Cops and Robber on Oriented Graphs

Cops and Robber is a vertex pursuit-evasion game played on graphs. The cops, who always play first, and the robber are positioned on different vertices. During a player’s turn, they either move on one edge to an adjacent vertex or stay put on their vertex. The cops win when one of them catches the robber by landing on the same vertex as the robber; the robber wins if they can avoid the cops forever. In this project, we will explore this game on oriented graphs. We will formulate winning strategies for the cops and robber and analyze the minimum number of cops needed to capture a robber on families of oriented graphs