On degree-based operators and topological descriptors of molecular graphs and their applications to QSPR analysis of carbon derivatives

This work initiates a concept of reduced reverse degree based \(\mathcal {RR_D\,M}\) ${\mathcal{RR}}_{\mathcal{D}}\mathcal{M}$ -Polynomial for a graph, and differential and integral operators by using this \(\mathcal {RR_D\,M}\) ${\mathcal{RR}}_{\mathcal{D}}\mathcal{M}$ -Polynomial. In this study twelve reduced reverse degree-based topological descriptors are formulated using the \(\mathcal {RR_D\,M}\) ${\mathcal{RR}}_{\mathcal{D}}\mathcal{M}$ -Polynomial. The topological descriptors, denoted as \(\mathbb{T}\mathbb{D}\) $\mathbb{T}\mathbb{D}$ ’s, are numerical invariants that offer significant insights into the molecular topology of a molecular graph. These descriptors are essential for conducting QSPR investigations and accurately estimating physicochemical attributes. The structural and algebraic characteristics of the graphene and graphdiyne are studied to apply this methodology. The study involves the analysis and estimation of Reduced reverse degree-based topological descriptors and physicochemical features of graphene derivatives using best-fit quadratic regression models. This work opens up new directions for scientists and researchers to pursue, taking them into new fields of study.