Chromatic Sums for Rooted Planar Triangulations: The Cases λ = 1 and λ = 2

Abstract

SummaryIn this paper we derive a functional equation whose solution would give the sum of the chromatic polynomialP(M,λ) over certain classes of rooted planar mapsMcalled “ triangulations” and “near-triangulations”. For an integral colour-number λ this sum is the number of λ-coloured rooted maps of the kind considered, but the sum can also be discussed for non-integral λ.