### 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 |
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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

Abiad Monge, A., Tait, M., & Cioaba, S. (2016). Spectral bounds for the k-independence number of a graph.

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