Consider an undirected graph G$.$ Suppose we perform a depth$-$first search $($DFS$)$ starting from vertex v$.$ Which of the following is true?

Group of answer choices

The DFS edges form a cycle that includes v$.$

The DFS edges form a tree that includes a path from v to every vertex in its connected component.

The back edges form a tree that includes a path from v to every vertex in its connected component.

The back edges form a cycle that includes v$.$