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We present exact calculations of the zero-temperature partition function forthe q-state Potts antiferromagnet (equivalently, the chromatic polynomial) fortwo families of arbitrarily long strip graphs of the square lattice withperiodic boundary conditions in the transverse direction and (i) periodic (ii)twisted periodic boundary conditions in the longitudinal direction, so that thestrip graphs are embedded on a (i) torus (ii) Klein bottle. In the limit ofinfinite length, we calculate the exponent of the entropy, W(q), show it to bethe same for (i) and (ii), and determine its analytic structure.Comment: 7 pages, latex, one postscript figur

T= 0 partition functions for Potts antiferromagnets on square lattice strips with (twisted) periodic boundary conditions