The Visited Array

To prevent infinite loops in graphs with cycles, you track which vertices you have already visited. Use a boolean array: visited[u] = true means you have been to vertex $u$. Before recursing to a neighbor, check if it is already visited.

If yes, skip it. If no, mark it visited and recurse. This simple mechanism prevents your DFS from looping forever. Without it, a graph like $1 \leftrightarrow 2$ would cause infinite recursion: visit $1$, go to $2$, go back to $1$, go to $2$, forever.