We treat a variation of graph domination which involves partition ( V 1 , 2 ,..., k ) the vertex set G and each class i over distance d where all vertices edges may be used in process. Strict upper bounds extremal graphs are presented; results collected three handy tables. Further, we compare high number classes dominators needed.

The walk distances in graphs are defined as the result of appropriate transformations of the ∑∞ k=0(tA) k proximity measures, where A is the weighted adjacency matrix of a graph and t is a sufficiently small positive parameter. The walk distances are graphgeodetic; moreover, they converge to the shortest path distance and to the so-called long walk distance as the parameter t approaches its lim...