The strong metric dimension of some generalized Petersen graphs

TL;DR

This paper investigates the strong metric dimension of generalized Petersen graphs, providing exact values for certain cases and bounds for others, advancing understanding of graph metric properties.

Contribution

It determines the exact strong metric dimension for specific classes of generalized Petersen graphs and offers bounds for additional cases.

Findings

Exact strong metric dimension for $n=4k$ and $n=4k+2$ cases.

Upper bounds for $n=4k+1$ cases.

Enhanced understanding of metric properties in generalized Petersen graphs.

Abstract

In this paper the strong metric dimension of generalized Petersen graphs $GP(n,2)$ is considered. The exact value is determined for cases $n=4k$ and $n=4k+2$, while for $n=4k+1$ an upper bound of the strong metric dimension is presented.