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Cliques and the spectral radius

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 01 Sep 2007Embargo end date: 01 Jan 2006 English Publisher:Elsevier BVJournal:Journal of Combinatorial Theory, Series B, volume 97, pages 859-865 (issn: 0095-8956, Copyright policy )Funded by:NSF | Collaborative Research: A..., NSF | ITR: Foundations of Hybri...
Authors: Béla Bollobás; Vladimir Nikiforov 0001;

doi: 10.1016/j.jctb.2006.12.002 , 10.48550/arxiv.math/0608453

arXiv: math/0608453

Cliques and the spectral radius

Abstract

We present a number of relations involving the number of cliques in a graph and its spectral radius.

Related Organizations
Keywords

spectral radius, Extremal problems in graph theory, Graphs and linear algebra (matrices, eigenvalues, etc.), stability, Mathematics - Commutative Algebra, Commutative Algebra (math.AC), clique number, Clique number, Theoretical Computer Science, Number of cliques, Computational Theory and Mathematics, number of cliques, FOS: Mathematics, Discrete Mathematics and Combinatorics, Mathematics - Combinatorics, Combinatorics (math.CO), 05C50, Spectral radius, Stability

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    selected citations
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    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).
    		 63
    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 1%
    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 1%
    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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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!
63
Top 1%
Top 1%
Average
Green
hybrid