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Tur\'an Graphs, Stability Number, and Fibonacci Index

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Type
Preprint
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Submission Date
Identifiers
DOI: 10.1007/978-3-540-85097-7_12
arXiv ID: 0802.3284
Source
arXiv
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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. 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.

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