Zero-Visibility Cops and Robber Game on Cage Graph

We consider zero-visibility cops and robber game that the cops lack of information on the location of the robber at all times, which is a variant of the classical cops and robbers game. First of all, we use the idea of splitting to study properties of cage graphs. Then we apply properties of cage graphs to investigate the lower bounds of cop number and the monotonic zero-visibility cop number of cage graphs. We also propose a searching algorithm to calculate the monotonic zero-visibility cop number of cage graphs.