Total Roman Domination Number of Rooted Product Graphs

Abel Cabrera Martínez, Suitberto Cabrera García, Andrés Carrión García and Frank A. Hernández Mira
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Abel Cabrera Martínez: Departament d’Enginyeria Informàtica i Matemàtiques, Universitat Rovira i Virgili, Av. Països Catalans 26, 43007 Tarragona, Spain
Suitberto Cabrera García: Departamento de Estadística e Investigación Operativa Aplicadas y Calidad, Universitat Politécnica de Valencia, Camino de Vera s/n, 46022 Valencia, Spain
Andrés Carrión García: Departamento de Estadística e Investigación Operativa Aplicadas y Calidad, Universitat Politécnica de Valencia, Camino de Vera s/n, 46022 Valencia, Spain
Frank A. Hernández Mira: Centro de Ciencias de Desarrollo Regional, Universidad Autónoma de Guerrero, Privada de Laurel 13, Col. El Roble, Acapulco, Guerrero 39640, Mexico

Mathematics, 2020, vol. 8, issue 10, 1-13

Abstract: Let G be a graph with no isolated vertex and f : V ( G ) → { 0 , 1 , 2 } a function. If f satisfies that every vertex in the set { v ∈ V ( G ) : f ( v ) = 0 } is adjacent to at least one vertex in the set { v ∈ V ( G ) : f ( v ) = 2 } , and if the subgraph induced by the set { v ∈ V ( G ) : f ( v ) ≥ 1 } has no isolated vertex, then we say that f is a total Roman dominating function on G . The minimum weight ω ( f ) = ∑ v ∈ V ( G ) f ( v ) among all total Roman dominating functions f on G is the total Roman domination number of G . In this article we study this parameter for the rooted product graphs. Specifically, we obtain closed formulas and tight bounds for the total Roman domination number of rooted product graphs in terms of domination invariants of the factor graphs involved in this product.

Keywords: total Roman domination; total domination; rooted product graph (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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