The difference between several metric dimension graph invariants

TL;DR

This paper investigates the extremal differences between various metric dimension graph invariants across all connected graphs of a given size, developing techniques to compute bounds and exact values.

Contribution

It introduces new methods to determine extremal values of differences between metric dimension invariants for connected graphs.

Findings

Computed extremal values for differences of metric invariants

Developed techniques for bounds and exact computations

Analyzed specific graph families for precise values

Abstract

In this paper extremal values of the difference between several graph invariants related to the metric dimension are studied: mixed metric dimension, edge metric dimension and strong metric dimension. These non-trivial extremal values are computed over all connected graphs of given order. To obtain such extremal values several techniques are developed. They use functions related to metric dimension graph invariants to obtain lower and/or upper bounds on these extremal values and exact computations when restricting to some specific families of graphs.