Pruned tree

Pruned tree --- сокращенное дерево.

If a leaf [math]\displaystyle{ v }[/math] (together with the unique edge [math]\displaystyle{ e }[/math] incident with [math]\displaystyle{ v }[/math]) of a nontrivial tree [math]\displaystyle{ T }[/math] is removed from [math]\displaystyle{ T }[/math], we say that [math]\displaystyle{ v }[/math] has been pruned from [math]\displaystyle{ T }[/math]. We refer to the removal of all the leaves of a tree [math]\displaystyle{ T }[/math] of order [math]\displaystyle{ n \geq 3 }[/math] as a pruning of [math]\displaystyle{ T }[/math]. The graph that results from a pruning of [math]\displaystyle{ T }[/math] is a (possibly trivial) tree [math]\displaystyle{ T^{\ast} }[/math], called the pruned tree of [math]\displaystyle{ T }[/math].