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 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 language | English |
|---|---|
| Pages (from-to) | 761-772 |
| Number of pages | 12 |
| Journal | Acta Cybernetica |
| Volume | 23 |
| Issue number | 3 |
| DOIs | |
| State | Published - 2018 |
Bibliographical note
Publisher Copyright:Copyright © 2018 Institute of Informatics, University of Szeged. All rights reserved.
Keywords
- 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