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Domination number in the annihilating-ideal graphs of commutative rings

Nikandish Reza (Jundi-Shapur University of Technology, Department of Mathematics, Dezful, Iran)
Maimani Hamid Reza (Shahid Rajaee Teacher Training University, Department of Basic Sciences, Mathematics Section, Tehran, Iran + School of Mathematics Institute for Research in Fundamental Sciences (IPM), Tehran, Iran)
Kiani Sima (Islamic Azad University, Science and Research Branch, Department of Mathematics Tehran, Iran)

Let R be a commutative ring with identity and A(R) be the set of ideals with nonzero annihilator. The annihilating-ideal graph of R is defined as the graph AG(R) with the vertex set A(R)* = A(R)\{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 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