Extremal Topological Indices for Graphs of Given Connectivity

Abstract

In this paper, we show that in the class of graphs of order n and given (vertex or edge) connectivity equal to k (or at most equal to k), 1<= k<= n - 1, the graph Kk+(K1UKn-k-1) is the unique graph such that zeroth-order general Randic index,
general sum-connectivity index and general Randic connectivity index are maximum and general hyper-Wiener index is minimum provided \alpha >= 1. Also, for 2-connected (or 2-edge connected) graphs and \alpha > 0 the unique graph minimizing these indices is the n-vertex cycle Cn.