Exercise 1 (a) Proof that (by an example with10) the number of terminal vertices in a binary tree with n vertices is (n 1)/2. (b) Give an example of a tree (n> 10) for which the diameter is not equal to the twice the radius. Find eccentricity, radius, diameter and center of the tree. (c) If a tree T has four vertices of degree 2, one vertex of degree 3, two vertices of degree 4, and one vertex of degree 5, then find the number of pendant vertices in T. (d) A rooted tree has eleven vertices whose six are pendant and four of degree 3. What is the degree of the root? (e) Proof that the number of terminal vertices in a binary tree with n vertices is (n1)/2