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

Aida Abiad, Sebastian Cioabă, Michael Tait

Published 2015-10-24Version 1

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.