GATE CS 2020 Set 1 — Question 59
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Engineering Mathematics → Graph Theory (Math) → Trees & Spanning Trees
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Question
Consider a graph , where , , and weight of the edge is . The weight of minimum spanning tree of is ______.
Correct answer
99 to 99
Solution
In the given graph , the vertices are and the weight of an edge between and is .
To find the Minimum Spanning Tree (MST), we want to connect all 100 vertices with 99 edges such that the total weight is minimized.
The minimum possible weight for any edge is .
Consider the set of edges .
Total weight of MST = .
To find the Minimum Spanning Tree (MST), we want to connect all 100 vertices with 99 edges such that the total weight is minimized.
The minimum possible weight for any edge is .
Consider the set of edges .
1.Each edge in has weight .
2.There are 99 such edges.
3.These edges form a path , which connects all 100 vertices.
Since we have connected all vertices using the minimum possible edge weights, this set of edges forms an MST.Total weight of MST = .
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