$3.$ Figure $2$ shows a graph G$,$ with a given DFS ordering of the vertices. On

the right side of the figure, the palm tree is drawn according to the first

part of Tarjan$-$Hopcroft algorithm for planarity testing.

$($a$)$ If we follow the DFS ordering, which vertex v has the first frond back

to the root $($vertex $1)?1$

$($b$)$ Let C be the cycle $1,2,...,$ v$.$ if we remove the edges of v$,$ what are

the connected components $($Gi for i $=1,2,...)$ we get? Draw them.