Colored distance

Colored distance --- раскрашенное расстояние.

The colored distance of a colored graph [math]\displaystyle{ G }[/math] is introduced as the sum of distances between all unordered pairs of vertices having different colors. The chromatic distance of [math]\displaystyle{ G }[/math], denoted by [math]\displaystyle{ d_{ind}(G) }[/math], is the mi\-ni\-mum colored distance of a proper coloring of the vertex set.