Question

Draw the subtree of the tree in Exercise \({\bf{3}}\) that is rooted at

\({\bf{a) a}}{\bf{.}}\)

\({\bf{b) c}}{\bf{.}}\)

\({\bf{c) e}}{\bf{.}}\)

Short answer

1. The root of the tree is the vertex at the top of the tree. Since, a is the root of the given tree, the subtree rooted at a is the entire tree itself.
2. The subtree rooted at c contains the part of the given tree that contains the vertex c and all descendants of c. Note that the root of the subtree then becomes the vertex
3. The subtree rooted at e contains the part of the given tree that contains the vertex e and all descendants of e. Note that the root of the subtree then becomes the vertex e and that e does not have any descendants.

Step-by-step solution

(a) The subtree of \({\bf{a}}\)

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

Since \({\bf{a}}\) is the root of the given tree, the subtree rooted at \({\bf{a}}\) is the entire tree itself.

(b) The subtree of \({\bf{c}}\)

The subtree rooted at c contains the part of the given tree that contains the vertex c and all descendants of c. Note that the root of the subtree then becomes the vertex c.

(c) The subtree of \({\bf{e}}\)

The subtree rooted at e contains the part of the given tree that contains the vertex e and all descendants of e. Note that the root of the subtree then becomes the vertex e and that e does not have any descendants.