A graph ???? = (????, ????) is said to be strongly *-graph if there exists a bijection ???? : ???? → {1,2, … , ????} in such a way that when an edge, whose vertices are labeled ???? and ????, is labeled with the value ???? + ???? + ????????, all edge labels are distinct. In this paper we get an upper bound for the number of edges of any graph with ???? vertices to be strongly*- graph, and we make an algorithm to check any graph if it is a strongly*- graph or not. Also, we study some new families to be strongly*- graphs.