investigating banhatti indices with m-polynomial approach on silicate

Silicates are the largest, most interesting and complex group of minerals. the basic chemical unit ofsilicates is tetrahedral (sio4). we consider the silicate sheet as a fixed connection parallel architecture and call ita silicate network. silicate-containing compounds are widely used in industry with an environmental protectionapproach. for example, because silicate is cheap, does not have toxic effects, and also because it does not haveharmful effects on the environment, it is used in the production of glue. also, silicate gels can be used to controlwater production in tanks and prevent wall leakage. silicate gels do not contain toxic chromium ions in theirstructure and are environmentally friendly. the use of silicate gels as a new solution free of toxic substances canbe considered to improve the performance of production and injection wells in the oil industry. in this work, wecalculated the first and second banhatti indices for the silicate network. for this purpose, first by introducing mpolynomial and then by defining suitable operators on the topological polynomial, we calculated the first andsecond indices of banhatti and announced the results as polynomials.