Lazy Cops and Robber on Certain Cayley Graph

Abstract

The lazy cop number is the minimum number of cops needed for the cops to have a winning strategy in the game of Cops and Robber where at most one cop may move in any one round. This variant of the game of Cops and Robber, called Lazy Cops and Robber, was introduced by Offner and Ojakian, who provided bounds for the lazy cop number of hypercubes. In this paper, we are interested in the game of Lazy Cops and Robber on a Cayley graph of n copies of Zm+1.