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