a multiplicative version of forgotten topological index

Let g be a simple graph with vertex set v (g) and edge set e(g). the multiplicative forgotten topological index of g are defined as: πf (g) = v∈v (g) dg(v)3, where dg(v) is the degree of the vertex v of g. in this paper, we present upper bounds for the multiplicative forgotten topological index of several graph operations such as sum, cartesian product, corona product, composition, strong product, disjunction and symmetric difference in terms of the f􀀀index and the first zagreb index of their components. also, we give explicit formulas for this new graph invariant under two graph operations such as union and tensor product. moreover, we obtain the expressions for this new graph invariant of subdivision graphs and vertex – semitotal graphs. finally, we compare the discriminating ability of indices.