Fibonacci numbers in the topological theory of benzenoid hydrocarbons and related graphs |
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| Authors: | Sherif El-Basil Douglas J Klein |
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| Institution: | (1) Department of Chemistry, University of Georgia, 30602 Athens, Georgia, USA;(2) Department of Marine Sciences, Texas A & M University at Galveston, 77553 Galveston, Texas, USA;(3) Present address: Faculty of Pharmacy, Kasr El-Aini Street, 11562 Cairo, Egypt |
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| Abstract: | Fibonacci numbers are studied with respect to the topological theory of benzenoid hydrocarbons. These numbers are identified as the number of Kekulé structures of nonbranched all-benzenoid hydrocarbons, the number of matchings of paths, the number of independent sets of vertices of paths, the number of nonattacking rooks of certain rook boards, as well as the number of Clar structures of certain benzenoid hydrocarbons. Fibonacci numbers were also identified as the number of conjugated circuits of certain benzenoid hydrocarbons and thus they were also related to the structure-resonance model. Maximal independent sets of caterpillar trees are also shown to be Fibonacci numbers. |
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