- 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. Download: [PDF]Entry Submitted: 02/22/2008Entry Accepted: 02/22/2008Entry Last Modified: 02/22/2008Modify/Update this entry Visitors Authors More about us Links Subscribe, Unsubscribe Digest Archive Search, Browse the Repository Submit Update Policies Coordinator's Board Classification Scheme Credits Give us feedback Optimization Journals, Sites, Societies Optimization Online is supported by the Mathematical Programming Society and by the Optimization Technology Center.