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From the quasi-total strong differential to quasi-total italian domination in graphs

  • Datos identificativos

    Identificador: imarina:9219146
    Autores:
    Cabrera Martinez, AbelEstrada-Moreno, AlejandroRodriguez-Velazquez, Juan Alberto
    Resumen:
    This paper is devoted to the study of the quasi-total strong differential of a graph, and it is a contribution to the Special Issue “Theoretical computer science and discrete mathematics” of Symmetry. Given a vertex x ∈ V(G) of a graph G, the neighbourhood of x is denoted by N(x). The neighbourhood of a set X ⊆ V(G) is defined to be N(X) =⋃ x∈X N(x), while the external neighbourhood of X is defined to be Ne (X) = N(X) \ X. Now, for every set X ⊆ V(G) and every vertex x ∈ X, the external private neighbourhood of x with respect to X is defined as the set Pe (x, X) = {y ∈ V(G) \ X: N(y) ∩ X = {x}}. Let Xw = {x ∈ X: Pe (x, X) ̸= ∅}. The strong differential of X is defined to be ∂s (X) = |Ne (X)| − |Xw |, while the quasi-total strong differential of G is defined to be ∂s ∗ (G) = max{∂s (X): X ⊆ V(G) and Xw ⊆ N(X)}. We show that the quasi-total strong differential is closely related to several graph parameters, including the domination number, the total domination number, the 2-domination number, the vertex cover number, the semitotal domination number, the strong differential, and the quasi-total Italian domination number. As a consequence of the study, we show that the problem of finding the quasi-total strong differential of a graph is NP-hard.
  • Otros:

    Autor según el artículo: Cabrera Martinez, Abel; Estrada-Moreno, Alejandro; Rodriguez-Velazquez, Juan Alberto
    Departamento: Enginyeria Informàtica i Matemàtiques
    Autor/es de la URV: CABRERA MARTÍNEZ, ABEL / Estrada Moreno, Alejandro / Rodríguez Velázquez, Juan Alberto
    Palabras clave: Strong differential Roman domination Quasi-total strong differential Quasi-total italian domination number Differentials in graphs strong differential quasi-total strong differential quasi-total italian domination number
    Resumen: This paper is devoted to the study of the quasi-total strong differential of a graph, and it is a contribution to the Special Issue “Theoretical computer science and discrete mathematics” of Symmetry. Given a vertex x ∈ V(G) of a graph G, the neighbourhood of x is denoted by N(x). The neighbourhood of a set X ⊆ V(G) is defined to be N(X) =⋃ x∈X N(x), while the external neighbourhood of X is defined to be Ne (X) = N(X) \ X. Now, for every set X ⊆ V(G) and every vertex x ∈ X, the external private neighbourhood of x with respect to X is defined as the set Pe (x, X) = {y ∈ V(G) \ X: N(y) ∩ X = {x}}. Let Xw = {x ∈ X: Pe (x, X) ̸= ∅}. The strong differential of X is defined to be ∂s (X) = |Ne (X)| − |Xw |, while the quasi-total strong differential of G is defined to be ∂s ∗ (G) = max{∂s (X): X ⊆ V(G) and Xw ⊆ N(X)}. We show that the quasi-total strong differential is closely related to several graph parameters, including the domination number, the total domination number, the 2-domination number, the vertex cover number, the semitotal domination number, the strong differential, and the quasi-total Italian domination number. As a consequence of the study, we show that the problem of finding the quasi-total strong differential of a graph is NP-hard.
    Áreas temáticas: Visual arts and performing arts Physics and astronomy (miscellaneous) Multidisciplinary sciences Modeling and simulation Mathematics, interdisciplinary applications Mathematics (miscellaneous) Mathematics (all) Matemática / probabilidade e estatística General mathematics Engineering (miscellaneous) Computer science (miscellaneous) Ciência da computação Chemistry (miscellaneous) Arts and humanities (miscellaneous) Architecture Applied mathematics
    Acceso a la licencia de uso: https://creativecommons.org/licenses/by/3.0/es/
    Direcció de correo del autor: alejandro.estrada@urv.cat juanalberto.rodriguez@urv.cat
    Identificador del autor: 0000-0001-9767-2177 0000-0002-9082-7647
    Fecha de alta del registro: 2024-10-26
    Versión del articulo depositado: info:eu-repo/semantics/publishedVersion
    Enlace a la fuente original: https://www.mdpi.com/2073-8994/13/6/1036
    URL Documento de licencia: https://repositori.urv.cat/ca/proteccio-de-dades/
    Referencia al articulo segun fuente origial: Symmetry-Basel. 13 (6): 1036-
    Referencia de l'ítem segons les normes APA: Cabrera Martinez, Abel; Estrada-Moreno, Alejandro; Rodriguez-Velazquez, Juan Alberto (2021). From the quasi-total strong differential to quasi-total italian domination in graphs. Symmetry-Basel, 13(6), 1036-. DOI: 10.3390/sym13061036
    DOI del artículo: 10.3390/sym13061036
    Entidad: Universitat Rovira i Virgili
    Año de publicación de la revista: 2021
    Tipo de publicación: Journal Publications
  • Palabras clave:

    Applied Mathematics,Architecture,Arts and Humanities (Miscellaneous),Chemistry (Miscellaneous),Computer Science (Miscellaneous),Engineering (Miscellaneous),Mathematics (Miscellaneous),Mathematics, Interdisciplinary Applications,Modeling and Simulation,Multidisciplinary Sciences,Physics and Astronomy (Miscellaneous),Visual Arts and Performi
    Strong differential
    Roman domination
    Quasi-total strong differential
    Quasi-total italian domination number
    Differentials in graphs
    strong differential
    quasi-total strong differential
    quasi-total italian domination number
    Visual arts and performing arts
    Physics and astronomy (miscellaneous)
    Multidisciplinary sciences
    Modeling and simulation
    Mathematics, interdisciplinary applications
    Mathematics (miscellaneous)
    Mathematics (all)
    Matemática / probabilidade e estatística
    General mathematics
    Engineering (miscellaneous)
    Computer science (miscellaneous)
    Ciência da computação
    Chemistry (miscellaneous)
    Arts and humanities (miscellaneous)
    Architecture
    Applied mathematics
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