Equiseparable trees

Equiseparable trees --- эквисепарабельные деревья.

Let [math]\displaystyle{ T }[/math] be a tree and [math]\displaystyle{ e }[/math] an arbitrary edge of [math]\displaystyle{ T }[/math]. Then [math]\displaystyle{ T-e }[/math] consists of two components with [math]\displaystyle{ n_{1}(e) }[/math] and [math]\displaystyle{ n_{2}(e) }[/math] vertices. Conventionally, [math]\displaystyle{ n_{1}(e) \leq n_{2}(e) }[/math]. If [math]\displaystyle{ T^{'} }[/math] and [math]\displaystyle{ T^{''} }[/math] are two trees of the same order [math]\displaystyle{ n }[/math] and if their edges can be labelled so that [math]\displaystyle{ n_{1}(e_{i}^{'}) = n_{1}(e_{i}^{''}) }[/math] holds for all [math]\displaystyle{ i = 1, 2, \ldots, n-1 }[/math], then [math]\displaystyle{ T^{'} }[/math] and [math]\displaystyle{ T^{''} }[/math] are said to be equiseparable.