Strong domatic number of a graph

A set [Formula: see text] of vertices of a simple graph [Formula: see text] is a strong dominating set, if for every vertex [Formula: see text] there is a vertex [Formula: see text] with [Formula: see text] and [Formula: see text]. The strong domination number [Formula: see text] is defined as the minimum cardinality of a strong dominating set. The strong domatic number [Formula: see text] is the maximum number of strong dominating sets into which the vertex set of [Formula: see text] can be partitioned. We initiate the study of the strong domatic number, and we present different sharp bounds on [Formula: see text]. In addition, we determine this parameter for some classes of graphs such as cubic graphs of order at most [Formula: see text].