四正则哈密尔顿平面地图的数目(英文)

The Number of 4 Regular Planar Hamiltonian Maps

一个地图称为哈密尔顿的若其上的所有顶点都在一个圈上．若一个平面地图的所有顶点是四次的，且又是哈密尔顿地图，则称该平面地图为四正则哈密尔顿平面图一个地图是近四正则的，是指除去根点外，其余顶点的次均为四．本文提供了四正则哈密尔顿平面地图计数的一个公式和四正则平面地图计数的一个显式．

A map is said to be Hamiltonian if all the vertices of the map are on one circuit. A 4 regular Hamiltonian planar map is a plannar map which is both 4 regular and Hamilitonian. A nearly 4 regular map is such a map that all of its vertices but the root vertex are 4 valent. In this paper, a formula on enumeration of 4 regular planar Hamiltionian maps and an explicit enumerating formula for nearly 4 regular planar maps are provided.