Articles producció científica> Enginyeria Informàtica i Matemàtiques

Perfect Domination, Roman Domination and Perfect Roman Domination in Lexicographic Product Graphs

  • Identification data

    Identifier: imarina:9262466
    Handle: https://hdl.handle.net/20.500.11797/imarina9262466
    Authors:
    Cabrera Martinez, AGarcia-Gomez, CRodriguez-Velazquez, J A
    Abstract:
    The aim of this paper is to obtain closed formulas for the perfect domination number, the Roman domination number and the perfect Roman domination number of lexicographic product graphs. We show that these formulas can be obtained relatively easily for the case of the first two parameters. The picture is quite different when it concerns the perfect Roman domination number. In this case, we obtain general bounds and then we give sufficient and/or necessary conditions for the bounds to be achieved. We also discuss the case of perfect Roman graphs and we characterize the lexicographic product graphs where the perfect Roman domination number equals the Roman domination number.

  • Others:

    Author, as appears in the article.: Cabrera Martinez, A; Garcia-Gomez, C; Rodriguez-Velazquez, J A
    Department: Enginyeria Informàtica i Matemàtiques
    URV's Author/s: CABRERA MARTÍNEZ, ABEL / García Gómez, Carlos / Rodríguez Velázquez, Juan Alberto
    Keywords: Roman domination Perfect roman domination Perfect domination Number Lexicographic product
    Abstract: The aim of this paper is to obtain closed formulas for the perfect domination number, the Roman domination number and the perfect Roman domination number of lexicographic product graphs. We show that these formulas can be obtained relatively easily for the case of the first two parameters. The picture is quite different when it concerns the perfect Roman domination number. In this case, we obtain general bounds and then we give sufficient and/or necessary conditions for the bounds to be achieved. We also discuss the case of perfect Roman graphs and we characterize the lexicographic product graphs where the perfect Roman domination number equals the Roman domination number.
    Thematic Areas: Theoretical computer science Mathematics, applied Matemática / probabilidade e estatística Information systems Engenharias iv Engenharias iii Computer science, software engineering Computational theory and mathematics Ciência da computação Astronomia / física Algebra and number theory
    licence for use: https://creativecommons.org/licenses/by/3.0/es/
    Author's mail: juanalberto.rodriguez@urv.cat carlos.garciag@urv.cat
    Author identifier: 0000-0002-9082-7647 0000-0002-8201-3192
    Record's date: 2024-10-26
    Papper version: info:eu-repo/semantics/acceptedVersion
    Licence document URL: https://repositori.urv.cat/ca/proteccio-de-dades/
    Papper original source: Fundamenta Informaticae. 185 (3): 201-220
    APA: Cabrera Martinez, A; Garcia-Gomez, C; Rodriguez-Velazquez, J A (2022). Perfect Domination, Roman Domination and Perfect Roman Domination in Lexicographic Product Graphs. Fundamenta Informaticae, 185(3), 201-220. DOI: 10.3233/FI-222108
    Entity: Universitat Rovira i Virgili
    Journal publication year: 2022
    Publication Type: Journal Publications

  • Keywords:

    Algebra and Number Theory,Computational Theory and Mathematics,Computer Science, Software Engineering,Information Systems,Mathematics, Applied,Theoretical Computer Science
    Roman domination
    Perfect roman domination
    Perfect domination
    Number
    Lexicographic product
    Theoretical computer science
    Mathematics, applied
    Matemática / probabilidade e estatística
    Information systems
    Engenharias iv
    Engenharias iii
    Computer science, software engineering
    Computational theory and mathematics
    Ciência da computação
    Astronomia / física
    Algebra and number theory

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