Adigraph is called strongly connected if for any pair of two distinct vertices u and v t...

Adigraph is called strongly connected if for any pair of two distinct vertices u and v there exists a directed path from u to v and a directed path from v to u. In general, a digraph’s vertices can be partitioned into disjoint maximal subsets of vertices that are mutually accessible via directed paths; these subsets are called strongly connected components of the digraph. There are two DFS based algorithms for identifying strongly connected components. Here is the simpler (but somewhat less efficient) one of the two:

Step 1 Perform a DFS traversal of the digraph given and number its vertices in the order they become dead ends.

Step 2 Reverse the directions of all the edges of the digraph.

Step 3 Perform a DFS traversal of the new digraph by starting (and, if necessary, restarting) the traversal at the highest numbered vertex among still unvisited vertices.

The strongly connected components are exactly the vertices of the DFS trees obtained during the last traversal.

a. Apply this algorithm to the following digraph to determine its strongly connected components:

b. What is the time efficiency class of this algorithm? Give separate answers for the adjacency matrix representation and adjacency list representation of an input digraph.

c. How many strongly connected components does a dag have?