Metric dimension and metric independence number of incidence graphs of symmetric designs

摘要

Let D be a symmetric (v, k, lambda) design and Gamma 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 Gamma are v/k+1-lambda, which induces the lower or upper bounds on the metric dimension and metric independence number of Gamma. 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.

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