Centroid sequence

Centroid sequence --- центроидная последовательность.

Let [math]\displaystyle{ T }[/math] be a nontrivial tree; that is, a tree of order [math]\displaystyle{ n \geq 2 }[/math]. A centroid sequence [math]\displaystyle{ A = \{a_{1}, a_{2}, \ldots, a_{n}\} }[/math] of [math]\displaystyle{ T }[/math] is a sequence of the weights of the vertices of [math]\displaystyle{ T }[/math], arranged in a non-increasing order [math]\displaystyle{ (a_{1} \geq a_{2} \geq \ldots \geq a_{n}) }[/math].