Question

Consider the following directed graph for each of the problems:

1. Perform a breadth-first search on the graph assuming that the vertices and adjacency lists
are listed in alphabetical order. Show the breadth-first search tree that is generated.
2. Perform a depth-first search on the graph assuming that the vertices and adjacency lists
are listed in alphabetical order. Classify each edge as tree, back or cross edge. Label each
vertex with its start and finish time.
3. Remove all the back edges from the graph so it becomes a DAG. Perform a depth-first
search recording the start and finish times. Using those finish times, provide the
topological order that is produced. Provide one other topological order for that graph.
4. Determine the strongly connected components of the graph using the algorithm in section
22.5 of the textbook. Show each step of the algorithm.

Answer 1

1) Breadth First search (BFS):-

The Breadth First search (BFS) the graph is given below in a step by step manner:

STEP 1:-

step 2:-

step 3:-

step 4:-

step 5:-

step 6:-

step 7:-

step 8:-

step 9:-

step 10:-

The final tree after Breath First search is as follows:

2) Depth First Search (DFS):-

The Depth First search (DFS) the graph is shown below:

The final tree after DFS is shown below:

Tree Edges: (A,B),(B,D),(D,F),(D,G),(B,H),(H,E),(E,C),(C,I),(I,J),(J,K)

Back Edges: (E,D),(G,F),(E,D),(J,C),(K,I),(H,A)