Zero-divisor graph of a poset with respect to an automorphism

被引：5

作者：

Patil, Avinash ^{[1
]}

Khairnar, Anil ^{[2
]}

Waphare, B. N. ^{[3
]}

机构：

[1] JETs ZB Patil Coll, Dept Math, Dhule 424002, Maharashtra, India

[2] MES Abasaheb Garware Coll, Dept Math, Pune 411004, Maharashtra, India

[3] Savitribai Phule Pune Univ, Ctr Adv Study Math, Dept Math, Pune 411007, Maharashtra, India

来源：

DISCRETE APPLIED MATHEMATICS | 2020年 / 283卷

关键词：

Automorphism of a poset; Zero-divisor graph; Clique number; Chromatic number;

D O I：

10.1016/j.dam.2020.02.015

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we introduce the zero-divisor graph of a poset with respect to an automorphism, called the generalized zero-divisor graph of a poset, as an extension of the zero-divisor graph of a poset. It is proved that for such graphs, the chromatic number and the clique number need not be equal. A sufficient condition is provided for the chromatic number and the clique number of the generalized zero-divisor graph to be equal, which extends the result of the zero-divisor graph of poset. Further, the connectedness, diameter and girth of such graphs are studied. (C) 2020 Elsevier B.V. All rights reserved.

引用

页码：604 / 612

页数：9

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