ISSN 1234-3099 (print version)

ISSN 2083-5892 (electronic version)

Discussiones Mathematicae Graph Theory

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Discussiones Mathematicae Graph Theory


Discussiones Mathematicae Graph Theory 25(1-2) (2005) 13-28
DOI: 10.7151/dmgt.1255


Michael A. Henning

School of Mathematics, Statistics, &
Information Technology, University of KwaZulu-Natal
Pietermaritzburg, 3209 South Africa


In a graph G, a vertex dominates itself and its neighbors. A subset S ⊆ V(G) is a double dominating set of G if S dominates every vertex of G at least twice. The minimum cardinality of a double dominating set of G is the double domination number γ ×2(G). If G ± C5 is a connected graph of order n with minimum degree at least 2, then we show that γ×2(G) ≤ 3n/4 and we characterize those graphs achieving equality.

Keywords: bounds, domination, double domination, minimum degree two.

2000 Mathematics Subject Classification: 05C69.


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[2] M. Blidia, M. Chellali, T.W. Haynes and M.A. Henning, Independent and double domination in trees, Utilitas Math., to appear.
[3] M. Chellali and T.W. Haynes, Paired and double domination in graphs, Utilitas Math., to appear.
[4] J. Harant and M.A Henning, On double domination in graphs, Discuss. Math. Graph Theory, to appear, doi: 10.7151/dmgt.1256.
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[9] C.S. Liao and G.J. Chang, k-tuple domination in graphs, Information Processing Letters 87 (2003) 45-50, doi: 10.1016/S0020-0190(03)00233-3.

Received 25 August 2003
Revised 20 May 2004