设计的本地化数量
The localization number of designs
摘要：
研究了设计关联图的局部化数。在图上玩的定位游戏中，警察试图通过距离探测器确定一个看不见的强盗的位置。图$G$的局部化数，写作$ζ(G)$，是确保抢劫者被捕获所需的最小警察数。给出了平衡不完全区组设计关联图局部化数的界。给出了射影平面和仿射平面的关联图的局部化数的精确值。给出了Steiner系统和横截设计的界。
英文摘要：
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 $ζ(G)$, 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.
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