# On double domination in graphs

Jochen Harant; Michael A. Henning

Discussiones Mathematicae Graph Theory (2005)

- Volume: 25, Issue: 1-2, page 29-34
- ISSN: 2083-5892

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topJochen Harant, and Michael A. Henning. "On double domination in graphs." Discussiones Mathematicae Graph Theory 25.1-2 (2005): 29-34. <http://eudml.org/doc/270158>.

@article{JochenHarant2005,

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 $γ_\{×2\}(G)$. A function f(p) is defined, and it is shown that $γ_\{×2\}(G) = min f(p)$, where the minimum is taken over the n-dimensional cube $Cⁿ = \{p = (p₁,...,pₙ) | p_i ∈ IR, 0 ≤ p_i ≤ 1,i = 1,...,n\}$. Using this result, it is then shown that if G has order n with minimum degree δ and average degree d, then $γ_\{×2\}(G) ≤ ((ln(1+d) + lnδ + 1)/δ)n$.},

author = {Jochen Harant, Michael A. Henning},

journal = {Discussiones Mathematicae Graph Theory},

keywords = {average degree; bounds; double domination; probabilistic method; dominating number},

language = {eng},

number = {1-2},

pages = {29-34},

title = {On double domination in graphs},

url = {http://eudml.org/doc/270158},

volume = {25},

year = {2005},

}

TY - JOUR

AU - Jochen Harant

AU - Michael A. Henning

TI - On double domination in graphs

JO - Discussiones Mathematicae Graph Theory

PY - 2005

VL - 25

IS - 1-2

SP - 29

EP - 34

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 $γ_{×2}(G) = min f(p)$, where the minimum is taken over the n-dimensional cube $Cⁿ = {p = (p₁,...,pₙ) | p_i ∈ IR, 0 ≤ p_i ≤ 1,i = 1,...,n}$. Using this result, it is then shown that if G has order n with minimum degree δ and average degree d, then $γ_{×2}(G) ≤ ((ln(1+d) + lnδ + 1)/δ)n$.

LA - eng

KW - average degree; bounds; double domination; probabilistic method; dominating number

UR - http://eudml.org/doc/270158

ER -

## References

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