Atapour, Maryam; Sheikholeslami, Seyed Mahmoud; Volkmann, Lutz Signed total \(k\)-domatic numbers of digraphs. (English) Zbl 1289.05344 Kragujevac J. Math. 35, No. 3, 359-368 (2011). Let \(D\) be a finite and simple digraph with vertex set \(V(D)\), and let \(f:V(D)\to\{-1,1\}\) be a two-valued function. This function \(f\) is a signed total \(k\)-dominating function on \(D\) if \(\sum_{x\in N^-(v)}f(x)\geq k\) for each \(v\in V(D)\), where the integer \(k\geq1\) and \(N^-(v)\) consists of all vertices of \(D\) from which arcs go into \(v\). A set \(\{f_1,f_2,\dots,f_d\}\) of distinct signed total \(k\)-dominating functions of \(D\) with the property that \(\sum_{i=1}^df_i(v)\leq1\), for each \(v\in V(D)\), is called a signed total \(k\)-dominating family of functions of \(D\). The maximum number of functions in a signed total \(k\)-dominating family of \(D\), denoted by \(d^t_{kS}(D)\), is the signed total \(k\)-domatic number of \(D\). The authors initiate the study of the signed total \(k\)-domatic numbers of digraphs and present some sharp upper bounds for this parameter. Reviewer: Olga Miljković (Beograd) MSC: 05C69 Vertex subsets with special properties (dominating sets, independent sets, cliques, etc.) 05C76 Graph operations (line graphs, products, etc.) 05C20 Directed graphs (digraphs), tournaments Keywords:signed total \(k\)-dominating function PDFBibTeX XMLCite \textit{M. Atapour} et al., Kragujevac J. Math. 35, No. 3, 359--368 (2011; Zbl 1289.05344)