For each exercise assume that the graph is a simple undirected graph.

Definition $1$: The Fibonacci sequence is $1,1,2,3,5,8,13,21,34,$dots, 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.

A$)$ Give a formula for, the number of edges in a non$-$empty tree, in terms of n$,$ the number of nodes $($vertices$)$ that the tree has. $[5$ points$]$

that consists of the first four Fibonacci trees. $[$Hint: The number of nodes in a Fibonacci tree of height h is f$\_($h$+3)-1][10$ points$]$

points$]$

solve a$,$ b$,$ c