Domatic number

Domatic number --- доматическое число.

The domatic number [math]\displaystyle{ d(G) }[/math] (or [math]\displaystyle{ dom(G) }[/math]) of [math]\displaystyle{ G }[/math] is the maximum cardinality of a domatic partition of [math]\displaystyle{ G }[/math]. The domatic number is one of the numerous domination invariants. It was introduced by Cockayne and Hedetniemi in 1977. Clearly, any graph [math]\displaystyle{ G }[/math] satisfies [math]\displaystyle{ d(G) \leq \delta(G) + 1 }[/math] ([math]\displaystyle{ \delta(G) }[/math] is a minimal degree of [math]\displaystyle{ G }[/math]). Graphs for which [math]\displaystyle{ d(G) }[/math] achieves this upper bound [math]\displaystyle{ \delta(G) + 1 }[/math] are called domatically full.