Edge Metric Dimension and Edge Basis of One-Heptagonal Carbon Nanocone Networks
oleh: Karnika Sharma, Vijay Kumar Bhat, Sunny Kumar Sharma
| Format: | Article |
|---|---|
| Diterbitkan: | IEEE 2022-01-01 |
Deskripsi
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 (<inline-formula> <tex-math notation="LaTeX">$HCN_{7}(q)$ </tex-math></inline-formula>). We prove that only three non-adjacent vertices are the minimum requirement for the identification of all the edges in <inline-formula> <tex-math notation="LaTeX">$HCN_{7}(q)$ </tex-math></inline-formula>, uniquely.