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Wiener Index of Trees: Theory and Applications

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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.

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Authors and Affiliations

  1. Sobolev Institute of Mathematics, Russian Academy of Sciences, Siberian Branch, Novosibirsk, 630090, Russia

    Andrey A. Dobrynin

  2. Department of Mathematics and Statistics, University of New Mexico, Albuquerque, NM, 87131, USA

    Roger Entringer

  3. Faculty of Science, University of Kragujevac, PO Box 60, YU-34000, Kragujevac, Yugoslavia

    Ivan Gutman

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  1. Andrey A. Dobrynin
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  2. Roger Entringer
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  3. Ivan Gutman
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Dobrynin, A.A., Entringer, R. & Gutman, I. Wiener Index of Trees: Theory and Applications. Acta Applicandae Mathematicae 66, 211–249 (2001). https://doi.org/10.1023/A:1010767517079

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