The metric dimension of two-dimensional extended meshes
We consider two-dimensional grids with diagonals, also called extended meshes or meshes. Such a graph consists of vertices of the form (i, j) for 1 ≤ i ≤ m and 1 ≤ j ≤ n, for given m, n ≥ 2. Two vertices are defined to be adjacent if the `∞ distance between their vectors is equal to 1. A landmark se...
Elmentve itt :
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| Dokumentumtípus: | Cikk |
| Megjelent: |
2018
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| Sorozat: | Acta cybernetica
23 No. 3 |
| Kulcsszavak: | Matematika, Metrikus dimenzió |
| Tárgyszavak: | |
| Online Access: | http://acta.bibl.u-szeged.hu/55675 |
| Tartalmi kivonat: | We consider two-dimensional grids with diagonals, also called extended meshes or meshes. Such a graph consists of vertices of the form (i, j) for 1 ≤ i ≤ m and 1 ≤ j ≤ n, for given m, n ≥ 2. Two vertices are defined to be adjacent if the `∞ distance between their vectors is equal to 1. A landmark set is a subset of vertices L ⊆ V , such that for any distinct pair of vertices u, v ∈ V , there exists a vertex of L with different distances to u and v. We analyze the metric dimension and show how to obtain a landmark set of minimum cardinality. |
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| Terjedelem/Fizikai jellemzők: | 761-772 |
| ISSN: | 0324-721X |