Repositori institucional URV
| Autor/es de la URV: | CABRERA MARTÍNEZ, ABEL / Montejano Cantoral, Luis Pedro / Rodríguez Velázquez, Juan Alberto |
| Autor según el artículo: | Cabrera Martinez, Abel; Montejano, Luis P; Rodriguez-Velazquez, Juan A |
| Direcció de correo del autor: | luispedro.montejano@urv.cat juanalberto.rodriguez@urv.cat |
| Identificador del autor: | 0000-0002-9082-7647 |
| Año de publicación de la revista: | 2019 |
| Tipo de publicación: | Journal Publications |
| ISSN: | 20738994 |
| e-ISSN: | 2073-8994 |
| Referencia de l'ítem segons les normes APA: | Cabrera Martinez, Abel; Montejano, Luis P; Rodriguez-Velazquez, Juan A (2019). Total Weak Roman Domination in Graphs. Symmetry-Basel, 11(6), 831-. DOI: 10.3390/sym11060831 |
| Referencia al articulo segun fuente origial: | Symmetry-Basel. 11 (6): 831- |
| 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. |
| DOI del artículo: | 10.3390/sym11060831 |
| Enlace a la fuente original: | https://www.mdpi.com/2073-8994/11/6/831 |
| Versión del articulo depositado: | info:eu-repo/semantics/publishedVersion |
| Acceso a la licencia de uso: | thttps://creativecommons.org/licenses/by/3.0/es/ |
| Departamento: | Enginyeria Informàtica i Matemàtiques |
| URL Documento de licencia: | https://repositori.urv.cat/ca/proteccio-de-dades/ |
| 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 |
| Palabras clave: | Weak roman domination Total roman domination Total domination Secure total domination Np-hard problem |
| Entidad: | Universitat Rovira i Virgili |
| Fecha de alta del registro: | 2024-10-26 |
| Volumen de revista: | 11 |
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| DocumentPrincipal | DocumentPrincipal | application/pdf |
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