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From paths to stars. (English) Zbl 0723.05077

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
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