Run the DFS$-$based topological ordering algorithm on the following graph. When$-$

ever you have a choice of vertices to explore, always pick the one that appears first in alphabetical order.

$($a$)$ Indicate the pre$-$ and post$-$ numbers of the nodes.

$($b$)$ What are the sources and sinks of the graph?

$($c$)$ Write down one topological ordering found by the algorithm.

$($d$)$ How many topological orderings does this graph have?