互连网络$C_n\times S_m$的谱特征及其能量

Spectral Characteristics and Energy of Interconnected Networks $C_n\times S_m$

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新的笛卡尔乘积互连网络$C_n\times S_m$ 。本文根据分析研究互连网络的拓扑结构，刻画了$C_n\times S_m$ 的邻接谱和Laplace谱。进一步，根据Laplace矩阵的Fiedler向量对$C_n\times S_m$ 进行了图划分。另外，我们还研究得到了谱能量表达式。

Abstract: The eigenvalue set and its multiplicity of a graph are called spectra, which can be used to obtain various topological properties of the graph, such as connectivity, resilience, etc. Shi Haizhong used the Cartesian product method of graphs to construct a new Cartesian product interconnection network $C_n\times S_m$ . This article describes the adjacency spectrum and Laplace spectrum of $C_n\times S_m$ based on the analysis and research of the topology structure of interconnected networks. Furthermore, $C_n\times S_m$ was graphically partitioned based on the Fiedler vector of the Laplace matrix. In addition, we have also studied the expression of spectral energy.