Alameddine, A. F. From paths to stars. (English) Zbl 0723.05077 Int. J. Math. Math. Sci. 14, No. 2, 345-348 (1991). Summary: The number of cycles in the complement \(T'\) of a tree T is known to increase with the diameter of the tree. A similar question is raised and settled for the number of complete subgraphs in \(T'\) for a special class of trees via Fibonacci numbers. A structural characterization of extremal trees is also presented. MSC: 05C38 Paths and cycles 05C05 Trees 05A15 Exact enumeration problems, generating functions Keywords:number of cycles; complete subgraphs; trees; Fibonacci numbers; extremal trees PDFBibTeX XMLCite \textit{A. F. Alameddine}, Int. J. Math. Math. Sci. 14, No. 2, 345--348 (1991; Zbl 0723.05077) Full Text: DOI EuDML