Autor según el artículo: Cabrera Martinez, A; Rodriguez-Velazquez, J A
Departamento: Enginyeria Informàtica i Matemàtiques
Autor/es de la URV: CABRERA MARTÍNEZ, ABEL / Rodríguez Velázquez, Juan Alberto
Palabras clave: Strong differential of a graph Semitotal domination Roman domination Italian domination Differential of a graph
Resumen: 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.
Áreas temáticas: Mathematics, applied Mathematics (miscellaneous) Mathematics (all) Mathematics Matemática / probabilidade e estatística General mathematics Ensino Engenharias iv
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/s00009-021-01866-7
URL Documento de licencia: https://repositori.urv.cat/ca/proteccio-de-dades/
Referencia al articulo segun fuente origial: Mediterranean Journal Of Mathematics. 18 (5): 228-
Referencia 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 del artículo: 10.1007/s00009-021-01866-7
Entidad: Universitat Rovira i Virgili
Año de publicación de la revista: 2021
Tipo de publicación: Journal Publications