4. During the execution of GraphDFS (G), if an edge leads to a vertex v that is still in the recursion stack (i.e., the recursive call DFSG, v) has not returned), then such an edge is called a back-edge. (a) (2 points) Show that a directed graph has a cycle if and only if one detects a back-edge while running GraphDFS (G). (b) (1 point) Use part (a) to design an algorithm to determine if a given directed graph has a cycle. Give pseudocode and discuss running time