Fibonacci Identities and Graph Colorings
Abstract
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 \[Fr+s+t = Fr+1Fs+1Ft+1 + Fr Fs Ft - Fr-1Fs-1Ft-1.\]
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