Structural Insights into Neighbor Degree-Based Topological Indices for Hexagonal Chain Structures

Background/Objectives: Topological indices serve as essential tools in chemical graph theory, offering numerical descriptors that correlate molecular structure with physicochemical properties. This study introduces and analyzes new topological indices for hexagonal chain-based molecular graphs, focusing on their structural significance and predictive capabilities. Methods: We compute the neighbor degree based redefined third Zagreb index, forgotten index, and reduced Zagreb index for three distinct hexagonal chain structures: hammer-like benzenoid chains, linear hexagonal chains, and armchair hexagonal chains. By leveraging degree-based invariants, we establish mathematical formulations that enhance the understanding of molecular connectivity and stability. Findings: The results provide a deeper insight into the mathematical foundations of molecular descriptors and their interdisciplinary applications in computational chemistry, drug design, and material science. Novelty: Our work provides a simple yet effective way to analyze these graphs and opens new possibilities for studying their applications in chemistry.