Bounds on the global offensive k-alliance number in graphs

• Autorzy: Mustapha Chellali , Teresa W. Haynes , Bert Randerath , Lutz Volkmann
• Języki publikacji: EN

Abstrakty

EN

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 $γₒ^k(G)$ is the minimum cardinality of a global offensive k-alliance in G. We present different bounds on $γₒ^k(G)$ in terms of order, maximum degree, independence number, chromatic number and minimum degree.

Słowa kluczowe

EN

global offensive k-alliance number; independence number; chromatic number

Kategorie tematyczne

• 05C69: Dominating sets, independent sets, cliques

• Wydawca: De Gruyter Open
• Czasopismo: Discussiones Mathematicae Graph Theory
• Rocznik: 2009
• Tom: 29
• Numer: 3
• Strony: 597-613

Daty

wydano

2009

otrzymano

2008-07-08

poprawiono

2008-12-08

zaakceptowano

2008-12-08

Twórcy

autor

Mustapha Chellali

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

autor

Teresa W. Haynes

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

autor

Bert Randerath

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

autor

Lutz Volkmann

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

Bibliografia

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Identyfikatory

DOI

10.7151/dmgt.1467