Journal of Combinatorial Optimization

, Volume 18, Issue 3, pp 207-228

First online:

Fibonacci index and stability number of graphs: a polyhedral study

  • Véronique BruyèreAffiliated withDepartment of Theoretical Computer Science, Université de Mons-Hainaut
  • , Hadrien MélotAffiliated withDepartment of Theoretical Computer Science, Université de Mons-Hainaut Email author 

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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. 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.


Stable set Fibonacci index Merrifield-Simmons index Turán graph α-critical graph GraPHedron