  The Gruenberg-Kegel graph $\Gamma(G)$ of a finite group $G$ is the graph
whose vertex set is the set of prime divisors of $|G|$ and in which two
distinct vertices $r$ and $s$ are adjacent if and only if there exists an
element of order $rs$ in $G$.
  A finite group $G$ is called almost recognizable (by Gruenberg-Kegel graph)
if there is only finite number of pairwise non-isomorphic finite groups having
Gruenberg-Kegel graph as $G$. If $G$ is not almost recognizable, then it is
called unrecognizable (by Gruenberg--Kegel graph).
  Recently P.J. Cameron and the first author have proved that if a finite group
is almost recognizable, then the group is almost simple. Thus, the question of
which almost simple groups (in particular, finite simple groups) are almost
recognizable is of prime interest. We prove that every finite simple
exceptional group of Lie type, which is isomorphic to neither
${^2}B_2(2^{2n+1})$ with $n\geq1$ nor $G_2(3)$ and whose Gruenberg-Kegel graph
has at least three connected components, is almost recognizable. Moreover,
groups $ {^2}B_2(2^{2n+1})$, where $n\geq1$, and $G_2(3)$ are unrecognizable.
