Achromatic status

Achromatic status --- ахроматический статус.

Let [math]\displaystyle{ G }[/math] be a connected graph with its achromatic number [math]\displaystyle{ \psi(G) = k }[/math]. The achromatic status [math]\displaystyle{ \sum \psi(G) }[/math] is the minimum value of the total status for a set [math]\displaystyle{ X }[/math] of [math]\displaystyle{ k }[/math] vertices each from a different set [math]\displaystyle{ V_{i} }[/math] in the partition of [math]\displaystyle{ V }[/math], where minimum is taken over all possible partitions of [math]\displaystyle{ V }[/math] that satisfy (1) and (2) from the definition of achromatic number.