  For non-Hermitian equilateral q-pointed star-shaped quantum graphs of paper I
[Can. J. Phys. 90, 1287 (2012), arXiv 1205.5211] we show that due to certain
dynamical aspects of the model as controlled by the external,
rotation-symmetric complex Robin boundary conditions, the spectrum is
obtainable in a closed asymptotic-expansion form, in principle at least.
Explicit formulae up to the second order are derived for illustration, and a
few comments on their consequences are added.
