论文标题
设计的本地化数量
The localization number of designs
论文作者
论文摘要
我们研究了设计的发射率图的定位次数。在图表上播放的本地化游戏中，警察试图通过距离探针确定无形强盗的位置。图$ g $的本地化数字，书面$ζ（g）$是确保强盗俘虏所需的最小警察数量。我们介绍了平衡不完整块设计的发射率图的本地化数量。给出了针对投影和仿射平面的发射率图的确切值。为Steiner系统和横向设计提供了界限。
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.
