# Running time of Breath-First-Search — Proof

Running time of Breath-First-Search is **(V+E)**, where V — number of vertexes and E — number of edges.

**Pseudocode for BFS.**

· Enqueue and dequeue operations take **O(1)** time, so the total time for queuing is** O(V)**.

· Since each adjacency list is explored at most once the sum of all the adjacency list is **O(E)**. So the total time for exploring adjacency lists is **O(E)**.

Therefore the total running time of BFS is **O(V+E)**.