Autor segons l'article: Martinez, Abel Cabrera; Rodriguez-Velazquez, Juan Alberto;
Departament: Enginyeria Informàtica i Matemàtiques
Autor/s de la URV: CABRERA MARTÍNEZ, ABEL / Rodríguez Velázquez, Juan Alberto
Paraules clau: Total roman domination Total domination Lexicographic product graph
Resum: Let G be a graph with no isolated vertex and f: V (G) -> {0, 1, 2} a function. Let V-i = {x is an element of V(G): f(x) = i} for every i is an element of {0, 1, 2}. We say that f is a total Roman dominating function on G if every vertex in V-0 is adjacent to at least one vertex in V-2 and the subgraph induced by V-1 boolean OR V-2 has no isolated vertex. The weight of f is omega(f) = Sigma(v is an element of V(G)) f (v). The minimum weight among all total Roman dominating functions on G is the total Roman domination number of G, denoted by gamma(tR)circle(G). It is known that the general problem of computing gamma(tR)(G) is NP-hard. In this paper, we show that if G is a graph with no isolated vertex and H is a nontrivial graph, then the total Roman domination number of the lexicographic product graph G circle H is given bygamma(tR)(G o H) = {2 gamma t(G) if gamma(H) >= 2,xi(G) if gamma(H) =1,where gamma(H) is the domination number of H, gamma(t)(G) is the total domination number of G and xi(G) is a domination parameter defined on G.
Àrees temàtiques: Theoretical computer science Mathematics, applied Mathematics Matemática / probabilidade e estatística Geometry and topology Discrete mathematics and combinatorics Algebra and number theory
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: 2023-02-19
Versió de l'article dipositat: info:eu-repo/semantics/publishedVersion
Enllaç font original: https://amc-journal.eu/index.php/amc/article/view/2284
URL Document de llicència: http://repositori.urv.cat/ca/proteccio-de-dades/
Referència a l'article segons font original: Ars Mathematica Contemporanea. 20 (2): 233-241
Referència de l'ítem segons les normes APA: Martinez, Abel Cabrera; Rodriguez-Velazquez, Juan Alberto; (2021). Closed formulas for the total Roman domination number of lexicographic product graphs. Ars Mathematica Contemporanea, 20(2), 233-241. DOI: 10.26493/1855-3974.2284.aeb
DOI de l'article: 10.26493/1855-3974.2284.aeb
Entitat: Universitat Rovira i Virgili
Any de publicació de la revista: 2021
Tipus de publicació: Journal Publications
Repositori URV