On Resolvability of a Graph Associated to a Finite Vector Space

TL;DR

This paper determines the metric dimension of a graph linked to a finite vector space, explores the exchange property for resolving sets, and relates findings to intersection graphs, advancing understanding of graph resolvability in algebraic structures.

Contribution

It provides the first determination of the metric dimension for the non-component graph of a finite vector space and analyzes the exchange property of resolving sets.

Findings

Metric dimension of the non-component graph is explicitly determined.

The exchange property holds for resolving sets except in a specific case.

Results connect the properties of the graph to intersection graph theory.

Abstract

The metric dimension of non-component graph, associated to a finite vector space, is determined. It is proved that the exchange property holds for resolving sets of the graph, except a special case. Some results are also related to an intersection graph.