Edge metric dimension of some generalized Petersen graphs

TL;DR

This paper investigates the edge metric dimension of generalized Petersen graphs, providing exact formulas for specific cases and bounds for others, advancing understanding of their mathematical properties.

Contribution

It offers the first exact formulas for the edge metric dimension of $GP(n,1)$ and $GP(n,2)$, and establishes lower bounds for other parameters.

Findings

Exact formulas for $GP(n,1)$ and $GP(n,2)$

Lower bounds for other $k$ values

Mathematical properties of edge metric representations

Abstract

The edge metric dimension problem was recently introduced, which initiated the study of its mathematical properties. The theoretical properties of the edge metric representations and the edge metric dimension of generalized Petersen graphs $GP(n,k)$ are studied in this paper. We prove the exact formulae for $GP(n,1)$ and $GP(n, 2)$, while for the other values of $k$ the lower bound is stated.