Spectra of products of digraphs

Minerva Catral, Lorenzo Ciardo, Leslie Hogben, Carolyn Reinhart
2020 The Electronic Journal of Linear Algebra  
A unified approach to the determination of eigenvalues and eigenvectors of specific matrices associated with directed graphs is presented. Matrices studied include the new distance matrix, with natural extensions to the distance Laplacian and distance signless Laplacian, in addition to the new adjacency matrix, with natural extensions to the Laplacian and signless Laplacian. Various sums of Kronecker products of nonnegative matrices are introduced to model the Cartesian and lexicographic
more » ... exicographic 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.
doi:10.13001/ela.2020.5243 fatcat:rxop3iqbmbexpkwks2b6r3av3i