On the outer-independent total (Roman) domination number of some graph operators

¹ Universidad Autónoma de Guerrero, Facultad de Matemáticas, Carlos E. Adame 54, Col. La Garita 39650, Acapulco, Guerrero, Mexico
² Universidad de Córdoba, Departamento de Matemáticas, Campus de Rabanales, 14071 Córdoba, Spain

^* Corresponding author: This email address is being protected from spambots. You need JavaScript enabled to view it.

Received: 31 August 2024
Accepted: 23 April 2026

Abstract

The goal of this article is to obtain closed formulas for the outer-independent total domina- tion number and the outer-independent total Roman domination number of the following well-known graph operators defined from a connected graph G: the central graph C(G) the middle graph M(G) the graph R(G) and the total graph T(G). We show that these formulas can be obtained for the last three graph operators and for the outer-independent total domination number of C(G). The picture is quite different when it concerns the outer-independent total Roman domination number of C(G). In this case, we obtain tight bounds and, imposing some restrictions on G, we obtain closed formulas.