Protecting a Graph with Mobile Guards

TL;DR

This survey reviews various models of defending graphs with mobile guards, focusing on infinite attack sequences and configurations like dominating sets or vertex covers, summarizing existing literature on guard requirements.

Contribution

It provides a comprehensive overview of different guard defense models on graphs, emphasizing the case of infinite attacks and specific guard configurations.

Findings

Summarizes key results on guard numbers for different models.

Highlights the importance of guard configurations like dominating sets.

Provides a unified view of existing research in this area.

Abstract

Mobile guards on the vertices of a graph are used to defend it against attacks on either its vertices or its edges. Various models for this problem have been proposed. In this survey we describe a number of these models with particular attention to the case when the attack sequence is infinitely long and the guards must induce some particular configuration before each attack, such as a dominating set or a vertex cover. Results from the literature concerning the number of guards needed to successfully defend a graph in each of these problems are surveyed.