Cubic graphs with no eigenvalues in the interval (-1,1)
Combinatorics
2024-09-05 v1
Abstract
We give a complete characterisation of the cubic graphs with no eigenvalues in the open interval . There are two infinite families, one due to Guo and Mohar [Linear Algebra Appl. 449:68--75] the other due to Koll\'ar and Sarnak [Communications of the AMS. 1,1--38], and "sporadic" graphs on at most vertices. This allows us to show that is a maximal spectral gap set for cubic graphs. Our techniques including examination of various substructure and an application of the classification of generalized line graphs.
Keywords
Cite
@article{arxiv.2409.02678,
title = {Cubic graphs with no eigenvalues in the interval (-1,1)},
author = {Krystal Guo and Gordon F. Royle},
journal= {arXiv preprint arXiv:2409.02678},
year = {2024}
}