Simple Groups with the Same Prime Graph as $^2D_n(q)$

Behrooz Khosravi, A. Babai

In 2006, Vasil'ev posed the problem: \emph{Does there exist a positive integer $k$ such that there are no $k$ pairwise nonisomorphic nonabelian finite simple groups with the same graphs of primes? Conjecture: $k=5$.} In 2013, Zvezdina, confirmed the conjecture for the case when one of the groups is alternating. We continue this work and determine all nonabelian simple groups having the same prime graphs as the nonabelian simple group $^2D_n(q)$.