-ideal graph; zero-divisor graph; domination number; minimal prime ideal Classification (MSC2000): 13A15; 05C75 Full text of the article: (for faster download, first choose a mirror)
Electronic fulltext finalized on: 16 Apr 2015. This page was last modified: 21 Apr 2015.
© 2015 Mathematical Institute of the Serbian Academy of Science and Arts
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