A game of cops and robbers played on products of graphs Original Research Article

The game of cops and robbers is played with a set of ‘cops’ and a ‘robber’ who occupy some vertices of a graph. Both sides have perfect information and they move alternately to adjacent vertices. The robber is captured if at least one of the cops occupies the same vertex as the robber. The problem is to determine on a given graph, G, the least number of cops sufficient to capture the robber, called the cop-number, c(G). We investigate this game on three products of graphs: the Cartesian, categorical, and strong products.