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ON THE PERFECT DIFFERENTIAL OF A GRAPH

  • Identification data

    Identifier: imarina:9150984
    Authors:
    Cabrera Martinez, ARodriguez-Velazquez, J A
    Abstract:
    Let G be a graph of order n(G) and vertex set V(G). Given a set S subset of V(G), we define the perfect neighbourhood of S as the set N-p(S) of all vertices in V(G)\S having exactly one neighbour in S. The perfect differential of S is defined to be partial differential partial derivative(p)(S) = vertical bar N-p(S)vertical bar - vertical bar S vertical bar. In this paper, we introduce the study of the perfect differential of a graph, which we define as partial derivative(p)(G) = max{partial derivative(p)(S): S subset of V(G)}. Among other results, we obtain general bounds on partial derivative(p)(G) and we prove a Gallai-type theorem, which states that partial differential partial derivative(p)(G) + gamma(p)(R)(G) = n(G), where gamma(p)(R)(G) denotes the perfect Roman domination number of G. As a consequence of the study, we show some classes of graphs satisfying a conjecture stated by Bermudo
  • Others:

    Author, as appears in the article.: Cabrera Martinez, A; Rodriguez-Velazquez, J A
    Department: Enginyeria Informàtica i Matemàtiques
    URV's Author/s: CABRERA MARTÍNEZ, ABEL / Rodríguez Velázquez, Juan Alberto
    Keywords: Roman domination number Roman domination Perfect roman domination Perfect domination Perfect differential of a graph Differential of a graph
    Abstract: Let G be a graph of order n(G) and vertex set V(G). Given a set S subset of V(G), we define the perfect neighbourhood of S as the set N-p(S) of all vertices in V(G)\S having exactly one neighbour in S. The perfect differential of S is defined to be partial differential partial derivative(p)(S) = vertical bar N-p(S)vertical bar - vertical bar S vertical bar. In this paper, we introduce the study of the perfect differential of a graph, which we define as partial derivative(p)(G) = max{partial derivative(p)(S): S subset of V(G)}. Among other results, we obtain general bounds on partial derivative(p)(G) and we prove a Gallai-type theorem, which states that partial differential partial derivative(p)(G) + gamma(p)(R)(G) = n(G), where gamma(p)(R)(G) denotes the perfect Roman domination number of G. As a consequence of the study, we show some classes of graphs satisfying a conjecture stated by Bermudo
    Thematic Areas: Mathematics (miscellaneous) Mathematics Matemática / probabilidade e estatística
    licence for use: https://creativecommons.org/licenses/by/3.0/es/
    Author's mail: juanalberto.rodriguez@urv.cat
    Author identifier: 0000-0002-9082-7647
    Record's date: 2024-10-26
    Papper version: info:eu-repo/semantics/submittedVersion
    Link to the original source: https://www.tandfonline.com/doi/abs/10.2989/16073606.2020.1858992?journalCode=tqma20
    Licence document URL: https://repositori.urv.cat/ca/proteccio-de-dades/
    Papper original source: Quaestiones Mathematicae. 45 (3): 327-345
    APA: Cabrera Martinez, A; Rodriguez-Velazquez, J A (2022). ON THE PERFECT DIFFERENTIAL OF A GRAPH. Quaestiones Mathematicae, 45(3), 327-345. DOI: 10.2989/16073606.2020.1858992
    Article's DOI: 10.2989/16073606.2020.1858992
    Entity: Universitat Rovira i Virgili
    Journal publication year: 2022
    Publication Type: Journal Publications
  • Keywords:

    Mathematics,Mathematics (Miscellaneous)
    Roman domination number
    Roman domination
    Perfect roman domination
    Perfect domination
    Perfect differential of a graph
    Differential of a graph
    Mathematics (miscellaneous)
    Mathematics
    Matemática / probabilidade e estatística
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