Autor según el artículo: Kuziak, D; Rodríguez-Velázquez, JA
Departamento: Enginyeria Informàtica i Matemàtiques
Autor/es de la URV: Rodríguez Velázquez, Juan Alberto
Palabras clave: Total mutual-visibility set Total mutual-visibility number Mutual-visibility Lexicographic product General position problem Cartesian product total mutual-visibility set mutual-visibility lexicographic product cartesian product
Resumen: Given a connected graph G, the total mutual-visibility number of G, denoted μt(G) , is the cardinality of a largest set S⊆ V(G) such that for every pair of vertices x, y∈ V(G) there is a shortest x, y-path whose interior vertices are not contained in S. Several combinatorial properties, including bounds and closed formulae, for μt(G) are given in this article. Specifically, we give several bounds for μt(G) in terms of the diameter, order and/or connected domination number of G and show characterizations of the graphs achieving the limit values of some of these bounds. We also consider those vertices of a graph G that either belong to every total mutual-visibility set of G or does not belong to any of such sets, and deduce some consequences of these results. We determine the exact value of the total mutual-visibility number of lexicographic products in terms of the orders of the factors, and the total mutual-visibility number of the first factor in the product. Finally, we give some bounds and closed formulae for the total mutual-visibility number of Cartesian product graphs.
Áreas temáticas: Mathematics (miscellaneous) Mathematics (all) Mathematics General mathematics
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: 2024-02-18
Versión del articulo depositado: info:eu-repo/semantics/publishedVersion
Enlace a la fuente original: https://link.springer.com/article/10.1007/s40840-023-01590-3
URL Documento de licencia: http://repositori.urv.cat/ca/proteccio-de-dades/
Referencia al articulo segun fuente origial: Bulletin Of The Malaysian Mathematical Sciences Society. 46 (6):
Referencia de l'ítem segons les normes APA: Kuziak, D; Rodríguez-Velázquez, JA (2023). Total Mutual-Visibility in Graphs with Emphasis on Lexicographic and Cartesian Products. Bulletin Of The Malaysian Mathematical Sciences Society, 46(6), -. DOI: 10.1007/s40840-023-01590-3
DOI del artículo: 10.1007/s40840-023-01590-3
Entidad: Universitat Rovira i Virgili
Año de publicación de la revista: 2023
Tipo de publicación: Journal Publications
Repositori URV