Geodesic
Domination Number in the Annihilating-Ideal Graphs of Commutative Rings
Publications de l'Institut Mathématique, _N_S_97 (2015) no. 111, p. 225 .

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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.
DOI : 10.2298/PIM140222001N
Classification : 13A15 05C75
Keywords: annihilating-ideal graph, zero-divisor graph, domination number, minimal prime ideal 
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Reza Nikandish; Hamid Reza Maimani; Sima Kiani. Domination Number in the Annihilating-Ideal Graphs of Commutative Rings. Publications de l'Institut Mathématique, _N_S_97 (2015) no. 111, p. 225 . doi : 10.2298/PIM140222001N. http://geodesic.mathdoc.fr/articles/10.2298/PIM140222001N/

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