URV's Author/s:  CABRERA MARTÍNEZ, ABEL / Montejano Cantoral, Luis Pedro / Rodríguez Velázquez, Juan Alberto

Author, as appears in the article.:  CabreraMartínez, A; Montejano, LP; RodríguezVelázquez, JA

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

Author identifier:  0000000290827647

Journal publication year:  2023

Publication Type:  Journal Publications

APA:  CabreraMartínez, A; Montejano, LP; RodríguezVelázquez, JA (2023). From wDomination in Graphs to Domination Parameters in Lexicographic Product Graphs. Bulletin Of The Malaysian Mathematical Sciences Society, 46(3), . DOI: 10.1007/s40840023015025

Papper original source:  Bulletin Of The Malaysian Mathematical Sciences Society. 46 (3):

Abstract:  A wide range of parameters of domination in graphs can be defined and studied through a common approach that was recently introduced in [https://doi.org/10.26493/18553974.2318.fb9] under the name of wdomination, where w= (w, w1, ⋯ , wl) is a vector of nonnegative integers such that w≥ 1. Given a graph G, a function f: V(G) ⟶ { 0 , 1 , ⋯ , l} is said to be a wdominating function if ∑ u∈N(v)f(u) ≥ wi for every vertex v with f(v) = i, where N(v) denotes the open neighbourhood of v∈ V(G). The weight of f is defined to be ω(f) = ∑ v∈V(G)f(v) , while the wdomination number of G, denoted by γw(G) , is defined as the minimum weight among all wdominating functions on G. A wide range of wellknown domination parameters can be defined and studied through this approach. For instance, among others, the vector w= (1 , 0) corresponds to the case of standard domination, w= (2 , 1) corresponds to double domination, w= (2 , 0 , 0) corresponds to Italian domination, w= (2 , 0 , 1) corresponds to quasitotal Italian domination, w= (2 , 1 , 1) corresponds to total Italian domination, w= (2 , 2 , 2) corresponds to total { 2 } domination, while w= (k, k 1 , ⋯ , 1 , 0) corresponds to { k} domination. In this paper, we show that several domination parameters of lexicographic product graphs G∘ H are equal to γw(G) for some vector w∈ { 2 } × { 0 , 1 , 2 } l and l∈ { 2 , 3 }. The decision on whether the equality holds for a specific vector w will depend on the value of some domination parameters of H. In particular, we focus on quasitotal Italian domination, total Italian domination, 2domination, double domination, total { 2 } domination, and double total domination of lexicographic product graphs.

Article's DOI:  10.1007/s40840023015025

Link to the original source:  https://link.springer.com/article/10.1007/s40840023015025

Papper version:  info:eurepo/semantics/publishedVersion

licence for use:  https://creativecommons.org/licenses/by/3.0/es/

Department:  Enginyeria Informàtica i Matemàtiques

Licence document URL:  https://repositori.urv.cat/ca/protecciodedades/

Thematic Areas:  Mathematics (miscellaneous) Mathematics (all) Mathematics General mathematics

Keywords:  Wdomination Quasitotal italian domination Lexicographic product graph Double domination 2domination (total) italian domination

Entity:  Universitat Rovira i Virgili

Record's date:  20240803
