Author, as appears in the article.: Barragán-Ramírez G, Estrada-Moreno A, Ramírez-Cruz Y, Rodríguez-Velázquez J

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: 2023-07-31

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

Papper original source: Symmetry-Basel. 9 (8):

APA: Barragán-Ramírez G, Estrada-Moreno A, Ramírez-Cruz Y, Rodríguez-Velázquez J (2017). The simultaneous local metric dimension of graph families. Symmetry-Basel, 9(8), -. DOI: 10.3390/sym9080132

Article's DOI: 10.3390/sym9080132

Entity: Universitat Rovira i Virgili

Journal publication year: 2017

Publication Type: Journal Publications