Chromatic sums of general maps on the sphere and the projective plane

In this paper, we study the chromatic sum functions of rooted general maps on the sphere and the projective plane. The chromatic sum function equations of such maps are obtained. From the chromatic sum equations of such maps, the enumerating function equations of rooted loopless maps, bipartite maps and Eulerian maps are also derived. Moreover, some explicit expressions of enumerating functions are also derived.