Zetaequivalent digraphs: Simultaneous cospectrality
Abstract
We introduce a zeta function of digraphs that determines, and is determined by, the spectra of all linear combinations of the adjacency matrix, its transpose, the outdegree matrix, and the indegree matrix. In particular, zetaequivalence of graphs encompasses simultaneous cospectrality with respect to the adjacency, the Laplacian, the signless Laplacian, and the normalized Laplacian matrix, respectively. In addition, we express zetaequivalence in terms of Markov chains and in terms of invasions where each edge is replaced by a fixed digraph. We finish with a method for constructing zetaequivalent digraphs.
 Publication:

arXiv eprints
 Pub Date:
 December 2014
 arXiv:
 arXiv:1412.4763
 Bibcode:
 2014arXiv1412.4763H
 Keywords:

 Mathematics  Spectral Theory;
 Mathematics  Combinatorics
 EPrint:
 15 pages, 1 figure