Turán Graphs, Stability Number, and Fibonacci Index

Authors:
Véronique Bruyère;Hadrien Mélot
Affiliations:
Department of Theoretical Computer Science, Université de Mons-Hainaut, Mons, Belgium B-7000;Department of Theoretical Computer Science, Université de Mons-Hainaut, Mons, Belgium B-7000
Venue:
COCOA 2008 Proceedings of the 2nd international conference on Combinatorial Optimization and Applications
Year:
2008

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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. Turán graphs frequently appear in extremal graph theory. We show that Turán graphs and a connected variant of them are also extremal for these particular problems.