Recently, the arithmetic–geometric index (AG) was introduced, inspired by the well-known and studied geometric–arithmetic index (GA). In this work, we obtain new bounds on the arithmetic–geometric index, improving upon some already known bounds. In particular, we show families of graphs where such bounds are attained.

中文翻译：

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算术-几何索引的某些性质

最近，受著名和研究的几何算术指数（GA）的启发，引入了算术几何指数（AG）。在这项工作中，我们在算术几何索引上获得了新的界线，并改进了一些已知的界线。特别是，我们显示了达到此类界限的图族。