Gap Sets for the Spectra of Cubic Graphs
Mathematical Physics
2021-01-18 v4 Combinatorics
math.MP
Number Theory
Spectral Theory
Abstract
We study gaps in the spectra of the adjacency matrices of large finite cubic graphs. It is known that the gap intervals and achieved in cubic Ramanujan graphs and line graphs are maximal. We give constraints on spectra in [-3,3] which are maximally gapped and construct examples which achieve these bounds. These graphs yield new instances of maximally gapped intervals. We also show that every point in can be gapped by cubic graphs, even by planar ones. Our results show that the study of spectra of cubic, and even planar cubic, graphs is subtle and very rich.
Cite
@article{arxiv.2005.05379,
title = {Gap Sets for the Spectra of Cubic Graphs},
author = {Alicia J. Kollár and Peter Sarnak},
journal= {arXiv preprint arXiv:2005.05379},
year = {2021}
}