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

Aida Abiad; Sebastian Cioabă; Michael Tait

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

Combinatorics 2016-08-19 v2

Authors: Aida Abiad , Sebastian Cioabă , Michael Tait

Abstract

In this paper, we obtain two spectral upper bounds for the $k$ -independence number of a graph which is 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.

Keywords

k-independence number spectral upper bound graph theory eigenvalue distance in graphs

Cite

@article{arxiv.1510.07186,
  title  = {Spectral bounds for the $k$-independence number of a graph},
  author = {Aida Abiad and Sebastian Cioabă and Michael Tait},
  journal= {arXiv preprint arXiv:1510.07186},
  year   = {2016}
}

Comments

The manuscript has been improved by comments from the referees. To appear in Linear Algebra and its Applications

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