degree-based function index of graphs with given connectivity

We investigate the index if (g) =(g) f(dg(v), dg(w)) of a graph g, where f is a symmetric function of two variables satisfying certain condi-tions, e(g) is the edge set of g, and dg(v) and dg(w) are the degrees of vertices v and w in g, respectively. those conditions are satisfied by functions that can be used to define the general sum-connectivity index χa, general randi¢ index ra, general reduced second zagreb index grma for some a ∈ r, general sombor index soa,b, general augmented zagreb index azia,b and by one other generalization ma,b for some a, b ∈ r. the general augmented zagreb index is a new index defined in this paper.we obtain a sharp upper bound on if for graphs with given order and connectivity, and a sharp lower bound on if for 2-connected graphs with given order. our upper bound holds for ma,b and soa,b where a, b ≥ 1; χa and ra where a ≥ 1; and grma where a > −1. our lower bound holds for ma,b where a ≥ 0 and b ≥ −a; soa,b where a, b ≥ 0 or a, b ≤ 0; azia,b where a ≥ −2 and b ≥ 0; χa and ra where a ≥ 0; and grma where a > −2.