This paper introduces five new degree-based topological indices based on the neighborhood degree of vertices in molecular graphs. These indices are designed to provide a more nuanced characterization of molecular graphs, focusing on local structural information. The indices are applied to various nanostructures, including hexagonal parallelogram nanotubes, triangular benzenoid systems, zigzag-edge coronoid fused with starphene nanotubes, dominating derived networks, and various dendrimers. The computation of these indices for different nanostructures is facilitated by standard computational techniques and algebraic methods for edge partitioning. The results demonstrate the effectiveness of the proposed indices in capturing the complex topology of these systems. The paper also includes detailed proofs for the computation of these indices for specific nanostructures, such as hexagonal parallelogram nanotubes, triangular benzenoid systems, and various dendrimers. The findings contribute to the theoretical advancements in topological index theory and practical applications in the field of mathematical chemistry.This paper introduces five new degree-based topological indices based on the neighborhood degree of vertices in molecular graphs. These indices are designed to provide a more nuanced characterization of molecular graphs, focusing on local structural information. The indices are applied to various nanostructures, including hexagonal parallelogram nanotubes, triangular benzenoid systems, zigzag-edge coronoid fused with starphene nanotubes, dominating derived networks, and various dendrimers. The computation of these indices for different nanostructures is facilitated by standard computational techniques and algebraic methods for edge partitioning. The results demonstrate the effectiveness of the proposed indices in capturing the complex topology of these systems. The paper also includes detailed proofs for the computation of these indices for specific nanostructures, such as hexagonal parallelogram nanotubes, triangular benzenoid systems, and various dendrimers. The findings contribute to the theoretical advancements in topological index theory and practical applications in the field of mathematical chemistry.