Autor segons l'article: Kuziak, D; Rodríguez-Velázquez, JA
Departament: Enginyeria Informàtica i Matemàtiques
Autor/s de la URV: Rodríguez Velázquez, Juan Alberto
Paraules clau: 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
Resum: 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.
Àrees temàtiques: Mathematics (miscellaneous) Mathematics (all) Mathematics General mathematics
Accès a la llicència d'ús: https://creativecommons.org/licenses/by/3.0/es/
Adreça de correu electrònic de l'autor: juanalberto.rodriguez@urv.cat
Identificador de l'autor: 0000-0002-9082-7647
Data d'alta del registre: 2024-02-18
Versió de l'article dipositat: info:eu-repo/semantics/publishedVersion
Enllaç font original: https://link.springer.com/article/10.1007/s40840-023-01590-3
URL Document de llicència: http://repositori.urv.cat/ca/proteccio-de-dades/
Referència a l'article segons font original: Bulletin Of The Malaysian Mathematical Sciences Society. 46 (6):
Referència 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 de l'article: 10.1007/s40840-023-01590-3
Entitat: Universitat Rovira i Virgili
Any de publicació de la revista: 2023
Tipus de publicació: Journal Publications
Repositori URV