  We present $N$-body simulations of globular clusters, exploring the effect of
different galactic potentials on cluster sizes, $r_h$. For various
galactocentric distances, $R_G$, we assess how cluster sizes change when we
vary the virial mass and concentration of the host galaxy's dark-matter halo.
We show that sizes of GCs are determined by the local galactic mass density
rather than the virial mass of the host galaxy. We find that clusters evolving
in the inner haloes of less concentrated galaxies are significantly more
extended than those evolving in more concentrated ones, while the sizes of
those orbiting in the outer halo are almost independent of concentration.
Adding a baryonic component to our galaxy models does not change these results
much, since its effect is only significant in the very inner halo. Our
simulations suggest that there is a relation between $r_h$ and $R_G$, which
systematically depends on the physical parameters of the halo. Hence, observing
such relations in individual galaxies can put a new observational constraint on
dark-matter halo characteristics. However, by varying the halo mass in a wide
range of $10^{9}\leq M_{vir}/\msun \leq10^{13}$, we find that the $r_h-R_G$
relationship will be nearly independent of halo mass, if one assumes $M_{vir}$
and $c_{vir}$ as two correlated parameters, as is suggested by cosmological
simulations.
