On the limiting distribution of the metric dimension for random forests

TL;DR

This paper studies the metric dimension of random forests, showing that it follows a normal distribution in two different models, providing insights into the probabilistic behavior of this graph parameter.

Contribution

It introduces the first normal limit distribution results for the metric dimension in two models of random forests, advancing understanding of this parameter's probabilistic properties.

Findings

Metric dimension follows a normal distribution in the studied models

Provides theoretical foundation for probabilistic analysis of metric dimension

Enhances understanding of structural properties of random forests

Abstract

The metric dimension of a graph G is the minimum size of a subset S of vertices of G such that all other vertices are uniquely determined by their distances to the vertices in S. In this paper we investigate the metric dimension for two different models of random forests, in each case obtaining normal limit distributions for this parameter.