Question

Q6: 20 pts) For the directed graph assigned to you, run the Depth First Search algorithm. (a) Clearly show the order in which the vertices are pushed and popped. (b) Clearly write the list of edges and their classification into one of the four categories as determined using DFS. (c) Determine whether the directed graph assigned to you is a DAG or not? If it is a DAG. write the topological sort of the vertices.

Answer 1

Depth first Search algorithm works with Stack mechanism.

1) Node 1, is pushed into the stack and then selecting any arbitrary node(2,5). If node 2 is selected then node2 will be pushed into the Stack. And then there is only one directed unvisted node(5).

1-->2-->5

From node 5, there is no way to visit the unvisited nodes.

3 2. 1. 1 4t 1254-3 esa n e a, is dou b

Now we will be backtracking(pop operation) to node 2. From node 2, there is no possible way to visit the unvisited nodes.

Again from node 2, we will be backtracking(pop operation) to node 1. From node 1, it will search for possible ways to unvisited nodes.Yes,from node 1,there is way to node 4(which is unvisited node).

1-->4-->3

From node 4, there is way to node 3(unvisited).

From node 3, it will search for other directed node(2). But node 2 is already visited. Now all the nodes are visited.