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Secure w-domination in graphs

  • Dades identificatives

    Identificador: imarina:9138920
    Autors:
    Cabrera Martinez, AbelEstrada-Moreno, AlejandroRodriguez-Velazquez, Juan A
    Resum:
    © 2020 by the authors. Licensee MDPI, Basel, Switzerland. This paper introduces a general approach to the idea of protection of graphs, which encompasses the known variants of secure domination and introduces new ones. Specifically, we introduce the study of secure w-domination in graphs, where w = (w0, w1, …, wl) is a vector of nonnegative integers such that w0 ≥ 1. The secure w-domination number is defined as follows. Let G be a graph and N(v) the open neighborhood of v ∈ V(G). We say that a function f: V(G) −→ {0, 1, …, l} is a w-dominating function if f (N(v)) = ∑u N(v) f (u) ≥ wi for every vertex v with f (v) = i. The weight of f is defined to be ω(f) = ∑v∈V(G) f (v). Given a w-dominating function f and any pair of adjacent vertices v, u V(G) with f (v) = 0 and f (u) > 0, the function fu→v is defined by fu→v (v) = 1, fu→v (u) = f (u) − 1 and fu→v (x) = f (x) for every x V(G) \ {u, v}. We say that a w-dominating function f is a secure w-dominating function if for every v with f (v) = 0, there exists u N(v) such that f (u) > 0 and fu→v is a w-dominating function as well. The secure w-domination number of G, denoted by γw(G),s is the minimum weight among all secure w-dominating functions. This paper provides fundamental results on γw(G)s and raises the challenge of conducting a detailed study of the topic.
  • Altres:

    Autor segons l'article: Cabrera Martinez, Abel; Estrada-Moreno, Alejandro; Rodriguez-Velazquez, Juan A
    Departament: Enginyeria Informàtica i Matemàtiques
    e-ISSN: 2073-8994
    Autor/s de la URV: CABRERA MARTÍNEZ, ABEL / Estrada Moreno, Alejandro / Rodríguez Velázquez, Juan Alberto
    Paraules clau: Weak roman domination W-domination Secure italian domination Secure domination
    Resum: © 2020 by the authors. Licensee MDPI, Basel, Switzerland. This paper introduces a general approach to the idea of protection of graphs, which encompasses the known variants of secure domination and introduces new ones. Specifically, we introduce the study of secure w-domination in graphs, where w = (w0, w1, …, wl) is a vector of nonnegative integers such that w0 ≥ 1. The secure w-domination number is defined as follows. Let G be a graph and N(v) the open neighborhood of v ∈ V(G). We say that a function f: V(G) −→ {0, 1, …, l} is a w-dominating function if f (N(v)) = ∑u N(v) f (u) ≥ wi for every vertex v with f (v) = i. The weight of f is defined to be ω(f) = ∑v∈V(G) f (v). Given a w-dominating function f and any pair of adjacent vertices v, u V(G) with f (v) = 0 and f (u) > 0, the function fu→v is defined by fu→v (v) = 1, fu→v (u) = f (u) − 1 and fu→v (x) = f (x) for every x V(G) \ {u, v}. We say that a w-dominating function f is a secure w-dominating function if for every v with f (v) = 0, there exists u N(v) such that f (u) > 0 and fu→v is a w-dominating function as well. The secure w-domination number of G, denoted by γw(G),s is the minimum weight among all secure w-dominating functions. This paper provides fundamental results on γw(G)s and raises the challenge of conducting a detailed study of the topic.
    Àrees temàtiques: 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
    Accès a la llicència d'ús: https://creativecommons.org/licenses/by/3.0/es/
    Adreça de correu electrònic de l'autor: alejandro.estrada@urv.cat juanalberto.rodriguez@urv.cat
    Identificador de l'autor: 0000-0001-9767-2177 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.mdpi.com/2073-8994/12/12/1948
    URL Document de llicència: https://repositori.urv.cat/ca/proteccio-de-dades/
    Referència a l'article segons font original: Symmetry-Basel. 12 (12): 1-11
    Referència de l'ítem segons les normes APA: Cabrera Martinez, Abel; Estrada-Moreno, Alejandro; Rodriguez-Velazquez, Juan A (2020). Secure w-domination in graphs. Symmetry-Basel, 12(12), 1-11. DOI: 10.3390/sym12121948
    DOI de l'article: 10.3390/sym12121948
    Entitat: Universitat Rovira i Virgili
    Any de publicació de la revista: 2020
    Tipus de publicació: Journal Publications
  • Paraules clau:

    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
    Weak roman domination
    W-domination
    Secure italian domination
    Secure domination
    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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