Arithmetic–geometric index and its relations with geometric–arithmetic index

•Bounds for arithmetic-geometric index.•Relations between geometric-arithmetic and arithmetic-geometric indices.•Conjectures on graphs that minimize (or maximize) arithmetic-geometric index and various combinations of geometric-arithmetic and arithmetic-geometric indices. The arithmetic–geometric index (AG(G)) was recently introduced as a modification of the well-known geometric–arithmetic index (GA(G)). This paper reports results on searching for extremal AG-graphs for various classes of simple graphs. Additionally, relations between these two indices are elaborated. Results on combinations AG+GA,AG−GA,AG · GA, and AG/GA are given. The paper is concluded with four conjectures that have been derived based on computer investigations.