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On graphs with smallest eigenvalue at least −3 and their lattices

On graphs with smallest eigenvalue at least \(-3\) and their lattices
descriptionPublicationkeyboard_double_arrow_right Article , Preprint 01 Nov 2018Embargo end date: 01 Apr 2018 English Publisher:Elsevier BVJournal:Advances in Mathematics, volume 338, pages 847-864 (issn: 0001-8708, Copyright policy )
Authors: Koolen, Jack H.; Yang, Jae Young; Yang, Qianqian;

doi: 10.1016/j.aim.2018.09.004 , 10.48550/arxiv.1804.00369

arXiv: 1804.00369

On graphs with smallest eigenvalue at least −3 and their lattices

Abstract

In this paper, we show that a connected graph with smallest eigenvalue at least -3 and large enough minimal degree is 2-integrable. This result generalizes a 1977 result of Hoffman for connected graphs with smallest eigenvalue at least -2.

Related Organizations
Keywords

Connectivity, Graphs and linear algebra (matrices, eigenvalues, etc.), Hoffman graph, \(s\)-integrability, 05C50, 11H99, Geometry of numbers, root lattice, FOS: Mathematics, eigenvalue, Mathematics - Combinatorics, Combinatorics (math.CO), lattice

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    popularity
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    influence
    This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
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    This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
15
Top 10%
Top 10%
Top 10%
Green
bronze