Repositori institucional URV
| Autor/s de la URV: | CABRERA MARTÍNEZ, ABEL / Montejano Cantoral, Luis Pedro / Rodríguez Velázquez, Juan Alberto |
| Autor segons l'article: | Cabrera Martinez, Abel; Montejano, Luis P; Rodriguez-Velazquez, Juan A |
| Adreça de correu electrònic de l'autor: | luispedro.montejano@urv.cat juanalberto.rodriguez@urv.cat |
| Identificador de l'autor: | 0000-0002-9082-7647 |
| Any de publicació de la revista: | 2019 |
| Tipus de publicació: | Journal Publications |
| ISSN: | 20738994 |
| e-ISSN: | 2073-8994 |
| Referència 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 |
| Referència a l'article segons font original: | Symmetry-Basel. 11 (6): 831- |
| Resum: | 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 de l'article: | 10.3390/sym11060831 |
| Enllaç font original: | https://www.mdpi.com/2073-8994/11/6/831 |
| Versió de l'article dipositat: | info:eu-repo/semantics/publishedVersion |
| Accès a la llicència d'ús: | thttps://creativecommons.org/licenses/by/3.0/es/ |
| Departament: | Enginyeria Informàtica i Matemàtiques |
| URL Document de llicència: | https://repositori.urv.cat/ca/proteccio-de-dades/ |
| Àrees temàtiques: | 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 |
| Paraules clau: | Weak roman domination Total roman domination Total domination Secure total domination Np-hard problem |
| Entitat: | Universitat Rovira i Virgili |
| Data d'alta del registre: | 2024-10-26 |
| Volum de revista: | 11 |
| Cerca el teu registre a: |   |
| Fitxer | Descripció | Format | |
|---|---|---|---|
| DocumentPrincipal | DocumentPrincipal | application/pdf |
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