Adar Ron and Epstein Leah:
*The metric dimension of two-dimensional extended meshes.*
In: Acta cybernetica, (23) 3.
pp. 761-772. (2018)

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## Abstract

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.

Item Type: | Article |
---|---|

Journal or Publication Title: | Acta cybernetica |

Date: | 2018 |

Volume: | 23 |

Number: | 3 |

ISSN: | 0324-721X |

Page Range: | pp. 761-772 |

Language: | English |

Place of Publication: | Szeged |

Related URLs: | http://acta.bibl.u-szeged.hu/55467/ |

Uncontrolled Keywords: | Matematika, Metrikus dimenzió |

Additional Information: | Bibliogr.: p. 771-772. ; összefoglalás angol nyelven |

Subjects: | 01. Natural sciences 01. Natural sciences > 01.01. Mathematics 01. Natural sciences > 01.02. Computer and information sciences |

Date Deposited: | 2018. Nov. 07. 14:47 |

Last Modified: | 2022. Jun. 20. 15:53 |

URI: | http://acta.bibl.u-szeged.hu/id/eprint/55675 |

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