Investigating Metric Dimension and Edge Metric Dimension of Hexagonal Boron Nitride and Carbon Nanotubes

When there is a difference in the distance between two vertices in a simple linked graph, then a vertex x resolves both u and v. If at least one vertex in S distinguishes each pair of distinct vertices in G, then a set S of vertices in G is referred to as a resolving set. G's metric dimension is the minimum number of vertices required in a resolving set. A subset S of vertices in a simple connected graph is called an edge metric generator if each vertex can tell any two distinct edges e₁ and e₂ apart by their respective distances from each other. The edge metric dimension (EMD), denoted as dim_e(G), is the smallest cardinality of such a subset S that serves as an edge metric generator for G. The primary objective of this study is to investigate the edge metric dimension (EMD) of hexagonal boron nitride and carbon nanotube structures.