GATE CS 2024 Set 1 Q.60: Graph Traversals, Topological Sort and Connectivity

The number of edges present in the forest generated by the DFS traversal of an undirected graph $G$ with 100 vertices is 40. The number of connected components in $G$ is _________

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Official answer and solution

Official answer: 60
From: Official GATE 2024 answer key

Solution

Use the forest relation $E_{\text{forest}} = V - C$ , where $V$ is the number of vertices and $C$ is the number of connected components (trees in the DFS forest).

A DFS traversal of an undirected graph $G$ with $V$ vertices and $C$ connected components produces a spanning forest consisting of $C$ trees and $E_{\text{forest}} = V - C$ tree edges. Given $V = 100$ and $E_{\text{forest}} = 40$ :

C = V - E_{\text{forest}} = 100 - 40 = 60

Final answer

The answer is the one in the official GATE answer key. The solution is this site's own explanation.

Source

Paper: GATE 2024 Computer Science and Information Technology - Set 1 (CS1)
Question: 60 of 65
Section: Computer Science and Information Technology

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