General sum-connectivity index of a graph and its line graph

For a real number beta, the general sum-connectivity index chi(beta)(G) of a graph G is defined as Sigma(xy is an element of E(G))(d(x) + d(y))(beta), where d(x) denote the degree of a vertex x in G . In this paper, we show that for every graph G not congruent to P-n, if beta >= 0 , then chi(beta) (L(G)) >= {chi(beta)(G) for delta(G) <= 2 , 2 chi(beta) (G ) for delta(G) >= 3. In addition, for beta < 0 , we present the lower bound for chi(beta)(L(G)) in terms of chi(beta)(G). Finally, we establish sharp bounds for chi(beta)(G) + chi(beta)(L(G)), and characterize the extremal graphs attaining the bounds. (c) 2022 Elsevier Inc. All rights reserved.