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 back-circulant 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 $n+O\left(\frac{\log{n}}{\log{\log{n}}}\right)$ on the localization number of a latin square graph of order $n.$
翻译:我们调查了拉丁平方图上的各种追寻-回避参数,包括警察编号、公尺尺寸和地方化编号。 研究了拉丁方图的警号, 并给出了 $k$- MOLS$( n) 的警号。 如果$>( k+1) $2, 那么警号显示是 $+2. 美元 的下限和上限, 是 latin 平方图的公尺尺寸和本地化号 。 拉丁方图的内限值显示, 下限接近 。 最近关于拉丁方的覆盖值和部分转折结果提供了 $+O\left (\ frac\ log{ log_ log} right) 的上限值, 是 latin 方图的本地化号 $n。