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. Furthermore, if the domination number D of a graph G is known, than d(G)<=⌊( left bracketing bar G right bracketing bar )/(D(G)) ⌋, where left bracketing bar G right bracketing bar denotes the vertex count of G and ⌊x⌋ is the floor function.
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