Abstract
Fibonacci numbers are studied with respect to the topological theory of benzenoid hydrocarbons. These numbers are identified as the number of Kekule 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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