The necessary distinction can be made by first partitioning the edges, i . e ., defining the binary tree as triplet ( V, E 1, E 2 ), where ( V, E 1 * " E 2 ) is a rooted tree ( equivalently arborescence ) and E 1 ) " E 2 is empty, and also requiring that for all " j " " { 1, 2 } every node has at most one E " j " child.
