Wiener Index and Graph Energy of Zero Divisor Graph for Commutative Rings

IF 0.5 Q3 MATHEMATICS

Asian-European Journal of Mathematics Pub Date : 2023-10-04 DOI:10.1142/s179355712350211x

Clement Johnson Rayer, Ravi Sankar Jeyaraj

引用次数: 0

Abstract

Let [Formula: see text] be commutative ring and [Formula: see text] be the set of all non-zero zero divisors of [Formula: see text]. Then [Formula: see text] is said to be the zero divisor graph if and only if [Formula: see text] where [Formula: see text] and [Formula: see text]. Graph energy [Formula: see text] is defined as the sum of the absolute eigenvalues of the adjacency matrix [Formula: see text], then [Formula: see text]. Wiener index [Formula: see text] is defined as the sum of all distance between pairs of vertices [Formula: see text] and [Formula: see text], then [Formula: see text]. In this paper, we compute the graph energy from the adjacency matrix of the zero divisor graph and the Wiener index from the zero divisor graph associated with commutative rings.

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交换环上零因子图的Wiener指数与图能

设[公式:见文]为交换环，[公式:见文]为[公式:见文]的所有非零零因子的集合。那么，当且仅当[公式:见文]和[公式:见文]中[公式:见文]和[公式:见文]是零因子图时，称[公式:见文]为零因子图。图能量[公式:见文]定义为邻接矩阵[公式:见文]的绝对特征值之和，则[公式:见文]。维纳指数[公式:见文]定义为顶点对之间的所有距离[公式:见文]与[公式:见文]之和，则[公式:见文]。本文从交换环上的零因子图的邻接矩阵和零因子图的Wiener索引计算了图的能量。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Asian-European Journal of Mathematics MATHEMATICS-

CiteScore

1.30

自引率

12.50%

发文量

169

期刊介绍： Asian-European Journal of Mathematics is an international journal which is devoted to original research in the field of pure and applied mathematics. The aim of the journal is to provide a medium by which new ideas can be discussed among researchers from diverse fields in mathematics. It publishes high quality research papers in the fields of contemporary pure and applied mathematics with a broad range of topics including algebra, analysis, topology, geometry, functional analysis, number theory, differential equations, operational research, combinatorics, theoretical statistics and probability, theoretical computer science and logic. Although the journal focuses on the original research articles, it also welcomes survey articles and short notes. All papers will be peer-reviewed within approximately four months.