Oxide and silicate networks: computation and analysis of face neighborhood index

Chemical graph theory provides useful mathematical tools for studying the structural properties of molecular networks through topological descriptors. In recent years, neighborhood-based indices have gained significant interest because of their applications in chemistry and material science. Previous studies reported strong correlations between chemical structures and bond energies, with correlation coefficients of at least 0.999 for boiling points and 0.990 for bond energies. Motivated by these observations, the present paper studies the face neighborhood index (FNI) of the dominating oxide network DOX(n), dominating the silicate lattice DSL(n), and copper oxide network CUO(m,n). By employing suitable face and vertex partitions, exact closed expressions for the considered structures are obtained. The derived results may contribute to further investigations of neighborhood-based topological descriptors and their chemical applications.