Articles producció científica> Enginyeria Informàtica i Matemàtiques

From the Strong Differential to Italian Domination in Graphs

  • Identification data

    Identifier: imarina:9228569
    Authors:
    Cabrera Martinez, ARodriguez-Velazquez, J A
    Abstract:
    Given a graph G and a subset of vertices D subset of V (G), the external neighbourhood of D is defined as N-e(D) = {u is an element of V (G)\D : N(u) boolean AND D not equal O}, where N(u) denotes the open neighbourhood of u. Now, given a subset D subset of V (G) and a vertex v. D, the external private neighbourhood of v with respect to D is defined to be epn(v, D) = {u is an element of V(G)\D : N(u)boolean AND D = {v}}. The strong differential of a set D subset of V (G) is defined as partial derivative(s)(D) = vertical bar N-e(D)vertical bar - vertical bar D-w vertical bar, where D-w = {v is an element of D : epn(v, D) v not equal O}. In this paper, we focus on the study of the strong differential of a graph, which is defined aspartial derivative(s)(G) = max{partial derivative(s)(D) : D subset of V (G)}.Among other results, we obtain general bounds on partial derivative(s)(G) and we prove a Gallai-type theorem, which states that partial derivative(s)(G) + gamma(I)(G) = n(G), where gamma(I)G) denotes the Italian domination number of G. Therefore, we can see the theory of strong differential in graphs as a new approach to the theory of Italian domination. One of the advantages of this approach is that it allows us to study the Italian domination number without the use of functions. As we can expect, we derive new results on the Italian domination number of a graph.
  • 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: Strong differential of a graph Semitotal domination Roman domination Italian domination Differential of a graph
    Abstract: Given a graph G and a subset of vertices D subset of V (G), the external neighbourhood of D is defined as N-e(D) = {u is an element of V (G)\D : N(u) boolean AND D not equal O}, where N(u) denotes the open neighbourhood of u. Now, given a subset D subset of V (G) and a vertex v. D, the external private neighbourhood of v with respect to D is defined to be epn(v, D) = {u is an element of V(G)\D : N(u)boolean AND D = {v}}. The strong differential of a set D subset of V (G) is defined as partial derivative(s)(D) = vertical bar N-e(D)vertical bar - vertical bar D-w vertical bar, where D-w = {v is an element of D : epn(v, D) v not equal O}. In this paper, we focus on the study of the strong differential of a graph, which is defined aspartial derivative(s)(G) = max{partial derivative(s)(D) : D subset of V (G)}.Among other results, we obtain general bounds on partial derivative(s)(G) and we prove a Gallai-type theorem, which states that partial derivative(s)(G) + gamma(I)(G) = n(G), where gamma(I)G) denotes the Italian domination number of G. Therefore, we can see the theory of strong differential in graphs as a new approach to the theory of Italian domination. One of the advantages of this approach is that it allows us to study the Italian domination number without the use of functions. As we can expect, we derive new results on the Italian domination number of a graph.
    Thematic Areas: Mathematics, applied Mathematics (miscellaneous) Mathematics (all) Mathematics Matemática / probabilidade e estatística General mathematics Ensino Engenharias iv
    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/publishedVersion
    Link to the original source: https://link.springer.com/article/10.1007/s00009-021-01866-7
    Licence document URL: https://repositori.urv.cat/ca/proteccio-de-dades/
    Papper original source: Mediterranean Journal Of Mathematics. 18 (5): 228-
    APA: Cabrera Martinez, A; Rodriguez-Velazquez, J A (2021). From the Strong Differential to Italian Domination in Graphs. Mediterranean Journal Of Mathematics, 18(5), 228-. DOI: 10.1007/s00009-021-01866-7
    Article's DOI: 10.1007/s00009-021-01866-7
    Entity: Universitat Rovira i Virgili
    Journal publication year: 2021
    Publication Type: Journal Publications
  • Keywords:

    Mathematics,Mathematics (Miscellaneous),Mathematics, Applied
    Strong differential of a graph
    Semitotal domination
    Roman domination
    Italian domination
    Differential of a graph
    Mathematics, applied
    Mathematics (miscellaneous)
    Mathematics (all)
    Mathematics
    Matemática / probabilidade e estatística
    General mathematics
    Ensino
    Engenharias iv
  • Documents:

  • Cerca a google

    Search to google scholar