some new bounds on the general sum--connectivity index

Let g=(v,e) be a simple connected graph with n vertices, m edges and sequence of vertex degrees d1≥d2≥⋯≥dn>0, di=d(vi), where vi∈v. with i∼j we denote adjacency of vertices vi and vj. the general sum--connectivity index of graph is defined as χα(g)=∑i∼j(di+dj)α, where α is an arbitrary real number. in this paper we determine relations between χα+β(g) and χα+β−1(g), where α and β are arbitrary real numbers, and obtain new bounds for χα(g). also, by the appropriate choice of parameters α and β, we obtain a number of old/new inequalities for different vertex--degree--based topological indices.