On the general sum-connectivity index of connected graphs with given order and girth

In this paper, we show that in the class of connected graphs G of order n ≥3 having girth atleast equal to k, 3 ≤ k ≤ n, the unique graph G having minimum general sum-connectivity indexα(G) consists of Ck and nk pendant vertices adjacent to a unique vertex of Ck, if -1 ≤ α 0.This property does not hold for zeroth-order general Randi´c index 0Rα(G).