Discussiones Mathematicae Graph Theory 24(3) (2004)
423-430
DOI: https://doi.org/10.7151/dmgt.1241
SOME REMARKS ON α-DOMINATION
Franz Dahme
Lehrstuhl II für Mathematik, RWTH-Aachen | Dieter Rautenbach
Forschungsinstitut für Diskrete Mathematik
Lennéstr. 2, D-53113 Bonn, Germany | Lutz Volkmann
Lehrstuhl II für Mathematik, RWTH-Aachen |
Abstract
Let α ∈ (0,1) and let G = (VG,EG) be a graph. According to Dunbar, Hoffman, Laskar and Markus [3] a set D ⊆ VG is called an α-dominating set of G, if |NG(u)∩D| ≥ αdG(u) for all u ∈ VG∖D. We prove a series of upper bounds on the α-domination number of a graph G defined as the minimum cardinality of an α-dominating set of G.Keywords: α-domination; domination.
2000 Mathematics Subject Classification: 05C69.
References
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Received 31 March 2003
Revised 12 December 2003
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