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 $1)?$

b$)$ Let C be the cycle $1,2,...,$ v $($the vertex v is found in $3($a$)).$ if we remove the edges of cycle C$,$ what are the connected components $($Gi for i $=1,2,...)$ we get? Draw them.

c$)$ For each Gi from $3($b$),$ add the cycle C to it to construct G$$ i $.$ Draw all the G$$ i $$s$.$

PLEASE NOTE THE ANSWER TOO A$)$ IS VERTEX $5$

PLEASE ANSWER B AND C ACCORDINGLY