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Acta Applicandae Mathematica

, Volume 72, Issue 3, pp 247–294 | Cite as

Wiener Index of Hexagonal Systems

  • Andrey A. Dobrynin
  • Ivan Gutman
  • Sandi Klavžar
  • Petra Žigert
Article

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.

Wiener index hexagonal system hexagonal chain catacondensed hexagonal system isometric subgraph congruence relation Hosoya polynomial algorithm 

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Copyright information

© Kluwer Academic Publishers 2002

Authors and Affiliations

  • Andrey A. Dobrynin
    • 1
  • Ivan Gutman
    • 2
  • Sandi Klavžar
    • 3
  • Petra Žigert
    • 3
  1. 1.Sobolev Institute of MathematicsRussian Academy of Sciences Siberian BranchNovosibirskRussia
  2. 2.Faculty of ScienceUniversity of KragujevacKragujevacYugoslavia
  3. 3.Department of Mathematics, PEFUniversity of MariborMariborSlovenia

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