Repositori institucional URV
| URV's Author/s: | CABRERA MARTÍNEZ, ABEL / Montejano Cantoral, Luis Pedro / Rodríguez Velázquez, Juan Alberto |
| Author, as appears in the article.: | Cabrera-Martínez, A; Montejano, LP; Rodríguez-Velázquez, JA |
| Author's mail: | luispedro.montejano@urv.cat juanalberto.rodriguez@urv.cat |
| Author identifier: | 0000-0002-9082-7647 |
| Journal publication year: | 2023 |
| Publication Type: | Journal Publications |
| APA: | Cabrera-Martínez, A; Montejano, LP; Rodríguez-Velázquez, JA (2023). From w-Domination in Graphs to Domination Parameters in Lexicographic Product Graphs. Bulletin Of The Malaysian Mathematical Sciences Society, 46(3), -. DOI: 10.1007/s40840-023-01502-5 |
| 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/10.26493/1855-3974.2318.fb9] under the name of w-domination, where w= (w, w1, ⋯ , wl) is a vector of non-negative integers such that w≥ 1. Given a graph G, a function f: V(G) ⟶ { 0 , 1 , ⋯ , l} is said to be a w-dominating 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 w-domination number of G, denoted by γw(G) , is defined as the minimum weight among all w-dominating functions on G. A wide range of well-known 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 quasi-total 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 quasi-total Italian domination, total Italian domination, 2-domination, double domination, total { 2 } -domination, and double total domination of lexicographic product graphs. |
| Article's DOI: | 10.1007/s40840-023-01502-5 |
| Link to the original source: | https://link.springer.com/article/10.1007/s40840-023-01502-5 |
| Papper version: | info:eu-repo/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/proteccio-de-dades/ |
| Thematic Areas: | Mathematics (miscellaneous) Mathematics (all) Mathematics General mathematics |
| Keywords: | W-domination Quasi-total italian domination Lexicographic product graph Double domination 2-domination (total) italian domination |
| Entity: | Universitat Rovira i Virgili |
| Record's date: | 2024-08-03 |
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