Abstract
The Fibonacci number of a graph, defined by Prodinger and Tichy in 1982, is the number of independent sets on the graph. The Fibonacci number of the path graph, P n , is the Fibonacci number F n+2 and the Fibonacci number of the cycle graph, C n , is the Lucas number L n . This paper combines the visual nature of graph theory with combinatorial methods to prove new identities for the Fibonacci and Lucas numbers.
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DeMaio, J., Jacobson, J. (2013). Fibonacci and Lucas Identities via Graphs. In: Rychtář, J., Gupta, S., Shivaji, R., Chhetri, M. (eds) Topics from the 8th Annual UNCG Regional Mathematics and Statistics Conference. Springer Proceedings in Mathematics & Statistics, vol 64. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-9332-7_9
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DOI: https://doi.org/10.1007/978-1-4614-9332-7_9
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