Geometric-arithmetic index and minimum degree of connected graphs

In the present paper, we prove lower and upper bounds for each of the ratios GA/δ, as well as a lower bound on GA/√δ, in terms of the order n, over the class of connected graphs on n vertices, where GA and δ denote the geometric-arithmetic index and the minimum degree, respectively. We also characterize the extremal graphs corresponding to each of those bounds. In order to prove our results, we provide a modified statement of a well-known lower bound on the geometric-arithmetic index in terms of minimum degree.