Mixed Metric Dimension of Certain Carbon Nanocone Networks

Abstract

Chemical graph theory is an extension of mathematical chemistry that explores chemical phenomena and entities using the conceptual frameworks of graph theory. Chemical graph theory, in particular, uses chemical graphs to represent molecular structures. This chemical graph represents bonds and atoms, respectively, as edges and vertices. Cheminformatics predominantly uses chemical graphs as an essential data type for depicting chemical structures. The computable features of graphs lay the groundwork for (quantitative) structure-property and structure-activity predictions, which is an important component of cheminformatics. The physical and chemical characteristics of chemical compounds are thus reflected in these graphs, which can subsequently be reduced to graph-theoretical descriptors or indices. One of the most extensively researched distance-based graph descriptors is the resolving set W (metric dimension), which differentiates each pair of distinct vertices in every connected simple graph. The mixed metric dimension, which is the most significant variant of metric dimension, is determined for the complex molecular graph of a one-pentagonal carbon nanocone (PCN) in this manuscript. We show that only three distinct non-neighboring vertices (least possible requirement) from PCN can be adopted to uniquely identify all of the edges as well as vertices in PCN.

Keywords:

• Basis set
• resolving set
• mixed basis set
• mixed metric dimension
• one-pentagonal carbon nanocone

Acknowledgments

The author also thank the anonymous reviewers for a careful reading of this paper and for all their comments and suggestions, which lead to a number of improvements to the final manuscript.

Author contributions

All the authors have equally contributed to the final manuscript.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Data availability statement

Data sharing is not applicable to this article as no data sets were generated or analyzed during the current study.