GATE CS 2024 Set 1 — Question 60
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Programming & Data Structures → Graphs (Data Structure) → Connected Components
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Question
The number of edges present in the forest generated by the DFS traversal of an undirected graph with 100 vertices is 40. The number of connected components in is _________
Correct answer
60 to 60
Solution
In an undirected graph with vertices and connected components, any spanning forest (including one generated by DFS) will have exactly edges.Given:
Using the formula for the number of edges in a forest:Therefore, the number of connected components in is 60.
- Number of vertices () = 100
- Number of edges in the DFS forest = 40
Using the formula for the number of edges in a forest:Therefore, the number of connected components in is 60.
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