Degree-Based Topological Aspects of Polyphenylene Nanostructures

Abstract

In a molecular graph, molecules are associated with some numerical values these values are known as topological indices. From the M-polynomial of molecular structure we can derived degree based topological indices. We can derived chemical and physical properties of chemical compound from the topological indices. To find the strain energy, melting point, boiling point, distortion and stability of chemical compound usually mathematician used topological indices. Moreover topological indices also make relation between biological activities of compound with physical properties. In this paper, we determined the M-polynomials of the structure of the molecules of polyphenylene nanotube and nanotori. Then we derived some closed formulas for well-known topological indices, first Zagreb index, second Zagreb index, second Modified Zagreb index $m{M}_2(G),$ general Randić index, Symmetric division index, Harmonic index, inverse sum index for polyphenylene nanotube structure of molecules.

Keywords:

• M-polynomial
• topological indices
• polyphenylene nanotube
• molecules

Acknowledgment

The authors would like to thanks the two anonymous reviewers for their very constructive comments that helped us to enhance the quality of this manuscript.

Additional information

Funding

The research was supported by the National Natural Science Foundation of China (Grant Nos. 11971142, 11871202, 61673169, 11701176, 11626101, 11601485).