A Concealed Property of the Topological IndexZ

Abstract

Examination of the structure-dependence of the total π-electron energy leads to the equation F(G, x) = ln Z(G), where F(G, x) is the Coulson function (of the molecular graph G) and Z(G) is the corresponding topological index Z. The (positive and unique) solution of this equation is called the Z-point of G and is denoted by xH. By the analysis of the Z-points of trees and chemical trees the following generally valid regularities were established: (a) Not all trees have a Z-point, but all chemical trees have a Z-point. (b) The Z-points of all chemical trees (irrespective of their size and other structural features) are nearly equal; for all chemical trees, xH ≈ 1.2.