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

Xiaohong Chen

Abstract: For a real number β, the general sum-connectivity index χβ(G) of a graph G is defined as ∑xy∈E(G)(d(x)+d(y))β, where d(x) denote the degree of a vertex x in G. In this paper, we show that for every graph G≇Pn, if β≥0, thenχβ(L(G))≥{χβ(G)forδ(G)≤2,2χβ(G)forδ(G)≥3.In addition, for β<0, we present the lower bound for χβ(L(G)) in terms of χβ(G). Finally, we establish sharp bounds for χβ(G)+χβ(L(G)), and characterize the extremal graphs attaining the bounds.