FIBONACCI NUMBERS IN THE TOPOLOGICAL THEORY OF BENZENOID HYDROCARBONS AND RELATED GRAPHS Academic Article

abstract

• Fibonacci numbers are studied with respect to the topological theory of benzenoid hydrocarbons. These numbers are identified as the number of Kekul 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. 1989 J.C. Baltzer AG, Scientific Publishing Company.

authors

• Klein, Douglas

published proceedings

• JOURNAL OF MATHEMATICAL CHEMISTRY

author list (cited authors)

• El-Basil, S., & Klein, D. J.

citation count

• 10

complete list of authors

• El-Basil, Sherif||Klein, Douglas J

publication date

• January 1989

publisher

• Springer Nature  Publisher

published in

• Journal of Mathematical Chemistry  Journal

keywords

• 49 Mathematical Sciences
• 4901 Applied Mathematics
• 4904 Pure Mathematics

Digital Object Identifier (DOI)

• 10.1007/BF01171882

start page

• 1

end page

• 23

volume

• 3

issue

• 1

URL

• http://dx.doi.org/10.1007/bf01171882