2015/08/01 by James Alexander, Paul Hearding · 3 citations
Mathematics · Physics and Astronomy · #Advanced Mathematical Identities #Advanced Mathematical Theories and Applications #Analytic Number Theory Research #Artificial intelligence #Combinatorics #Computer science #Encoding (memory) #Fibonacci number #Fibonacci polynomials #Graph #Lucas number #Lucas sequence #Mathematics #Theoretical computer science
paper · doi:10.1080/00150517.2015.12428264
published in The Fibonacci Quarterly 53(3), 237-240 (The Fibonacci Association)
openalex publication_date 2015/08/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/07
Some well-known results of Prodinger and Tichy are that the number of independent sets in the n-vertex path graph is Fn+2, and that the number of independent sets in the n-vertex cycle graph is Ln. We generalize these results by introducing new classes of graphs whose independent set structures encode the Lucas sequences of both the first and second kind. We then use this class of graphs to provide new combinatorial interpretations of the terms of Dickson polynomials of the first and second kind.