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