Derivation of New Class of Topological Indices Through M-Polynomial

Abstract

A topological index (TI) is a numeral quantity computed from the molecule’s graphical model that provides insight into the physical, chemical, bioactive, and structural properties of the associated compound. Chemical graph theory (CGT) is the bridge between graph theory and mathematical chemistry, widely employs this tool to design and analyze existing and new compounds through QSPR/QSAR analyses. The M-Polynomial is a general ex- pression possessing abundant facts about myriad degree-related TIs. Recently, the class of K-Banhatti indices and some famous indices have been extracted from the M-Polynomial. The line graphs of the synthetic denture base polymers, namely bakelite BLst , vulcanite VUst , and polymethyl methacrylate PMst , are novel, intriguing and complex structures. In this work, initially, we aim to calculate the M-Polynomials of the above-described graphs. Using M-Polynomials, we extract several TIs such as the first and second simple, hyper, and modified K-Banhatti indices, respectively. Also, we derive harmonic K-Banhatti , GA, and ABC indices from M-Polynomials of graphs under study. Lastly, we examine the relation among the paraline graphs of bakelite BLst , vulcanite VUst , and polymethyl methacrylate PMst by comparing the computed TIs.