Graph searching and dynamic domination problems focus on the following question: how can the activity of an adversary be neutralized in a network? A collection of agents move around a network according to a rule set. In graph searching, the goal is generally to locate a hidden mobile adversary, while for dynamic domination problems, the goal is generally to defend against a sequence of adversarial attacks. The study of such network security problems has largely been inspired by foundational issues in discrete mathematics and theoretical computer science.