TY  - JOUR
ID  - Bouzefrane2009
LB  - Bouzefrane2009
AU  - Bouzefrane, Mohamed
AU  - Chellali, Mustapha
TI  - On the global offensive alliance number of a tree
ST  - On the global offensive alliance number of a tree
JO  - Opuscula Math.
JA  - Opuscula Math.
JF  - Opuscula Mathematica
PY  - 2009
VL  - 29
IS  - 3
SP  - 223
EP  - 228
DO  - http://dx.doi.org/10.7494/OpMath.2009.29.3.223
UR  - http://dx.doi.org/10.7494/OpMath.2009.29.3.223
AB  - For a graph \(G=(V,E)\), a set \(S \subseteq V\) is a dominating set if every vertex in \(V-S\) has at least a neighbor in \(S\). A dominating set \(S\) is a global offensive alliance if for every vertex \(v\) in \(V-S\), at least half of the vertices in its closed neighborhood are in \(S\). The domination number \(\gamma(G)\) is the minimum cardinality of a dominating set of \(G\) and the global offensive alliance number \(\gamma_o(G)\) is the minimum cardinality of a global offensive alliance of \(G\). We first show that every tree of order at least three with \(l\) leaves and \(s\) support vertices satisfies \(\gamma_o(T) \geq (n-l+s+1)/3\) and we characterize extremal trees attaining this lower bound. Then we give a constructive characterization of trees with equal domination and global offensive alliance numbers.
KW  - global offensive alliance number
KW  - domination number
KW  - trees
SN  - 1232-9274
ER  -