Arithmetical Semigroups Related to Trees and Polyhedra,II — Maps on Surfaces

This paper extends recent investigations by Arnold Knopfmacher and John Knopfmacher 10] of asymptotic enumeration questions concerning finite graphs, trees and polyhedra. The present emphasis is on the counting of non‐isomorphic maps of not necessarily connected finite graphs on arbitrary surfaces. A significant aid towards this goal is provided by an extended abstract prime number theorem, based partly on more delicate tools of analysis due to W. K. Hayman 8].