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arXiv · 2003.03412

Spectral theory of products of digraphs

Minerva Catral·Lorenzo Ciardo·Leslie Hogben·Carolyn Reinhart
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Abstract

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.

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Minerva Catral, Lorenzo Ciardo, Leslie Hogben, Carolyn Reinhart. 2020-03-06. Spectral theory of products of digraphs. https://arxiv.org/abs/2003.03412

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