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Total Protection of Lexicographic Product Graphs

  • Identification data

    Identifier: imarina:7980012
  • Authors:

    Martínez AC
    Rodríguez-Velázquez JA
  • Others:

    Author, as appears in the article.: Martínez AC; Rodríguez-Velázquez JA
    Department: Enginyeria Informàtica i Matemàtiques
    URV's Author/s: CABRERA MARTÍNEZ, ABEL / Rodríguez Velázquez, Juan Alberto
    Keywords: Total weak roman domination Total domination Secure total domination Lexicographic product Italian domination total domination secure total domination roman lexicographic product
    Abstract: © (V1 â V2) such that the function f′, defined by f′(v) = 1, f′(u) = f(u)-1 and f′(x) = f(x) whenever x â V (G) \ {u, v}, is a total dominating function as well. If f is a total weak Roman dominating function and V2 = â, then we say that f is a secure total dominating function. The weight of a function f is defined to be ω(f) = ςvâV(G) f(v). The total weak Roman domination number (secure total domination number) of a graph G is the minimum weight among all total weak Roman dominating functions (secure total dominating functions) on G. In this article, we show that these two parameters coincide for lexicographic product graphs. Furthermore, we obtain closed formulae and tight bounds for these parameters in terms of invariants of the factor graphs involved in the product. Given a graph G with vertex set V (G), a function f: V (G) → {0, 1, 2} is said to be a total dominating function if ςuâN(v) f(u) > 0 for every v â V (G), where N(v) denotes the open neighbourhood of v. Let Vi = {x â V (G): F(x) = i}. A total dominating function f is a total weak Roman dominating function if for every vertex v â V0 there exists a vertex u â N(v) â.
    Thematic Areas: Mathematics Matemática / probabilidade e estatística Discrete mathematics and combinatorics Ciência da computação Applied 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: 2024-09-07
    Papper version: info:eu-repo/semantics/publishedVersion
    Link to the original source: https://www.dmgt.uz.zgora.pl/publish/bbl_view_press.php?ID=27108
    Licence document URL: https://repositori.urv.cat/ca/proteccio-de-dades/
    Papper original source: Discussiones Mathematicae Graph Theory. 42 (3): 967-984
    APA: Martínez AC; Rodríguez-Velázquez JA (2022). Total Protection of Lexicographic Product Graphs. Discussiones Mathematicae Graph Theory, 42(3), 967-984. DOI: 10.7151/dmgt.2318
    Article's DOI: 10.7151/dmgt.2318
    Entity: Universitat Rovira i Virgili
    Journal publication year: 2022
    Publication Type: Journal Publications
  • Keywords:

    Applied Mathematics,Discrete Mathematics and Combinatorics,Mathematics
    Total weak roman domination
    Total domination
    Secure total domination
    Lexicographic product
    Italian domination
    total domination
    secure total domination
    roman
    lexicographic product
    Mathematics
    Matemática / probabilidade e estatística
    Discrete mathematics and combinatorics
    Ciência da computação
    Applied mathematics
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