Solve the minimal-spanning tree problem defined below:
A)total cost = 13
B)total cost = 15
C)total cost = 17
D)total cost = 11
E)None of the above

Question

Solve the minimal-spanning tree problem defined below: 
A)total cost = 13 
B)total cost = 15 
C)total cost = 17 
D)total cost = 11 
E)None of the above

Quizplus · Accepted Answer

The minimal spanning tree connects all nodes with the minimum possible total weight or cost. In the given problem, the weights/costs of the edges are:
AB = 5
AC = 3
BD = 3
CD = 4
CE = 4
DE = 2
To find the minimal spanning tree, we can start from any node and then add the shortest available edge that connects to an unconnected node. We repeat this process until all nodes are connected. 
Starting from A, we can add edge AC (weight = 3) to connect node C. Then we can add edge CD (weight = 4) to connect node D. Finally, we can add edge DE (weight = 2) to connect node E. The resulting tree connects all nodes and has a total weight/cost of 3 + 4 + 2 + 6 = 15. 
Therefore, the correct choice is B.

Solve the Minimal-Spanning Tree Problem Defined Below