Spectral theory of products of digraphs
Combinatorics
2020-08-04 v2
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.
Keywords
Cite
@article{arxiv.2003.03412,
title = {Spectral theory of products of digraphs},
author = {Minerva Catral and Lorenzo Ciardo and Leslie Hogben and Carolyn Reinhart},
journal= {arXiv preprint arXiv:2003.03412},
year = {2020}
}