Answer to Question #278225 in Discrete Mathematics for Aljon

Question

Exercise 9:

Draw a full binary tree having the following properties

1. Four internal vertices and five terminal vertices.

2. Height = 3 and nine terminal vertices.

3. Height = 4 and nine terminal vertices.

Answer 1

Full binary tree is a tree each vertcle of which has either 0 or 2 children. Internal verticle is a verticle that has children. Terminal verticle is a verticle that has no children

1) a, b, d, g - internal verticles. f, e, c, i, h - terminal verticles

2) Height of a tree is a max distance from its root to the terminal verticle. Full binary tree with height 3 has no more than $2^3=8$ terminal points, so there is no full binary tree with such properties

3) j, k, e, l, m, n, o, p, q - terminal verticles. Path with max distance is a-b-d-f-j(or k) - 4 steps