Neighborhood Sum VDB Indices and Entropy for Molecular Graphs of Supertriphenylene and Superphenalene

Abstract

The structural topology of molecular graphs can be correlated with physicochemical and biological features using topological indices (TIs), which are numerical descriptors. In this work, we calculate the neighborhood sum degree-based M-polynomial and provide closed-form analytical formulas for a wide range of topological indices based on degree and those based on the sum of neighborhood degrees of superphenalene and supertriphenylene, two polycyclic aromatic hydrocarbons (PAHs). Explicit formulas for indices like the Zagreb-type, GA, ABC, SDD, harmonic, inverse sum, and redefined Zagreb indices are produced through systematic vertex-edge partitioning and neighborhood degree-sum labeling. Additionally, structural complexity is measured using Shannon-type entropy metrics based on neighborhood information. Three-dimensional graphical representations and tabular computations are used for numerical validation and comparative studies. The findings give these PAHs—structures of growing importance in organic electronics, supramolecular chemistry, and carbon-based nanomaterials—new TI and entropy characterizations. These results support upcoming QSPR/QSAR research and add to the theoretical toolkit for benzenoid hydrocarbon analysis.