Resolving sets and semi-resolving sets in finite projective planes
| Autor: | Héger, Tamás, Takáts, Marcella |
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| Rok vydání: | 2012 |
| Předmět: | |
| Zdroj: | Electronic Journal of Combinatorics, Volume 19, Issue 4 (2012) |
| Druh dokumentu: | Working Paper |
| Popis: | 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 $\tau_2$ 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 $\mathrm{PG}(2,q)$, $|S|\geq \min \{2q+q/4-3, \tau_2-2\}$ holds. In particular, if $q\geq9$ is a square, then the smallest semi-resolving set in $\mathrm{PG}(2,q)$ has size $2q+2\sqrt{q}$. Comment: 21 pages, 3 figures. Version 3 contains clarifications and minor corrections regarding the list and the figure of the 32 types of smallest resolving sets, and a supplementary page explaining these modifications |
| Databáze: | arXiv |
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