Autor según el artículo: Martínez A, Montejano L, Rodríguez-Velázquez J

Departamento: Enginyeria Informàtica i Matemàtiques

e-ISSN: 2073-8994

Autor/es de la URV: CABRERA MARTÍNEZ, ABEL / Montejano Cantoral, Luis Pedro / Rodríguez Velázquez, Juan Alberto

Palabras clave: Weak roman domination Total roman domination Total domination Secure total domination Np-hard problem

Resumen: Given a graph G=(V,E) , a function f:V→{0,1,2,⋯} is said to be a total dominating function if ∑u∈N(v)f(u)>0 for every v∈V , where N(v) denotes the open neighbourhood of v. Let Vi={x∈V:f(x)=i} . We say that a function f:V→{0,1,2} is a total weak Roman dominating function if f is a total dominating function and for every vertex v∈V0 there exists u∈N(v)∩(V1∪V2) such that the function f′ , defined by f′(v)=1 , f′(u)=f(u)−1 and f′(x)=f(x) whenever x∈V\{u,v} , is a total dominating function as well. The weight of a function f is defined to be w(f)=∑v∈Vf(v). In this article, we introduce the study of the total weak Roman domination number of a graph G, denoted by γtr(G) , which is defined to be the minimum weight among all total weak Roman dominating functions on G. We show the close relationship that exists between this novel parameter and other domination parameters of a graph. Furthermore, we obtain general bounds on γtr(G) and, for some particular families of graphs, we obtain closed formulae. Finally, we show that the problem of computing the total weak Roman domination number of a graph is NP-hard.

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: thttps://creativecommons.org/licenses/by/3.0/es/

ISSN: 20738994

Direcció de correo del autor: luispedro.montejano@urv.cat juanalberto.rodriguez@urv.cat

Identificador del autor: 0000-0002-9082-7647

Fecha de alta del registro: 2023-07-31

Volumen de revista: 11

Versión del articulo depositado: info:eu-repo/semantics/publishedVersion

Enlace a la fuente original: https://www.mdpi.com/2073-8994/11/6/831

URL Documento de licencia: http://repositori.urv.cat/ca/proteccio-de-dades/

Referencia al articulo segun fuente origial: Symmetry-Basel. 11 (6):

Referencia de l'ítem segons les normes APA: Martínez A, Montejano L, Rodríguez-Velázquez J (2019). Total Weak Roman Domination in Graphs. Symmetry-Basel, 11(6), -. DOI: 10.3390/sym11060831

DOI del artículo: 10.3390/SYM11060831

Entidad: Universitat Rovira i Virgili

Año de publicación de la revista: 2019

Tipo de publicación: Journal Publications