Your friend is trying to find the strongly connected components of a directed graph $G.$ Recall that

this involves first running depth$-$first search on $G,$ and then running depth$-$first search on the

reverse graph, $G^R,$ using the decreasing order of finish time. Your friend has done this and found the

following table. Here, $a,b,c,d,e,f,g,h,$i are the vertices of $G.$

Now answer the following questions.

a$)$ Find a vertex in $G$ that is guaranteed to be contained in a source connected component.

Recall that a source connected component in an SCC DAG is a node that has indegree zero.

For example, in the following SCC DAG, $\{a,b,e\}$ is a source connected component.

This image is just an example to show how SCC can convert a graph into DAG, and the source connected component

b$)$ Let $x$ be your answer to $($a$).$ Find all the vertices in the strongly connected component that

contains $x.$

c$)$ If the vertices you found in $($b$)$ are deleted from $G,$ which set of vertices is guaranteed to be

a source connected component of the resulting graph? Write the list of those vertices.

d$)$ How many strongly connected components does $G$ have? Just write the answer.

e$)$ Draw the DAG of the strongly connected components of $G.$ There is more than one correct

answer, anyone of those will be accepted.