Signed total Roman domination in graphs

Let be a finite and simple graph with vertex set . A signed total Roman dominating function (STRDF) on a graph is a function satisfying the conditions that (i) for each vertex , where is the neighborhood of , and (ii) every vertex for which is adjacent to at least one vertex for which . The weight of an SRTDF is . The signed total Roman domination number of is the minimum weight of an STRDF on . In this paper we initiate the study of the signed total Roman domination number of graphs, and we present different bounds on . In addition, we determine the signed total Roman domination number of some classes of graphs.