LAUSR

Abstract 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.