Chromatic sums of general simple maps on the plane

Abstract

In this paper we study the chromatic sum functions for rooted general simple maps on the plane. The chromatic sum function equations for such maps are obtained. The enumerating function equation of such maps is derived by the chromatic sum equation of such maps. From the chromatic sum equation of such maps, the enumerating function equation of rooted simple bipartite maps on the plane is also derived. Moreover, some explicit expressions of enumerating functions are also derived.