PT Journal
AU Harant, J
   Henning, M
AU Workshop on Graph Theory: Colourings, Independence and Domination (CID) ; 10 (Karpacz) : 2003.09.22-26
TI On double domination in graphs
SO Discussiones mathematicae: Graph theory
PY 2005
BP 29
EP 34
VL 25, 2005
IS 1/2
PU De Gruyter Open
DI 10.7151/dmgt.1256
WP https://www.db-thueringen.de/receive/dbt_mods_00040542
LA en
DE average degree; bounds; double domination; probabilistic method
SN 2083-5892
AB 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.
PI Warsaw
ER