On the metric determination of linear dependence graph

The metric on a connected graph G is a mapping which assigns to each pair (u,v) of vertices in G the length of a shortest path between u and v. In this article, we consider the linear dependence graph associated with a finite dimensional vector space and determine its metric properties, namely, the center, the periphery, metric-degree sequence, metric-degree polynomial, metric dimension, connected metric dimension, local metric dimension, strong metric dimension, and the metric polynomial.