The cops and robber game on some graph families

The inspiration for studying this game on graphs comes from an analysis of the popular video game Pac-Man. In this game, each move corresponds to an edge in the graph. The game involves two players: the cop and the robber. The number of players is limited by the vertices of the graph. At the beginning of the game, each player selects a vertex, and in each round, they can either move to adjacent vertices or remain in their current positions. The objective of the game is to capture the robber using the minimum number of cops. This minimum number of cops required to catch the robber is called the cop number of the graph. The main focus of this thesis is to determine the cop number for specific graphs. It explores how the cop number changes when the game is played on various subgraphs of the original graph. Furthermore, a new version of the game is introduced and compared to the classical version.