We present exact calculations of the partition function of the zero-temperature Potts antiferromagnet (equivalently, the chromatic polynomial) for graphs of arbitrarily great length composed of repeated complete subgraphs Kb with b=5, 6 which have periodic or twisted periodic boundary condition in the longitudinal direction. In the Lx → ∞ limit, the continuous accumulation set of the chromatic zeros ℬ is determined. We give some results for arbitrary b including the extrema of the eigenvalues with coefficients of degree b-1 and the explicit forms of some classes of eigenvalues. We prove that the maximal point where ℬ crosses the real axis, qc, satisfies the inequality qc ≤ b for 2 ≤ b, the minimum value of q at which ℬ crosses the real q axis is q = 0, and we make a conjecture concerning the structure of the chromatic polynomial for Klein bottle strips.
|Number of pages||30|
|Journal||Physica A: Statistical Mechanics and its Applications|
|Publication status||Published - 2002 Oct 15|
All Science Journal Classification (ASJC) codes
- Statistics and Probability
- Condensed Matter Physics