Characterizations of the simple group Dn(3) by prime graph and spectrum

We prove that $D_n(3)$, where $n\geq6$ is even, is uniquely determined by its prime graph. Also, if $G$ is a finite group with the same prime graph as $D_4(3)$, then $G\cong D_4(3), B_3(3), C_3(3)$ or $G/O_2(G)\cong {\rm Aut}({}^2B_2(8))$.