ZERO-DIVISOR GRAPH OF AN IDEAL OF A NEAR-RING

被引：8
|
作者：
Chelvam, T. Tamizh [1 ]
Nithya, S. [1 ]
机构：
[1] Manonmaniam Sundaranar Univ, Dept Math, Tirunelveli 627012, India
来源：
DISCRETE MATHEMATICS ALGORITHMS AND APPLICATIONS | 2013年 / 5卷 / 01期
关键词：
zero-divisor graph; near-ring; minimal ideals; coloring;
D O I：
10.1142/S1793830913500079
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we associate the graph Gamma(I)(N) to an ideal I of a near-ring N. We exhibit some properties and structure of Gamma(I) (N). For a commutative ring R, Beck conjectured that both chromatic number and clique number of the zero-divisor graph Gamma(R) of R are equal. We prove that Beck's conjecture is true for Gamma(I) (N). Moreover, we characterize all right permutable near-rings N for which the graph Gamma(I) (N) is finitely colorable.
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页数：11
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