Analytical study of degree-based graphical invariants in subdivided hexagonal cage networks

Graphical invariants and degree-based topological indices are important tools in graph theory, network science, and mathematical modeling for characterizing the structural properties of complex graph families. In this paper, we investigated subdivided hexagonal cage networks and derived exact analytical expressions for several important graphical invariants, including the general Randić index, the first Zagreb index, the second Zagreb index, the third Zagreb index, the atom-bond connectivity index, and the hyper-Zagreb index. By employing graph-theoretical techniques together with edge partition methods, explicit closed-form formulas were obtained in terms of the subdivision parameter of the underlying network. The derived results demonstrate the impact of subdivision operations on the structural behavior, branching characteristics, and quantitative complexity of the considered networks. Moreover, these graphical invariants provide useful insights into the structural characteristics, connectivity patterns, and complexity of the considered subdivision networks. The presented framework enriches the study of graphical invariants for nanostructures and complex graph and network models, while also contributing to applications in mathematical chemistry, materials science, and graph-based network analysis.