Articles producció científica> Enginyeria Informàtica i Matemàtiques

Total Weak Roman Domination in Graphs

  • Dades identificatives

    Identificador: imarina:5745867
    Autors:
    Cabrera Martinez, AbelMontejano, Luis PRodriguez-Velazquez, Juan A
    Resum:
    Given a graph G=(V,E) , a function f:V→{0,1,2,⋯} is said to be a total dominating function if ∑u∈N(v)f(u)>0 for every v∈V , where N(v) denotes the open neighbourhood of v. Let Vi={x∈V:f(x)=i} . We say that a function f:V→{0,1,2} is a total weak Roman dominating function if f is a total dominating function and for every vertex v∈V0 there exists u∈N(v)∩(V1∪V2) such that the function f′ , defined by f′(v)=1 , f′(u)=f(u)−1 and f′(x)=f(x) whenever x∈V\{u,v} , is a total dominating function as well. The weight of a function f is defined to be w(f)=∑v∈Vf(v). In this article, we introduce the study of the total weak Roman domination number of a graph G, denoted by γtr(G) , which is defined to be the minimum weight among all total weak Roman dominating functions on G. We show the close relationship that exists between this novel parameter and other domination parameters of a graph. Furthermore, we obtain general bounds on γtr(G) and, for some particular families of graphs, we obtain closed formulae. Finally, we show that the problem of computing the total weak Roman domination number of a graph is NP-hard.
  • Altres:

    Autor segons l'article: Cabrera Martinez, Abel; Montejano, Luis P; Rodriguez-Velazquez, Juan A
    Departament: Enginyeria Informàtica i Matemàtiques
    e-ISSN: 2073-8994
    Autor/s de la URV: CABRERA MARTÍNEZ, ABEL / Montejano Cantoral, Luis Pedro / Rodríguez Velázquez, Juan Alberto
    Paraules clau: Weak roman domination Total roman domination Total domination Secure total domination Np-hard problem
    Resum: Given a graph G=(V,E) , a function f:V→{0,1,2,⋯} is said to be a total dominating function if ∑u∈N(v)f(u)>0 for every v∈V , where N(v) denotes the open neighbourhood of v. Let Vi={x∈V:f(x)=i} . We say that a function f:V→{0,1,2} is a total weak Roman dominating function if f is a total dominating function and for every vertex v∈V0 there exists u∈N(v)∩(V1∪V2) such that the function f′ , defined by f′(v)=1 , f′(u)=f(u)−1 and f′(x)=f(x) whenever x∈V\{u,v} , is a total dominating function as well. The weight of a function f is defined to be w(f)=∑v∈Vf(v). In this article, we introduce the study of the total weak Roman domination number of a graph G, denoted by γtr(G) , which is defined to be the minimum weight among all total weak Roman dominating functions on G. We show the close relationship that exists between this novel parameter and other domination parameters of a graph. Furthermore, we obtain general bounds on γtr(G) and, for some particular families of graphs, we obtain closed formulae. Finally, we show that the problem of computing the total weak Roman domination number of a graph is NP-hard.
    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: thttps://creativecommons.org/licenses/by/3.0/es/
    ISSN: 20738994
    Adreça de correu electrònic de l'autor: luispedro.montejano@urv.cat juanalberto.rodriguez@urv.cat
    Identificador de l'autor: 0000-0002-9082-7647
    Data d'alta del registre: 2024-10-26
    Volum de revista: 11
    Versió de l'article dipositat: info:eu-repo/semantics/publishedVersion
    Enllaç font original: https://www.mdpi.com/2073-8994/11/6/831
    URL Document de llicència: https://repositori.urv.cat/ca/proteccio-de-dades/
    Referència a l'article segons font original: Symmetry-Basel. 11 (6): 831-
    Referència de l'ítem segons les normes APA: Cabrera Martinez, Abel; Montejano, Luis P; Rodriguez-Velazquez, Juan A (2019). Total Weak Roman Domination in Graphs. Symmetry-Basel, 11(6), 831-. DOI: 10.3390/sym11060831
    DOI de l'article: 10.3390/sym11060831
    Entitat: Universitat Rovira i Virgili
    Any de publicació de la revista: 2019
    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
    Total roman domination
    Total domination
    Secure total domination
    Np-hard problem
    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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