Graph theoretical characterization and QSPR modeling of aluminum and magnesium hydroxide networks through integrated face degree topological indices.

Aluminum hydroxide (gibbsite) and magnesium hydroxide (brucite) rank among the most prevalent hydroxide minerals and function as structural prototypes for diverse layered materials, including phyllosilicates, layered double hydroxides, and emerging two-dimensional halides. An exciting feature of these materials is their novel electronic and spintronic functionalities. Gibbsite adopts a dioctahedral framework with one-third of its octahedral sites vacant and stabilized by hydrogen bonding, whereas brucite forms a fully occupied trioctahedral lattice bound by van der Waals interactions. Such structural differences critically influence their stability, reactivity, and functional versatility. The present study develops a topological framework by employing classical degree-based indices, along with face degree and degree-sum variants, to characterize their network structures and compute their properties. We employ univariate and bivariate regression models in conjunction with the quantitative structure-property relationship (QSPR) approach to predict physicochemical properties of aluminum and magnesium hydroxide configurations, such as log P (base 10), molecular weight, and molar refractivity. The integrated methodology demonstrates improved structural discrimination and predictive reliability, highlighting the utility of topological indices in QSPR analysis.