Group for Research in Decision Analysis

# Geometric-arithmetic index and minimum degree of connected graphs

## Mustapha Aouchiche, Issmail El Hallaoui, and Pierre Hansen

In the present paper, we prove lower and upper bounds for each of the ratios $$GA/\delta$$, as well as a lower bound on $$GA/\sqrt{\delta}$$, in terms of the order $$n$$, over the class of connected graphs on $$n$$ vertices, where $$GA$$ and $$\delta$$ 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.

, 11 pages