Reverse Degree-Based Polynomial Descriptors in Corrosion-Related Systems: Exploratory Analysis of Organic Inhibitors and Nanoporous Graphene

Mild steel remains one of the most widely used structural materials in mechanical and industrial engineering due to its favorable mechanical performance and low cost. However, its high susceptibility to corrosion continues to cause significant operational and economic losses across engineering systems. This study presents a unified analytical framework for analyzing corrosion-related molecular and nanostructured systems using reverse degree-based topological descriptors, namely, the Reverse M-polynomial and Reverse NM-polynomial. The framework is demonstrated in two complementary stages relevant to corrosion engineering. First, an exploratory structure–property correlation analysis based on Quantitative Structure–Property Relationship (QSPR) principles is conducted for furan-based organic inhibitors reported in the literature, examining the relationship between reverse degree-based descriptors and inhibition efficiency on mild steel surfaces. The analysis reveals a strong statistical correlation within the analyzed dataset (r = 0.958), indicating the sensitivity of selected reverse topological descriptors to molecular structural variations. The statistical significance of the correlations was evaluated using p-values and F-statistics, confirming the reliability of the observed associations within the analyzed dataset. However, owing to the limited dataset size, no claims of external predictivity are made. Second, the framework is extended to advanced protective materials through the analytical formulation of reverse descriptors for nanoporous graphene nanoribbons containing 14-annulene pores, focusing exclusively on structural and topological characterization. These graphene structures are considered as potential physical barrier materials; however, in this study, the analysis is limited to structural descriptor characterization without modeling corrosion performance. This work provides analytical results for reverse degree-based descriptors of such graphene architectures. Overall, the findings establish a versatile analytical framework that supports exploratory structure–property investigations of organic inhibitors and provides descriptor-based structural benchmarks for graphene nanostructures, offering theoretical insights relevant to corrosion mitigation research.