相关论文: Propagation time for weighted zero forcing
The zero forcing number of a simple graph, written $Z(G)$, is a NP-hard graph invariant which is the result of the zero forcing color change rule. This graph invariant has been heavily studied by linear algebraists, physicists, and graph…
Zero forcing and power domination are iterative processes on graphs where an initial set of vertices are observed, and additional vertices become observed based on some rules. In both cases, the goal is to eventually observe the entire…
We develop the theory of the edge coloring of infinite lattice graphs, proving a necessary and sufficient condition for a proper edge coloring of a patch of a lattice graph to induce a proper edge coloring of the entire lattice graph by…
Expectation propagation is a general approach to fast approximate inference for graphical models. The existing literature treats models separately when it comes to deriving and coding expectation propagation inference algorithms. This comes…
In this paper, we propose computational approaches for the zero forcing problem, the connected zero forcing problem, and the problem of forcing a graph within a specified number of timesteps. Our approaches are based on a combination of…
Zero forcing is a process that models the spread of information throughout a graph as white vertices are forced to turn blue using a color change rule. The idea of throttling, introduced in 2013 by Butler and Young, is to optimize the…
Modeling how information travels throughout a network has vast applications across social sciences, cybersecurity, and graph-based neural networks. In this paper, we consider the zero forcing model for information diffusion on iterative…
For a graph $G$ in which vertices are either black or white, a zero forcing process is an iterative vertex color changing process such that the only white neighbor of a black vertex becomes black in the next time step. A zero forcing set is…
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 tight upper bound $\operatorname{pt}_+(G) \leq \left\lceil \frac{\left\vert \operatorname{V}(G) \right\vert - \operatorname{Z}_+(G)}{2} \right\rceil$ is established for the positive semidefinite propagation time of a graph in terms of…
Twisted hypercubes are graphs that generalize the structure of the hypercube by relaxing the symmetry constraint while maintaining degree-regularity and connectivity. We study the zero forcing number of twisted hypercubes. Zero forcing is a…
Zero forcing can be described as a combinatorial game on a graph that uses a color change rule in which vertices change white vertices to blue. The throttling number of a graph minimizes the sum of the number of vertices initially colored…
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…
We introduce a generalization of the concept of a chronological list of forces, called a relaxed chronology. This concept is used to introduce a new way of formulating the standard zero forcing process, which we refer to as parallel…
Zero forcing is a process that colors the vertices of a graph blue by starting with some vertices blue and applying a color change rule. Throttling minimizes the sum of the number of initial blue vertices and the time to color the graph. In…
Zero forcing is a process on a graph in which the goal is to force all vertices to become blue by applying a color change rule. Throttling minimizes the sum of the number of vertices that are initially blue and the number of time steps…
Zero forcing is a combinatorial game played on graphs that can be used to model the spread of information with repeated applications of a color change rule. In general, a zero forcing parameter is the minimum number of initial blue vertices…
In this paper, we study the impact of edge weights on distances in diluted random graphs. We interpret these weights as delays, and take them as i.i.d exponential random variables. We analyze the weighted flooding time defined as the…
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…
Say that an edge of a graph $G$ dominates itself and every other edge adjacent to it. An edge dominating set of a graph $G=(V,E)$ is a subset of edges $E' \subseteq E$ which dominates all edges of $G$. In particular, if every edge of $G$ is…