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  • $\begingroup$ Thanks. However, I am still confused. I have added an example to explain my confusion. Could you please have a look at it? $\endgroup$ Commented Oct 22, 2018 at 5:40
  • $\begingroup$ :) I am waiting (both on the Internet and in my university). $\endgroup$ Commented Oct 22, 2018 at 6:01
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    $\begingroup$ OK. Now I think I understand it. I have misunderstood the statement in the exercise as "classifying $(u,v)$ as a tree edge if $(u,v)$ is encountered before $(v,u)$, otherwise classifying it a back edge". To make sure: Each edge $\{u,v\}$ will be encountered twice in a DFS. The definition in the text uses the first "type" according to the ordering, and that in the exercise uses the type the first "time" the edge is classified. Is this right? $\endgroup$ Commented Oct 22, 2018 at 12:40
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    $\begingroup$ Yes, that is correct. Either the earlier "type" or the first "time". That is, the first time always goes together with the earlier type. $\endgroup$ Commented Oct 22, 2018 at 12:54
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    $\begingroup$ @JohnL. " 1. The earliest type of edge (according to that ordering) as which either $(u,v)$ or $(v,u)$ can be classified, then $e$ is classified as that kind of edge. " Your answer is great but could you please elaborate the above definition. I feel that somewhere the entire meaning is not conveyed to me. And pardon me for asking a doubt in an old question's answer. Thank you... $\endgroup$ Commented Aug 5, 2020 at 16:10