Domination number of graphs associated with rings

被引：4

作者：

Hashemi, Ebrahim ^{[1
]}

Abdi, Mona ^{[1
]}

Alhevaz, Abdollah ^{[1
]}

Su, Huadong ^{[2
]}

机构：

[1] Shahrood Univ Technol, Fac Math Sci, POB 316-3619995161, Shahrood, Iran

[2] Nanning Normal Univ, Sch Math & Stat, Nanning 530001, Peoples R China

来源：

JOURNAL OF ALGEBRA AND ITS APPLICATIONS | 2020年 / 19卷 / 01期

基金：

中国国家自然科学基金;

关键词：

Zero-divisor graph; compressed zero-divisor graph; unit graph; domination number; ZERO-DIVISOR GRAPH; UNIT GRAPHS;

D O I：

10.1142/S0219498820500097

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The present work aims to exploit the interplay between the algebraic properties of rings and the graph-theoretic structures of their associated graphs. Let R be an associative (not necessarily commutative) ring. We focus on the domination number of the zero-divisor graph Gamma(R), the compressed zero-divisor graph Gamma(E) (R) and the unit graph G(R). We find some relations between the domination number of the zero-divisor graph and that of the compressed zero-divisor graph. Moreover, some relations between the domination number of Gamma(R) and Gamma(R[x; alpha, delta]) as well as the relations between the domination number of G(R) and G(R[[x; alpha]]), are studied.

引用

页数：12

共 25 条

[1] Unit graphs of rings of polynomials and power series [J].