图的规范化Laplace和规范化无符号Laplace特征多项式

Normalized Laplacian and Normalized Signless Laplacian Characteristic Polynomials of a Graph

利用行列式的性质,首先基于图G的Randic矩阵的特征多项式给出规范化Laplace和规范化无符号Laplace特征多项式;其次,借助导出子图的特征多项式表示出Randic矩阵以及规范化Laplace和规范化无符号Laplace矩阵的特征多项式;最后,给出图G的Middle图的特征多项式.

Using the properties of determinant,firstly,we gave the normalized Laplacian and normalized signless Laplacian characteristic polynomials based on the characteristic polynomial of the Randic matrix of a graph G.Secondly,we gave the characteristic polynomials of Randic matrix,normalized Laplacian matrix and normalized signless Laplacian matrix by means of the characteristic polynomials of the induced subgraphs.Finally,we gave the characteristic polynomial of the Middle graph of a graph G.