  Using the Luthar--Passi method, we investigate the classical Zassenhaus
conjecture for the normalized unit group of integral group rings of Janko
sporadic simple groups. As a consequence, we obtain that the Gruenberg-Kegel
graph of the Janko groups $J_1$, $J_2$ and $J_3$ is the same as that of the
normalized unit group of their respective integral group ring.
