SOME RECENT RESULTS IN THE THEORY OF THE WIENER NUMBER

The Wiener number (W) is equal to the sum of distances between all pai rs of vertices of the molecular graph. This important topological inde x was invented in the 1940s, 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 inte rmolecular forces (which, for the first time, provide a sound physico- chemical basis for various applications of W), (b) several novel techn iques for the calculation of W, (c) methods for the calculation of W o f composite, and highly branched molecular graphs, (d) the problem of isomer degeneracy of W, and (e) some novel mathematical results releva nt to the theory of W.