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.