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Total Protection of Lexicographic Product Graphs

  • Dades identificatives

    Identificador: imarina:7980012
    Autors:
    Cabrera Martinez, AbelAlberto Rodriguez-Velazquez, Juan
    Resum:
    © (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.
  • Altres:

    Autor segons l'article: Cabrera Martinez, Abel; Alberto Rodriguez-Velazquez, Juan
    Departament: Enginyeria Informàtica i Matemàtiques
    Autor/s de la URV: CABRERA MARTÍNEZ, ABEL / Rodríguez Velázquez, Juan Alberto
    Paraules clau: Total weak roman domination Total domination Secure total domination Lexicographic product Italian domination total domination secure total domination roman lexicographic product
    Resum: © (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.
    Àrees temàtiques: Mathematics Matemática / probabilidade e estatística Discrete mathematics and combinatorics Ciência da computação Applied 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: 2024-10-26
    Versió de l'article dipositat: info:eu-repo/semantics/publishedVersion
    Enllaç font original: https://www.dmgt.uz.zgora.pl/publish/bbl_view_press.php?ID=27108
    URL Document de llicència: https://repositori.urv.cat/ca/proteccio-de-dades/
    Referència a l'article segons font original: Discussiones Mathematicae Graph Theory. 42 (3): 967-984
    Referència de l'ítem segons les normes APA: Cabrera Martinez, Abel; Alberto Rodriguez-Velazquez, Juan (2022). Total Protection of Lexicographic Product Graphs. Discussiones Mathematicae Graph Theory, 42(3), 967-984. DOI: 10.7151/dmgt.2318
    DOI de l'article: 10.7151/dmgt.2318
    Entitat: Universitat Rovira i Virgili
    Any de publicació de la revista: 2022
    Tipus de publicació: Journal Publications
  • Paraules clau:

    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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