Autor según el artículo: Alberto Rodriguez-Velazquez, Juan;
Departamento: Enginyeria Informàtica i Matemàtiques
Autor/es de la URV: Rodríguez Velázquez, Juan Alberto
Palabras clave: Universal lines Product graphs Metric spaces Lines in graphs Distance in graph
Resumen: In a metric space M = (X, d), a line induced by two distinct points x, x ' is an element of X, denoted by L-M{x, x'}, is the set of points given byL-M{x, x'} = {z is an element of X : d(x, x') = d(x, z) + d(z, x') or d(x, x') = |d(x, z) - d(z, x')|}.A line L-M{x, x'} gis universal whenever L-M{x, x'} = X.Chen and Chvatal [Disc. Appl. Math. 156 (2008), 2101-2108.] conjectured that in any finite metric space M = (X, d) either there is a universal line, or there are at least |X| different (nonuniversal) lines. A particular problem derived from this conjecture consists of investigating the properties of M that determine the existence of a universal line, and the problem remains interesting even if we can check that M has at least |X| different lines. Since the vertex set of any connected graph, equipped with the shortest path distance, is a metric space, the problem automatically becomes of interest in graph theory. In this paper, we address the problem of characterizing graphs that have universal lines. We consider several scenarios in which the study can be approached by analysing the existence of such lines in primary subgraphs. We first discuss the wide class of separable graphs, and then describe some particular cases, including those of block graphs, rooted product graphs and corona graphs. We also discuss important classes of nonseparable graphs, including Cartesian product graphs, join graphs and lexicographic product graphs.
Áreas temáticas: Mathematics (miscellaneous) Mathematics Matemática / probabilidade e estatística
Acceso a la licencia de uso: https://creativecommons.org/licenses/by/3.0/es/
Direcció de correo del autor: juanalberto.rodriguez@urv.cat
Identificador del autor: 0000-0002-9082-7647
Fecha de alta del registro: 2023-02-19
Versión del articulo depositado: info:eu-repo/semantics/acceptedVersion
Enlace a la fuente original: https://www.tandfonline.com/doi/abs/10.2989/16073606.2021.1950862
URL Documento de licencia: http://repositori.urv.cat/ca/proteccio-de-dades/
Referencia al articulo segun fuente origial: Quaestiones Mathematicae. 45 (10): 1485-1500
Referencia de l'ítem segons les normes APA: Alberto Rodriguez-Velazquez, Juan; (2022). UNIVERSAL LINES IN GRAPHS. Quaestiones Mathematicae, 45(10), 1485-1500. DOI: 10.2989/16073606.2021.1950862
DOI del artículo: 10.2989/16073606.2021.1950862
Entidad: Universitat Rovira i Virgili
Año de publicación de la revista: 2022
Tipo de publicación: Journal Publications
Repositori URV