id: 05879548
dt: j
an: 05879548
au: Chellali, Mustapha; Volkmann, Lutz
ti: Independence and global offensive alliance in graphs.
so: Australas. J. Comb. 47, 125-131 (2010).
py: 2010
pu: Published for the Combinatorial Mathematics Society of Australasia by the
    Centre for Discrete Mathematics and Computing, the University of
    Queensland, Brisbane, QLD
la: EN
cc: 
ut: global strong offensive alliance number; connected bipartite graph;
    connected unicyclic graph; independence number; extremal bipartite
    graph
ci: 
li: 
ab: Summary: Let $G$ be a simple graph with vertex set $V(G)$. A non-empty set
    $S\subseteq V(G)$ is a global strong offensive alliance if for every
    vertex $v$ in $V(G)- S$, a strict majority of its closed neighborhood
    is in $S$. The global strong offensive alliance number $γ_{\widehat
    o}(G)$ is the minimum cardinality of a global strong offensive alliance
    of $G$. We show that if $G$ is a connected bipartite graph of order at
    least three, then $γ_{\widehat o}(G)\le {3\over 2}α(G)$ and if $G$ is
    a connected unicyclic graph, then $γ_{\widehat o}(G)\le{3\over
    2}α(G)+ 1$, where $α(G)$ is the independence number of $G$. Moreover,
    we characterize extremal bipartite graphs achieving equality in the
    first upper bound.
rv: