Question

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 v is a descendant of u in T
• B. {u, v} must be an edge in G, and u is a descendant of v in T
• C. If {u, v} is not an edge in G then u is a leaf in T
• D. If {u} is not an edge in G then u and v must have the same parent in T

Answer 1

The correct option is C If {u, v} is not an edge in G then u is a leaf in T

Draw some random graph and try to verify the options.