We present exact calculations of the zero-temperature partition function, , and ground-state degeneracy (per site), , for the q-state Potts antiferromagnet on a number of families of graphs for which the boundary of regions of analyticity of W in the complex q-plane is noncompact and has the properties that (i) in the -plane, the point z = 0 is a multiple point on and (ii) includes support for . These families are generated by the method of homeomorphic expansion. Our results give further insight into the conditions for the validity of large-q series expansions for the reduced function .