Question

What is the level of each vertex of the rooted tree in Exercise \(4\)?

Short answer

Level \(0\): \({\bf{a}}\)

Level \(1\): \(b,c,d\)

Level \(2\): \(e,f,g,h,i\)

Level \(3\): \(j,k,l,m,n,o,p\)

Level \(4\): \(q,r,s\)

Step-by-step solution

Definitions

The root of the tree is the vertex at the top of the tree.

The level of a vertex is the length of the path from the root to the vertex.

Finding the vertices from level \({\bf{0}},{\bf{1}},{\bf{2}}\)

The vertex at level 0 is the root of the tree.

Level \(0\): \({\bf{a}}\)

The vertices at level 1 are the children of the root of the tree.

Level \(1\): \(b,c,d\)

The vertices at level 2 are the children of the vertices at level 1

Level \(2\): \(e,f,g,h,i\)

Finding the vertices from level \({\bf{3}},{\bf{4}}\)

The vertices at level 3 are the children of the vertices at level 2

Level \(3\): \(j,k,l,m,n,o,p\)

The vertices at level 4 are the children of the vertices at level 3

Level \(4\): \(q,r,s\)