Fibonacci Identities and Graph Colorings

Details Fibonacci Identities and Graph Colorings Fibonacci Identities and Graph Colorings

2008-05-07

arxiv.org/abs/0805.0992v2

Mathematics

Combinatorics

5 pages, 1 figure

Scientific paper

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
\[F_{r+s+t} = F_{r+1}F_{s+1}F_{t+1} + F_r F_s F_t - F_{r-1}F_{s-1}F_{t-1}.\]

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