Abstract
Silicon, oxygen and aluminium are found in large quantities on the earth's surface. Silicates are the minerals which contain silicon and oxygen in tetrahedral \( (SiO)_{4}^{4-} \) units, which are linked together in several patterns. In chemical graph
theory, atoms are represented as vertices and chemical bonds as edges. In a silicate network, a tetrahedron comprises of one central silicon atom and four surrounding oxygen atoms. Cement, ceramic and glass industries use silicates for
manufacturing purposes. The computation of silicate networks using graph-invariant has been introduced in this article. Using graph-invariant parameters has applications in studying the topological properties of silicate networks. We consider
chain silicate \( (CS_{m}) \), cyclic silicate \( (CYS_{m}) \), double chain silicate \( (DCS_{m}) \), sheet silicate \( (SS_{m}) \), honeycomb network \( (HC_{m}) \) and m \( \times \) m grid network \( (G_{m \times m}) \). To compute
the topological properties of silicate networks, we investigate the graph-invariants such as maximum cliques(\( \omega \)), minimum chromatic number(\( \chi \)), maximum independence number(\( \alpha \)), matching ratio(\( m_{r} \)) and
minimum domination number(\( \gamma \)). Here, we observe the clique number of chain silicate, cyclic silicate, double chain silicate, and sheet silicate is 3, whereas honeycomb network and m \( \times \) m grid network is 2. Similarly,
the chromatic number of chain silicate, cyclic silicate and sheet silicate is 4. Moreover, the chromatic number of the honeycomb network, m \( \times \) m grid network is 2 and the double chain silicate is 4. Then, the independence number
of chain silicate, cyclic silicate, double chain silicate and sheet silicate is m. These characteristics show the structural behaviour of silicate networks. For instance, the clique number gives the molecular structure of the silicate
network whereas the chromatic number gives the least number of atom types necessary to represent a molecule.
