Graphs with large double domination numbers

Michael A. Henning

Discussiones Mathematicae Graph Theory (2005)

  • Volume: 25, Issue: 1-2, page 13-28
  • ISSN: 2083-5892

Abstract

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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 ) . If G ≠ C₅ is a connected graph of order n with minimum degree at least 2, then we show that γ × 2 ( G ) ≤ 3 n / 4 and we characterize those graphs achieving equality.

How to cite

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Michael A. Henning. "Graphs with large double domination numbers." Discussiones Mathematicae Graph Theory 25.1-2 (2005): 13-28. <http://eudml.org/doc/270356>.

@article{MichaelA2005,
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 $γ_\{×2\}(G)$. If G ≠ C₅ is a connected graph of order n with minimum degree at least 2, then we show that $γ_\{×2\}(G) ≤ 3n/4$ and we characterize those graphs achieving equality.},
author = {Michael A. Henning},
journal = {Discussiones Mathematicae Graph Theory},
keywords = {bounds; domination; double domination; minimum degree two},
language = {eng},
number = {1-2},
pages = {13-28},
title = {Graphs with large double domination numbers},
url = {http://eudml.org/doc/270356},
volume = {25},
year = {2005},
}

TY - JOUR
AU - Michael A. Henning
TI - Graphs with large double domination numbers
JO - Discussiones Mathematicae Graph Theory
PY - 2005
VL - 25
IS - 1-2
SP - 13
EP - 28
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 $γ_{×2}(G)$. If G ≠ C₅ is a connected graph of order n with minimum degree at least 2, then we show that $γ_{×2}(G) ≤ 3n/4$ and we characterize those graphs achieving equality.
LA - eng
KW - bounds; domination; double domination; minimum degree two
UR - http://eudml.org/doc/270356
ER -

References

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  1. [1] M. Blidia, M. Chellali, and T.W. Haynes, Characterizations of trees with equal paired and double domination numbers, submitted for publication. Zbl1100.05068
  2. [2] M. Blidia, M. Chellali, T.W. Haynes and M.A. Henning, Independent and double domination in trees, Utilitas Math., to appear. Zbl1110.05074
  3. [3] M. Chellali and T.W. Haynes, Paired and double domination in graphs, Utilitas Math., to appear. Zbl1069.05058
  4. [4] J. Harant and M.A Henning, On double domination in graphs, Discuss. Math. Graph Theory, to appear, doi: 10.7151/dmgt.1256. 
  5. [5] F. Harary and T.W. Haynes, Double domination in graphs, Ars Combin. 55 (2000) 201-213. Zbl0993.05104
  6. [6] T.W. Haynes, S.T. Hedetniemi, and P.J. Slater, Fundamentals of Domination in Graphs (Marcel Dekker, New York, 1998). Zbl0890.05002
  7. [7] T.W. Haynes, S.T. Hedetniemi, and P.J. Slater (eds), Domination in Graphs: Advanced Topics (Marcel Dekker, New York, 1998). Zbl0883.00011
  8. [8] C.S. Liao and G.J. Chang, Algorithmic aspects of k-tuple domination in graphs, Taiwanese J. Math. 6 (2002) 415-420. Zbl1047.05032
  9. [9] C.S. Liao and G.J. Chang, k-tuple domination in graphs, Information Processing Letters 87 (2003) 45-50, doi: 10.1016/S0020-0190(03)00233-3. 

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