GATE CS 2021 Set 1 — Question 27
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Algorithms → Graph Theory (Math) → Kruskal's MST
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Question
Consider the following undirected graph with edge weights as shown:
The number of minimum-weight spanning trees of the graph is _______.
Correct answer
3 to 3
Solution
To find the number of minimum-weight spanning trees (MSTs), we consider the edges with the minimum weight, which is 0.1.
Let the vertices be labeled as follows:
Top row:
Bottom row: From the graph, the edges with weight 0.1 are:
Let the vertices be labeled as follows:
Top row:
Bottom row: From the graph, the edges with weight 0.1 are:
1.
2.
3.
4.
5. (diagonal)
6. (diagonal)
There are 6 edges with weight 0.1. Let's check for cycles among these edges:- The edges form a cycle of length 3.
- No other cycles are formed by these 6 edges, and they connect all 6 vertices.
- Removing leaves a tree.
- Removing leaves a tree.
- Removing leaves a tree.
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