Extremal topological indices for graphs of given connectivity

Abstract

In this paper, weshow 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 + (K1 ∪ Kn-k-1) is the unique graph such that zeroth-order general Randić index, general sum-connectivity index and general Randić connectivity index are maximum and general hyper-Wiener index is minimum provided α ≥ 1. Also, for 2-connected (or 2-edge connected) graphs and α > 0 the unique graph minimizing these indices is the n-vertex cycle Cn.