Let G = (V, E), V = {v 1 , v 2 ,. .. , v n }, be a simple connected graph with n vertices, m edges and vertex degree sequence ∆ = d 1 ≥ d 2 ≥ · · · ≥ d n = δ > 0, d i = d(v i). General zeroth–order Randić index of G is defined as 0 R α (G) = n i=1 d α i , where α is an arbitrary real number. In this paper we establish relationships between 0 R α (G) and 0 R α−1 (G) and obtain new bounds for 0 R α (G). Also, we determine relationship between 0 R α (G), 0 R β (G) and 0 R 2α−β (G), where α and β are arbitrary real numbers. By the appropriate choice of parameters α and β, a number of old/new inequalities for different vertex–degree–based topological indices are obtained