This paper introduces five new degree-based topological indices based on the neighborhood degree of a vertex. These indices are computed for various nanostructures such as hexagonal parallelogram nanotubes, triangular benzenoid systems, zigzag-edge coronoid fused with starphene nanotubes, dominating derived networks, and dendrimers. The study employs standard computational techniques and algebraic methods for edge partitioning to calculate the topological indices efficiently and accurately. The results show that these new indices provide a more nuanced characterization of molecular graphs and can effectively capture the complex topology of nanostructures. The paper also discusses the theoretical and practical significance of these indices in the field of mathematical chemistry. The results are presented in the form of mathematical expressions for each nanostructure, demonstrating the applicability of the proposed indices to a wide range of chemical structures. The study contributes to the development of topological indices and their application in analyzing the structural properties of nanostructures.This paper introduces five new degree-based topological indices based on the neighborhood degree of a vertex. These indices are computed for various nanostructures such as hexagonal parallelogram nanotubes, triangular benzenoid systems, zigzag-edge coronoid fused with starphene nanotubes, dominating derived networks, and dendrimers. The study employs standard computational techniques and algebraic methods for edge partitioning to calculate the topological indices efficiently and accurately. The results show that these new indices provide a more nuanced characterization of molecular graphs and can effectively capture the complex topology of nanostructures. The paper also discusses the theoretical and practical significance of these indices in the field of mathematical chemistry. The results are presented in the form of mathematical expressions for each nanostructure, demonstrating the applicability of the proposed indices to a wide range of chemical structures. The study contributes to the development of topological indices and their application in analyzing the structural properties of nanostructures.