The maximum number of disjoint dominating sets in a domatic partition of a graph G is called its domatic number d(G). The domatic number should not be confused with the domination number, which is the size of the smallest individual dominating set. Let δ be the minimum vertex degree of a graph G, then d(G)<=δ + 1. The domatic number of a graph with one or more isolated points is therefore 1.

domatic partition | dominating set | minimal dominating set