Fibonacci Identities and Graph Colorings
Christopher J. Hillar, Troels Windfeldt · The Fibonacci Quarterly · 2008
We generalize both the Fibonacci and Lucas numbers to the context of graph colorings, and prove some identities involving these numbers. As a corollary we obtain new proofs of some known identities involving Fibonacci numbers such as Fr + s + t = Fr + 1Fs + 1Ft + 1 + FrFsFt − Fr − 1Fs − 1Ft − 1.