Repositori institucional URV
| URV's Author/s: | CABRERA MARTÍNEZ, ABEL / Montejano Cantoral, Luis Pedro / Rodríguez Velázquez, Juan Alberto |
| Author, as appears in the article.: | Martínez A, Montejano L, Rodríguez-Velázquez J |
| Author's mail: | luispedro.montejano@urv.cat juanalberto.rodriguez@urv.cat |
| Author identifier: | 0000-0002-9082-7647 |
| Journal publication year: | 2019 |
| Publication Type: | Journal Publications |
| ISSN: | 20738994 |
| e-ISSN: | 2073-8994 |
| APA: | Martínez A, Montejano L, Rodríguez-Velázquez J (2019). Total Weak Roman Domination in Graphs. Symmetry-Basel, 11(6), -. DOI: 10.3390/sym11060831 |
| Papper original source: | Symmetry-Basel. 11 (6): |
| Abstract: | 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. |
| Article's DOI: | 10.3390/sym11060831 |
| Link to the original source: | https://www.mdpi.com/2073-8994/11/6/831 |
| Papper version: | info:eu-repo/semantics/publishedVersion |
| licence for use: | thttps://creativecommons.org/licenses/by/3.0/es/ |
| Department: | Enginyeria Informàtica i Matemàtiques |
| Licence document URL: | https://repositori.urv.cat/ca/proteccio-de-dades/ |
| Thematic Areas: | 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 |
| Keywords: | Weak roman domination Total roman domination Total domination Secure total domination Np-hard problem |
| Entity: | Universitat Rovira i Virgili |
| Record's date: | 2024-07-27 |
| Journal volume: | 11 |
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