The Number of Rooted Simple Bipartite Maps on the Sphere

Shude Long1, Junliang Cai2
1Department of Mathematics, Chongqing University of Arts and Sciences, Chongqing 402160, P.R.China
2School of Mathematical Sciences, Beijing Normal University, Beijing 100875, P.R.China

Abstract

This paper investigates the number of rooted simple bipartite maps on the sphere and presents some formulae for such maps with the number of edges and the valency of the root-face as two parameters.