  An offensive alliance in a graph $\Gamma=(V,E)$ is a set of vertices
$S\subset V$ where for every vertex $v$ in its boundary it holds that the
majority of vertices in $v$'s closed neighborhood are in $S$. In the case of
strong offensive alliance, strict majority is required. An alliance $S$ is
called global if it affects every vertex in $V\backslash S$, that is, $S$ is a
dominating set of $\Gamma$. The global offensive alliance number
$\gamma_o(\Gamma)$ (respectively, global strong offensive alliance number
$\gamma_{\hat{o}}(\Gamma)$) is the minimum cardinality of a global offensive
(respectively, global strong offensive) alliance in $\Gamma$. If $\Gamma$ has
global independent offensive alliances, then the \emph{global independent
offensive alliance number} $\gamma_i(\Gamma)$ is the minimum cardinality among
all independent global offensive alliances of $\Gamma$. In this paper we study
mathematical properties of the global (strong) alliance number of cubic graphs.
For instance, we show that for all connected cubic graph of order $n$,
$$\frac{2n}{5}\le \gamma_i(\Gamma)\le \frac{n}{2}\le
\gamma_{\hat{o}}(\Gamma)\le \frac{3n}{4} \le \gamma_{\hat{o}}({\cal
L}(\Gamma))=\gamma_{o}({\cal L}(\Gamma))\le n,$$ where ${\cal L}(\Gamma)$
denotes the line graph of $\Gamma$. All the above bounds are tight.
