Investigating the Metric and Edge Metric Dimensions of H-Naphthalenic Nanotubes

Abstract

If the distances between two vertices in a simple connected network are different, then a vertex x resolves the pair u and v. A set S of vertices in G is referred to as a resolving set if every pair of distinct vertices in G can be identified by at least one vertex in S. The metric dimension (MD) of G is the minimum number of vertices required for a resolving set. Moreover, an edge metric generator is any subset S of vertices that can distinguish between any two distinct edges, e1 and e2, according to their respective distances. An edge metric dimension (EMD), dime(G), is an edge metric generator of the least size. This study aims to explore the metric dimension (MD) and edge metric dimension (EMD) of the H-Naphthalenic Nanotube.