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Linear Algebra and its Applications
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Linear Algebra and its Applications
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Toughness and spectrum of a graph

descriptionPublicationkeyboard_double_arrow_right Article 01 Sep 1995 Netherlands English Publisher:Elsevier BVJournal:Linear Algebra and its Applications, volume 226-228, pages 267-271 (issn: 0024-3795, Copyright policy )
Authors: Andries E. Brouwer;

doi: 10.1016/0024-3795(95)00154-j

Toughness and spectrum of a graph

Abstract

The author proves the following theorem: Let \(G\) be a connected non- complete regular graph of valency \(d\) and let \(\lambda\) be the maximum of the absolute values of the eigenvalues of \(G\) distinct from \(d\). Then the toughness \(t\) of \(G\) satisfies \(t> d/\lambda- 2\).

Country
Netherlands
Related Organizations
Keywords

Extremal problems in graph theory, Numerical Analysis, Algebra and Number Theory, Graphs and linear algebra (matrices, eigenvalues, etc.), eigenvalues, toughness, Discrete Mathematics and Combinatorics, Geometry and Topology

  • BIP!
    Impact byBIP!
    citations
    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).
    		 30
    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.
    		 Top 10%
    influence
    This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
    		 Top 10%
    impulse
    This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
    		 Average
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citations
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!
30
Top 10%
Top 10%
Average
hybrid
Related to Research communities
Netherlands Research Portal