Strong resolving graph of the intersection graph in commutative rings

TL;DR

This paper characterizes the structure of the resolving graph of the intersection graph of ideals in a commutative ring and calculates its strong metric dimension, contributing to algebraic graph theory.

Contribution

It provides a detailed characterization of the resolving graph of the intersection graph of ideals in commutative rings and computes its strong metric dimension.

Findings

Resolved the structure of the resolving graph for intersection graphs of ideals.

Calculated the strong metric dimension of these graphs.

Established connections between ring properties and graph invariants.

Abstract

The intersection graph of ideals associated with a commutative unitary ring $R$ is the graph $G(R)$ whose vertices all non-trivial ideals of $R$ and there exists an edge between distinct vertices if and only if the intersection of them is non-zero. In this paper, the structure of the resolving graph of $G(R)$ is characterized and as an application, we evaluate the strong metric dimension of $G(R)$.