# Article

 Title: On a problem concerning $k$-subdomination numbers of graphs (English) Author: Zelinka, Bohdan Language: English Journal: Czechoslovak Mathematical Journal ISSN: 0011-4642 (print) ISSN: 1572-9141 (online) Volume: 53 Issue: 3 Year: 2003 Pages: 627-629 Summary lang: English . Category: math . Summary: One of numerical invariants concerning domination in graphs is the $k$-subdomination number $\gamma ^{-11}_{kS}(G)$ of a graph $G$. A conjecture concerning it was expressed by J. H. Hattingh, namely that for any connected graph $G$ with $n$ vertices and any $k$ with $\frac{1}{2} n < k \leqq n$ the inequality $\gamma ^{-11}_{kS}(G) \leqq 2k - n$ holds. This paper presents a simple counterexample which disproves this conjecture. This counterexample is the graph of the three-dimensional cube and $k=5$. (English) Keyword: $k$-subdomination number of a graph Keyword: three-dimensional cube graph MSC: 05C69 idZBL: Zbl 1080.05526 idMR: MR2000058 . Date available: 2009-09-24T11:05:08Z Last updated: 2016-04-07 Stable URL: http://hdl.handle.net/10338.dmlcz/127828 . Reference: [1] E. J.  Cockayne and C. M.  Mynhardt: On a generalization of signed dominating functions of graphs.Ars Cobin. 43 (1996), 235–245. MR 1415993 Reference: [2] J. H.  Hattingh: Majority domination and its generalizations.In: Domination in Graphs. Advanced Topics, T. W.  Haynes, S. T.  Hedetniemi, P. J.  Slater (eds.), Marcel Dekker, Inc., New York-Basel-Hong Kong, 1998. Zbl 0891.05042, MR 1605689 .

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