D option is true ,
The ith iteration finds shortest paths in G of i or fewer edges, by the path relaxation property (see p. 587 in CLRS) .
A is false , just draw a directed connected graph and see counter example exist.
B is false bacause DFS is more closely related. The top-down approach to dynamic programming is effectively performing DFS on the subproblem dependence graph. The bottom-up approach means solving subproblems in the order of a reverse topological sort, which is also related to DFS.
C is false because The DFS forest may contain different numbers of trees (and tree edges) depending on the starting vertex and upon the order in which vertices are searched .