Topological Indices and Properties of the Prime Ideal Graph of a Commutative Ring and its Line Graph

被引：1

作者：

Syarifudin, Abdul Gazir ^{[1
]}

Muchtadi-Alamsyah, Intan ^{[2
]}

Suwastika, Erma ^{[3
]}

机构：

[1] Bandung Inst Technol, Math, Bandung 40116, Indonesia

[2] Bandung Inst Technol, Algebra Res Grp, Bandung 40116, Indonesia

[3] Bandung Inst Technol, Combinatorial Math Res Grp, Bandung 40116, Indonesia

来源：

CONTEMPORARY MATHEMATICS | 2024年 / 5卷 / 02期

关键词：

prime ideal graph; commutative ring; degree of vertices; diameter; topological indices; PARADIGMATIC APPROACH; TOTIENT; NUMBERS;

D O I：

10.37256/cm.5220243574

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let R be a commutative ring with identity and P be a prime ideal of R . The prime ideal graph, denoted by Gamma P , is the graph where the set of vertices is R \{0} and two vertices are joined by an edge if their product belongs to P . This paper will discuss topological indices and some properties of the prime ideal graph of a commutative ring and its line graph. Topological indices, such as the Wiener, first Zagreb, second Zagreb, Harary, Gutman, Schultz, and harmonic indices, are related to the degree of vertices and the diameter of the graphs. In this paper, we also discuss the independence and domination numbers of the line graph.

引用

页码：1349 / 1354

页数：6

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