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.