On double domination in graphs
Jochen Harant, Michael A. Henning (2005)
Discussiones Mathematicae Graph Theory
Similarity:
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 . A function f(p) is defined, and it is shown that , where the minimum is taken over the n-dimensional cube . Using this result, it is then shown that if G has order n with minimum degree δ and average degree d, then .