  If $G$ is a finite group, then the spectrum $\omega(G)$ is the set of all
element orders of $G$. The prime spectrum $\pi(G)$ is the set of all primes
belonging to $\omega(G)$. A simple graph $\Gamma(G)$ whose vertex set is
$\pi(G)$ and in which two distinct vertices $r$ and $s$ are adjacent if and
only if $rs \in \omega(G)$ is called the Gruenberg-Kegel graph or the prime
graph of $G$.
  In this paper, we prove that if $G$ is a group of even order, then the set of
vertices which are non-adjacent to $2$ in $\Gamma(G)$ form a union of cliques.
Moreover, we decide when a strongly regular graph is isomorphic to the
Gruenberg-Kegel graph of a finite group. Besides this, we prove that a complete
bipartite graph with each part of size at least $3$ can not be isomorphic to
the Gruenberg-Kegel graph of a finite group.
