DFS on Trees

A tree is a special graph: fully connected, no cycles, exactly $n-1$ edges for $n$ vertices. DFS on trees is simpler than on general graphs. You do not need to worry about cycles destroying your algorithm.

However, in an undirected tree, there is still a technical "cycle" issue: if you are at vertex $u$ and came from vertex $p$, there is an edge back to $p$. Without tracking the parent, you would immediately recurse back. Solution: pass the parent vertex as a parameter and skip it when iterating neighbors.