Pursuit-evasion games on latin square graphs

Abstract

We investigate various pursuit-evasion parameters on latin square graphs, including the cop number, metric dimension, and localization number. The cop number of latin square graphs is studied, and for k-MOLS(n), bounds for the cop number are given. If n > (k + 1) 2 , then the cop number is shown to be k + 2. Lower and upper bounds are provided for the metric dimension and localization number of latin square graphs. The metric dimension of backcirculant latin squares shows that the lower bound is close to tight. Recent results on covers and partial transversals of latin squares provide the upper bound of n + O log n log log n on the localization number of a latin square graph of order n.