Answer
-If an edge uv is not followed while we are processing vertex u during the depth-first search process,
-then it must be the case that the vertex v had already been visited.
Work Step by Step
-If an edge uv is not followed while we are processing vertex u during the depth-first search process,
-then it must be the case that the vertex v had already been visited. ----There are two cases. If vertex v was visited after we started processing u,
then,
- because we are not finished processing u yet, v must appear in the subtree rooted at u (and hence, must be a descendant of u).
-On the other hand, if the processing of v had already begun before we started processing u,
-then why wasn’t this edge followed at that time?
-It must be that we had not finished processing v,
--in other words,
that we are still forming the subtree rooted at v, sou is a descendant
of v, and hence, v is an ancestor of u.
