ISSN 1234-3099 (print version)

ISSN 2083-5892 (electronic version)

Discussiones Mathematicae Graph Theory

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Discussiones Mathematicae Graph Theory


Discussiones Mathematicae Graph Theory 29(3) (2009) 597-613


1 Mustapha Chellali,  2Teresa W. Haynes, 3 Bert Randerath  and  3Lutz Volkmann

1LAMDA-RO Laboratory, Department of Mathematics
University of Blida
B.P. 270, Blida, Algeria

2Department of Mathematics
East Tennessee State University
Johnson City, TN 37614 USA

3Lehrstuhl II für Mathematik
RWTH Aachen University
Templergraben 55, D-52056 Aachen, Germany


Let G = (V(G),E(G)) be a graph, and let k ≥1 be an integer. A set S ⊆V(G) is called a global offensive k-alliance if |N(v)∩S| ≥ |N(v)-S|+k for every v∈V(G)-S, where N(v) is the neighborhood of v. The global offensive k-alliance number γok(G) is the minimum cardinality of a global offensive k-alliance in G. We present different bounds on γok(G) in terms of order, maximum degree, independence number, chromatic number and minimum degree.

Keywords: global offensive k-alliance number, independence number, chromatic number.

2000 Mathematics Subject Classification: 05C69.


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Received 8 July 2008
Revised 8 December 2008
Accepted 8 December 2008