Autor segons l'article: Cabrera Martinez, Abel; Alberto Rodriguez-Velazquez, Juan
Departament: Enginyeria Informàtica i Matemàtiques
Autor/s de la URV: CABRERA MARTÍNEZ, ABEL / Rodríguez Velázquez, Juan Alberto
Paraules clau: Total weak roman domination Total domination Secure total domination Lexicographic product Italian domination total domination secure total domination roman lexicographic product
Resum: © (V1 â V2) such that the function f′, defined by f′(v) = 1, f′(u) = f(u)-1 and f′(x) = f(x) whenever x â V (G) \ {u, v}, is a total dominating function as well. If f is a total weak Roman dominating function and V2 = â, then we say that f is a secure total dominating function. The weight of a function f is defined to be ω(f) = ςvâV(G) f(v). The total weak Roman domination number (secure total domination number) of a graph G is the minimum weight among all total weak Roman dominating functions (secure total dominating functions) on G. In this article, we show that these two parameters coincide for lexicographic product graphs. Furthermore, we obtain closed formulae and tight bounds for these parameters in terms of invariants of the factor graphs involved in the product. Given a graph G with vertex set V (G), a function f: V (G) → {0, 1, 2} is said to be a total dominating function if ςuâN(v) f(u) > 0 for every v â V (G), where N(v) denotes the open neighbourhood of v. Let Vi = {x â V (G): F(x) = i}. A total dominating function f is a total weak Roman dominating function if for every vertex v â V0 there exists a vertex u â N(v) â.
Àrees temàtiques: Mathematics Matemática / probabilidade e estatística Discrete mathematics and combinatorics Ciência da computação Applied mathematics
Accès a la llicència d'ús: https://creativecommons.org/licenses/by/3.0/es/
Adreça de correu electrònic de l'autor: juanalberto.rodriguez@urv.cat
Identificador de l'autor: 0000-0002-9082-7647
Data d'alta del registre: 2024-10-26
Versió de l'article dipositat: info:eu-repo/semantics/publishedVersion
Enllaç font original: https://www.dmgt.uz.zgora.pl/publish/bbl_view_press.php?ID=27108
URL Document de llicència: https://repositori.urv.cat/ca/proteccio-de-dades/
Referència a l'article segons font original: Discussiones Mathematicae Graph Theory. 42 (3): 967-984
Referència de l'ítem segons les normes APA: Cabrera Martinez, Abel; Alberto Rodriguez-Velazquez, Juan (2022). Total Protection of Lexicographic Product Graphs. Discussiones Mathematicae Graph Theory, 42(3), 967-984. DOI: 10.7151/dmgt.2318
DOI de l'article: 10.7151/dmgt.2318
Entitat: Universitat Rovira i Virgili
Any de publicació de la revista: 2022
Tipus de publicació: Journal Publications