Wiener Index of Trees: Theory and Applications |
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Authors: | Andrey A. Dobrynin Roger Entringer Ivan Gutman |
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Affiliation: | (1) Sobolev Institute of Mathematics, Russian Academy of Sciences, Siberian Branch, Novosibirsk, 630090, Russia;(2) Department of Mathematics and Statistics, University of New Mexico, Albuquerque, NM 87131, USA;(3) Faculty of Science, University of Kragujevac, PO Box 60, YU-34000 Kragujevac, Yugoslavia |
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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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Keywords: | distance (in a graph) Wiener index trees |
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