On the Arithmetic-Geometric Index of Graphs

Very recently, the first geometric-arithmetic index GA and arithmetic-geometric index AG were introduced in mathematical chemistry. In the present paper, we first obtain some lower and upper bounds on AG and characterize the extremal graphs. We also establish various relations between AG and other topological indices, such as the first geometric-arithmetic index GA, atom-bond connectivity index ABC, symmetric division deg index SDD, chromatic number chi and so on. Finally, we present some sufficient conditions of GA(G) > GA(G - e) or AG(G) > AG(G - e) for an edge e of a graph G. In particular, for the first geometric-arithmetic index, we also give a refinement of Bollobas-Erdos-type theorem obtained in [3].