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Dominating the direct product of two graphs through total Roman strategies

  • Identification data

    Identifier: imarina:8505358
    Authors:
    Cabrera AKuziak DPeterin IYero IG
    Abstract:
    © 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.
  • Others:

    Author, as appears in the article.: Cabrera A; Kuziak D; Peterin I; Yero IG
    Department: Enginyeria Informàtica i Matemàtiques
    URV's Author/s: CABRERA MARTÍNEZ, ABEL
    Keywords: Total roman domination Roman domination Number Direct product graphs msc: 05c69 Direct product graphs 05c76
    Abstract: © 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.
    Thematic Areas: Química Mathematics (miscellaneous) Mathematics General mathematics Astronomia / física
    licence for use: https://creativecommons.org/licenses/by/3.0/es/
    Author's mail: abel.cabrera@urv.cat
    Author identifier: 0000-0003-2806-4842
    Record's date: 2021-10-10
    Papper version: info:eu-repo/semantics/publishedVersion
    Link to the original source: https://www.mdpi.com/2227-7390/8/9/1438
    Papper original source: Mathematics. 8 (9):
    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
    Licence document URL: https://repositori.urv.cat/ca/proteccio-de-dades/
    Article's DOI: 10.3390/MATH8091438
    Entity: Universitat Rovira i Virgili
    Journal publication year: 2020
    Publication Type: Journal Publications
  • Keywords:

    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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