LetG(m,s,t,λ)bethenumberofwaysofλ-coloringalltherootednonseparableouterplanarmapswhicharesimpleandhavetheedgenumberm,thevalencysoftheroot-face,andthevalencytoftheroot-vertex.Thechromaticenumeratingfunctiong(x,y,z;λ.)=G(m,s,t;λ)x~my~sz~tisdetermined.Meanwhile,anumberofexplicitformulaeforenumeratingthiskindofmapsingeneralcaseandinLipartitecaseareprovided.
