University of KashanIranian Journal of Mathematical Chemistry2228-64897120160301Three-center Harary Index and its Applications61681240210.22052/ijmc.2016.12402ENB.FurtulaFaculty of Science, University of KragujevacI.GutmanFaculty of Science, University of Kragujevac, Kragujevac, Serbia0000-0001-9681-1550V.KatanicFaculty of Science, University of KragujevacJournal Article20151118The 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 Hk, is achieved by employing the Steiner-type distance between k-tuples of atoms. We show that the linear combination H+x H3 is significantly better correlated with a variety of physico-chemical properties of alkanes than H itself.https://ijmc.kashanu.ac.ir/article_12402_ff64ec64188304a21bed1c7a4b1c22e4.pdf