A set Z of vertices of a graph G is a zero forcing set of G if iteratively adding to Z vertices from
V (G)∖ Z that are the unique neighbor in V (G)∖ Z of some vertex in Z, results in the entire …

A set Z of vertices of a graph G is a zero forcing set of G if initially labeling all vertices in Z
with 0 and all remaining vertices of G with 1, and then, iteratively and as long as possible …

A subset S of initially infected vertices of a graph G is called zero forcing if we can infect the
entire graph by iteratively applying the following process. At each step, any infected vertex …

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 …

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 …

Abstract Amos et al.(2015) introduced the notion of the k-forcing number of graph for a
positive integer k as the generalization of the zero forcing number of a graph. The k-forcing …

A total forcing set in a graph G is a forcing set (zero forcing set) in G which induces a
subgraph without isolated vertices. Total forcing sets were introduced and first studied by …

In this paper, we showcase the process of using an automated conjecturing program called
TxGraffiti written and maintained by the second author. We begin by proving a conjecture …

Zero forcing is an iterative graph coloring process, where given a set of initially colored
vertices, a colored vertex with a single uncolored neighbor causes that neighbor to become …

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 …