The zero-temperature q-state Potts model partition function for a lattice
strip of fixed width Ly and arbitrary length Lx has the form
P(G,q)=∑j=1NG,λcG,j(λG,j)Lx, and is
equivalent to the chromatic polynomial for this graph. We present exact
zero-temperature partition functions for strips of several lattices with
(FBCy,PBCx), i.e., cyclic, boundary conditions. In particular, the
chromatic polynomial of a family of generalized dodecahedra graphs is
calculated. The coefficient cG,j of degree d in q is
c(d)=U2d(2q), where Un(x) is the Chebyshev
polynomial of the second kind. We also present the chromatic polynomial for the
strip of the square lattice with (PBCy,PBCx), i.e., toroidal, boundary
conditions and width Ly=4 with the property that each set of four vertical
vertices forms a tetrahedron. A number of interesting and novel features of the
continuous accumulation set of the chromatic zeros, B are found.Comment: 41 pages, latex, 18 figure