CID 2003 Abstracts - Colourings, Independence and Domination
CID 2003 Abstracts - Colourings, Independence and Domination
CID 2003 Abstracts - Colourings, Independence and Domination
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32 abstracts<br />
GRAPHS WITH LARGE DOUBLE DOMINATION NUMBER<br />
Michael A. Henning<br />
University of Natal, Pietermaritzburg, Republic of South Africa<br />
In a graph G = (V, E), a vertex dominates itself <strong>and</strong> its neighbors. A<br />
subset of vertices S of V is a double dominating set if every vertex in V is<br />
dominated at least twice. The minimum cardinality of a double dominating set<br />
of G is the double domination number of G, denoted γ ×2 (G). If G ≠ C 5 is a<br />
connected graph of order n with minimum degree at least 2, then we show that<br />
γ ×2 (G) ≤ 3n/4 <strong>and</strong> we characterize those graphs achieving equality.
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