The metric dimension of two-dimensional extended meshes

Ron Adar, Leah Epstein

Research output: Contribution to journalArticlepeer-review


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 ℓ∞ 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.

Original languageEnglish
Pages (from-to)761-772
Number of pages12
JournalActa Cybernetica
Issue number3
StatePublished - 2018

Bibliographical note

Publisher Copyright:
Copyright © 2018 Institute of Informatics, University of Szeged. All rights reserved.


  • Grid graph
  • Landmark set
  • Mesh graph
  • Metric dimension
  • Resolving set

ASJC Scopus subject areas

  • Software
  • Computer Science (miscellaneous)
  • Computer Vision and Pattern Recognition
  • Management Science and Operations Research
  • Information Systems and Management
  • Electrical and Electronic Engineering


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