Fault-Tolerant Partition Resolvability in Chemical Graphs

Abstract

Apart from many branches in mathematical sciences, the main share of applications of graph theory nowadays is in chemistry. The graph-theoretical ideas have been used by many chemists for more than two centuries but over the last 30 years, the great significance of graph theory in chemistry has been extensively acknowledged. In a chemical graph, the vertices can symbolize atoms, orbitals, bonds, collection of atoms, molecules, or group of molecules and the edges symbolize the connection between chemical substances and are used to describe reactions, chemical bonds, kinetic models, reaction mechanisms, or other interactions and alterations of the chemical substances. Benzene is the archetypal aromatic molecule, showing exceptional chemical stability as compared with other unsaturated hydrocarbons. Fullerenes are a unique family of carbon-based cage molecules having remarkable properties. Fullerene has potential applications in medicinal chemistry due to its size, hydrophobicity, three-dimensionality, and electronic configurations. In this paper, we will calculate the fault-tolerant partition dimension of classes of fullerene graphs, n-linear benzene graph and partition dimension of polyphenyl chains.

Keywords:

• Fullerene graph
• benzene graph
• polyphenyl chains
• metric dimension
• partition dimension
• fault-tolerant partition dimension

Acknowledgement

The authors are grateful to the reviewer’s valuable comments that improved the manuscript.

Disclosure statement

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

Additional information

Funding

This work was supported by UMT Research Fund.