please no hand writing please no hand writing Answer the que

please no hand writing please no hand writing

Answer the questions for the following tree with root a Find the levels of vertices d and f What is the height of the tree? Which vertices are internal? Which vertices are leaves? Above tree is balance tree

Solution

a) we know that The level of a vertex is the number of edges along the unique path between it and the root. Here the root is a,

So for vertex d the level is 1.

And for the vertex f the level is 2.

b) We know that The height of a rooted tree is the maximum level to any vertex of the tree. Here the vertices at the ends are all having level 3.

So the Height of the tree is 3

c) A vertex of degree greater than 1 in a tree is called an internal vertex or a branch vertex.

So for the given tree a, b, c, d, e, f, g, h, i, j

Are internal vertices

d) the vertices which are at the end are called leaves

So for the above graph the leaves are

k, l, m, n, o, p, q, r, s, t

Are leaves