Definition $1$: The Fibonacci sequence is $1,1,2,3,5,8,13,21,34,...,$ where the first and second terms of the sequence are $1$ and every other term is determined by adding its two immediate predecessors.

Definition $2$: A tree is an acyclic$$ connected graph.

Definition $3$: A forest is a graph that consists of components that are trees.

Definition $4$: A Fibonacci tree$$of height h is a balanced binary tree that is minimal with respect to number of nodes and contains no right$-$high subtree. A subtree is right$-$high if its right subtree is taller than its left subtree.