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INDEPENDENT TRANSVERSAL TOTAL DOMINATION VERSUS TOTAL DOMINATION IN TREES

  • Identification data

    Identifier: imarina:9093097
    Authors:
    Cabrera Martinez, AbelPeterin, IztokYero, Ismael G.
    Abstract:
    A subset of vertices in a graph G is a total dominating set if every vertex in G is adjacent to at least one vertex in this subset. The total domination number of G is the minimum cardinality of any total dominating set in G and is denoted by gamma(t)(G). A total dominating set of G having nonempty intersection with all the independent sets of maximum cardinality in G is an independent transversal total dominating set. The minimum cardinality of any independent transversal total dominating set is denoted by gamma(u) (G). Based on the fact that for any tree T, gamma(t) (T) <= gamma(u) (T) <= gamma(t) (T) + 1, in this work we give several relationship(s) between gamma(u) (T) and gamma(t) (T) for trees T which are leading to classify the trees which are satisfying the equality in these bounds.
  • Others:

    Author, as appears in the article.: Cabrera Martinez, Abel; Peterin, Iztok; Yero, Ismael G.;
    Department: Enginyeria Informàtica i Matemàtiques
    URV's Author/s: CABRERA MARTÍNEZ, ABEL / GONZÁLEZ YERO, ISMAEL
    Keywords: Trees Total domination number Independent transversal total domination number Independence number
    Abstract: A subset of vertices in a graph G is a total dominating set if every vertex in G is adjacent to at least one vertex in this subset. The total domination number of G is the minimum cardinality of any total dominating set in G and is denoted by gamma(t)(G). A total dominating set of G having nonempty intersection with all the independent sets of maximum cardinality in G is an independent transversal total dominating set. The minimum cardinality of any independent transversal total dominating set is denoted by gamma(u) (G). Based on the fact that for any tree T, gamma(t) (T) <= gamma(u) (T) <= gamma(t) (T) + 1, in this work we give several relationship(s) between gamma(u) (T) and gamma(t) (T) for trees T which are leading to classify the trees which are satisfying the equality in these bounds.
    Thematic Areas: Mathematics Matemática / probabilidade e estatística Discrete mathematics and combinatorics Ciência da computação Applied mathematics
    licence for use: https://creativecommons.org/licenses/by/3.0/es/
    ISSN: 1234-3099
    Author's mail: abel.cabrera@urv.cat
    Author identifier: 0000-0003-2806-4842
    Last page: 224
    Record's date: 2021-10-10
    Journal volume: 41
    Papper version: info:eu-repo/semantics/publishedVersion
    Link to the original source: https://www.dmgt.uz.zgora.pl/publish/bbl_view_pdf.php?ID=42027
    Papper original source: Discussiones Mathematicae Graph Theory. 41 (1): 213-224
    APA: Cabrera Martinez, Abel; Peterin, Iztok; Yero, Ismael G.; (2021). INDEPENDENT TRANSVERSAL TOTAL DOMINATION VERSUS TOTAL DOMINATION IN TREES. Discussiones Mathematicae Graph Theory, 41(1), 213-224. DOI: 10.7151/dmgt.2200
    Licence document URL: https://repositori.urv.cat/ca/proteccio-de-dades/
    Article's DOI: 10.7151/dmgt.2200
    Entity: Universitat Rovira i Virgili
    Journal publication year: 2021
    First page: 213
    Publication Type: Journal Publications
  • Keywords:

    Applied Mathematics,Discrete Mathematics and Combinatorics,Mathematics
    Trees
    Total domination number
    Independent transversal total domination number
    Independence number
    Mathematics
    Matemática / probabilidade e estatística
    Discrete mathematics and combinatorics
    Ciência da computação
    Applied mathematics
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