图的特征方程的推广及应用

Generalization and Application of the Characteristic Equation of Matrix with Applications

文章将代数的二次型、行列式运算和图的同构相联系,将矩阵的特征方程加以推广,给出广义特征方程列的概念,从而通过计算反映了图的与标号无关的信息,并给出图同构的一些必要条件。

In this paper, the relation among quadratic form, determinant and graphic isomorphism is discussed. We give a population in the characteristic equation of the matrix and the notion of column.Then, through calculation, some information,which is irrelevant to graphic labeling is discussed. In the end, some isomorphic necessary conditions are given.