Consider the following graph:
Graph
Which edges would be included in the minimum spanning tree using Prim’s algorithm starting from vertex A?
Options: a) b) c) d)
(A)
AB, BD, DE, EF, FC
(B)
AC, CD, DE, EB, BF
(C)
AB, BD, DE, EC, CF
(D)
AC, CD, DE, EB, FE
Answer: (A)
Explanation:
Let’s go through the steps of Prim’s algorithm starting from vertex A:
Start from vertex A and initialize the MST with just vertex A.
Find the minimum-weight edge that connects a vertex in the MST to a vertex outside the MST. The possible edges are AB (weight 5) and AC (weight 4).
Choose the minimum-weight edge, which is AC (weight 4), and add it to the MST.
Now, the MST includes vertices A and C. Look for the minimum-weight edge that connects a vertex in the MST to a vertex outside the MST. The possible edges are BC (weight 2), BD (weight 3), and CD (weight 6).
Choose the minimum-weight edge, which is BC (weight 2), and add it to the MST.
Now, the MST includes vertices A, B, and C. Look for the minimum-weight edge that connects a vertex in the MST to a vertex outside the MST. The possible edges are BD (weight 3), CD (weight 6), and DE (weight 3).
Choose the minimum-weight edge, which is BD (weight 3), and add it to the MST.
Now, the MST includes vertices A, B, C, and D. Look for the minimum-weight edge that connects a vertex in the MST to a vertex outside the MST. The possible edges are CD (weight 6), DE (weight 3), and EF (weight 5).
Choose the minimum-weight edge, which is DE (weight 3), and add it to the MST.
Now, the MST includes vertices A, B, C, D, and E. Look for the minimum-weight edge that connects a vertex in the MST to a vertex outside the MST. The possible edges are CD (weight 6), EF (weight 5), EC (weight 3), and FC (weight 2).
Choose the minimum-weight edge, which is FC (weight 2), and add it to the MST.
After going through all the steps, the minimum spanning tree (MST) using Prim’s algorithm starting from vertex A includes the following edges: AB, BC, BD, DE, and FC.
Therefore, the correct answer is option c) AB, BD, DE, EC, CF.
Quiz of this Question
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