Fibonacci Index and Stability Number of Graphs: a Polyhedral Study

V. Bruyère(veronique.bruyereumh.ac.be)
H. 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. Turan graphs frequently appear in extremal graph theory. We show that Turan graphs and a connected variant of them are also extremal for these particular problems. We also make a polyhedral study by establishing all the optimal linear inequalities for the stability number and the Fibonacci index, inside the classes of general and connected graphs of order n.

Keywords: Stable set; Fibonacci index; Merrifield-Simmons index; Turan graph; alpha-critical graph; GraPHedron

Category 1: Combinatorial Optimization (Graphs and Matroids )

Citation: Submitted (November 2008)

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Entry Submitted: 11/10/2008
Entry Accepted: 11/11/2008
Entry Last Modified: 11/10/2008

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