关于一个简单图的色数及其相邻矩阵的特征多项式

摘要

把图论中的着色问题同数论中的整数论相结合，并且引入代数中的矩阵、特征多项式等数学工具，在讨论图的色数为2，3的结论基础上，给出了色数为4时图的性质和相邻矩阵的特征多项式等一些基本的结论。%The present paper integrates the color in graph theory and the integer in number theory ,and introduces some mathematic tools, such as matrices and characteristic polynomial in algebra. On the basis of the previous conclusion when the chromatic number is 2 or 3,some basic conclusions are given when the chromatic number is 4 and characteristic polynomial of the adjacent matrices.