Related papers: Propagation processes on (hyper)graphs: where zero…
The concept of zero forcing involves a dynamic coloring process by which blue vertices cause white vertices to become blue, with the goal of forcing the entire graph blue while choosing as few as possible vertices to be initially blue. Past…
A procedure called \textit{graph burning} was introduced to facilitate the modelling of spread of an alarm, a social contagion, or a social influence or emotion on graphs and networks. Graph burning runs on discrete time-steps (or rounds).…
Graph burning is a natural discrete graph algorithm inspired by the spread of social contagion. Despite its simplicity, some open problems remain steadfastly unsolved, notably the burning number conjecture, which says that every connected…
Zero forcing is a graph coloring process that was defined as a tool for bounding the minimum rank and maximum nullity of a graph. It has also been used for studying control of quantum systems and monitoring electrical power networks. One of…
Zero forcing is a process on a graph that colors vertices blue by starting with some of the vertices blue and applying a color change rule. Throttling minimizes the sum of the size of the initial blue vertex set and the number of the time…
Graph burning is a discrete-time process that models the spread of influence in a network. Vertices are either burning or unburned, and in each round, a burning vertex causes all of its neighbours to become burning before a new fire source…
The problem of graph burning was firstly introduced as a model for different processes of social and network interactions. Recently, the authors of the present paper developed methods of algebraic topology for investigation of this problem.…
In this paper, we study the graph classification problem in vertex-labeled graphs. Our main goal is to classify the graphs comparing their higher-order structures thanks to heat diffusion on their simplices. We first represent…
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…
While a number of bounds are known on the zero forcing number $Z(G)$ of a graph $G$ expressed in terms of the order of a graph and maximum or minimum degree, we present two bounds that are related to the (upper) total domination number…
The Burning Number Problem (BNP) models the spread of information or contagion in a network through a discrete-time process on a graph. At each step, one new vertex is selected as a burning source, while fire simultaneously spreads from…
In this paper a new parameter for hypergraphs called hypergraph infection is defined. This concept generalizes zero forcing in graphs to hypergraphs. The exact value of the infection number of complete and complete bipartite hypergraphs is…
The concept of graph burning and burning number ($bn(G)$) of a graph G was introduced recently [1]. Graph burning models the spread of contagion (fire) in a graph in discrete time steps. $bn(G)$ is the minimum time needed to burn a graph…
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…
Graph coloring is a problem with varied applications in industry and science such as scheduling, resource allocation, and circuit design. The purpose of this paper is to establish if a new gradient based iterative solver framework known as…
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 colored. A zero forcing set is a set of initially colored…
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…
Let $G=(V,E)$ be a finite connected graph along with a coloring of the vertices of $G$ using the colors in a given set $X$. In this paper, we introduce multi-color forcing, a generalization of zero-forcing on graphs, and give conditions in…
Graph-based semi-supervised learning usually involves two separate stages, constructing an affinity graph and then propagating labels for transductive inference on the graph. It is suboptimal to solve them independently, as the correlation…
The zero forcing number $Z(G)$ of a graph $G$ is the minimum cardinality of a set $S$ with colored (black) vertices which forces the set $V(G)$ to be colored (black) after some times. "color change rule": a white vertex is changed to a…