Graph Algorithms

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?

Consider the following undirected graph G: Choose a value for $x$ that will maximize the number of minimum weight spanning trees (MWSTs) of G. The number of MWSTs of G for this value of $x$ is _____.