  We study the conformational properties of complex Gaussian polymers
containing $f_c$ linear branches and $f_r$ closed loops, periodically tethered
at $n$ branching points to either a linear polymer backbone (generalized
bottlebrush structures) or closed polymer ring (decorated ring structure).
Applying the path integration method, based on Edwards continuous chain model,
we obtain in particular the exact values for the size ratios comparing the
gyration radii of considered complex structures and linear chains of the same
total molecular weight, as functions of $n$, $f_c$ and $f_r$. Compactification
of the overall effective size of branched macromolecules with the increasing
number of loops is quantitatively confirmed. Our results are supported by
numerical estimates obtained by application of Wei's method.
