Autor según el artículo: Cabrera Martinez, Abel; Estrada-Moreno, Alejandro; Rodriguez-Velazquez, Juan A
Departamento: Enginyeria Informàtica i Matemàtiques
e-ISSN: 2073-8994
Autor/es de la URV: CABRERA MARTÍNEZ, ABEL / Estrada Moreno, Alejandro / Rodríguez Velázquez, Juan Alberto
Palabras clave: Weak roman domination W-domination Secure italian domination Secure domination
Resumen: © 2020 by the authors. Licensee MDPI, Basel, Switzerland. This paper introduces a general approach to the idea of protection of graphs, which encompasses the known variants of secure domination and introduces new ones. Specifically, we introduce the study of secure w-domination in graphs, where w = (w0, w1, …, wl) is a vector of nonnegative integers such that w0 ≥ 1. The secure w-domination number is defined as follows. Let G be a graph and N(v) the open neighborhood of v ∈ V(G). We say that a function f: V(G) −→ {0, 1, …, l} is a w-dominating function if f (N(v)) = ∑u N(v) f (u) ≥ wi for every vertex v with f (v) = i. The weight of f is defined to be ω(f) = ∑v∈V(G) f (v). Given a w-dominating function f and any pair of adjacent vertices v, u V(G) with f (v) = 0 and f (u) > 0, the function fu→v is defined by fu→v (v) = 1, fu→v (u) = f (u) − 1 and fu→v (x) = f (x) for every x V(G) \ {u, v}. We say that a w-dominating function f is a secure w-dominating function if for every v with f (v) = 0, there exists u N(v) such that f (u) > 0 and fu→v is a w-dominating function as well. The secure w-domination number of G, denoted by γw(G),s is the minimum weight among all secure w-dominating functions. This paper provides fundamental results on γw(G)s and raises the challenge of conducting a detailed study of the topic.
Áreas temáticas: Visual arts and performing arts Physics and astronomy (miscellaneous) Multidisciplinary sciences Modeling and simulation Mathematics, interdisciplinary applications Mathematics (miscellaneous) Mathematics (all) Matemática / probabilidade e estatística General mathematics Engineering (miscellaneous) Computer science (miscellaneous) Ciência da computação Chemistry (miscellaneous) Arts and humanities (miscellaneous) Architecture Applied mathematics
Acceso a la licencia de uso: https://creativecommons.org/licenses/by/3.0/es/
Direcció de correo del autor: alejandro.estrada@urv.cat juanalberto.rodriguez@urv.cat
Identificador del autor: 0000-0001-9767-2177 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://www.mdpi.com/2073-8994/12/12/1948
URL Documento de licencia: https://repositori.urv.cat/ca/proteccio-de-dades/
Referencia al articulo segun fuente origial: Symmetry-Basel. 12 (12): 1-11
Referencia de l'ítem segons les normes APA: Cabrera Martinez, Abel; Estrada-Moreno, Alejandro; Rodriguez-Velazquez, Juan A (2020). Secure w-domination in graphs. Symmetry-Basel, 12(12), 1-11. DOI: 10.3390/sym12121948
DOI del artículo: 10.3390/sym12121948
Entidad: Universitat Rovira i Virgili
Año de publicación de la revista: 2020
Tipo de publicación: Journal Publications