Data Structures | Graph | Question 5

Consider an undirected unweighted graph G. Let a breadth-first traversal of G be done starting from a node r. Let d(r, u) and d(r, v) be the lengths of the shortest paths from r to u and v respectively, in G. lf u is visited before v during the breadth-first traversal, which of the following statements is correct? (GATE CS 2001)
(A) d(r, u) < d (r, v)
(B) d(r, u) > d(r, v)
(C) d(r, u) <= d (r, v)
(D) None of the above

Answer: (C)

Explanation: d(r, u) and d(r, v) will be equal when u and v are at same level, otherwise d(r, u) will be less than d(r, v)

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