000K  utf8
0100  827726732
0500  Ou
1100  $c2005
1500  eng
2050  urn:nbn:de:gbv:ilm1-2020200102
2051  10.7151/dmgt.1256
2240  
3000  Harant, Jochen
3010  Henning, Mike
4000  On double domination in graphs  [Harant, Jochen]
4060  6 Seiten
4209  In a graph G, a vertex dominates itself and its neighbors. A subset S ⊆ V(G) is a double dominating set of G if S dominates every vertex of G at least twice. The minimum cardinality of a double dominating set of G is the double domination number γ ×2(G). A function f(p) is defined, and it is shown that γ ×2(G) = minf(p), where the minimum is taken over the n-dimensional cube Cn = {p = (p1,…,pn) | pi ∈ IR, 0 ≤ pi ≤ 1,i = 1,…,n}. Using this result, it is then shown that if G has order n with minimum degree δ and average degree d, then γ×2(G) ≤ ((ln(1+d)+lnδ+1)/δ)n.
4950  https://doi.org/10.7151/dmgt.1256$xR$3Volltext$534
4950  https://nbn-resolving.org/urn:nbn:de:gbv:ilm1-2020200102$xR$3Volltext$534
4961  http://uri.gbv.de/document/gvk:ppn:827726732
5051  510
5550  average degree
5550  bounds
5550  double domination
5550  probabilistic method