Edge Metric Dimension and Edge Basis of One-Heptagonal Carbon Nanocone Networks

Abstract

A molecular (chemical) graph is a simple connected graph, where the vertices represent the compound’s atoms and the edges represent bonds between the atoms, and the degree (valence) of every vertex (atom) is not more than four. In this paper, we determine the edge metric basis and edge metric dimension (EMD) of the complex molecular graph of a one-heptagonal carbon nanocone ( $HCN_{7}(q)$ ). We prove that only three non-adjacent vertices are the minimum requirement for the identification of all the edges in $HCN_{7}(q)$ , uniquely.

Keywords

• Connected graph
• edge metric basis
• edge metric dimension
• independent set
• one-heptagonal carbon nanocone
• resolving set