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INDEPENDENT TRANSVERSAL TOTAL DOMINATION VERSUS TOTAL DOMINATION IN TREES

  • Identification data

    Identifier:  imarina:9093097
    Authors:  Cabrera Martinez, Abel; Peterin, Iztok; Yero, 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:

    Link to the original source: https://www.dmgt.uz.zgora.pl/publish/bbl_view_pdf.php?ID=42027
    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
    Paper original source: Discussiones Mathematicae Graph Theory. 41 (1): 213-224
    Article's DOI: 10.7151/dmgt.2200
    Journal publication year: 2021
    Entity: Universitat Rovira i Virgili
    Paper version: info:eu-repo/semantics/publishedVersion
    Record's date: 2021-10-10
    First page: 213
    URV's Author/s: CABRERA MARTÍNEZ, ABEL / GONZÁLEZ YERO, ISMAEL
    Department: Enginyeria Informàtica i Matemàtiques
    Licence document URL: https://repositori.urv.cat/ca/proteccio-de-dades/
    Publication Type: Journal Publications
    Last page: 224
    ISSN: 1234-3099
    Author, as appears in the article.: Cabrera Martinez, Abel; Peterin, Iztok; Yero, Ismael G.;
    licence for use: https://creativecommons.org/licenses/by/3.0/es/
    Journal volume: 41
    Thematic Areas: Mathematics, Matemática / probabilidade e estatística, Discrete mathematics and combinatorics, Ciência da computação, Applied mathematics
    Author's mail: abel.cabrera@urv.cat
  • Keywords:

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