Spectral bounds for the k-independence number of a graph

Aida Abiad Monge, Michael Tait, Sebastian Cioaba

Research output: Contribution to journalArticleAcademicpeer-review

Abstract

In this paper, we obtain two spectral upper bounds for the k-independence number of a graph which is the maximum size of a set of vertices at pairwise distance greater than k. We construct graphs that attain equality for our first bound and show that our second bound compares favorably to previous bounds on the k-independence number. 

Original languageEnglish
Pages (from-to)160-170
Number of pages11
JournalLinear Algebra and Its Applications
Volume510
DOIs
Publication statusPublished - Dec 2016

Keywords

  • k-independence number
  • Graph powers
  • Eigenvalues
  • Expander-mixing lemma
  • DISTANCE-REGULAR GRAPHS
  • POLYNOMIALS
  • DIAMETERS

Cite this

Abiad Monge, Aida ; Tait, Michael ; Cioaba, Sebastian. / Spectral bounds for the k-independence number of a graph. In: Linear Algebra and Its Applications. 2016 ; Vol. 510. pp. 160-170.
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Spectral bounds for the k-independence number of a graph. / Abiad Monge, Aida; Tait, Michael; Cioaba, Sebastian.

In: Linear Algebra and Its Applications, Vol. 510, 12.2016, p. 160-170.

Research output: Contribution to journalArticleAcademicpeer-review

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AB - In this paper, we obtain two spectral upper bounds for the k-independence number of a graph which is the maximum size of a set of vertices at pairwise distance greater than k. We construct graphs that attain equality for our first bound and show that our second bound compares favorably to previous bounds on the k-independence number. 

KW - k-independence number

KW - Graph powers

KW - Eigenvalues

KW - Expander-mixing lemma

KW - DISTANCE-REGULAR GRAPHS

KW - POLYNOMIALS

KW - DIAMETERS

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