Revan Topological Indices of Quadrilateral Snake Graphs: Polynomial Formulations, Python Implementation, and Applications

Abstract

This study presents a detailed exploration of the Revan family of topological indices and their polynomial representations for diverse classes of quadrilateral snake graphs. Originating from the concept introduced by V. R. Kulli, Revan indices integrate both the minimum and maximum vertex degrees, which provide a refined measure of graph connectivity and structure. The research systematically derives explicit analytical expressions for Revan indices and their corresponding polynomials for four principal graph variants: standard, alternate, double, and cyclic quadrilateral snake graphs, highlighting their distinctive structural characteristics and degree-based relationships. To complement the theoretical formulations, a Python-based computational framework was developed to automate the calculation and symbolic representation of these indices. This implementation enables efficient validation of analytical results and facilitates the extension of Revan-based metrics to larger and more complex graph families. The findings underscore the potential of Revan indices as powerful structural descriptors in mathematical chemistry and network theory, with promising applications in quantitative modeling, cheminformatics, and the broader field of graph-based molecular design.