@Article{dbt_mods_00040542,
  author = 	{Harant, Jochen
		and Henning, Mike
		and {Workshop on Graph Theory: Colourings, Independence and Domination (CID) ; 10 (Karpacz) : 2003.09.22-26}},
  title = 	{On double domination in graphs},
  journal = 	{Discussiones mathematicae: Graph theory},
  year = 	{2005},
  publisher = 	{De Gruyter Open},
  address = 	{Warsaw},
  volume = 	{25, 2005},
  number = 	{1/2},
  pages = 	{29--34},
  keywords = 	{average degree; bounds; double domination; probabilistic method},
  abstract = 	{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 $\gamma$ {\texttimes}2(G). A function f(p) is defined, and it is shown that $\gamma$ {\texttimes}2(G) = minf(p), where the minimum is taken over the n-dimensional cube Cn = {\{}p = (p1,{\ldots},pn) | pi ∈ IR, 0 ≤ pi ≤ 1,i = 1,{\ldots},n{\}}. Using this result, it is then shown that if G has order n with minimum degree $\delta$ and average degree d, then $\gamma${\texttimes}2(G) ≤ ((ln(1+d)+ln$\delta$+1)/$\delta$)n.},
  note = 	{Faculty of Mathematics, Computer Science and Econometrics, University of Zielona G{\'o}ra},
  note = 	{Nachgewiesen 15.1995 -},
  note = 	{Urh. bis 2000: Institute of Mathematics, Technical University of Zielona G{\'o}ra; bis 2004: University of Zielona G{\'o}ra},
  issn = 	{2083-5892},
  doi = 	{10.7151/dmgt.1256},
  url = 	{https://www.db-thueringen.de/receive/dbt_mods_00040542},
  url = 	{http://uri.gbv.de/document/gvk:ppn:827726732},
  url = 	{http://uri.gbv.de/document/gvk:ppn:633752266},
  url = 	{https://doi.org/10.7151/dmgt.1256},
  file = 	{:https://www.db-thueringen.de/servlets/MCRFileNodeServlet/dbt_derivate_00046438/2083-5892_25_2005_1_2_29-34.pdf:PDF},
  language = 	{en}
}