Bounds on the signed total Roman 2-domination in graphs

Let k >= 1 be an integer and G be a simple and finite graph with vertex set V (G). A signed total Roman k-dominating function (STRkDF) on a graph G is a function f : V (G) -> {- 1, 1, 2} such that (i) every vertex v with f(v) = -1 is adjacent to at least one vertex u with f(u) = 2 and (ii) Sigma(u is an element of N(v)) f(u) >= k holds for any vertex v. The weight of an STRkDF f is Sigma(u is an element of V) ((G)) f (u) and the minimum weight of an STRkDF is the signed total Roman k-domination number gamma(k)(stR) (G) of G. In this paper, we establish some sharp bounds on the signed total Roman 2-domination number.