Some recent results in the theory of the Wiener number

Abstract

The Wiener number (W) is equal to the some of distances between all pairs of vertices of the molecular graph. This important topological index was invented in the 1940, but vigorous research on both its theory and its applications is still going on. The aim of this article is to outline the state of the art of the theory of the Wiener number, with emphasis on the progress achieved in the last few years. In particular, we present (a) the recent results on the relation between W and intermolecular forces (which, for the first time, provide a sound physico-chemical basis for various applications of W), (b) several novel techniques for the calculation of W, (c) methods for the calculation of W of composite and highly branched molecular graphs, (d) the problem of isomer degeneracy of W, and (e) some novel mathematical results relevant to the theory of W.