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signed dominating function; signed domination number; directed graph; tournament; directed Hamiltonian cycle
The concept of signed domination number of an undirected graph (introduced by J. E. Dunbar, S. T. Hedetniemi, M. A. Henning and P. J. Slater) is transferred to directed graphs. Exact values are found for particular types of tournaments. It is proved that for digraphs with a directed Hamiltonian cycle the signed domination number may be arbitrarily small.
[1] J. F. Dunbar, S. T. Hedetniemi, M. A. Henning and P.  J. Slater: Signed domination in graphs. In: Graph Theory, Combinatorics and Applications. Proc. 7th Internat. conf. Combinatorics, Graph Theory, Applications, Vol. 1, Y.  Alavi, A. J. Schwenk (eds.), John Wiley & Sons, Inc., 1995, pp. 311–322. MR 1405819
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