Some new upper bounds for the inverse sum indeg index of graphs

Let G = (V,E) be a simple connected graph with the vertex set V = {1,2,...,n} and sequence of vertex degrees (d1,d2,...,dn) where di denotes the degree of a vertex i ∈ V. With i ∼ j, we denote the adjacency of the vertices i and j in the graph G. The inverse sum indeg (ISI) index of the graph G is defined as ISI(G)=∑i∼j(didj)/(di+dj). Some new upper bounds for the ISI index are obtained in this paper.