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Signed domination numbers of directed graphs. (English) Zbl 1081.05042

Summary: 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 (Zbl 0842.05051)) 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.

MSC:

05C20 Directed graphs (digraphs), tournaments
05C69 Vertex subsets with special properties (dominating sets, independent sets, cliques, etc.)
05C45 Eulerian and Hamiltonian graphs

Citations:

Zbl 0842.05051
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References:

[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. · Zbl 0842.05051
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