On the arithmetic-geometric index of graphs

Shu-Yu Cui; Weifan Wang; Gui-Xian Tian; Baoyindureng Wu

paper

On the arithmetic-geometric index of graphs

arXiv:2010.03748

Abstract

Very recently, the first geometric-arithmetic index $G A$ and arithmetic-geometric index $A G$ were introduced in mathematical chemistry. In the present paper, we first obtain some lower and upper bounds on $A G$ and characterize the extremal graphs. We also establish various relations between $A G$ and other topological indices, such as the first geometric-arithmetic index $G A$ , atom-bond-connectivity index $A B C$ , symmetric division deg index $S D D$ , chromatic number $χ$ and so on. Finally, we present some sufficient conditions of $G A (G) > G A (G - e)$ or $A G (G) > A G (G - e)$ 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].

24 pages, 4 figures, 32 conferences