Valency-based topological descriptors of chemical networks and their applications

A topological descriptor/index (or molecular structure descriptor) is a numerical value associated with chemical constitution for correlation of chemical structure/network with various physical properties, chemical reactivity or biological activity. Quantitative structure-activity and structure-property relationships of chemical networks require expressions for the topological properties of these networks. Topological indices provide these expressions of topological properties. Valency-based topological descriptors are the oldest and most successful class of descriptors so far. A chemical graph/network is a representation of the structural formula of a chemical compound whose vertices correspond to the atoms of the compound and edges correspond to chemical bonds. In this paper, we study valency-based topological indices of chemical networks. By using some real world data, we performed certain comparative testings to investigate the performance of almost all well-known valency-based indices. Dependence on the molecular structure is studied for topological indices which are best in performance. We calculated explicit formulas for well-performed indices of some infinite families of carbon nanotubes, carbon nanocones and a newly proposed family of organic networks called tetrahedral diamond networks. Tetrahedral diamond networks arises by recurrently joining graphene layers in a diamond cluster. Significance and applicability of the obtained results are reported.