  Topology of the space of periodic ground states in the antiferromagnetic
Ising and Potts (3-state) models is analysed in selected spatial structures.
The states are treated as graph nodes, connected by one-spin-flip transitions.
The spatial structures are the triangular lattice, the Archimedean ($3,12^{2}$)
lattice and the cubic Laves C15 lattice with the periodic boundary conditions.
In most cases the ground states are isolated nodes, but for selected systems we
obtain connected graphs. The latter means that the magnetisation can vary in
time with zero energy cost. The ground states are classified according to their
degree and type of neighbours.
