Avoiding Cycles in Trees

Here's the tree DFS template with parent tracking:

function dfs(u, parent):
    process(u)
    for each neighbor v of u:
        if v != parent:
            dfs(v, u)

When you call dfs(v, u), you pass the current vertex as the child's parent. The child knows not to recurse back to where it came from. Start with dfs(root, -1) where $-1$ means no parent.

This single check eliminates the need for a visited array on trees. You save memory and simplify your code. Every tree problem uses this pattern.