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Total Roman Domination Number of Rooted Product Graphs

  • Dades identificatives

    Identificador: imarina:9048284
    Autors:
    Cabrera Martinez, AbelCabrera Garcia, SuitbertoCarrion Garcia, AndresHernandez Mira, Frank A.
    Resum:
    Let G be a graph with no isolated vertex and f:V(G)->{0,1,2} a function. If f satisfies that every vertex in the set {v is an element of V(G):f(v)=0} is adjacent to at least one vertex in the set {v is an element of V(G):f(v)=2}, and if the subgraph induced by the set {v is an element of V(G):f(v)>= 1} has no isolated vertex, then we say that f is a total Roman dominating function on G. The minimum weight omega(f)= n-ary sumation v is an element of V(G)f(v) among all total Roman dominating functions f on G is the total Roman domination number of G. In this article we study this parameter for the rooted product graphs. Specifically, we obtain closed formulas and tight bounds for the total Roman domination number of rooted product graphs in terms of domination invariants of the factor graphs involved in this product.
  • Altres:

    Autor segons l'article: Cabrera Martinez, Abel; Cabrera Garcia, Suitberto; Carrion Garcia, Andres; Hernandez Mira, Frank A.;
    Departament: Enginyeria Informàtica i Matemàtiques
    Autor/s de la URV: CABRERA MARTÍNEZ, ABEL
    Paraules clau: Total roman domination Total domination Rooted product graph
    Resum: Let G be a graph with no isolated vertex and f:V(G)->{0,1,2} a function. If f satisfies that every vertex in the set {v is an element of V(G):f(v)=0} is adjacent to at least one vertex in the set {v is an element of V(G):f(v)=2}, and if the subgraph induced by the set {v is an element of V(G):f(v)>= 1} has no isolated vertex, then we say that f is a total Roman dominating function on G. The minimum weight omega(f)= n-ary sumation v is an element of V(G)f(v) among all total Roman dominating functions f on G is the total Roman domination number of G. In this article we study this parameter for the rooted product graphs. Specifically, we obtain closed formulas and tight bounds for the total Roman domination number of rooted product graphs in terms of domination invariants of the factor graphs involved in this product.
    Àrees temàtiques: Química Mathematics (miscellaneous) Mathematics General mathematics Astronomia / física
    Accès a la llicència d'ús: https://creativecommons.org/licenses/by/3.0/es/
    Adreça de correu electrònic de l'autor: abel.cabrera@urv.cat
    Identificador de l'autor: 0000-0003-2806-4842
    Data d'alta del registre: 2021-10-10
    Versió de l'article dipositat: info:eu-repo/semantics/publishedVersion
    Enllaç font original: https://www.mdpi.com/2227-7390/8/10/1850
    Referència a l'article segons font original: Mathematics. 8 (10): 1-13
    Referència de l'ítem segons les normes APA: Cabrera Martinez, Abel; Cabrera Garcia, Suitberto; Carrion Garcia, Andres; Hernandez Mira, Frank A.; (2020). Total Roman Domination Number of Rooted Product Graphs. Mathematics, 8(10), 1-13. DOI: 10.3390/math8101850
    URL Document de llicència: https://repositori.urv.cat/ca/proteccio-de-dades/
    DOI de l'article: 10.3390/math8101850
    Entitat: Universitat Rovira i Virgili
    Any de publicació de la revista: 2020
    Tipus de publicació: Journal Publications
  • Paraules clau:

    Mathematics,Mathematics (Miscellaneous)
    Total roman domination
    Total domination
    Rooted product graph
    Química
    Mathematics (miscellaneous)
    Mathematics
    General mathematics
    Astronomia / física
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