Consider the following graph:Which one of the following is NOT the sequence of edges added to the minimum spanning tree using Kruskal's algorithm?Marks : 1Negative Marks : 0Answer here(b,e)(e,f)(b,c)(a,c)(f,g)(c,d)(b,e)(e,f)(a,c)(b,c)(f,g)(c,d)(b,e)(e,f)(a,c)(f,g)(b,c)(c,d)(b,e)(a,c)(e,f)(b,c)(f,g)(c,d)
Question
Consider the following graph:Which one of the following is NOT the sequence of edges added to the minimum spanning tree using Kruskal's algorithm?Marks : 1Negative Marks : 0Answer here(b,e)(e,f)(b,c)(a,c)(f,g)(c,d)(b,e)(e,f)(a,c)(b,c)(f,g)(c,d)(b,e)(e,f)(a,c)(f,g)(b,c)(c,d)(b,e)(a,c)(e,f)(b,c)(f,g)(c,d)
Solution
To determine which one of the given sequences is NOT the sequence of edges added to the minimum spanning tree using Kruskal's algorithm, we need to compare each sequence with the steps of Kruskal's algorithm.
Kruskal's algorithm for finding a minimum spanning tree works as follows:
- Sort all the edges in non-decreasing order of their weights.
- Initialize an empty set to store the minimum spanning tree.
- Iterate through each edge in the sorted order: a. If adding the current edge to the minimum spanning tree does not create a cycle, add it to the tree. b. Otherwise, discard the edge.
Now, let's compare each given sequence with the steps of Kruskal's algorithm:
Sequence (b,e)(e,f)(b,c)(a,c)(f,g)(c,d):
- (b,e): This edge can be added to the minimum spanning tree.
- (e,f): This edge can be added to the minimum spanning tree.
- (b,c): This edge can be added to the minimum spanning tree.
- (a,c): This edge can be added to the minimum spanning tree.
- (f,g): This edge can be added to the minimum spanning tree.
- (c,d): This edge can be added to the minimum spanning tree.
The given sequence (b,e)(e,f)(b,c)(a,c)(f,g)(c,d) is a valid sequence of edges added to the minimum spanning tree using Kruskal's algorithm.
Therefore, the answer is none of the given sequences is NOT the sequence of edges added to the minimum spanning tree using Kruskal's algorithm.
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