Graphs, partitions and Fibonacci numbers

Authors:
Arnold Knopfmacher;Robert F. Tichy;Stephan Wagner;Volker Ziegler
Affiliations:
The John Knopfmacher Centre for Applicable Analysis and Number Theory, University of the Witwatersrand, Johannesburg, Private Bag 3, WITS 2050, South Africa;Department of Mathematics, Graz University of Technology, Steyrergasse 30, A-8010 Graz, Austria;Department of Mathematics, Graz University of Technology, Steyrergasse 30, A-8010 Graz, Austria;Department of Mathematics, Graz University of Technology, Steyrergasse 30, A-8010 Graz, Austria
Venue:
Discrete Applied Mathematics
Year:
2007

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Abstract

The Fibonacci number of a graph is the number of independent vertex subsets. In this paper, we investigate trees with large Fibonacci number. In particular, we show that all trees with n edges and Fibonacci number 2^n^-^1+5 have diameter =~. This is proved by using a natural correspondence between partitions of integers and star-like trees.