PDF

Discussiones Mathematicae Graph Theory 25(1-2) (2005) 13-28
DOI: https://doi.org/10.7151/dmgt.1255

GRAPHS WITH LARGE DOUBLE DOMINATION NUMBERS

Michael A. Henning

School of Mathematics, Statistics, &
Information Technology, University of KwaZulu-Natal
Pietermaritzburg, 3209 South Africa
e-mail: henning@ukzn.ac.za

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.

Keywords: bounds, domination, double domination, minimum degree two.

2000 Mathematics Subject Classification: 05C69.

References

[1]	M. Blidia, M. Chellali, and T.W. Haynes, Characterizations of trees with equal paired and double domination numbers, submitted for publication.
[2]	M. Blidia, M. Chellali, T.W. Haynes and M.A. Henning, Independent and double domination in trees, Utilitas Math., to appear.
[3]	M. Chellali and T.W. Haynes, Paired and double domination in graphs, Utilitas Math., to appear.
[4]	J. Harant and M.A Henning, On double domination in graphs, Discuss. Math. Graph Theory, to appear, doi: 10.7151/dmgt.1256.
[5]	F. Harary and T.W. Haynes, Double domination in graphs, Ars Combin. 55 (2000) 201-213.
[6]	T.W. Haynes, S.T. Hedetniemi, and P.J. Slater, Fundamentals of Domination in Graphs (Marcel Dekker, New York, 1998).
[7]	T.W. Haynes, S.T. Hedetniemi, and P.J. Slater (eds), Domination in Graphs: Advanced Topics (Marcel Dekker, New York, 1998).
[8]	C.S. Liao and G.J. Chang, Algorithmic aspects of k-tuple domination in graphs, Taiwanese J. Math. 6 (2002) 415-420.
[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.

Received 25 August 2003
Revised 20 May 2004