GATE | GATE-CS-2000 | Question 49

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

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