Karami, H.; Sheikholeslami, S. M.; Khodkar, Abdollah Lower bounds on the signed domination numbers of directed graphs. (English) Zbl 1211.05117 Discrete Math. 309, No. 8, 2567-2570 (2009). Summary: A numerical invariant of directed graphs concerning domination which is named signed domination number \(\gamma _S\) is studied in this paper. We present some sharp lower bounds for \(\gamma _S\) in terms of the order, the maximum degree and the chromatic number of a directed graph. Cited in 2 ReviewsCited in 7 Documents MSC: 05C69 Vertex subsets with special properties (dominating sets, independent sets, cliques, etc.) 05C20 Directed graphs (digraphs), tournaments Keywords:signed dominating function; signed domination number; directed graph PDFBibTeX XMLCite \textit{H. Karami} et al., Discrete Math. 309, No. 8, 2567--2570 (2009; Zbl 1211.05117) Full Text: DOI References: [1] Szekeres, G.; Wilf, H. S., An inequality for the chromatic number of a graph, Journal of Combinatorial Theory, 4, 1-3 (1968) · Zbl 0171.44901 [2] West, D. B., Introduction to Graph Theory (2000), Prentice-Hall, Inc [3] Zelinka, B., Signed domination numbers of directed graphs, Czechoslovak Mathematical Journal, 55, 479-482 (2005) · Zbl 1081.05042 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.