Author, as appears in the article.: Yero, Ismael G.; Estrada-Moreno, Alejandro; Rodriguez-Velazquez, Juan A.;
Department: Enginyeria Informàtica i Matemàtiques
URV's Author/s: Estrada Moreno, Alejandro / Rodríguez Velázquez, Juan Alberto
Keywords: Product Np-hard problem Np-complete problem Metric dimension Landmarks K-metric dimensional graph K-metric dimension Graph algorithms
Abstract: Given a connected graph G = (V, E), a set S subset of V is a k-metric generator for G if for any two different vertices u, v is an element of V, there exist at least k vertices w(1), ... ,W-k is an element of S such that d(G)(u, w(i)) not equal d(G) (v, w(i)) for every i is an element of {1, ... , k}. A metric generator of minimum cardinality is called a k-metric basis and its cardinality the k-metric dimension of G. We make a study concerning the complexity of some k-metric dimension problems. For instance, we show that the problem of computing the k-metric dimension of graphs is NP-hard. However, the problem is solved in linear time for the particular case of trees. (C) 2016 Elsevier Inc. All rights reserved.
Thematic Areas: Saúde coletiva Química Nutrição Medicina iii Medicina ii Mathematics, applied Materiais Matemática / probabilidade e estatística Interdisciplinar Geociências Filosofia/teologia:subcomissão filosofia Ensino Engenharias iv Engenharias iii Engenharias ii Engenharias i Computational mathematics Ciências biológicas iii Ciências biológicas ii Ciências ambientais Ciências agrárias i Ciência da computação Biodiversidade Astronomia / física Arquitetura, urbanismo e design Applied mathematics
licence for use: https://creativecommons.org/licenses/by/3.0/es/
Author's mail: alejandro.estrada@urv.cat juanalberto.rodriguez@urv.cat
Author identifier: 0000-0001-9767-2177 0000-0002-9082-7647
Record's date: 2023-04-29
Papper version: info:eu-repo/semantics/acceptedVersion
Link to the original source: https://www.sciencedirect.com/science/article/abs/pii/S0096300316307317
Papper original source: Applied Mathematics And Computation. 300 60-69
APA: Yero, Ismael G.; Estrada-Moreno, Alejandro; Rodriguez-Velazquez, Juan A.; (2017). Computing the k-metric dimension of graphs. Applied Mathematics And Computation, 300(), 60-69. DOI: 10.1016/j.amc.2016.12.005
Licence document URL: http://repositori.urv.cat/ca/proteccio-de-dades/
Article's DOI: 10.1016/j.amc.2016.12.005
Entity: Universitat Rovira i Virgili
Journal publication year: 2017
Publication Type: Journal Publications
Repositori URV