Sharp bounds on the Arithmetic-geometric index of graphs and line graphs

As a degree-based topological index, the arithmetic-geometric index was firstly introduced by Shegehall and Kanabur and was defined as AG = AG(G) = Sigma(uv is an element of EG) du+dv/2 root d(u)d(v) for a nontrivial graph G, where d(v) is the degree of v in G. In this paper, we determine some sharp upper and lower bounds on AG of graphs and characterize the corresponding extremal graphs, respectively. Through the relation between the graph G and its line graph L(G), some sharp upper and lower bounds on AG(L(G)) are studied and the corresponding extremal graphs are also characterized. (C) 2022 Elsevier B.V. All rights reserved.