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

Authors

  • Abdul Gazir Syarifudin Master’s Program in Mathematics, Bandung Institute of Technology, Bandung 40116, Indonesia
  • Intan Muchtadi-Alamsyah Algebra Research Group, Bandung Institute of Technology, Bandung 40116, Indonesia https://orcid.org/0000-0001-7059-3196
  • Erma Suwastika Combinatorial Mathematics Research Group, Bandung Institute of Technology, Bandung, 40116, Indonesia

DOI:

https://doi.org/10.37256/cm.5220243574

Keywords:

prime ideal graph, commutative ring, degree of vertices, diameter, topological indices

Abstract

Let R be a commutative ring with identity, and P be a prime ideal of R. The prime ideal graph, denoted by Γp, 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.

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Published

2024-04-26

How to Cite

1.
Syarifudin AG, Muchtadi-Alamsyah I, Suwastika E. Topological Indices and Properties of the Prime Ideal Graph of a Commutative Ring and its Line Graph. Contemp. Math. [Internet]. 2024 Apr. 26 [cited 2024 Jun. 17];5(2):1342-54. Available from: https://ojs.wiserpub.com/index.php/CM/article/view/3574