摘要: 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。
Abstract:
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.