Author, as appears in the article.: Gispert-Fernandez, Adria; Rodriuez-Velazquez, Juan Alberto
Department: Enginyeria Informàtica i Matemàtiques
URV's Author/s: Rodríguez Velázquez, Juan Alberto
Keywords: Distance-equalizer Distances in graph Distances in graphs Equidistant dimension Lexicographic product Np-complete problem
Abstract: Let V ( G ) be the vertex set of a simple and connected graph G . A subset S subset of V ( G ) is a distance -equalizer set of G if, for every pair of vertices u , v E V ( G ) \ S , there exists a vertex in S that is equidistant to u and v . The minimum cardinality among the distance -equalizer sets of G is the equidistant dimension of G , denoted by xi ( G ). In this paper, we studied the problem of finding xi ( G o H ), where G o H denotes the lexicographic product of two graphs G and H . The aim was to express xi ( G o H ) in terms of parameters of G and H . In particular, we considered the cases in which G has a domination number equal to one, as well as the cases where G is a path or a cycle, among others. Furthermore, we showed that xi ( G )
Thematic Areas: General mathematics Mathematics Mathematics (all) Mathematics (miscellaneous) Mathematics, applied
licence for use: https://creativecommons.org/licenses/by/3.0/es/
Author's mail: juanalberto.rodriguez@urv.cat
Author identifier: 0000-0002-9082-7647
Record's date: 2024-10-26
Papper version: info:eu-repo/semantics/publishedVersion
Papper original source: Aims Mathematics. 9 (6): 15325-15345
APA: Gispert-Fernandez, Adria; Rodriuez-Velazquez, Juan Alberto (2024). The equidistant dimension of graphs: NP-completeness and the case of lexicographic product graphs. Aims Mathematics, 9(6), 15325-15345. DOI: 10.3934/math.2024744
Licence document URL: https://repositori.urv.cat/ca/proteccio-de-dades/
Entity: Universitat Rovira i Virgili
Journal publication year: 2024
Publication Type: Journal Publications
Repositori URV