Three-center Harary index and its applications

Abstract

The Harary index \(H\) can be viewed as a molecular structure descriptor composed of increments representing interactions between pairs of atoms, such that their magnitude decreases with the increasing distance between the respective two atoms. A generalization of the Harary index, denoted by \(H_k\), is achieved by employing the Steiner-type distance between \(k\)-tuples of atoms. We show that the linear combination \(H + \lambda\,H_3\) is significantly better correlated with a variety of physico-chemical properties of alkanes than \(H\) itself.