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Wiener Index of Hexagonal Systems |
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| Authors: | Andrey A Dobrynin Ivan Gutman Sandi Klavžar Petra Žigert |
| Institution: | (1) Sobolev Institute of Mathematics, Russian Academy of Sciences Siberian Branch, Novosibirsk, 630090, Russia;(2) Faculty of Science, University of Kragujevac, PO Box 60, YU-34000 Kragujevac, Yugoslavia;(3) Department of Mathematics, PEF, University of Maribor, Koro ka 160, SI-2000 Maribor, Slovenia |
| 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. |
| Keywords: | Wiener index hexagonal system hexagonal chain catacondensed hexagonal system isometric subgraph congruence relation Hosoya polynomial algorithm |
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