DMGT

ISSN 1234-3099 (print version)

ISSN 2083-5892 (electronic version)

https://doi.org/10.7151/dmgt

Discussiones Mathematicae Graph Theory

IMPACT FACTOR 2018: 0.741

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Discussiones Mathematicae Graph Theory

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Discussiones Mathematicae Graph Theory 24(3) (2004) 423-430
DOI: 10.7151/dmgt.1241

SOME REMARKS ON α-DOMINATION

Franz Dahme

Lehrstuhl II für Mathematik, RWTH-Aachen
52056 Aachen, Germany

e-mail: franz.dahme@web.de

Dieter Rautenbach

Forschungsinstitut für Diskrete Mathematik
Lennéstr. 2, D-53113 Bonn, Germany

e-mail: rauten@or.uni-bonn.de

Lutz Volkmann

Lehrstuhl II für Mathematik, RWTH-Aachen
52056 Aachen, Germany

e-mail: volkm@math2.rwth-aachen.de

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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[3] J.E. Dunbar, D.G. Hoffman, R.C. Laskar and L.R. Markus, α-domination, Discrete Math. 211 (2000) 11-26, doi: 10.1016/S0012-365X(99)00131-4.
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Received 31 March 2003
Revised 12 December 2003