A domatic partition is a partition of the vertices of a graph into disjoint dominating sets.

The maximum number of disjoint dominating sets in a domatic partition of a graph is called its domatic number.

Finding a domatic partition of size 1 is trivial and finding a domatic partition of size 2 (or establishing that none exists) is easy, but finding a maximum-size domatic partition (i.e., the domatic number), is computationally hard.

More things to try:

Weisstein, Eric W. "Domatic Partition." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/DomaticPartition.html