On the monotonicity of topological indices and the connectivity of a graph

Let I(G) be a topological index of a graph. If I(G+e)I(G), respectively) for each edge e∉G, then I(G) decreases (or increases, respectively) with addition of edges. In this paper, we determine the extremal values of some monotonic topological indices in terms of the number of cut vertices, or the number of cut edges, or the vertex connectivity, or the edge connectivity of a graph, and characterize the corresponding extremal graphs among all graphs of order n.