Related papers: Protecting a Graph with Mobile Guards
\textsc{Cops and Robber} is a game played on graphs where a set of \textit{cops} aim to \textit{capture} the position of a single \textit{robber}. The main parameter of interest in this game is the \textit{cop number}, which is the minimum…
Recent studies have shown that graph neural networks (GNNs) are vulnerable to adversarial attacks, posing significant challenges to their deployment in safety-critical scenarios. This vulnerability has spurred a growing focus on designing…
A graph environment must be explored by a collection of mobile robots. Some of the robots, a priori unknown, may turn out to be unreliable. The graph is weighted and each node is assigned a deadline. The exploration is successful if each…
Interdicting a criminal with limited police resources is a challenging task as the criminal changes location over time. The size of the large transportation network further adds to the difficulty of this scenario. To tackle this issue, we…
The spread of an infection, a contagion, meme, emotion, message and various other spreadable objects have been discussed in several works. Burning and firefighting have been discussed in particular on static graphs. Graph burning simulates…
Recent developments have made autonomous vehicles (AVs) closer to hitting our roads. However, their security is still a major concern among drivers as well as manufacturers. Although some work has been done to identify threats and possible…
We consider the problem of finding decentralized strategies for multi-agent perimeter defense games. In this work, we design a graph neural network-based learning framework to learn a mapping from defenders' local perceptions and the…
Existing studies have shown that Message-Passing Graph Neural Networks (MPNNs) are highly susceptible to adversarial attacks. In contrast, despite the increasing importance of Graph Transformers (GTs), their robustness properties are…
We introduce a new class of network allocation games called graphical distance preservation games. Here, we are given a graph, called a topology, and a set of agents that need to be allocated to its vertices. Moreover, every agent has an…
Graph learning is a popular approach for performing machine learning on graph-structured data. It has revolutionized the machine learning ability to model graph data to address downstream tasks. Its application is wide due to the…
In the `Covering' pursuit game on a graph, a robber and a set of cops play alternately, with the cops each moving to an adjacent vertex (or not moving) and the robber moving to a vertex at distance at most 2 from his current vertex. The aim…
A new graph invariant called the secure vertex cover pebbling number, which is a combination of two graph invariants, namely secure vertex cover and cover pebbling number, is introduced in this paper. The secure vertex cover pebbling number…
In many variants of the game of Cops and Robbers on graphs, multiple cops play against a single robber. In 2019, Cox and Sanaei introduced a variant of the game that gives the robber a more active role than simply evading the cop. In their…
Let $G = (V,E)$ be a plane graph. A face $f$ of $G$ is guarded by an edge $vw \in E$ if at least one vertex from $\{v,w\}$ is on the boundary of $f$. For a planar graph class $\mathcal{G}$ we ask for the minimal number of edges needed to…
In order to improve the resilience of computer infrastructure against cyber attacks and finding ways to mitigate their impact we need to understand their structure and dynamics. Here we propose a novel network-based influence spreading…
Extensive research has highlighted the vulnerability of graph neural networks (GNNs) to adversarial attacks, including manipulation, node injection, and the recently emerging threat of backdoor attacks. However, existing defenses typically…
We consider a variation of cop vs.\ robber on graph in which the robber is not restricted by the graph edges; instead, he picks a time-independent probability distribution on $V(G)$ and moves according to this fixed distribution. The cop…
When securing complex infrastructures or large environments, constant surveillance of every area is not affordable. To cope with this issue, a common countermeasure is the usage of cheap but wide-ranged sensors, able to detect suspicious…
The 'Cheating Robot' version of Cops and Robbers is played on a finite, simple, connected graph. The players move in the same time period. However, before moving, the robot observes to which vertices the cops are moving and it is fast…
We consider the well-studied cops and robbers game in the context of oriented graphs, which has received surprisingly little attention to date. We examine the relationship between the cop numbers of an oriented graph and its underlying…