5,079 research outputs found
Chromatic Polynomials for Strip Graphs and their Asymptotic Limits
We calculate the chromatic polynomials for -vertex strip graphs of the
form , where and are various subgraphs on the
left and right ends of the strip, whose bulk is comprised of -fold
repetitions of a subgraph . The strips have free boundary conditions in the
longitudinal direction and free or periodic boundary conditions in the
transverse direction. This extends our earlier calculations for strip graphs of
the form . We use a generating function method. From
these results we compute the asymptotic limiting function ; for this has physical significance as
the ground state degeneracy per site (exponent of the ground state entropy) of
the -state Potts antiferromagnet on the given strip. In the complex
plane, is an analytic function except on a certain continuous locus . In contrast to the strip graphs, where
(i) is independent of , and (ii) consists of arcs and possible line segments
that do not enclose any regions in the plane, we find that for some
strip graphs, (i) does depend on and
, and (ii) can enclose regions in the plane. Our study elucidates the
effects of different end subgraphs and and of boundary conditions on
the infinite-length limit of the strip graphs.Comment: 33 pages, Latex, 7 encapsulated postscript figures, Physica A, in
press, with some typos fixe
- …