Applications of the inverse degree index to molecular structures

The inverse degree index, also called inverse index, first attracted attention through numerous conjectures generated by the computer programme Graffiti. Since then its relationship with other graph invariants has been studied by several authors. In this paper we obtain new inequalities involving the inverse degree index, and we characterize graphs which are extremal with respect to them. In particular, we obtain several inequalities relating the inverse degree index with the first and second Zagreb indices, the general first and second Zagreb indices, the Forgotten index, the general sum-connectivity index, the Sombor index and the misbalance indeg index, and several parameters of the molecular graph as the number of vertices, the number of edges, the minimum degree and the maximum degree. Also, we compute the inverse degree index for some classes of chemical graphs. Furthermore, some applications are given to the study of the physicochemical properties of three classes of compounds: polyaromatic hydrocarbons, polychlorobiphenyls, and octane isomers.