Let \(G\) be a simple undirected graph. Let \(T_D\) be a depth first search…

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?