Show that in an undirected graph, classifying an edge (u, ) as a tree edge or a back edge according to whether (u, ) or

Show that in an undirected graph, classifying an edge (u, ν) as a tree edge or a back edge according to whether (u, ν) or (ν, u) is encountered first during the depth-first search is equivalent to classifying it according to the ordering of the four types in the classification scheme.