Problem 32 Using the DFS method, construct ... [FREE SOLUTION]

Chapter 9: Problem 32

Using the DFS method, construct a spanning tree for each graph with the given adjacency list.

Short Answer

Expert verified

Starting from vertex 1, perform DFS traversal and visit connected vertices: visit vertex 2 and add edge (1,2) to the spanning tree. Move to vertex 2, visit vertex 3 and add edge (2,3) to the spanning tree. Move to vertex 3, visit vertex 4 and add edge (3,4) to the spanning tree. The final spanning tree is: ``` 1---2 | 3 | 4 ``` With edge set: {(1,2), (2,3), (3,4)}.

Step by step solution

Choose the starting vertex

Choose any vertex as the starting point for the DFS algorithm. In this example, we will choose vertex 1 as our starting vertex.

Start DFS traversal

Starting from vertex 1, we will perform the DFS traversal, visiting each connected vertex following the depths of the graph before backtracking.

DFS traversal from vertex 1

Begin from vertex 1, mark it as visited, and visit the next connected unvisited vertex. In our adjacency list, vertex 2 is connected to vertex 1. So we will visit vertex 2 and add the edge (1,2) to our spanning tree.

DFS traversal from vertex 2

Then move from vertex 1 to vertex 2, mark it as visited, and visit the next connected unvisited vertex. In this case, vertex 3 is connected to vertex 2. So we will visit vertex 3 and add the edge (2,3) to our spanning tree.

DFS traversal from vertex 3

Move from vertex 2 to vertex 3, mark it as visited, and visit the next connected unvisited vertex. Vertex 4 is connected to vertex 3. We will visit vertex 4 and add the edge (3,4) to our spanning tree.

Complete DFS traversal

Since we have visited all the vertices, our DFS traversal is complete, and we have obtained the following spanning tree: ``` 1---2 | 3 | 4 ``` The edge set of this spanning tree is {(1,2), (2,3), (3,4)}, and we have successfully constructed a spanning tree for the given graph using the DFS method.

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91影视

Using the DFS method, construct a spanning tree for each graph with the given adjacency list.

Short Answer

Step by step solution

Choose the starting vertex

Start DFS traversal

DFS traversal from vertex 1

DFS traversal from vertex 2

DFS traversal from vertex 3

Complete DFS traversal

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