GATE CS 2014 Set 2 — Question 62
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Algorithms → Graph Theory (Math) → Kruskal's MST
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Question
The number of distinct minimum spanning trees for the weighted graph below is ______
Correct answer
6 to 6
Solution
Label the vertices of the left part as (top-left), (top-right), (left), (centre), (right), (bottom), and the triangle on the right as (apex), (bottom-left), (bottom-right). The graph has vertices, so every spanning tree has edges.Edges of weight 1: . They form no cycle, so (by Kruskal's algorithm) every MST contains all five of them. They leave four components:Edges of weight 2: . We need exactly of them to join the four components into a tree:
- and lie inside and can never be used.
- –: any one of , , → choices.
- –: only → choice (forced).
- –: either or → choices.
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