The Fibonacci Edge Labeling on Fibonacci Trees

We present a novel graph labeling problem called Fibonacci edge labeling. The constraint in this labeling is placed on the allowable edge label which is the difference between the labels of endvertices of an edge. Each edge label should be (3m+2)-th Fibonacci numbers. We show that every Fibonacci tree can be labeled Fibonacci edge labeling. The labelings on the Fibonacci trees are applied to their embeddings into Fibonacci Circulants.