Author, as appears in the article.: Estrada-Moren, A; Yero, I G; Rodriguez-Velazquez, J A
Department: Enginyeria Informàtica i Matemàtiques
e-ISSN: 1460-2067
URV's Author/s: Estrada Moreno, Alejandro / Rodríguez Velázquez, Juan Alberto
Keywords: Strong metric dimension Positive integers Nondeterministic polynomial time Metric spaces Metric space Metric dimensions Metric dimension K-metric dimension K-adjacency dimension K points Graph theory Graph g Geodesic distances Connected graph nondeterministic polynomial time metric space lexicographic product k-metric dimension k-adjacency dimension corona
Abstract: Let (X; d) be a metric space. A set S X is said to be a k-metric generator for X if and only if for any pair of dierent points u; v 2 X, there exist at least k points w1;w2; : : :wk 2 S such that d(u;wi) 6= d(v;wi); for all i 2 f1; : : : kg: Let Rk(X) be the set of metric generators for X. The k-metric dimension dimk(X) of (X; d) is dened as dimk(X) = inffjSj : S 2 Rk(X)g: Here, we discuss the k-metric dimension of (V; dt), where V is the set of vertices of a simple graph G and the metric dt : V V ! N [ f0g is dened by dt(x; y) = minfd(x; y); tg from the geodesic distance d in G and a positive integer t. The case t D(G), where D(G) denotes the diameter of G, corresponds to the original theory of k-metric dimension and the case t = 2 corresponds to the theory of k- adjacency dimension. Furthermore, this approach allows us to extend the theory of k-metric dimension to the general case of non-necessarily connected graphs. Finally, we analyse the computational complexity of determining the k-metric dimension of (V; dt) for the metric dt.
licence for use: https://creativecommons.org/licenses/by/3.0/es/
ISSN: 0010-4620
Author's mail: alejandro.estrada@urv.cat juanalberto.rodriguez@urv.cat
Author identifier: 0000-0001-9767-2177 0000-0002-9082-7647
Record's date: 2024-10-26
Papper version: info:eu-repo/semantics/submittedVersion
Link to the original source: https://academic.oup.com/comjnl/advance-article-abstract/doi/10.1093/comjnl/bxaa009/5808798?redirectedFrom=fulltext
Licence document URL: https://repositori.urv.cat/ca/proteccio-de-dades/
Papper original source: The Computer Journal. 64 (5): 707-720
APA: Estrada-Moren, A; Yero, I G; Rodriguez-Velazquez, J A (2021). On The (k,t)-Metric Dimension Of Graphs. The Computer Journal, 64(5), 707-720. DOI: 10.1093/comjnl/bxaa009
Article's DOI: 10.1093/comjnl/bxaa009
Entity: Universitat Rovira i Virgili
Journal publication year: 2021
Publication Type: Journal Publications
Repositori URV