Abstract
The authors present some analytical results for the Potts model, using the symmetry group (acting on its parameters) generated by the inverse relation and other symmetries of this model. In particular, they find the critical manifolds and study the relationship between this group and the Lee-Yang singularities in the complex plane. For those cases where the symmetry group is finite, they look at the possible consequences for some colouring problems in graph theory and more specifically for chromatic polynomials.