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

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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

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Received 25 August 2003
Revised 20 May 2004