  We analyze exact ground-state energies of two-dimensional Ising spin glasses
with either Gaussian or bimodal nearest-neighbor interactions for large system
sizes and for three types of boundary conditions: free on both axes, periodic
on both axes, and free on one axis and periodic on the other. We find accurate
values for bulk-, edge-, and corner-site energies. Fits for the system with
Gaussian bonds are excellent for all types of boundary conditions over the
whole range of system sizes. In particular, the leading behavior for non-free
boundary conditions is governed by the stiffness exponent ~ -0.28 describing
the scaling of domain-wall and droplet excitations. For the system with a
bimodal distribution of bonds the fit is good for free boundary conditions but
worse for other geometries, particularly for periodic-free boundary conditions
where there appear to be unorthodox corrections to scaling up to large sizes.
Finally, by introducing hard bonds we test explicitly for the Gaussian case the
relationship between domain walls and the standard scaling behavior.
