### 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 language | English |
---|---|

Pages (from-to) | 160-170 |

Number of pages | 11 |

Journal | Linear Algebra and Its Applications |

Volume | 510 |

DOIs | |

Publication status | Published - Dec 2016 |

### Keywords

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

### Cite this

*Linear Algebra and Its Applications*,

*510*, 160-170. https://doi.org/10.1016/j.laa.2016.08.024

}

*Linear Algebra and Its Applications*, vol. 510, pp. 160-170. https://doi.org/10.1016/j.laa.2016.08.024

**Spectral bounds for the k-independence number of a graph.** / Abiad Monge, Aida; Tait, Michael; Cioaba, Sebastian.

Research output: Contribution to journal › Article › Academic › peer-review

TY - JOUR

T1 - Spectral bounds for the k-independence number of a graph

AU - Abiad Monge, Aida

AU - Tait, Michael

AU - Cioaba, Sebastian

N1 - No data used.

PY - 2016/12

Y1 - 2016/12

N2 - 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.

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

U2 - 10.1016/j.laa.2016.08.024

DO - 10.1016/j.laa.2016.08.024

M3 - Article

VL - 510

SP - 160

EP - 170

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

SN - 0024-3795

ER -