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, RodríguezVelázquez J

Author's mail:  luispedro.montejano@urv.cat juanalberto.rodriguez@urv.cat

Author identifier:  0000000290827647

Journal publication year:  2019

Publication Type:  Journal Publications

ISSN:  20738994

eISSN:  20738994

APA:  Martínez A, Montejano L, RodríguezVelázquez J (2019). Total Weak Roman Domination in Graphs. SymmetryBasel, 11(6), . DOI: 10.3390/sym11060831

Papper original source:  SymmetryBasel. 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 NPhard.

Article's DOI:  10.3390/sym11060831

Link to the original source:  https://www.mdpi.com/20738994/11/6/831

Papper version:  info:eurepo/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/protecciodedades/

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 Nphard problem

Entity:  Universitat Rovira i Virgili

Record's date:  20240727

Journal volume:  11
