What is the time complexity of a depth-first search (DFS) on a graph?

What is the time complexity of a depth-first search (DFS) on a graph?

Step 1: Understand that a graph consists of vertices (nodes) and edges (connections between nodes).
Step 2: Recognize that during a depth-first search (DFS), we explore each vertex in the graph.
Step 3: Note that for each vertex we visit, we also look at all the edges connected to that vertex.
Step 4: Realize that in the worst case, we will visit every vertex (V) and every edge (E) in the graph.
Step 5: Combine the visits to vertices and edges to express the total work done: O(V) for vertices and O(E) for edges.
Step 6: Conclude that the overall time complexity of DFS is O(V + E).

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