Remarks on general zeroth-order Randić and general sum-connectivity indices

Abstract

Let G = (V,E ), V = [v \,v2, . . . , vn}, be a simple connected graph with n vertices, m edges and vertex degree sequence d1 > d2 > ■■■ > dn > 0, di = d(vi ). General zeroth-order Randic index of G is defined as °Ra (G) = Ση=ι > and general sum-connectivity index as Xa(G) = (di + d j)α, where a is an arbitrary real number. In this paper we establish a relationship between 0Rα+β (G), ^ α -β ^ ) and °Ra (G), as well as χ α+β (G), χ α -β ^ ) and Xa (G), where α and β are arbitrary real numbers. By the appropriate choice of parameters α and β, a number of new/old inequalities that reveal relationships between various vertex and edge degree-based topological indices are obtained.