Tur\'an Graphs, Stability Number, and Fibonacci Index
Discrete Mathematics
2024-03-11 v1
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
Cite
@article{arxiv.0802.3284,
title = {Tur\'an Graphs, Stability Number, and Fibonacci Index},
author = {Véronique Bruyère and Hadrien Mélot},
journal= {arXiv preprint arXiv:0802.3284},
year = {2024}
}
Comments
11 pages, 3 figures