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Nanoscience has progressed exponentially during the previous few decades, moving from bench science to complex applied technologies. Nanomaterials found their application in large number of industrial products which includes filters, paints, insulation, electronic components, lubricant additives, biomedical applications, etc. One such important nanomaterial is lead sulphide, an inorganic compound with the chemical formula PbS, and is one of the most common ore of Galena. The graphical depiction of the molecular structure determines how the atoms are organised in real three-dimensional space. Graphical representation encloses a detailed study of the physical and chemical properties of molecules for the calculation of degree and distance-based graph parameters. Such parameters are termed as topological indices of graph and are usually numerical parameters. The resolvability parameters of a graph are a highly innovative topic in which the entire structure is molded to obtain each atom's unique position. In this work, we consider some degree and distance-based graph parameters of an inorganic compound, namely, lead sulphide. In particular, we study its metric dimension and fault-tolerant metric dimension. We also obtain first, second, and third Zagreb index for PbS.

Mathematical analysis of one-dimensional lead sulphide crystal structure using molecular graph theory