Zelinka, Bohdan Semidomatic numbers of directed graphs. (English) Zbl 0602.05038 Math. Slovaca 34, 371-374 (1984). E. J. Cockayne and S. T. Hedetniemi have introduced the domatic number of an undirected graph. Here its variants for directed graphs are studied. An inside-dominating (or outside-dominating) set in a directed graph G is a subset D of the vertex set V(G) of G such that for each vertex \(x\in V(G)-D\) there exists a vertex \(y\in D\) such that the edge xy (or yx respectively) exists in G. A dominating set in G is a set which is simultaneously inside-semidomatic and outside-semidomatic. The maximum number of classes of a partition of V(G) into dominating (or inside- semidominating, or outside-semidominating) sets is the domatic number (or inside-semidomatic number, or outside-semidomatic number respectively) of G. Fundamental properties of these concepts are described. A special attention is paid to tournaments. Cited in 2 Documents MSC: 05C35 Extremal problems in graph theory 05C20 Directed graphs (digraphs), tournaments 05C99 Graph theory Keywords:domatic number of a digraph; directed graph; inside-semidomatic number; outside-semidomatic number PDFBibTeX XMLCite \textit{B. Zelinka}, Math. Slovaca 34, 371--374 (1984; Zbl 0602.05038) Full Text: EuDML References: [1] COCKAYNE E. J., HEDETNIEMI S. T.: Towards a theory of domination in graphs. Networks 7, 1977, 247-261. · Zbl 0384.05051 · doi:10.1002/net.3230070305 [2] ZELINKA B.: Domatic numbers of directed graphs. Czech. Math. J. · Zbl 0847.05063 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.