Related papers: Connected forcing density and related problems
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…
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. We provide sharp upper and lower bounds on the connected…
In a graph G, a dominating set Df subset of V (G) is called a dom-forcing set if the sub-graph induced by Df must form a zero forcing set. The minimum cardinality of such a set is known as the dom-forcing number of the graph G, denoted by…
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…
A subset $S$ of initially infected vertices of a graph $G$ is called forcing if we can infect the entire graph by iteratively applying the following process. At each step, any infected vertex which has a unique uninfected neighbour, infects…
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…
A dynamic coloring of the vertices of a graph $G$ starts with an initial subset $S$ of colored vertices, with all remaining vertices being non-colored. At each discrete time interval, a colored vertex with exactly one non-colored neighbor…
The positive zero forcing number of a graph is a graph parameter that arises from a non-traditional type of graph colouring, and is related to a more conventional version of zero forcing. We establish a relation between the zero forcing and…
A graph in which all minimal zero forcing sets are in fact minimum size is called ``well-forced." This paper characterizes well-forced trees and presents an algorithm for determining which trees are well-forced. Additionally, we…
In zero forcing, the focus is typically on finding the minimum cardinality of any zero forcing set in the graph; however, the number of cardinalities between $0$ and the number of vertices in the graph for which there are both zero forcing…
A forcing set for a perfect matching of a graph is defined as a subset of the edges of that perfect matching such that there exists a unique perfect matching containing it. A complete forcing set for a graph is a subset of its edges, such…
This paper begins the study of reconfiguration of zero forcing sets, and more specifically, the zero forcing graph. Given a base graph $G$, its zero forcing graph, $\mathscr{Z}(G)$, is the graph whose vertices are the minimum zero forcing…
Let $G$ be a simple and finite graph without isolated vertices. In this paper we study forcing sets (zero forcing sets) which induce a subgraph of $G$ without isolated vertices. Such a set is called a total forcing set, introduced and first…
In this paper, controllability of systems defined on graphs is discussed. We consider the problem of controllability of the network for a family of matrices carrying the structure of an underlying directed graph. A one-to-one correspondence…
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.…
Power domination in graphs arises from the problem of monitoring an electric power system by placing as few measurement devices in the system as possible. A power dominating set of a graph is a set of vertices that observes every vertex in…
A dynamic coloring of the vertices of a graph $G$ starts with an initial subset $S$ of colored vertices, with all remaining vertices being non-colored. At each discrete time interval, a colored vertex with exactly one non-colored neighbor…
A set $Z$ of vertices of a graph $G$ is a zero forcing set of $G$ if initially labeling all vertices in $Z$ with $1$ and all remaining vertices of $G$ with $0$, and then, iteratively and as long as possible, changing the label of some…
The zero forcing number is the minimum number of black vertices that can turn a white graph black following a single neighbour colour forcing rule. The zero forcing number provides topological information about linear algebra on graphs,…
A connected dominating set in a graph is a dominating set of vertices that induces a connected subgraph. Following analogous studies in the literature related to independent sets, dominating sets, and total dominating sets, we study in this…