Generalized M-polynomial and graphical invariants of silicate cage networks with applications to property prediction

This study introduces a generalized M-polynomial framework for the structural analysis of silicate cage molecular networks. From the molecular graph representation, several degree-based topological indices are derived, including Zagreb indices, the Randić index, the inverse Randić index, the symmetric division index, the harmonic index, the sum inverse index, and the augmented Zagreb index. The proposed formulation incorporates degree-weighted parameters, enabling a systematic characterization of structural complexity in terms of network parameters such as the number of layers and replicated units. Case-wise analysis for different structural configurations shows consistent trends in all indices, reflecting their sensitivity to molecular growth and connectivity. Overall, the results demonstrate that the proposed framework provides a unified and scalable approach for analyzing silicate cage networks. The obtained indices effectively capture structural variations and offer useful insights for graph-theoretical studies of complex molecular systems.