The arithmetic-geometric index is a newly proposed degree-based graph invariant in mathematical chemistry. We give a sharp upper bound on the value of this invariant for connected chemical graphs of given order and size and characterize the connected chemical graphs that reach the bound. We also prove that the removal of the constraint that extremal chemical graphs must be connected does not allow to increase the upper bound.

翻译：算术-几何指数是数学化学中一种新提出的基于度的图不变量。本文给出了给定阶数和规模的连通化学图在该不变量上的一个紧上界，并刻画了达到该上界的连通化学图。我们还证明了，移除极值化学图必须连通的约束条件并不会使该上界增大。