On recognition of the sporadic simple groups $hs$, $j_3$, $suz$, $o'n$, $ly$, $th$, $fi_{23}$, and $fi_{24}'$ by the gruenberg–kegel graph

The Gruenberg–Kegel graph (the prime graph) of a finite group $G$ is the graph whose vertices are the prime divisors of the order of $G$ and two different vertices $p$ and $q$ are adjacent if and only if $G$ contains an element of order $pq$. We find all finite groups with the same Gruenberg–Kegel graph as $S$ for each of the sporadic groups $S$ isomorphic to $HS$, $J_3$, $Suz$, $O'N$, $Ly$, $Th$, $Fi_{23}$, or $Fi_{24}'$. In particular, we establish the recognition by the Gruenberg–Kegel graph for these eight groups $S$.