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Turán Graphs, Stability Number, and Fibonacci Index

By Véronique Bruyère and Hadrien Mélot


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

Topics: Stable sets, Fibonacci index, Merrifield-Simmons index, Turán graph
Year: 2008
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