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We propose and unify classes of different models for information propagation over graphs. In a first class, propagation is modelled as a wave which emanates from a set of \emph{known} nodes at an initial time, to all other \emph{unknown}…

Numerical Analysis · Mathematics 2025-09-10 Oliver R. A. Dunbar , Charles M. Elliott , Lisa Maria Kreusser

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…

Combinatorics · Mathematics 2023-07-21 Leslie Hogben , Mark Hunnell , Kevin Liu , Houston Schuerger , Ben Small , Yaqi Zhang

We study a very restrictive graph exploration problem. In our model, an agent without persistent memory is placed on a vertex of a graph and only sees the adjacent vertices. The goal is to visit every vertex of the graph, return to the…

Data Structures and Algorithms · Computer Science 2023-02-01 Hans-Joachim Böckenhauer , Fabian Frei , Walter Unger , David Wehner

Consider a graph G with n nodes and m edges, which represents a social network, and assume that initially each node is blue or white. In each round, all nodes simultaneously update their color to the most frequent color in their…

Data Structures and Algorithms · Computer Science 2023-02-15 Ahad N. Zehmakan

Zero forcing is a combinatorial game played on a graph where the goal is to start with all vertices unfilled and to change them to filled at minimal cost. In the original variation of the game there were two options. Namely, to fill any one…

We consider a random graph in which vertices can have one of two possible colours. Each vertex switches its colour at a rate that is proportional to the number of vertices of the other colour to which it is connected by an edge. Each edge…

Probability · Mathematics 2026-04-21 Siva Athreya , Frank den Hollander , Adrian Röllin

We study feature propagation on graph, an inference process involved in graph representation learning tasks. It's to spread the features over the whole graph to the $t$-th orders, thus to expand the end's features. The process has been…

Social and Information Networks · Computer Science 2018-04-18 Biao Xiang , Ziqi Liu , Jun Zhou , Xiaolong Li

A leak is a vertex that is not allowed to perform a force during the zero forcing process. Leaky forcing was recently introduced as a new variation of zero forcing in order to analyze how leaks in a network disrupt the zero forcing process.…

Combinatorics · Mathematics 2020-08-18 Joseph S. Alameda , Jürgen Kritschgau , Nathan Warnberg , Michael Young

A power dominating set of a graph $G=(V,E)$ is a set $S\subset V$ that colors every vertex of $G$ according to the following rules: in the first timestep, every vertex in $N[S]$ becomes colored; in each subsequent timestep, every vertex…

Combinatorics · Mathematics 2018-10-03 Boris Brimkov , Joshua Carlson , Illya V. Hicks , Rutvik Patel , Logan Smith

The power domination number arises from the monitoring of electrical networks and its determination is an important problem. Upper bounds for power domination numbers can be obtained by constructions. Lower bounds for the power domination…

The \emph{metric dimension} $\dim(G)$ of a graph $G$ is the minimum number of vertices such that every vertex of $G$ is uniquely determined by its vector of distances to the chosen vertices. The \emph{zero forcing number} $Z(G)$ of a graph…

Combinatorics · Mathematics 2017-06-20 Linda Eroh , Cong X. Kang , Eunjeong Yi

We study the stabilization time of two common types of influence propagation. In majority processes, nodes in a graph want to switch to the most frequent state in their neighborhood, while in minority processes, nodes want to switch to the…

Discrete Mathematics · Computer Science 2021-07-06 Pál András Papp , Roger Wattenhofer

In quantum gravity, we study the evolution of a two-dimensional planar open frozen spin network, in which the color (i.e. the twice spin of an edge) labeling edge changes but the underlying graph remains fixed. The mainly considered…

General Relativity and Quantum Cosmology · Physics 2009-01-06 Jian-Zhen Chen , Jian-Yang Zhu

Deduction is a recently introduced graph searching process in which searchers clear the vertex set of a graph with one move each, with each searcher's movement determined by which of its neighbors are protected by other searchers. In this…

Combinatorics · Mathematics 2024-10-31 Andrea Burgess , Danny Dyer , Kerry Ojakian , Lusheng Wang , Mingyu Xiao , Boting Yang

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…

Combinatorics · Mathematics 2024-09-24 Karen Gunderson , William Kellough , JD Nir , Hritik Punj

Graph burning is a deterministic, discrete-time process that models how influence or contagion spreads in a graph. Associated to each graph is its burning number, which is a parameter that quantifies how quickly the influence spreads. We…

Combinatorics · Mathematics 2020-09-23 Anthony Bonato

We analyze the stabilization time of minority processes in graphs. A minority process is a dynamically changing coloring, where each node repeatedly changes its color to the color which is least frequent in its neighborhood. First, we…

Discrete Mathematics · Computer Science 2019-07-05 Pál András Papp , Roger Wattenhofer

We consider the influence maximization problem over a temporal graph, where there is a single fixed source. We deviate from the standard model of influence maximization, where the goal is to choose the set of most influential vertices.…

Computational Complexity · Computer Science 2023-03-24 Argyrios Deligkas , Michelle Döring , Eduard Eiben , Tiger-Lily Goldsmith , George Skretas

In this paper we compare the brushing number of a graph with the zero-forcing number of its line graph. We prove that the zero-forcing number of the line graph is an upper bound for the brushing number by constructing a brush configuration…

Combinatorics · Mathematics 2020-08-25 Aras Erzurumluoglu , David Pike , Karen Meagher

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…

Methodology · Statistics 2018-01-17 Wilson Y. Chen , Matt P. Wand