A Class of Fibonacci Matrices, Graphs, and Games

Valentin E. Brimkov and Reneta P. Barneva ()
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Valentin E. Brimkov: Mathematics Department, SUNY Buffalo State, Buffalo, NY 14222, USA
Reneta P. Barneva: School of Business, State University of New York at Fredonia, Fredonia, NY 14063, USA

Mathematics, 2022, vol. 10, issue 21, 1-9

Abstract: In this paper, we define a class of Fibonacci graphs as graphs whose adjacency matrices are obtained by alternating binary Fibonacci words. We show that Fibonacci graphs are close in size to Turán graphs and that their size-stability tradeoff defined as the product of their size and stability number is very close to the maximum possible over all bipartite graphs. We also consider a combinatorial game based on sequential vertex deletions and show that the Fibonacci graphs are extremal regarding the number of rounds in which the game can terminate.

Keywords: Fibonacci array; Fibonacci matrix; Fibonacci graph; bipartite graph; Turán graph (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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