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Total Mutual-Visibility in Graphs with Emphasis on Lexicographic and Cartesian Products

  • Identification data

    Identifier: imarina:9331242
  • Authors:

    Kuziak, D
    Rodríguez-Velázquez, JA
    Bulletin Of The Malaysian Mathematical Sciences Society
    10.1007/s40840-023-01590-3
    Bulletin Of The Malaysian Mathematical Sciences Society. 46 (6):
  • Others:

    Author, as appears in the article.: Kuziak, D; Rodríguez-Velázquez, JA
    Department: Enginyeria Informàtica i Matemàtiques
    URV's Author/s: Rodríguez Velázquez, Juan Alberto
    Keywords: 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
    Abstract: 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.
    Thematic Areas: Mathematics (miscellaneous) Mathematics (all) Mathematics General mathematics
    licence for use: https://creativecommons.org/licenses/by/3.0/es/
    Author's mail: juanalberto.rodriguez@urv.cat
    Author identifier: 0000-0002-9082-7647
    Record's date: 2024-07-20
    Papper version: info:eu-repo/semantics/publishedVersion
    Link to the original source: https://link.springer.com/article/10.1007/s40840-023-01590-3
    Licence document URL: http://repositori.urv.cat/ca/proteccio-de-dades/
    Papper original source: Bulletin Of The Malaysian Mathematical Sciences Society. 46 (6):
    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
    Article's DOI: 10.1007/s40840-023-01590-3
    Entity: Universitat Rovira i Virgili
    Journal publication year: 2023
    Publication Type: Journal Publications
  • Keywords:

    Mathematics,Mathematics (Miscellaneous)
    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
    Mathematics (miscellaneous)
    Mathematics (all)
    Mathematics
    General mathematics
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