BFS and DFS

BFS. Start at a root $r$. Visit all neighbors of $r$, then all unvisited neighbors of those, etc. Uses a queue (FIFO). Computes distances from $r$ in unweighted graphs.

DFS. Start at $r$, recursively explore as deep as possible before backtracking. Uses a stack or recursion. Used for topological sorting, cycle detection, connected components.

Complexity. Both run in $O(|V|+|E|)$.

Conclusion. BFS explores level by level; DFS explores depth-first.