The metric dimension of annihilator graphs of commutative rings

被引：8

作者：

Soleymanivarniab, V ^{[1
]}

Tehranian, A. ^{[1
]}

Nikandish, R. ^{[2
]}

机构：

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

[2] Jundi Shapur Univ Thchnol, Dept Basic Sci, Dezful, Iran

来源：

JOURNAL OF ALGEBRA AND ITS APPLICATIONS | 2020年 / 19卷 / 05期

关键词：

Metric dimension; zero-divisor; annihilator graph; commutative ring;

D O I：

10.1142/S0219498820500899

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 nonzero identity. The annihilator graph of R, denoted by AG(R), is the (undirected) graph whose vertex set is the set of all nonzero zerodivisors of R and two distinct vertices x and y are adjacent if and only if ann (R)(xy) not equal ann (R)(x) U ann (R)(y). In this paper, we study the metric dimension of annihilator graphs associated with commutative rings and some metric dimension formulae for annihilator graphs are given.

引用

页数：12

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