Reverse M-polynomial of a Graph

Chemical graph theory is an important field of mathematical chemistry that deals with the mathematical modeling of chemical compound structures. A graph consisting of non-hydrogen atoms is known as a molecular graph. The reverse degree-based topological indices are an important tool in mathematical chemistry to encode the structural information of a molecular graph in the form of a fixed quantity. In this study, we are going to introduce a concept of a polynomial based on the reverse degree of a graph. Let [Formula: see text] be a graph and let [Formula: see text] be the number of [Formula: see text]-edges of [Formula: see text] such that [Formula: see text] We introduce the idea of the Reverse M-polynomial (RM-polynomial) of [Formula: see text], which is defined as [Formula: see text] This investigation presents the derivation of novel closed-form expressions for well-known reverse degree-based topological indices. Rather than employing conventional mathematical definitions, our approach utilizes the RM-polynomial framework to compute these indices for the oxide networks and the antiviral pharmaceutical agent Zanamivir. The RM-polynomial offers significant computational advantages by enabling the calculation of multiple reverse degree-based topological indices and reducing computational complexity. Furthermore, this study provides a comprehensive analysis of the graphical representations and the behavioral characteristics exhibited by the RM-polynomial and the reverse degree-based topological indices of graphs corresponding to the oxide networks and the Zanamivir graph. These results demonstrate the practical utility of the RM-polynomial approach in the field of mathematical chemistry.