The total {k}-domatic number of digraphs
Seyed Mahmoud Sheikholeslami, Lutz Volkmann (2012)
Discussiones Mathematicae Graph Theory
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For a positive integer k, a total k-dominating function of a digraph D is a function f from the vertex set V(D) to the set 0,1,2, ...,k such that for any vertex v ∈ V(D), the condition is fulfilled, where N¯(v) consists of all vertices of D from which arcs go into v. A set of total k-dominating functions of D with the property that for each v ∈ V(D), is called a total k-dominating family (of functions) on D. The maximum number of functions in a total k-dominating family on D is...