Question: 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

4. During the execution of GraphDFS (G), if an edge leads

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

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