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arXiv · 1207.5469

Resolving sets and semi-resolving sets in finite projective planes

Tamás Héger·Marcella Takáts
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Abstract

We show that the metric dimension of a finite projective plane of order $q\geq 23$ is $4q-4$, and describe all resolving sets of that size. Let $τ_2$ denote the size of the smallest double blocking set in $\mathrm{PG}(2,q)$, the Desarguesian projective plane of order $q$. We prove that for a semi-resolving set $S$ in the incidence graph of $\mathrm{PG}(2,q)$, $|S|\geq \min \{2q+q/4-3, τ_2-2\}$ holds. In particular, if $q\geq9$ is a square, then the smallest semi-resolving set in $\mathrm{PG}(2,q)$ has size $2q+2\sqrt{q}$.

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Tamás Héger, Marcella Takáts. 2017-01-30. Resolving sets and semi-resolving sets in finite projective planes. https://arxiv.org/abs/1207.5469

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