  A comparative simulation study of polymer brushes formed by grafting at a
planar surface either flexible linear polymers (chain length $N_L$) or
(non-catenated) ring polymers (chain length $N_R=2 N_L$) is presented. Two
distinct off-lattice models are studied, one by Monte Carlo methods, the other
by Molecular Dynamics, using a fast implementation on graphics processing units
(GPUs). It is shown that the monomer density profiles $\rho(z)$ in the
$z$-direction perpendicular to the surface for rings and linear chains are
practically identical, $\rho_R(2 N_L, z)=\rho_L(N_L, z)$. The same applies to
the pressure, exerted on a piston at hight z, as well. While the gyration radii
components of rings and chains in $z$-direction coincide, too, and increase
linearly with $N_L$, the transverse components differ, even with respect to
their scaling properties: $R_{gxy}^{(L)} \propto N_L^{1/2}$, $R_{gxy}^{(R)}
\propto N_L^{0.4}$. These properties are interpreted in terms of the
statistical properties known for ring polymers in dense melts.
