Abstract Let D be a symmetric ( v , k , λ ) design and Γ be its incidence graph. This paper focuses on the metric dimension and metric independence number of the incidence graphs of symmetric designs, along with their fractional versions. It proves that both the fractional metric dimension and the fractional metric independence number of Γ are v k + 1 − λ , which induces the lower or upper bounds on the metric dimension and metric independence number of Γ . In particular, it determines the metric dimension number or metric independence number, and their basis, of finite projective planes, finite biplanes, and trivial symmetric designs.

中文翻译：

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对称设计的关联图的度量维数和度量独立数

摘要 设 D 为对称 ( v , k , λ ) 设计，Γ 为其关联图。本文重点介绍对称设计的关联图的度量维数和度量独立数，以及它们的分数版本。证明了Γ的分数阶度量维数和分数度量独立数都是vk + 1 − λ ，由此推导出Γ 的度量维数和度量独立数的下界或上限。特别是，它确定了有限射影平面、有限双平面和平凡对称设计的度量维数或度量独立数及其基础。