Spectral bounds for the zero forcing number of a graph

Abstract

Let Z(G) be the zero forcing number of a simple connected graph G. In this paper, we study the relationship between the zero forcing number of a graph and its (normalized) Laplacian eigenvalues. We provide the upper and lower bounds on Z(G) in terms of its (normalized) Laplacian eigenvalues, respectively. Our bounds extend the existing bounds for regular graphs.