Let $G$ be a simple undirected graph, $T_D$ be a DFS tree on $G$, and $T_B$ be the BFS tree on $G$. Consider the following statements.
Statement $I$: No edge of $G$ is a cross with respect to $T_D$
Statement $II$: For every edge $(u,v)$ of $G$, if $u$ is at depth $i$ and $v$ is at depth $j$ in $T_B$ then $\mid i-j \mid =1$
In the light of the above statements, choose the correct answer from the options given below
- Both Statement $I$ and Statement $II$ are true
- Both Statement $I$ and Statement $II$ are false
- Statement $I$ is correct but Statement $II$ is false
- Statement $I$ is incorrect but Statement $II$ is true