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In this paper the metric dimension of (the incidence graphs of) particular partial linear spaces is considered. We prove that the metric dimension of an affine plane of order $q\geq13$ is $3q-4$ and describe all resolving sets of that size if $q\geq
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::36a959ab117d032c65269d0d815b633e
http://arxiv.org/abs/1706.06583
http://arxiv.org/abs/1706.06583
Autor:
H��ger, Tam��s, Nagy, Zolt��n L��r��nt
Publikováno v:
J COMB DES JOURNAL OF COMBINATORIAL DESIGNS.
We describe small dominating sets of the incidence graphs of finite projective planes by establishing a stability result which shows that dominating sets are strongly related to blocking and covering sets. Our main result states that if a dominating
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::7ddab9a03073badc3b2e0abd9b8cae78
http://hdl.handle.net/10831/48894
http://hdl.handle.net/10831/48894
A $t$-semiarc is a pointset ${\cal S}_t$ with the property that the number of tangent lines to ${\cal S}_t$ at each of its points is $t$. We show that if a small $t$-semiarc ${\cal S}_t$ in $\mathrm{PG}(2,q)$ has a large collinear subset ${\cal K}$,
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::557e604ee81cdcd5219ff2e383c003a2
http://arxiv.org/abs/1310.7207
http://arxiv.org/abs/1310.7207