几类图的推广的拉普拉斯矩阵的特征多项式 The Characteristic Polynomial of Generalized Laplace Matrix of Several Kinds of Graphs

本文主要研究几类图的推广的拉普拉斯矩阵的特征多项式。用A(G)表示有n个顶点的简单图G的邻接矩阵，D(G)表示图G的顶点度对角矩阵。图G的拉普拉斯矩阵为，推广的拉普拉斯矩阵设为 。根据完全图和二部图的推广的拉普拉斯矩阵的特征多项式的结果，可以知道推广式中k分别取−1、0、1时，即是无符号拉普拉斯矩阵、邻接矩阵、拉普拉斯矩阵的相应的结果。 In this paper, we mainly study the characteristic polynomial of the generalized Laplace matrix of several kinds of graphs. The adjacency matrix of a simple graph with n vertexes represented by A(G), D(G) represents the vertex degree diagonal matrix of graph G. The Laplace matrix of G is , the generalized Laplace matrix is set to . We can know the promotion of the k are taken −1, 0, 1. That is, the corresponding results of the unsigned Laplace matrix, adjacency matrix and the Laplace matrix.