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 d(1) >= d(2) >= ... >= d(n) > 0, d(i) = d(v(i)), where v(i) is an element of V. With i similar to j we denote adjacency of vertices v(i) and v(j). The general sum-connectivity index of graph is defined as chi(alpha)(G) = Sigma(i similar to j)(d(i) + d(j))(alpha), where alpha is an arbitrary real number. In this paper we determine relations between chi(alpha+beta)(G) and chi alpha+beta-1 (G), where alpha and beta are arbitrary real numbers, and obtain new bounds for chi alpha(G). Also, by the appropriate choice of parameters alpha and beta, we obtain a number of old/new inequalities for different vertex-degree-based topological indices.