**4. Concluding Remarks**

It is well-known that the problem of finding the secure total domination number of a graph is NP-hard. This suggests the challenge of finding closed formulas or giving tight bounds for this parameter. In this paper we develop the theory for the class of rooted product graph. The study shows that if the root vertex is strong leaf, a support, or a universal vertex, then there exists a formula for the secure total domination number of the rooted product graph. In the remaining cases, two different behaviours are observed depending on whether the root vertex is a weak leaf or not. Although in a different way, in both cases we were able to give the intervals to which the parameter belongs. The endpoints of these intervals are expressed in terms of other domination parameters of the graphs *G* and *H* involved in the product, which allows us to obtain closed formulas when certain conditions are imposed on *G* or *H*.

**Author Contributions:** All authors contributed equally to this work. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research received no external funding.

**Conflicts of Interest:** The authors declare no conflict of interest.
