Articles producció científica> Enginyeria Informàtica i Matemàtiques

From Italian domination in lexicographic product graphs to w-domination in graphs

  • Identification data

    Identifier: imarina:9220190
    Authors:
    Cabrera Martinez, AbelEstrada-Moreno, AlejandroAlberto Rodriguez-Velazquez, Juan
    Abstract:
    In this paper, we show that the Italian domination number of every lexicographic product graph G o H can be expressed in terms of five different domination parameters of G. These parameters can be defined under the following unified approach, which encompasses the definition of several well-known domination parameters and introduces new ones. Let N(v) denote the open neighbourhood of v ∈ V (G), and let w = (w0,w1,⋯, wl) be a vector of nonnegative integers such that w0≥ 1. We say that a function f : V (G) → {0, 1,⋯, l} is a w-dominating function if f(N(v)) = Σu∈N(v)f(u) ≥ wifor every vertex v with f(v) = i. The weight of f is defined to be ω(f) = Σv∈V (G)f(v). The w-domination number of G, denoted by γw(G), is the minimum weight among all w-dominating functions on G. Specifically, we show that γI(G 0 H) = γw(G), where w ∈ {2} × {0, 1, 2}land l ∈ {2, 3}. The decision on whether the equality holds for specific values of w0,⋯, wlwill depend on the value of the domination number of H. This paper also provides preliminary results on γw(G) and raises the challenge of conducting a detailed study of the topic.
  • Others:

    Author, as appears in the article.: Cabrera Martinez, Abel; Estrada-Moreno, Alejandro; Alberto Rodriguez-Velazquez, Juan
    Department: Enginyeria Informàtica i Matemàtiques
    URV's Author/s: CABRERA MARTÍNEZ, ABEL / Estrada Moreno, Alejandro / Rodríguez Velázquez, Juan Alberto
    Keywords: W-domination Lexicographic product graph K-tuple domination K-domination Italian domination
    Abstract: In this paper, we show that the Italian domination number of every lexicographic product graph G o H can be expressed in terms of five different domination parameters of G. These parameters can be defined under the following unified approach, which encompasses the definition of several well-known domination parameters and introduces new ones. Let N(v) denote the open neighbourhood of v ∈ V (G), and let w = (w0,w1,⋯, wl) be a vector of nonnegative integers such that w0≥ 1. We say that a function f : V (G) → {0, 1,⋯, l} is a w-dominating function if f(N(v)) = Σu∈N(v)f(u) ≥ wifor every vertex v with f(v) = i. The weight of f is defined to be ω(f) = Σv∈V (G)f(v). The w-domination number of G, denoted by γw(G), is the minimum weight among all w-dominating functions on G. Specifically, we show that γI(G 0 H) = γw(G), where w ∈ {2} × {0, 1, 2}land l ∈ {2, 3}. The decision on whether the equality holds for specific values of w0,⋯, wlwill depend on the value of the domination number of H. This paper also provides preliminary results on γw(G) and raises the challenge of conducting a detailed study of the topic.
    Thematic Areas: Theoretical computer science Mathematics, applied Mathematics Matemática / probabilidade e estatística Geometry and topology Discrete mathematics and combinatorics Algebra and number theory
    licence for use: https://creativecommons.org/licenses/by/3.0/es/
    Author's mail: alejandro.estrada@urv.cat juanalberto.rodriguez@urv.cat
    Author identifier: 0000-0001-9767-2177 0000-0002-9082-7647
    Record's date: 2024-10-26
    Papper version: info:eu-repo/semantics/publishedVersion
    Link to the original source: https://amc-journal.eu/index.php/amc/article/view/2318
    Licence document URL: https://repositori.urv.cat/ca/proteccio-de-dades/
    Papper original source: Ars Mathematica Contemporanea. 22 (1):
    APA: Cabrera Martinez, Abel; Estrada-Moreno, Alejandro; Alberto Rodriguez-Velazquez, Juan (2022). From Italian domination in lexicographic product graphs to w-domination in graphs. Ars Mathematica Contemporanea, 22(1), -. DOI: 10.26493/1855-3974.2318.fb9
    Article's DOI: 10.26493/1855-3974.2318.fb9
    Entity: Universitat Rovira i Virgili
    Journal publication year: 2022
    Publication Type: Journal Publications
  • Keywords:

    Algebra and Number Theory,Discrete Mathematics and Combinatorics,Geometry and Topology,Mathematics,Mathematics, Applied,Theoretical Computer Science
    W-domination
    Lexicographic product graph
    K-tuple domination
    K-domination
    Italian domination
    Theoretical computer science
    Mathematics, applied
    Mathematics
    Matemática / probabilidade e estatística
    Geometry and topology
    Discrete mathematics and combinatorics
    Algebra and number theory
  • Documents:

  • Cerca a google

    Search to google scholar