Related papers: Connected zero forcing sets and connected propagat…

Zero forcing (also called graph infection) on a simple, undirected graph $G$ is based on the color-change rule: If each vertex of $G$ is colored either white or black, and vertex $v$ is a black vertex with only one white neighbor $w$, then…

Zero forcing in a graph refers to the evolution of vertex states under repeated application of a color change rule. Typically the states are chosen to be blue and white, and a forcing set is an initial set of blue vertices such that all of…

The \emph{zero forcing number}, $Z(G)$, of a graph $G$ is the minimum cardinality of a set $S$ of black vertices (whereas vertices in $V(G) \setminus S$ are colored white) such that $V(G)$ is turned black after finitely many applications of…

Zero forcing is a dynamic graph coloring process whereby a colored vertex with a single uncolored neighbor forces that neighbor to be colored. This forcing process has been used to approximate certain linear algebraic parameters, as well as…

Zero forcing is a dynamic coloring process on graphs. Initially, each vertex of a graph is assigned a color of either blue or white, and then a process begins by which blue vertices force white vertices to become blue. The zero forcing…

Let each vertex of a graph G = (V(G), E(G)) be given one of two colors, say, "black" and "white". Let Z denote the (initial) set of black vertices of G. The color-change rule converts the color of a vertex from white to black if the white…

Zero forcing is an iterative graph coloring process where at each discrete time step, a colored vertex with a single uncolored neighbor forces that neighbor to become colored. The zero forcing number of a graph is the cardinality of the…

Zero forcing is an iterative process on a graph used to bound the maximum nullity. The process begins with select vertices as colored, and the remaining vertices can become colored under a specific color change rule. The goal is to find a…

\emph{Zero forcing number}, $Z(G)$, of a graph $G$ is the minimum cardinality of a set $S$ of black vertices (whereas vertices in $V(G) \setminus S$ are colored white) such that $V(G)$ is turned black after finitely many applications of…

The zero forcing number of a graph $G$, denoted by $Z(G)$, is the minimum cardinality of a set $S$ of black vertices (where vertices in $V(G)\setminus S$ are colored white) such that $V(G)$ is turned black after finitely many applications…

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 vertex with exactly one white neighbor forces…

Zero forcing is an iterative graph coloring process whereby a colored vertex with a single uncolored neighbor forces that neighbor to be colored. It is NP-hard to find a minimum zero forcing set - a smallest set of initially colored…

The \emph{zero forcing number} $Z(G)$ of a graph $G$ is the minimum cardinality of a set $S$ of black vertices (whereas vertices in $V(G)\setminusS$ are colored white) such that $V(G)$ is turned black after finitely many applications of…

Let $G$ be a graph, and $Z$ a subset of its vertices, which we color black, while the remaining are colored white. We define the skew color change rule as follows: if $u$ is a vertex of $G$, and exactly one of its neighbors $v$, is white,…

Let $G$ be a simple, finite, and undirected graph with vertices each given an initial coloring of either blue or white. Zero forcing on graph $G$ is an iterative process of forcing its white vertices to become blue after a finite…

Let $S$ be a set of vertices of a graph $G$. Let $cl(S)$ be the set of vertices built from $S$, by iteratively applying the following propagation rule: if a vertex and all but exactly one of its neighbors are in $cl(S)$, then the remaining…

Probabilistic zero forcing is a coloring game played on a graph where the goal is to color every vertex blue starting with an initial blue vertex set. As long as the graph is connected, if at least one vertex is blue then eventually all of…

Zero forcing is a coloring game played on a graph that was introduced more than ten years ago in several different applications. The goal is to color all the vertices blue by repeated use of a (deterministic) color change rule.…

Zero forcing is a binary coloring game on a graph where a set of filled vertices can force non-filled vertices to become filled following a color change rule. In 2008, the zero forcing number of a graph was shown to be an upper bound on its…

Zero forcing in graphs is a coloring process where a colored vertex can force its unique uncolored neighbor to be colored. A zero forcing set is a set of initially colored vertices capable of eventually coloring all vertices of the graph.…