Author, as appears in the article.: Cabrera Martinez, Abel; Montejano, Luis P; Rodriguez-Velazquez, Juan A
Department: Enginyeria Informàtica i Matemàtiques
e-ISSN: 2073-8994
URV's Author/s: CABRERA MARTÍNEZ, ABEL / Montejano Cantoral, Luis Pedro / Rodríguez Velázquez, Juan Alberto
Keywords: Weak roman domination Total roman domination Total domination Secure total domination Np-hard problem
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.
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licence for use: thttps://creativecommons.org/licenses/by/3.0/es/
ISSN: 20738994
Author's mail: luispedro.montejano@urv.cat juanalberto.rodriguez@urv.cat
Author identifier: 0000-0002-9082-7647
Record's date: 2024-10-26
Journal volume: 11
Papper version: info:eu-repo/semantics/publishedVersion
Link to the original source: https://www.mdpi.com/2073-8994/11/6/831
Licence document URL: https://repositori.urv.cat/ca/proteccio-de-dades/
Papper original source: Symmetry-Basel. 11 (6): 831-
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
Article's DOI: 10.3390/sym11060831
Entity: Universitat Rovira i Virgili
Journal publication year: 2019
Publication Type: Journal Publications