Autor según el artículo: Martínez AC; Rodríguez-Velázquez JA

Departamento: Enginyeria Informàtica i Matemàtiques

Autor/es de la URV: CABRERA MARTÍNEZ, ABEL / Rodríguez Velázquez, Juan Alberto

Palabras clave: Total weak roman domination Total domination Secure total domination Lexicographic product Italian domination total domination secure total domination roman lexicographic product

Resumen: © (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.

Áreas temáticas: Mathematics Matemática / probabilidade e estatística Discrete mathematics and combinatorics Ciência da computação Applied mathematics

Acceso a la licencia de uso: https://creativecommons.org/licenses/by/3.0/es/

Direcció de correo del autor: juanalberto.rodriguez@urv.cat

Identificador del autor: 0000-0002-9082-7647

Fecha de alta del registro: 2023-02-19

Versión del articulo depositado: info:eu-repo/semantics/publishedVersion

Enlace a la fuente original: https://www.dmgt.uz.zgora.pl/publish/bbl_view_press.php?ID=27108

URL Documento de licencia: http://repositori.urv.cat/ca/proteccio-de-dades/

Referencia al articulo segun fuente origial: Discussiones Mathematicae Graph Theory. 42 (3): 967-984

Referencia de l'ítem segons les normes APA: Martínez AC; Rodríguez-Velázquez JA (2022). Total Protection of Lexicographic Product Graphs. Discussiones Mathematicae Graph Theory, 42(3), 967-984. DOI: 10.7151/dmgt.2318

DOI del artículo: 10.7151/dmgt.2318

Entidad: Universitat Rovira i Virgili

Año de publicación de la revista: 2022

Tipo de publicación: Journal Publications