The metric dimension of the annihilating-ideal graph of a finite commutative ring

TL;DR

This paper calculates the metric dimension of the annihilating-ideal graph for specific classes of finite commutative rings, providing exact values and bounds for these algebraic structures.

Contribution

It determines the metric dimension for local finite commutative principal rings and rings with two maximal ideals, and establishes bounds for general finite commutative principal rings.

Findings

Exact metric dimension for local finite commutative principal rings

Metric dimension for rings with two maximal ideals

Bounds for metric dimension in arbitrary finite commutative principal rings

Abstract

We determine the metric dimension of the annihilating-ideal graph of a local finite commutative principal ring and a finite commutative principal ring with two maximal ideals. We also find the bounds for the metric dimension of the annihilating-ideal graph of an arbitrary finite commutative principal ring.