New Results On The Zero-Visibility Cops And Robber Game

We study the zero-visibility cops and robber game, a variant of the cops and robber game in which the robber is invisible. We give a method for proving lower bounds on the zero-visibility cop number. Using this method, we investigate graph joins, lexicographic products of graphs, complete multipartite graphs and split graphs. Lower bounds and upper bounds, along with rigorous proofs, are given for the zero-visibility cop number of each of these types of graphs.