Irregularity strength

Irregularity strength --- степень иррегулярности.

The irregularity strength [math]\displaystyle{ s(G) }[/math] of a graph [math]\displaystyle{ G }[/math] is defined as the minimum integer [math]\displaystyle{ t }[/math], for which the edges of [math]\displaystyle{ G }[/math] can be weighted with [math]\displaystyle{ 1, 2, \ldots, t }[/math] in such a way that the weighted degrees, i.e. the sum of weights of the adjacent edges in each vertex, are distinct numbers.

It is known that the irregularity strength of any tree with no vertices of degree 2 is its number of pendant vertices.