A variation of Cops and Robbers on Graphs

Abstract

"We consider a variation of game of cops and robber where the cop seeks to determine the location of the robber by selecting a vertex v in the graph and receiving distance from v to the invisible robber. The movement of robber is restricted to adjacent vertices except for the vertices just probed by the cop. We use multiple probes per turn for the cop to determine strategies to locate the robber in the Gr otzsch graph, the Petersen graph, and split graphs and conclude that it takes at most 3 turns to locate the robber in Gr otzsch graph and the Petersen graph. We also provide strategies to locate robber on different split graphs"