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?