%0 Journal Article
%T 互连网络<math display='inline' xmlns='http://www.w3.org/1998/Math/MathML'> <mrow>  <msub>   <mstyle mathvariant='bold' mathsize='normal'><mi>C</mi></mstyle>   <mstyle mathvariant='bold' mathsize='normal'><mi>n</mi></mstyle>  </msub>  <mo>&#x00D7;</mo><msub>   <mstyle mathvariant='bold' mathsize='normal'><mi>S</mi></mstyle>   <mstyle mathvariant='bold' mathsize='normal'><mi>m</mi></mstyle>  </msub>  </mrow></math>的谱特征及其能量<br>Spectral Characteristics and Energy of Interconnected Networks <math display='inline' xmlns='http://www.w3.org/1998/Math/MathML'> <mrow>  <msub>   <mstyle mathvariant='bold' mathsize='normal'><mi>C</mi></mstyle>   <mstyle mathvariant='bold' mathsize='normal'><mi>n</mi></mstyle>  </msub>  <mo>&#x00D7;</mo><msub>   <mstyle mathvariant='bold' mathsize='normal'><mi>S</mi></mstyle>   <mstyle mathvariant='bold' mathsize='normal'><mi>m</mi></mstyle>  </msub>  </mrow></math>
%A 杨金娜
%A 陈语哲
%A 梁志鹏
%J Pure Mathematics
%P 262-272
%@ 2160-7605
%D 2025
%I Hans Publishing
%R 10.12677/pm.2025.153101
%X 图的特征值集及其多重性称为谱&#65292;它可以用来获得图的各种拓扑性质&#65292;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<math display='inline' xmlns='http://www.w3.org/1998/Math/MathML'>
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   <mstyle mathvariant='bold' mathsize='normal'><mi>m</mi></mstyle>
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。本文根据分析研究互连网络的拓扑结构&#65292;刻画了<math display='inline' xmlns='http://www.w3.org/1998/Math/MathML'>
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的邻接谱和Laplace谱。进一步&#65292;根据Laplace矩阵的Fiedler向量对<math display='inline' xmlns='http://www.w3.org/1998/Math/MathML'>
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进行了图划分。另外&#65292;我们还研究得到了谱能量表达式。<br>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 <math display='inline' xmlns='http://www.w3.org/1998/Math/MathML'>
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   <mstyle mathvariant='bold' mathsize='normal'><mi>S</mi></mstyle>
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. This article describes the adjacency spectrum and Laplace spectrum of <math display='inline' xmlns='http://www.w3.org/1998/Math/MathML'>
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%K 互连网络&#65292
%K 邻接谱&#65292
%K Laplace谱&#65292
%K 能量<br>Interconnected Network
%K Adjacency Spectrum
%K Laplace Spectrum
%K Energy
%U http://www.hanspub.org/journal/PaperInformation.aspx?PaperID=110091