Let G be an undirected graph. Consider a depth-first traversal of G, and let T be the resulting depth-first search tree. Let u be a vertex in G and let v be the first new (unvisited) vertex visited after visiting u in the traversal. Which of the following statements is always true?
(A) {u,v} must be an edge in G, and u is a descendant of v in T
(B) {u,v} must be an edge in G, and v is a descendant of u in T
(C) If {u,v} is not an edge in G then u is a leaf in T
(D) If {u,v} is not an edge in G then u and v must have the same parent in T
Answer: (C)
Explanation:
In DFS, if 'v' is visited
after 'u', then one of the following is true.
1) (u, v) is an edge.
u
/ \
v w
/ / \
x y z
2) 'u' is a leaf node.
w
/ \
x v
/ / \
u y z In DFS, after visiting a node, we first recur for all unvisited children. If there are no unvisited children (u is leaf), then control goes back to parent and parent then visits next unvisited children.
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