Chromatic Sums for Rooted Planar Triangulations II: The Case λ = τ + 1

Abstract

SummaryIn an earlier paper [2] we denned the chromatic sums g, q, l and h. We determined the derivatives of these sums with respect to the colour-number λ at the special values λ = 1 and λ = 2. In the present paper we find parametric equations for h, l and q in the case λ = τ + 1, where τ is the golden ratio. We obtain h, l and the basic indeterminate z explicitly in terms of the parameter u, but for q we exhibit only a cubic equation with coefficients depending on u. We obtain an exact formula for the coefficients in h by applying Lagrange's theorem to the parametric equations.