Here i have option III is doubt.how option III always correct.one counter example is if i choose a tree where s is root node and v1& v2 are its child node then above question property i.e the vertices V1 and V2 that are simultaneously on the function call stack at some point during the execution of depth-first search from vertex s in a digraph is satisfies.but there is no any path from v1 to v2 or from v2 to v1.