  Let $\Gamma(G)$ be the Gruenberg-Kegel graph of a finite group $G$. We prove
that if $G$ is solvable and $\sigma$ is a cut-set for $\Gamma(G)$, then $G$ has
a $\sigma$-series of length $5$ whose factors are controlled. As a consequence,
we prove that if $G$ is a solvable group and $\Gamma(G)$ has a cut-vertex $p$,
then the Fitting length $\ell_F(G)$ of $G$ is bounded and the bound obtained is
the best possible. A cut-set is said \emph{minimal} if it does not contain any
other proper subset that is a cut-set for the graph. For a finite solvable
group $G$, we give a geometrical description of $\Gamma(G)$ when it has a
minimal cut-set of size $2$, for a finite solvable group $G$.
