Wiener index

In chemical graph theory, the Wiener index (also Wiener number) is a topological index of a molecule, defined as the sum of the numbers of edges in the shortest paths in a chemical graph between all pairs of non-hydrogen atoms in a molecule. It was introduced by H. Wiener in 1947. [H. Wiener, J. Am. Chem. Soc., 1947, 69, 17.] Wiener index may be calculated using the Floyd–Warshall algorithm. Bojan Mohar and Tomaž Pisanski presented an efficient algorithm for computing the Wiener index of a tree. [Bojan Mohar, Tomaž Pisanski, "How to compute the Wiener index of a graph" "J. Math. Chemistry" 2 (1988) pp. 267-277]

Wiener index is the oldest topological index related to molecular branching. [Roberto Todeschini, Viviana Consonni (2000) "Handbook of Molecular Descriptors", "Wiley-VCH", ISBN 3527299130 ] A tentative explanation of the relevance of the Wiener index in research of QSPR and QSAR is that it correlates with the van der Waals surface area of the molecule. [Ivan Gutman, T. Körtvélyesi, "Wiener indices and molecular surfaces" "Z. Naturforsch." 50a (1995) pp. 669-671] Also, different modifications of Wiener index were introduced (for example, Extended Wiener index [S. S. Tratch, M. I. Stankevitch, and N. S. Zefirov, "J. Comp. Chem.", 1990, 11, 899.] ).

References