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Let G be a graph with n vertices and m edges. What is the tightest upper bound on the running time of Depth First Search on G, when G is represented as an adjacency matrix?

1. Θ(n)
2. Θ(n + m)
3. Θ(n²)
4. Θ(m²)

Correct answer: Θ(n²)

Solution

When a graph is represented as an adjacency matrix, checking for the existence of edges requires examining each entry in the n x n matrix. This results in a time complexity of Θ(n²) for Depth First Search, as every vertex and its potential connections must be considered.

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