Let G be an undirected graph Consider a depth first traversal of G and let T be the resulting depth first search tree GATE CSE 2000

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## Let G be an undirected graph. Consider a depth-first traversal of G, and let T be the resulting depth-first search tree GATE CSE 2000

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

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Answer:C=If {u,v} is not an edge in G then u is a leaf in T. 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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