Ground-state degeneracy of Potts antiferromagnets: homeomorphic classes with noncompact W boundaries

We present exact calculations of the zero-temperature partition function Z(G,q,T=0) and ground-state degeneracy W({G},q) for the q-state Potts antiferromagnet on a number of families of graphs G for which (generalizing q from to ) the boundary of regions of analyticity of W in the complex q plane is noncompact, passing through z=1/q=0. For these types of graphs, since the reduced function Wred=q−1W is nonanalytic at z=0, there is no large-q Taylor series expansion of Wred. The study of these graphs thus gives insight into the conditions for the validity of the large-q expansions. It is shown how such (families of) graphs can be generated from known families by homeomorphic expansion.