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Dominating the direct product of two graphs through total Roman strategies

  • Datos identificativos

    Identificador: imarina:8505358
    Autores:
    Cabrera AKuziak DPeterin IYero IG
    Resumen:
    © 2020 by the authors. Given a graph G without isolated vertices, a total Roman dominating function for G is a function f: V(G) → [0, 1, 2] such that every vertex u with f (u) = 0 is adjacent to a vertex v with f (v) = 2, and the set of vertices with positive labels induces a graph of minimum degree at least one. The total Roman domination number γtR(G) of G is the smallest possible value of ΣvεV(G) f (v) among all total Roman dominating functions f . The total Roman domination number of the direct product G× H of the graphs G and H is studied in this work. Specifically, several relationships, in the shape of upper and lower bounds, between γtR(G× H) and some classical domination parameters for the factors are given. Characterizations of the direct product graphs G× H achieving small values (≤ 7) for γtR(G× H) are presented, and exact values for γtR(G× H) are deduced, while considering various specific direct product classes.
  • Otros:

    Autor según el artículo: Cabrera A; Kuziak D; Peterin I; Yero IG
    Departamento: Enginyeria Informàtica i Matemàtiques
    Autor/es de la URV: CABRERA MARTÍNEZ, ABEL
    Palabras clave: Total roman domination Roman domination Number Direct product graphs msc: 05c69 Direct product graphs 05c76
    Resumen: © 2020 by the authors. Given a graph G without isolated vertices, a total Roman dominating function for G is a function f: V(G) → [0, 1, 2] such that every vertex u with f (u) = 0 is adjacent to a vertex v with f (v) = 2, and the set of vertices with positive labels induces a graph of minimum degree at least one. The total Roman domination number γtR(G) of G is the smallest possible value of ΣvεV(G) f (v) among all total Roman dominating functions f . The total Roman domination number of the direct product G× H of the graphs G and H is studied in this work. Specifically, several relationships, in the shape of upper and lower bounds, between γtR(G× H) and some classical domination parameters for the factors are given. Characterizations of the direct product graphs G× H achieving small values (≤ 7) for γtR(G× H) are presented, and exact values for γtR(G× H) are deduced, while considering various specific direct product classes.
    Áreas temáticas: Química Mathematics (miscellaneous) Mathematics General mathematics Astronomia / física
    Acceso a la licencia de uso: https://creativecommons.org/licenses/by/3.0/es/
    Direcció de correo del autor: abel.cabrera@urv.cat
    Identificador del autor: 0000-0003-2806-4842
    Fecha de alta del registro: 2021-10-10
    Versión del articulo depositado: info:eu-repo/semantics/publishedVersion
    Enlace a la fuente original: https://www.mdpi.com/2227-7390/8/9/1438
    Referencia al articulo segun fuente origial: Mathematics. 8 (9):
    Referencia de l'ítem segons les normes APA: Cabrera A; Kuziak D; Peterin I; Yero IG (2020). Dominating the direct product of two graphs through total Roman strategies. Mathematics, 8(9), -. DOI: 10.3390/MATH8091438
    URL Documento de licencia: https://repositori.urv.cat/ca/proteccio-de-dades/
    DOI del artículo: 10.3390/MATH8091438
    Entidad: Universitat Rovira i Virgili
    Año de publicación de la revista: 2020
    Tipo de publicación: Journal Publications
  • Palabras clave:

    Mathematics,Mathematics (Miscellaneous)
    Total roman domination
    Roman domination
    Number
    Direct product graphs msc: 05c69
    Direct product graphs
    05c76
    Química
    Mathematics (miscellaneous)
    Mathematics
    General mathematics
    Astronomia / física
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