Graphs with large double domination numbers
Michael A. Henning (2005)
Discussiones Mathematicae Graph Theory
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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 . If G ≠ C₅ is a connected graph of order n with minimum degree at least 2, then we show that and we characterize those graphs achieving equality.