  Due to their unique topology of having no chain ends, dilute solutions of
ring polymers exhibit behaviour distinct from their linear chain counterparts.
The universality of their static and dynamic properties, as a function of
solvent quality $z$ in the thermal crossover regime between $\theta$ and
athermal solvents, is studied here using Brownian dynamics simulations. The
universal ratio $U_{\text{RD}}$ of the radius of gyration $R_g$ to the
hydrodynamic radius $R_H$ is determined, and a comparative study of the
swelling ratio $\alpha_g$ of the radius of gyration, the swelling ratio
$\alpha_H$ of the hydrodynamic radius, and the swelling ratio $\alpha_X$ of the
mean polymer stretch $X$ along the $x$-axis, for linear and ring polymers, is
carried out. The ratio $U_{\text{RD}}$ for dilute ring polymer solutions is
found to converge asymptotically to a constant value as $z \to \infty$, which
is a major difference from the behaviour of solutions of linear chains, where
no such asymptotic limit exists. Additionally, the ratio of the mean stretch
along the $x$-axis to the hydrodynamic radius, $(X/R_H)$, is found to be
independent of $z$ for polymeric rings, unlike in the case for linear polymers.
These results indicate a fundamental difference in the scaling of static and
dynamic properties of rings and linear chains in the thermal crossover regime.
