On the secure Italian domination in lexicographic product graphs

In this paper, we study the problem of expressing the secure Italian domination number of lexicographic product graphs [Formula: see text] in terms of a domination parameter of the graph [Formula: see text]. For this purpose we use the approach of [Formula: see text]-domination introduced in [Ars Math. Contemp. 22 (2022), no. 1, Paper No. 4, 25 pp], where [Formula: see text] is a vector whose components are integers and whose values depend on the value of some domination parameters of the graph [Formula: see text].