TY  - JOUR
ID  - Chellali2010
LB  - Chellali2010
AU  - Chellali, Mustapha
TI  - Trees with equal global offensive k-alliance and k-domination numbers
ST  - Trees with equal global offensive k-alliance and k-domination numbers
JO  - Opuscula Math.
JA  - Opuscula Math.
JF  - Opuscula Mathematica
PY  - 2010
VL  - 30
IS  - 3
SP  - 249
EP  - 254
DO  - http://dx.doi.org/10.7494/OpMath.2010.30.3.249
UR  - http://dx.doi.org/10.7494/OpMath.2010.30.3.249
AB  - Let \(k \geq 1\) be an integer. A set \(S\) of vertices of a graph \(G = (V(G),E(G))\) is called a global offensive \(k\)-alliance if \(|N(v) \cap S| \geq |N(v) - S| + k\) for every \(v \in V(G)- S\), where \(N(v)\) is the neighborhood of \(v\). The subset \(S\) is a \(k\)-dominating set of \(G\) if every vertex in \(V(G) - S\) has at least \(k\) neighbors in \(S\). The global offensive \(k\)-alliance number \(\gamma_0^k (G)\) is the minimum cardinality of a global offensive \(k\)-alliance in \(G\) and the \(k\)-domination number \(\gamma _k (G)\) is the minimum cardinality of a \(k\)-dominating set of \(G\). For every integer \(k \geq 1\) every graph \(G\) satisfies \(\gamma_0^k (G) \geq \gamma_k (G)\). In this paper we provide for \(k \geq 2\) a characterization of trees \(T\) with equal \(\gamma_0^k (T)\) and \(\gamma_k (T)\).
KW  - global offensive \(k\)-alliance number
KW  - \(k\)-domination number
KW  - trees
SN  - 1232-9274
ER  -