论文标题
挖掘产品的光谱理论
Spectral theory of products of digraphs
论文作者
论文摘要
提出了一种与有向图相关的特定矩阵的特征值和特征向量确定的统一方法。研究的矩阵还包括距离矩阵，距离拉普拉斯和无距离的Laplacian，除了邻接矩阵，Laplacian和无标志性的Laplacian。引入了非负矩阵的各种Kronecker产品，以建模Digraphs的笛卡尔和词典产物。约旦规范形式广泛应用于光谱和特征向量的分析。分析表明，笛卡尔产品提供了一种用于建立无限传输常规挖掘家庭的方法，而距离很少有特征值。
A unified approach to the determination of eigenvalues and eigenvectors of specific matrices associated with directed graphs is presented. Matrices studied include the distance matrix, distance Laplacian, and distance signless Laplacian, in addition to the adjacency matrix, Laplacian, and signless Laplacian. Various sums of Kronecker products of nonnegative matrices are introduced to model the Cartesian and lexicographic products of digraphs. The Jordan canonical form is applied extensively to the analysis of spectra and eigenvectors. The analysis shows that Cartesian products provide a method for building infinite families of transmission regular digraphs with few distinct distance eigenvalues.
