This paper investigates ultrafilters in the context of connectivity systems, defined as pairs
$(X, f) $ where $ X $ is a finite set and $ f $ is a symmetric submodular function. Ultrafilters …

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 …

In this note, we study a dynamic vertex coloring for a graph G. In particular, one starts with a
certain set of vertices black, and all other vertices white. Then, at each time step, a black …

In this paper, we determine the graphs (respectively, trees) with maximum spectral radius
among all graphs (respectively, trees) with zero forcing number at most $ k $. As an …

A unified framework for the Expander Mixing Lemma for irregular graphs using adjacency
eigenvalues is presented, as well as two new versions of it. While the existing Expander …

Zero forcing is a deterministic iterative graph coloring process in which vertices are colored
either blue or white, and in every round, any blue vertices that have a single white neighbor …

We give an algorithm that finds a zero forcing set which approximates the optimal size by a
factor of $\text {pw}(G)+ 1$, where $\text {pw}(G) $ is the pathwidth of $ G $. Starting from a …

Zero forcing is a coloring process on a graph that was introduced more than fifteen years
ago in several different applications. The goal is to color all the vertices blue by repeated …

This article studies the problem of computing a minimum zero forcing set (ZFS) in undirected
graphs and presents new approaches to reducing the size of the minimum ZFS via edge …

This paper studies resilient strong structural controllability (SSC) in networks with
misbehaving agents and edges. We consider various misbehavior models and identify the …