We study the localization number of incidence graphs of designs. In the localization game played on a graph, the cops attempt to determine the location of an invisible robber via distance probes. The localization number of a graph $G$, written $\zeta(G)$, is the minimum number of cops needed to ensure the robber's capture. We present bounds on the localization number of incidence graphs of balanced incomplete block designs. Exact values of the localization number are given for the incidence graphs of projective and affine planes. Bounds are given for Steiner systems and for transversal designs.

中文翻译：

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设计本土化数量

我们研究了设计关联图的定位数。在图形上进行的定位游戏中，警察试图通过距离探测器确定一个隐形强盗的位置。图 $G$ 的定位数，写作 $\zeta(G)$，是确保劫匪被捕所需的最少警察数量。我们提出了平衡不完全块设计的关联图的定位数的界限。为投影和仿射平面的关联图给出了定位数的确切值。给出了 Steiner 系统和横向设计的界限。