On generalized zero divisor graph of a poset

被引：11
|
作者：
Joshi, Vinayak [1 ]
Waphare, B. N. [1 ]
Pourali, H. Y. [1 ]
机构：
[1] Univ Pune, Dept Math, Pune 411007, Maharashtra, India
来源：
DISCRETE APPLIED MATHEMATICS | 2013年 / 161卷 / 10-11期
关键词：
Zero divisor graph; Clique number; Chromatic number; r-partite graph; Semi-ideal; Ideal; Prime ideal; Semiprime ideal; IDEALS;
D O I：
10.1016/j.dam.2012.12.019
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we introduce the generalized ideal based zero divisor graph of a poset P, denoted by <(G(I)(P))over cap>. A representation theorem is obtained for generalized zero divisor graphs. It is proved that a graph is complete r-partite with r >= 2 if and only if it is a generalized zero divisor graph of a poset. As a consequence of this result, we prove a form of a Beck's Conjecture for generalized zero divisor graphs of a poset. Further, it is proved that a generalized zero divisor graph <(G({0})(P))over cap> of a section semi-complemented poset P with respect to the ideal (0] is a complete graph. (C) 2013 Elsevier By. All rights reserved.
引用
收藏
页码：1490 / 1495
页数：6
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