The problem is to determine the number of `cops’ needed to capture a `robber’ where the game is played with perfect information with the cops and the robber alternating moves. The `cops’ capture the `robber’ if one of them occupies the same vertex as the robber at any time in the game. Here we show that a graph with strong isometric dimension two requires no more than two cops.
Citation
Shannon L. Fitzpatrick, Richard J. Nowakowski. Copnumber of Graphs With Strong Isometric Dimension Two[J], Ars Combinatoria, Volume 059. 65-73. .