CHROMATIC ENUMERATION FORROOTED OUTERPLANAR MAPS

Let G(m,s,t,λ)be the number of ways of λ-coloring all the rooted nonseparableouterplanar maps which are simple and have the edge number m,the valency s of theroot-face,and the valency t of the root-vertex.The chromatic enumerating functiong(x,y,z;λ.)=G(m,s,t;λ)x~my~sz~tis determined.Meanwhile,a number of explicit formulae for enumerating this kindofmaps in general case and in Lipartite case are provided.