On Properties of Prime Ideal Graphs of Commutative Rings

Abstract

The prime ideal graph of in a finite commutative ring with unity, denoted by , is a graph with elements of as its vertices and two elements in are adjacent if their product is in . In this paper, we explore some interesting properties of . We determined some properties of such as radius, diameter, degree of vertex, girth, clique number, chromatic number, independence number, and domination number. In addition to these properties, we study dimensions of prime ideal graphs, including metric dimension, local metric dimension, and partition dimension; furthermore, we examined topological indices such as atom bond connectivity index, Balaban index, Szeged index, and edge-Szeged index.

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

“…Rings are represented by the zero divisor [10], prime [11], and Jacobson [12,13] graphs. Vertices and edges in each type of graph are determined based on the definitions of the respective graphs [14][15][16].…”