Author, as appears in the article.: Martínez AC; Rodríguez-Velázquez JA

Department: Enginyeria Informàtica i Matemàtiques

URV's Author/s: CABRERA MARTÍNEZ, ABEL / Rodríguez Velázquez, Juan Alberto

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

Abstract: © (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.

Thematic Areas: Mathematics Matemática / probabilidade e estatística Discrete mathematics and combinatorics Ciência da computação Applied mathematics

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

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

Author identifier: 0000-0002-9082-7647

Record's date: 2023-02-19

Papper version: info:eu-repo/semantics/publishedVersion

Link to the original source: https://www.dmgt.uz.zgora.pl/publish/bbl_view_press.php?ID=27108

Licence document URL: http://repositori.urv.cat/ca/proteccio-de-dades/

Papper original source: Discussiones Mathematicae Graph Theory. 42 (3): 967-984

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

Article's DOI: 10.7151/dmgt.2318

Entity: Universitat Rovira i Virgili

Journal publication year: 2022

Publication Type: Journal Publications