GATE 2018
Let G be a simple undirected graph. Let T_D be a depth first search tree of G. Let T_B be a breadth first search tree of G. Consider the following statements:
(I) No edge of G is a cross edge with respect to T_D. (A cross edge in G is between two nodes neither of which is an ancestor of the other in T_D)
(II) For every edge (u, v) of G, if u is at depth i and v is at depth j in T_B, then |i - j| = 1.
Which of the statements above must necessarily be true?