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Acta Applicandae Mathematica

, Volume 66, Issue 3, pp 211–249 | Cite as

Wiener Index of Trees: Theory and Applications

  • Andrey A. Dobrynin
  • Roger Entringer
  • Ivan Gutman
Article

Abstract

The Wiener index W is the sum of distances between all pairs of vertices of a (connected) graph. The paper outlines the results known for W of trees: methods for computation of W and combinatorial expressions for W for various classes of trees, the isomorphism–discriminating power of W, connections between W and the center and centroid of a tree, as well as between W and the Laplacian eigenvalues, results on the Wiener indices of the line graphs of trees, on trees extremal w.r.t. W, and on integers which cannot be Wiener indices of trees. A few conjectures and open problems are mentioned, as well as the applications of W in chemistry, communication theory and elsewhere.

distance (in a graph) Wiener index trees 

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Copyright information

© Kluwer Academic Publishers 2001

Authors and Affiliations

  • Andrey A. Dobrynin
    • 1
  • Roger Entringer
    • 2
  • Ivan Gutman
    • 3
  1. 1.Sobolev Institute of MathematicsRussian Academy of Sciences, Siberian BranchNovosibirskRussia
  2. 2.Department of Mathematics and StatisticsUniversity of New MexicoAlbuquerqueUSA
  3. 3.Faculty of ScienceUniversity of KragujevacKragujevacYugoslavia

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