Articles producció científica> Enginyeria Informàtica i Matemàtiques

On the 2-Packing Differential of a Graph

  • Datos identificativos

    Identificador: imarina:9227041
    Autores:
    Cabrera Martinez, APuertas, M LRodriguez-Velazquez, J A
    Resumen:
    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 external neighbourhood of S as the set Ne(S) of all vertices in V (G)\S having at least one neighbour in S. The differential of S is defined to be partial derivative(S) = vertical bar N-e(S)vertical bar - vertical bar S vertical bar. In this paper, we introduce the study of the 2-packing differential of a graph, which we define as partial derivative(2p)(G) = max{partial derivative(S) : S subset of V(G) is a 2-packing}. We show that the 2-packing differential is closely related to several graph parameters, including the packing number, the independent domination number, the total domination number, the perfect differential, and the unique response Roman domination number. In particular, we show that the theory of 2-packing differentials is an appropriate framework to investigate the unique response Roman domination number of a graph without the use of functions. Among other results, we obtain a Gallai-type theorem, which states that partial derivative(2p)(G)+ mu(R)(G) = n(G), where mu(R)(G) denotes the unique response Roman domination number of G. As a consequence of the study, we derive several combinatorial results on mu(R)(G), and we show that the problem of finding this parameter is NP-hard. In addition, the particular case of lexicographic product graphs is discussed.
  • Otros:

    Autor según el artículo: Cabrera Martinez, A; Puertas, M L; Rodriguez-Velazquez, J A
    Departamento: Enginyeria Informàtica i Matemàtiques
    Autor/es de la URV: CABRERA MARTÍNEZ, ABEL / Rodríguez Velázquez, Juan Alberto
    Palabras clave: Unique response roman domination Response roman domination Number Lexicographic product Efficient open domination Differential of a graph 2-packing differential
    Resumen: 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 external neighbourhood of S as the set Ne(S) of all vertices in V (G)\S having at least one neighbour in S. The differential of S is defined to be partial derivative(S) = vertical bar N-e(S)vertical bar - vertical bar S vertical bar. In this paper, we introduce the study of the 2-packing differential of a graph, which we define as partial derivative(2p)(G) = max{partial derivative(S) : S subset of V(G) is a 2-packing}. We show that the 2-packing differential is closely related to several graph parameters, including the packing number, the independent domination number, the total domination number, the perfect differential, and the unique response Roman domination number. In particular, we show that the theory of 2-packing differentials is an appropriate framework to investigate the unique response Roman domination number of a graph without the use of functions. Among other results, we obtain a Gallai-type theorem, which states that partial derivative(2p)(G)+ mu(R)(G) = n(G), where mu(R)(G) denotes the unique response Roman domination number of G. As a consequence of the study, we derive several combinatorial results on mu(R)(G), and we show that the problem of finding this parameter is NP-hard. In addition, the particular case of lexicographic product graphs is discussed.
    Áreas temáticas: Mathematics, applied Mathematics (miscellaneous) Mathematics Matemática / probabilidade e estatística Ensino Economia Applied mathematics
    Acceso a la licencia de uso: https://creativecommons.org/licenses/by/3.0/es/
    Direcció de correo del autor: juanalberto.rodriguez@urv.cat
    Identificador del autor: 0000-0002-9082-7647
    Fecha de alta del registro: 2024-10-26
    Versión del articulo depositado: info:eu-repo/semantics/publishedVersion
    Enlace a la fuente original: https://link.springer.com/article/10.1007/s00025-021-01473-8
    URL Documento de licencia: https://repositori.urv.cat/ca/proteccio-de-dades/
    Referencia al articulo segun fuente origial: Results In Mathematics. 76 (3): 157-
    Referencia de l'ítem segons les normes APA: Cabrera Martinez, A; Puertas, M L; Rodriguez-Velazquez, J A (2021). On the 2-Packing Differential of a Graph. Results In Mathematics, 76(3), 157-. DOI: 10.1007/s00025-021-01473-8
    DOI del artículo: 10.1007/s00025-021-01473-8
    Entidad: Universitat Rovira i Virgili
    Año de publicación de la revista: 2021
    Tipo de publicación: Journal Publications
  • Palabras clave:

    Applied Mathematics,Mathematics,Mathematics (Miscellaneous),Mathematics, Applied
    Unique response roman domination
    Response roman domination
    Number
    Lexicographic product
    Efficient open domination
    Differential of a graph
    2-packing differential
    Mathematics, applied
    Mathematics (miscellaneous)
    Mathematics
    Matemática / probabilidade e estatística
    Ensino
    Economia
    Applied mathematics
  • Documentos:

  • Cerca a google

    Search to google scholar