Author, as appears in the article.: A. Estrada-Moreno, I.G. Yero, J.A. Rodríguez-Velázquez

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: 2023-09-30

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: http://repositori.urv.cat/ca/proteccio-de-dades/

Papper original source: 64 (5): 707-720

APA: A. Estrada-Moreno, I.G. Yero, J.A. Rodríguez-Velázquez (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