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

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.

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

References in corpus (1)

• Eigenvalue interlacing and weight parameters of graphs