On the k-metric Dimension of Metric Spaces

TL;DR

This paper explores the concept of k-metric dimension in general metric spaces, extending previous graph-based definitions to broader metric space contexts, and discusses its properties and implications.

Contribution

It generalizes the k-metric dimension concept from graphs to arbitrary metric spaces, providing new insights and potential applications.

Findings

Extension of k-metric dimension to general metric spaces

Analysis of properties of k-metric dimension in metric spaces

Potential applications in metric space analysis

Abstract

The metric dimension of a general metric space was defined in 1953, applied to the set of vertices of a graph metric in 1975, and developed further for metric spaces in 2013. It was then generalised in 2015 to the k-metric dimension of a graph for each positive integer k, where k=1 corresponds to the original definition. Here, we discuss the k-metric dimension of general metric spaces.