Spanning Paths in Fibonacci-Sum Graphs
Kyle J. Fox, William B. Kinnersley, Daniel Cooper McDonald, Nathan Orlow, Gregory J. Puleo · The Fibonacci Quarterly · 2014
Motivated by a problem posed by Barwell, we apply graph theory to determine all n for which the numbers 1, . . . , n can be ordered so that the sum of any two consecutive terms is a Fibonacci number. We prove that such an ordering exists if and only if n is 9, 11, a Fibonacci number, or one less than a Fibonacci number. For each such n, we also prove that at most two such orderings exist, up to symmetry.