A new lower bound for doubly metric dimension and related extremal differences

TL;DR

This paper introduces a new graph invariant that provides a tight lower bound for the doubly metric dimension, with exact values for common graph classes and analysis of extremal differences.

Contribution

It presents a novel invariant based on the minimal hitting set problem that bounds the doubly metric dimension from below and explores its properties.

Findings

New invariant is a tight lower bound for doubly metric dimension.

Exact values computed for paths, stars, complete graphs, and bipartite graphs.

Identifies extremal differences between related graph invariants.

Abstract

In this paper a new graph invariant based on the minimal hitting set problem is introduced. It is shown that it represents a tight lower bound for the doubly metric dimension of a graph. Exact values of new invariant for paths, stars, complete graphs and complete bipartite graph are obtained. The paper analyzes some tight bounds for the new invariant in general case. Also several extremal differences between some related invariants are determined.