CUT STRUCTURES IN ZERO-DIVISOR GRAPHS OF COMMUTATIVE RINGS

被引：5

作者：

Axtell, M. ^{[1
]}

Baeth, N. ^{[2
]}

Stickles, J. ^{[3
]}

机构：

[1] Univ St Thomas, Dept Math, St Paul, MN 55105 USA

[2] Univ Cent Missouri, Dept Math & Comp Sci, Warrensburg, MO 64093 USA

[3] Millikin Univ, Dept Math, Decatur, IL 62522 USA

来源：

JOURNAL OF COMMUTATIVE ALGEBRA | 2016年 / 8卷 / 02期

关键词：

Commutative ring; cut vertex; cut-set; bridge; zero divisor graph; VERTICES;

D O I：

10.1216/JCA-2016-8-2-143

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Zero-divisor graphs, and more recently, compressed zero-divisor graphs are well represented in the commutative ring literature. In this work, we consider various cut structures, sets of edges or vertices whose removal disconnects the graph, in both compressed and non compressed zero-divisor graphs. In doing so, we connect these graph-theoretic concepts with algebraic notions and provide realization theorems of zero-divisor graphs for commutative rings with identity.

引用

页码：143 / 171

页数：29

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