两类互连网络的谱特征

Spectral Characteristics of Two Classes Interconnection Networks

摘要: 图的特征值集及其多重性称为谱，它可以用来获得图的各种拓扑性质，如连通性、韧性等。师海忠利用图的笛卡尔乘积方法构建了两类新的笛卡尔乘积互连网络$C_n\times Q_m$ 和$P_n\times Q_m$ 。本文分析研究了此两类互连网络的拓扑结构，得到了两类互连网络的邻接矩阵和拉普拉斯矩阵的特征值及其多重性，刻画了两类互连网络的谱特征，从而增加了已知谱图的类。

Abstract: The eigenvalues and its multiplicity of a graph are called spectrum, which can be used to obtain various topological properties of the graph, such as connectivity, toughness, etc. Shi Haizhong constructed new Cartesian product interconnection networks $C_n\times Q_m$ and $P_n\times Q_m$ using the Cartesian product method of graphs. This article analyzes and studies the topological structures of two types of interconnected networks, obtains the eigenvalues and multiplicities of the adjacency matrix and Laplace matrix of the two types of interconnected networks, characterizes the spectral characteristics of the two types of interconnected networks, so as to increase the classes of the graph with known spectra.