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On the Roman domination number of generalized Sierpiński graphs

  • Dades identificatives

    Identificador: imarina:5132236
    Autors:
    Ramezani, FRodriguez-Bazan, E DRodriguez-Velazquez, J A
    Resum:
    A map f : V → {0, 1, 2} is a Roman dominating function on a graph G = (V, E) if for every vertex v ∈ V with f (v) = 0, there exists a vertex∑ u, adjacent to v, such that f (u) = 2. The weight of a Roman dominating function is given by f (V) =u∈V f (u). The minimum weight among all Roman dominating functions on G is called the Roman domination number of G. In this article we study the Roman domination number of Generalized Sierpiński graphs S(G, t). More precisely, we obtain a general upper bound on the Roman domination number of S(G, t) and discuss the tightness of this bound. In particular, we focus on the cases in which the base graph G is a path, a cycle, a complete graph or a graph having exactly one universal vertex.
  • Altres:

    Autor segons l'article: Ramezani, F; Rodriguez-Bazan, E D; Rodriguez-Velazquez, J A
    Departament: Enginyeria Informàtica i Matemàtiques
    Autor/s de la URV: Rodríguez Velázquez, Juan Alberto
    Paraules clau: Sierpiński graph Roman domination number Generalized sierpiński graph
    Resum: A map f : V → {0, 1, 2} is a Roman dominating function on a graph G = (V, E) if for every vertex v ∈ V with f (v) = 0, there exists a vertex∑ u, adjacent to v, such that f (u) = 2. The weight of a Roman dominating function is given by f (V) =u∈V f (u). The minimum weight among all Roman dominating functions on G is called the Roman domination number of G. In this article we study the Roman domination number of Generalized Sierpiński graphs S(G, t). More precisely, we obtain a general upper bound on the Roman domination number of S(G, t) and discuss the tightness of this bound. In particular, we focus on the cases in which the base graph G is a path, a cycle, a complete graph or a graph having exactly one universal vertex.
    Àrees temàtiques: Mathematics, applied Mathematics (miscellaneous) Mathematics (all) Mathematics General mathematics Engenharias iii Economia Ciências agrárias i
    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://journal.pmf.ni.ac.rs/filomat/index.php/filomat/article/view/4403
    URL Document de llicència: https://repositori.urv.cat/ca/proteccio-de-dades/
    Referència a l'article segons font original: Filomat. 31 (20): 6515-6528
    Referència de l'ítem segons les normes APA: Ramezani, F; Rodriguez-Bazan, E D; Rodriguez-Velazquez, J A (2017). On the Roman domination number of generalized Sierpiński graphs. Filomat, 31(20), 6515-6528. DOI: 10.2298/FIL1720515R
    DOI de l'article: 10.2298/FIL1720515R
    Entitat: Universitat Rovira i Virgili
    Any de publicació de la revista: 2017
    Tipus de publicació: Journal Publications
  • Paraules clau:

    Mathematics,Mathematics (Miscellaneous),Mathematics, Applied
    Sierpiński graph
    Roman domination number
    Generalized sierpiński graph
    Mathematics, applied
    Mathematics (miscellaneous)
    Mathematics (all)
    Mathematics
    General mathematics
    Engenharias iii
    Economia
    Ciências agrárias i
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