On the multiplicities of digraph eigenvalues
Combinatorics
2020-11-05 v3
Abstract
We show various upper bounds for the order of a digraph (or a mixed graph) whose Hermitian adjacency matrix has an eigenspace of prescribed codimension. In particular, this generalizes the so-called absolute bound for (simple) graphs first shown by Delsarte, Goethals, and Seidel (1977) and extended by Bell and Rowlinson (2003). In doing so, we also adapt the Blokhuis' theory (1983) of harmonic analysis in real hyperbolic spaces to that in complex hyperbolic spaces.
Keywords
Cite
@article{arxiv.1911.11055,
title = {On the multiplicities of digraph eigenvalues},
author = {Alexander L. Gavrilyuk and Sho Suda},
journal= {arXiv preprint arXiv:1911.11055},
year = {2020}
}
Comments
Sections 4 and 5 added