given the graph below use kruskals algorithm to determine the minimum spanning tree.
given the graph below use kruskals algorithm to determine the minimum spanning tree.
Answer
Explanation:
Step1: Sort edges by weight
Sort the edges in ascending order of their weights: (B - A, 1), (D - E, 2), (B - C, 3), (C - D, 4), (A - E, 5), (A - C, 7), (A - D, 10).
Step2: Select edges for MST
Start adding edges to the minimum - spanning tree (MST) as long as they don't create a cycle. Add (B - A) with weight 1. Add (D - E) with weight 2. Add (B - C) with weight 3. Add (C - D) with weight 4. Adding (A - E) would not create a cycle, so add it with weight 5.
Step3: Calculate total weight
The edges in the MST are (B - A), (D - E), (B - C), (C - D), (A - E). The total weight of the MST is (1 + 2+3 + 4+5=15).
Answer:
The minimum - spanning tree has edges (B - A), (D - E), (B - C), (C - D), (A - E) with a total weight of 15.