Mathematical study of silicate and oxide networks through Revan topological descriptors for exploring molecular complexity and connectivity.

Oxide and silicate frameworks, known for their structural adaptability, play a pivotal role in gas storage, drug delivery, electronics, and catalysis. In this study, we explore the structural complexities of silicate and oxide networks through the lens of chemical graph theory, focusing on their molecular topology and its implications for real-world applications. By representing these materials as molecular graphs-where atoms are represented by vertices, and edges depict bonds-we employ various Revan topological indices namely, first Revan index, second Revan index, third Revan index, first modified Revan index, second modified Revan index, the first hyper Revan index, second hyper Revan index, sum connectivity Revan index, product connectivity Revan index, harmonic Revan index, geometric arithmetic Revan index, arithmetic geometric Revan index, F-Revan index, and Sombor Revan index for chain silicates, chain oxide frameworks, sheet oxide frameworks, and sheet silicate frameworks to quantitatively assess their structural and physicochemical properties. Through graphical and numerical analyses, this study offers new insights into the structure-property relationships of these networks. Our work opens the door for more efficient application of these materials across industries, particularly in nanotechnology, environmental remediation, and material science, where understanding topological features is critical to enhancing performance. The results also contribute to a deeper understanding of chemical networks, advancing both theoretical knowledge and practical applications in chemistry and material science.