Wiener index

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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. [1] Wiener index may be calculated using the Floyd algorithm. Bojan Mohar and Tomaž Pisanski presented an efficient algorithm for computing the Wiener index of a tree. [2]

Wiener index is the oldest topological index related to molecular branching.[3] 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. [4] Also, different modifications of Wiener index were introduced (for example, Extended Wiener index[5]).


[edit] References

  1. ^ H. Wiener, J. Am. Chem. Soc., 1947, 69, 17.
  2. ^ Bojan Mohar, Tomaž Pisanski, "How to compute the Wiener index of a graph" J. Math. Chemistry 2 (1988) pp. 267-277
  3. ^ Roberto Todeschini, Viviana Consonni (2000) "Handbook of Molecular Descriptors", Wiley-VCH, ISBN 3527299130
  4. ^ Ivan Gutman, T. Körtvélyesi, "Wiener indices and molecular surfaces" Z. Naturforsch. 50a (1995) pp. 669-671
  5. ^ S. S. Tratch, M. I. Stankevitch, and N. S. Zefirov, J. Comp. Chem., 1990, 11, 899.
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