Topological indices of advanced nanotube architectures: hexagonal, zigzag-edge coronoid and starphene fusions

Chemical graph theory (CGT) utilizes graph-theoretical tools to model molecular structures and predict their physicochemical properties. Topological indices (TIs), as numerical descriptors derived from molecular graphs, serve as essential tools in theoretical chemistry and nanotechnology. In this study, we investigate advanced nanotube architectures, specifically hexagonal parallelogram nanotubes, triangular benzenoids, and zigzag-edge coronoids fused with starphene units. Using a systematic algebraic approach, we derive novel neighborhood M-polynomials (NM-polynomials) for these nanostructures. From the NMpolynomials, we compute various neighborhood-based topological indices, including the second Zagreb index, harmonic index, and forgotten index. The proposed methodology simplifies the computation of TIs and provides closed-form expressions for complex fused structures. The findings have promising implications for the design and analysis of nanomaterials in fields such as drug delivery, molecular electronics, and material science.