PERFECT ESSENTIAL GRAPHS

被引：1
|
作者：
Nikmehr, M. Javad [1 ]
Azadi, A. [1 ]
Soleymanzadeh, B. [1 ]
机构：
[1] KN Tossi Univ Technol, Fac Math, Tehran, Iran
来源：
MATEMATICHE | 2019年 / 74卷 / 02期
关键词：
Annihilator; Weakly perfect graph; Perfect graph; Chromatic number; Clique number;
D O I：
10.4418/2019.74.2.4
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Let R be a commutative ring with identity, and let Z(R) be the set of zero-divisors of R. Let EG(R) be a simple undirected graph associated with R whose vertex set is the set of all nonzero zero-divisors of R and and two distinct vertices x, y in this graph are joined by an edge if and only if Ann(R)(xy) is an essential ideal. A perfect graph is a graph in which the chromatic number of every induced subgraph equals the size of the largest clique of that subgraph. In this paper, we characterize all Artinian rings whose EG(R) is perfect.
引用
收藏
页码：279 / 287
页数：9
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