On the arithmetic-geometric index of graphs

Abstract

Very recently, the first geometric-arithmetic index GA and arithmeticgeometric 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 χ 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 Bollobás-Erdős-type theorem obtained in [3].