Tur\'an Graphs, Stability Number, and Fibonacci Index

Véronique Bruyère (veronique.bruyereumh.ac.be)
Hadrien Mélot (hadrien.melotumh.ac.be)

Abstract: The Fibonacci index of a graph is the number of its stable sets. This parameter is widely studied and has applications in chemical graph theory. In this paper, we establish tight upper bounds for the Fibonacci index in terms of the stability number and the order of general graphs and connected graphs. Tur\'an graphs frequently appear in extremal graph theory. We show that Tur\'an graphs and a connected variant of them are also extremal for these particular problems.

Keywords: Stable sets; Fibonacci index; Merrifield-Simmons index; Tur\'an graph; $\alpha$-critical graph.

Category 1: Combinatorial Optimization (Graphs and Matroids )

Citation: Submitted, February 2008.

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Entry Submitted: 02/22/2008
Entry Accepted: 02/22/2008
Entry Last Modified: 02/22/2008

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