Let G be a graph whose vertices are the integers 1 through 8, and let the...

Let G be a graph whose vertices are the integers 1 through 8, and let the adjacent vertices of each vertex be given by the table below:

vertex	adjacent vertices
1	(2, 3, 4)
2	(1, 3, 4)
3	(1, 2, 4)
4	(1, 2, 3, 6)
5	(6, 7, 8)
6	(4, 5, 7)
7	(5, 6, 8)
8	(5, 7)

Assume that, in a traversal of G, the adjacent vertices of a given vertex are returned in the same order as they are listed in the above table.

Order the vertices as they are visited in a DFS traversal starting at vertex 1.
Order the vertices as they are visited in a BFS traversal starting at vertex 1.

Expert Solution

Answer:-

(1) Order the vertices as they are visited in a DFS traversal starting at vertex 1.

We use the following steps to implement DFS traversal...

Step 1 - Define a Stack of size total number of vertices in the graph.
Step 2 - Select any vertex as starting point for traversal. Visit that vertex and push it on to the Stack.
Step 3 - Visit any one of the non-visited adjacent vertices of a vertex which is at the top of stack and push it on to the stack.
Step 4 - Repeat step 3 until there is no new vertex to be visited from the vertex which is at the top of the stack.
Step 5 - When there is no new vertex to visit then use back tracking and pop one vertex from the stack.
Step 6 - Repeat steps 3, 4 and 5 until stack becomes Empty.
Step 7 - When stack becomes Empty, then produce final spanning tree by removing unused edges from the graph

After applying above STEPS the DFS values are as follws:-

DFS: 1-2-3-4-6-5-7-8

(2) Order the vertices as they are visited in a BFS traversal starting at vertex 1.

We use the following steps to implement BFS traversal...

Step 1 - Define a Queue of size total number of vertices in the graph.
Step 2 - Select any vertex as starting point for traversal. Visit that vertex and insert it into the Queue.
Step 3 - Visit all the non-visited adjacent vertices of the vertex which is at front of the Queue and insert them into the Queue.
Step 4 - When there is no new vertex to be visited from the vertex which is at front of the Queue then delete that vertex.
Step 5 - Repeat steps 3 and 4 until queue becomes empty.
Step 6 - When queue becomes empty, then produce final spanning tree by removing unused edges from the graph.

After applying above STEPS the BFS values are as follws:-

BFS: 1-2-3-4-6-5-7-8

venereology answered 2 years ago

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