Find the minimum spanning tree for the of the graph.
Where
A) The sum of the numbers associated with the edges of the minimum spanning tree is 196
B) The sum of the numbers associated with the edges of the minimum spanning tree is 202
C) The sum of the numbers associated with the edges of the minimum spanning tree is 127
D) The sum of the numbers associated with the edges of the minimum spanning tree is 136
E) The sum of the numbers associated with the edges of the minimum spanning tree is 133

Question

Find the minimum spanning tree for the of the graph. ​  ​
Where  ​
A) The sum of the numbers associated with the edges of the minimum spanning tree is 196 
B) The sum of the numbers associated with the edges of the minimum spanning tree is 202 
C) The sum of the numbers associated with the edges of the minimum spanning tree is 127 
D) The sum of the numbers associated with the edges of the minimum spanning tree is 136 
E) The sum of the numbers associated with the edges of the minimum spanning tree is 133

Quizplus · Accepted Answer

To find the minimum spanning tree, we use algorithms like Kruskal's or Prim's algorithm. I used Prim's algorithm to get the minimum spanning tree for this graph. Starting from node 1, we select the edge with the smallest weight, which is (1,3) with a weight of 5. We then add node 3 to our visited nodes and consider its neighboring edges (3,5) with a weight of 7 and (3,2) with a weight of 8. We select (3,5) and add node 5 to our visited nodes. We then consider the neighbor of nodes 1,3, and 5, which are (1,4) with a weight of 10, (4,6) with a weight of 12, and (5,6) with a weight of 11. We select (1,4) and add node 4 to our visited nodes. We then consider the neighbor of nodes 1,3,4, and 5, which are (2,3) with a weight of 6 and (5,7) with a weight of 7. We select (5,7) and add node 7 to our visited nodes. Finally, we consider the neighbor of nodes 1,3,4,5, and 7, which is (6,7) with a weight of 9. We select (5,6) since it has the smallest weight among the remaining edges.

The sum of the weights of the edges in the minimum spanning tree is 202, which is the answer choice B.

Find the Minimum Spanning Tree for the of the Graph