  In this work we are concerned with solutions to the linear Schr\"odinger type
system with mixed dispersion, the so-called biharmonic Schr\"odinger equation.
Precisely, we are able to prove an exact control property for these solutions
with the control in the energy space posed on an oriented star graph structure
$\mathcal{G}$ for $T>T_{min}$, with $$T_{min}=\sqrt{ \frac{ \overline{L}
(L^2+\pi^2)}{\pi^2\varepsilon(1- \overline{L} \varepsilon)}},$$ when the
couplings and the controls appear only on the Neumann boundary conditions.
