The Handbook of Linear Algebra provides comprehensive coverage of linear algebra
concepts, applications, and computational software packages in an easy-to-use handbook …

This book provides an introduction to the inverse eigenvalue problem for graphs (IEP-$ G $)
and the related area of zero forcing, propagation, and throttling. The IEP-$ G $ grew from the …

For a given graph G and an associated class of real symmetric matrices whose off-diagonal
entries are governed by the adjacencies in G, the collection of all possible spectra for such …

The minimum rank problem for a (simple) graph $ G $ is to determine the smallest possible
rank over all real symmetric matrices whose $ ij $ th entry (for $ i\neq j $) is nonzero …

The positive semidefinite zero forcing number Z+(G) of a graph G was introduced in Barioli
et al.(2010)[4]. We establish a variety of properties of Z+(G): Any vertex of G can be in a …

The minimum rank of a graph G is the minimum of the ranks of all symmetric adjacency
matrices of G. We present a new combinatorial bound for the minimum rank of an arbitrary …

We investigate the zero-forcing number for triangle-free graphs. We improve upon the trivial
bound, $\delta\le Z (G) $ where $\delta $ is the minimum degree, in the triangle-free case. In …

In this paper, we study (zero) forcing sets which induce connected subgraphs of a graph.
The minimum cardinality of such a set is called the connected forcing number of the graph …

Abstract We propose a Nordhaus–Gaddum conjecture for q (G), the minimum number of
distinct eigenvalues of a symmetric matrix corresponding to a graph G: for every graph G …

The zero forcing number is used to study the maximum nullity/minimum rank of the family of
symmetric matrices described by a simple, undirected graph. We study the positive …