  The degree pattern of a finite group is the degree sequence of its prime
graph in ascending order of vertices. We say that the problem of
OD-characterization is solved for a finite group if we determine the number of
pairwise nonisomorphic finite groups with the same order and degree pattern as
the group under consideration. In this article the problem of
OD-characterization is solved for some simple unitary groups. It was shown, in
particular, that the simple unitary groups $U_3(q)$ and $U_4(q)$ are
OD-characterizable, where $q$ is a prime power $<10^2$.
