On the general sum-connectivity index of connected unicyclic graphs with kk pendant vertices

In this paper, we show that in the class of connected unicyclic graphs GG of order n≥3n≥3 having 0≤k≤n−30≤k≤n−3 pendant vertices, the unique graph GG having minimum general sum-connectivity index χα(G)χα(G) consists of Cn−kCn−k and kk pendant vertices adjacent to a unique vertex of Cn−kCn−k, if −1≤α<0−1≤α<0. This property does not hold for zeroth-order general Randić index 0Rα(G)0Rα(G).