GRAPH THEORY IMPLEMENTATION ON THE LOCATING ROBBER PROBLEM IN COP-ROBBER GAME

Abstract

Cop and robber game is one of the pursuit games that is currently being developed with various problems to analyze a graph is a locatable or non-locatable graph. One of the problems in this game is determining the strategy for finding robber on a graph by guessing the distance with the player is a cop and a robber. The robber is in a graph and the cop is outside the graph. The cop tried to guess the vertex that was occupied by robber in a graph consider the distance that informed by the robber. A graph where the cop have a strategy to find the location of robber is called locatable graph otherwise if on a graph the cop does not have a strategy to find the location of the robber is called non-locatable graph. The locatable graph describes the cop strategy that in t-th probe the cop know the distance from t-th probe to the set of vertices that may be occupied by robber is single. This final project describes that path graph, graph cycle with n more than 6 vertices and graph girth 6 is locatable while graph cycle with n less than equal to 6 vertices, bipartite graph girth 6 and m-subdivision complete graph n vertices with m less than half the number of vertices is non-locatable. Keywords: Cop-robber, Graph Theory, Locatable, Non-Locatable