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Wiener Index of Hexagonal Systems

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Abstract

The Wiener index W is the sum of distances between all pairs of vertices of a (connected) graph. Hexagonal systems (HS's) are a special type of plane graphs in which all faces are bounded by hexagons. These provide a graph representation of benzenoid hydrocarbons and thus find applications in chemistry. The paper outlines the results known for W of the HS: method for computation of W, expressions relating W with the structure of the respective HS, results on HS's extremal w.r.t. W, and on integers that cannot be the W-values of HS's. A few open problems are mentioned. The chemical applications of the results presented are explained in detail.

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

    Ivan Gutman

  3. Department of Mathematics, PEF, University of Maribor, Koroška 160, SI-2000, Maribor, Slovenia

    Sandi Klavžar & Petra Žigert

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  1. Andrey A. Dobrynin
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Dobrynin, A.A., Gutman, I., Klavžar, S. et al. Wiener Index of Hexagonal Systems. Acta Applicandae Mathematicae 72, 247–294 (2002). https://doi.org/10.1023/A:1016290123303

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