DOMINATION NUMBER IN THE ANNIHILATING-IDEAL GRAPHS OF COMMUTATIVE RINGS

被引：10

作者：

Nikandish, Reza ^{[1
]}

Maimani, Hamid Reza ^{[2
,3
]}

Kiani, Sima ^{[4
]}

机构：

[1] Jundi Shapur Univ Technol, Dept Math, Dezful, Iran

[2] Shahid Rajaee Teacher Training Univ, Dept Basic Sci, Math Sect, Tehran, Iran

[3] Inst Res Fundamental Sci IPM, Sch Math, Tehran, Iran

[4] Islamic Azad Univ, Sci & Res Branch, Dept Math, Tehran, Iran

来源：

PUBLICATIONS DE L INSTITUT MATHEMATIQUE-BEOGRAD | 2015年 / 97卷 / 111期

关键词：

annihilating-ideal graph; zero-divisor graph; domination number; minimal prime ideal;

D O I：

10.2298/PIM140222001N

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页码：225 / 231

页数：7

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