Author, as appears in the article.: Barragan-Ramirez, Gabriel A; Estrada-Moreno, Alejandro; Ramirez-Cruz, Yunior; Rodriguez-Velazquez, Juan A
Department: Enginyeria Informàtica i Matemàtiques
e-ISSN: 2073-8994
URV's Author/s: Estrada Moreno, Alejandro / Rodríguez Velázquez, Juan Alberto
Keywords: Simultaneity Local metric dimension Lexicographic product Corona product Complexity
Abstract: In a graph G = (V, E), a vertex v ¿ V is said to distinguish two vertices x and y if dG(v, x) ¿ dG(v, y). A set S ¿ V is said to be a local metric generator for G if any pair of adjacent vertices of G is distinguished by some element of S. A minimum local metric generator is called a local metric basis and its cardinality the local metric dimension of G. A set S ¿ V is said to be a simultaneous local metric generator for a graph family G = (G1, G2, . . . , Gk), defined on a common vertex set, if it is a local metric generator for every graph of the family. A minimum simultaneous local metric generator is called a simultaneous local metric basis and its cardinality the simultaneous local metric dimension of G. We study the properties of simultaneous local metric generators and bases, obtain closed formulae or tight bounds for the simultaneous local metric dimension of several graph families and analyze the complexity of computing this parameter.
Thematic Areas: Visual arts and performing arts Physics and astronomy (miscellaneous) Multidisciplinary sciences Modeling and simulation Mathematics, interdisciplinary applications Mathematics (miscellaneous) Mathematics (all) Matemática / probabilidade e estatística General mathematics Engineering (miscellaneous) Computer science (miscellaneous) Ciência da computação Chemistry (miscellaneous) Arts and humanities (miscellaneous) Architecture Applied mathematics
licence for use: https://creativecommons.org/licenses/by/3.0/es/
ISSN: 20738994
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
Journal volume: 9
Papper version: info:eu-repo/semantics/publishedVersion
Link to the original source: https://www.mdpi.com/2073-8994/9/8/132
Licence document URL: https://repositori.urv.cat/ca/proteccio-de-dades/
Papper original source: Symmetry-Basel. 9 (8): 132-
APA: Barragan-Ramirez, Gabriel A; Estrada-Moreno, Alejandro; Ramirez-Cruz, Yunior; Rodriguez-Velazquez, Juan A (2017). The simultaneous local metric dimension of graph families. Symmetry-Basel, 9(8), 132-. DOI: 10.3390/sym9080132
Article's DOI: 10.3390/sym9080132
Entity: Universitat Rovira i Virgili
Journal publication year: 2017
Publication Type: Journal Publications
Repositori URV