Enumeration of Unicursal Planar Near-Triangulation

Yongli Zhang1, Yanpei Liu1, Junliang Cai2
1Department of Mathematics, Beijing Jiaotong University 100044, Beijing, China
2Laboratory of Mathematics and Complex Systems School of Mathematical Sciences, Beijing Normal University 100875, Beijing, China

Abstract

A map is called Unicursal if it has exactly two vertices of odd valency. A near-triangulation is a map with all but one of its faces triangles. We use the enufunction approach to enumerate rooted Unicursal planar near-triangulations with the valency of the root-face and the number of non-rooted faces as parameters.