Metric dimension of line graph of the subdivision of the graphs of convex polytopes

Abstract

The metric generator for the simple connected graph Γ is the set of vertices Y ⊆ V(Γ) with the property that every pair of vertices u, v(u 6= v) ∈ V are determined (or resolved) by some vertex of Y. The minimum possible cardinality of this metric generator is called the metric dimension of Γ, denoted by dim(Γ)or β(Γ). In this article, we determine the exact metric dimension and some other properties of the line graph of the subdivision graph of the graph of convex polytope Dn (exists in the literature).