Maximum General Sum-Connectivity Index for Trees with Given Independence Number

Des, Xu and Gutman [MATCH Commun. Math. Comput. Chem. 70(2013) 301-314] proved that in the class of trees of order n and independence number s, the spur S-n,S-s maximizes both first and second Zagreb indices and this graph is unique with these properties. In this paper, we show that in the same class of trees T, S-n,S-s is the unique graph maximizing zeroth-order general Randie index R-0(alpha)(T) for alpha > 1 and general sum-connectivity index x(alpha)(T) for alpha >= 1. This property does not hold for general Rancho index R-alpha(T) if alpha >= 2.