EXAMPLE $2$ In the rooted tree $T($with root $a)$ shown in Figure $5,$ find the parent of $c,$ the children of $g,$ the

siblings of $h,$ all ancestors of $e,$ all descendants of $b,$ all intemal vertices, and all leaves. What

is the subtree rooted at $g?$

Solution: The parent of $c$ is $b.$ The children of $g$ are $h,i,$ and $j.$ The siblings of $h$ are i and $j.$

The ancestors of $e$ are $c,b,$ and $a.$ The descendants of $b$ are $c,d,$ and $e.$ The internal vertices

are $a,b,c,g,h,$ and $j.$ The leaves are $d,e,f,i,k,l,$ and $m.$ The subtree rooted at $g$ is shown

in Figure $6.$

FIGURE $5$ A Rooted Tree $T.$

Subtree Rooted at $g.$