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arXiv · 2409.02678

Cubic graphs with no eigenvalues in the interval (-1,1)

Krystal Guo·Gordon F. Royle
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Abstract

We give a complete characterisation of the cubic graphs with no eigenvalues in the open interval $(-1,1)$. There are two infinite families, one due to Guo and Mohar [Linear Algebra Appl. 449:68--75] the other due to Kollár and Sarnak [Communications of the AMS. 1,1--38], and $14$ "sporadic" graphs on at most $32$ vertices. This allows us to show that $(-1,1)$ 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.

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Krystal Guo, Gordon F. Royle. 2024-09-04. Cubic graphs with no eigenvalues in the interval (-1,1). https://arxiv.org/abs/2409.02678

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