Recognition by prime graph of $^2 D_{2^m + 1} (3)$

As shown in 1] the simple group ² D_{2^m + 1} (3)^2 D_{2^m + 1} (3) is recognizable by spectrum. The main result of this paper generalizes the above, stating that ² D_{2^m + 1} (3)^2 D_{2^m + 1} (3) is recognizable by prime graph. In other words, we show that if G is a finite group satisfying G(G) = G(² D_{2^m + 1} (3))\Gamma (G) = \Gamma (^2 D_{2^m + 1} (3)) then G @ ² D_{2^m + 1} (3)G \cong ^2 D_{2^m + 1} (3).