  The prime graph, or Gruenberg--Kegel graph, of a finite group $G$ is the
graph $\Gamma(G)$ whose vertices are the prime divisors of $|G|$, and whose
edges are the pairs $\{p,q\}$ for which $G$ contains an element of order $pq$.
A finite group $G$ is recognisable by its prime graph if every finite group $H$
with $\Gamma(H)=\Gamma(G)$ is isomorphic to $G$. By a result of Cameron and
Maslova, every such group must be almost simple, so one natural case to
investigate is that in which $G$ is one of the $26$ sporadic simple groups.
Existing work of various authors answers the question of recognisability by
prime graph for all but three of these groups, namely the Monster, $\text{M}$,
the Baby Monster, $\text{B}$, and the first Conway group, $\text{Co}_1$. We
prove that these three groups are recognisable by their prime graphs.
