The game of Cops and Robber on circulant graphs

Abstract

We examine the game of Cops and Robber on circulant graphs, and determine the copnumbers of all circulant graphs of degree at most four. We then look at wreath products, and show how they can be used to determine the copnumbers for additional classes of circulant graphs. Finally, we show how expressing a circulant graph as a wreath product relates to dismantling that graph via corners and open corners.