Pursuit-evasion games on latin square graphs

09/29/2021

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by   Shreya Ahirwar, et al.

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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(logn/loglogn) on the localization number of a latin square graph of order n.