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From the Strong Differential to Italian Domination in Graphs

  • Dades identificatives

    Identificador: imarina:9228569
    Autors:
    Cabrera Martinez, ARodriguez-Velazquez, J A
    Resum:
    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.
  • Altres:

    Autor segons l'article: Cabrera Martinez, A; Rodriguez-Velazquez, J A
    Departament: Enginyeria Informàtica i Matemàtiques
    Autor/s de la URV: CABRERA MARTÍNEZ, ABEL / Rodríguez Velázquez, Juan Alberto
    Paraules clau: Strong differential of a graph Semitotal domination Roman domination Italian domination Differential of a graph
    Resum: 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.
    Àrees temàtiques: Mathematics, applied Mathematics (miscellaneous) Mathematics (all) Mathematics Matemática / probabilidade e estatística General mathematics Ensino Engenharias iv
    Accès a la llicència d'ús: https://creativecommons.org/licenses/by/3.0/es/
    Adreça de correu electrònic de l'autor: juanalberto.rodriguez@urv.cat
    Identificador de l'autor: 0000-0002-9082-7647
    Data d'alta del registre: 2024-10-26
    Versió de l'article dipositat: info:eu-repo/semantics/publishedVersion
    Enllaç font original: https://link.springer.com/article/10.1007/s00009-021-01866-7
    URL Document de llicència: https://repositori.urv.cat/ca/proteccio-de-dades/
    Referència a l'article segons font original: Mediterranean Journal Of Mathematics. 18 (5): 228-
    Referència de l'ítem segons les normes 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
    DOI de l'article: 10.1007/s00009-021-01866-7
    Entitat: Universitat Rovira i Virgili
    Any de publicació de la revista: 2021
    Tipus de publicació: Journal Publications
  • Paraules clau:

    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
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