中文摘要：

研究平面剖分图的着色性质,通过讨论图的色多项式的零点问题,分析对图的着色保证相邻的两个区域着不同颜色的最少方法数目,进而给出了平面剖分图的着色方法数目的重要性质.主要研究方法是对平面图的着色提供了一个新的研究渠道,即通过色多项式计算,得出平面剖分前后的着色数目,进而再计算球面剖分图的着色数目.首先,研究＂具有一条公共边的两个区域G_n和G_m,及广义剖分图＂的着色问题;其次,研究＂简单正多面体及球面的三角剖分图＂的着色问题.

英文摘要：

In this paper,we study properties of division plane graph with coloring by discussing the zeros of chromatic polynomial of graphs.We analyze the minimum number of ways to faces by coloring the graph,so that no two adjacent faces receive the same color,giving the important properties of the number of ways to color plane division figure.This paper gives a new study method of coloring plane division figure.We compute the dichromatic polynomial of graphs,summarize the coloring properties of decomposing plane before and after,and discuss the coloring properties of sphere division figure.We discuss the coloring number of the regional figure Gnand Gm with a public side and their generalized division figure,and also discuss the coloring number of the triangulation figure of simple polyhedron and sphere.